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Platnica SV-JME 57(2011)7-8_04.pdf 1 12.8.2011 10:33:08

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME)

© 2011 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website. The journal is subsidized by Slovenian Book Agency.

Strojniški vestnik - Journal of Mechanical Engineering is also available on http://www.sv-jme.eu, where you access also to papers’ supplements, such as simulations, etc.

Editor in ChiefVincenc ButalaUniversity of Ljubljana Faculty of Mechanical Engineering, Slovenia

Co-EditorBorut BuchmeisterUniversity of MariborFaculty of Mechanical Engineering, Slovenia

Technical EditorPika ŠkrabaUniversity of Ljubljana Faculty of Mechanical Engineering, Slovenia

Editorial OfficeUniversity of Ljubljana (UL)Faculty of Mechanical EngineeringSV-JMEAškerčeva 6, SI-1000 Ljubljana, SloveniaPhone: 386-(0)1-4771 137Fax: 386-(0)1-2518 567E-mail: [email protected]://www.sv-jme.eu

Founders and PublishersUniversity of Ljubljana (UL)Faculty of Mechanical Engineering, Slovenia

University of Maribor (UM)Faculty of Mechanical Engineering, Slovenia

Association of Mechanical Engineers of Slovenia

Chamber of Commerce and Industry of SloveniaMetal Processing Industry Association

International Editorial BoardKoshi Adachi, Graduate School of Engineering,Tohoku University, JapanBikramjit Basu, Indian Institute of Technology, Kanpur, IndiaAnton Bergant, Litostroj Power, Slovenia Franci Čuš, UM, Faculty of Mech. Engineering, SloveniaNarendra B. Dahotre, University of Tennessee, Knoxville, USAMatija Fajdiga, UL, Faculty of Mech. Engineering, SloveniaImre Felde, Bay Zoltan Inst. for Mater. Sci. and Techn., HungaryJože Flašker, UM, Faculty of Mech. Engineering, SloveniaBernard Franković, Faculty of Engineering Rijeka, CroatiaJanez Grum, UL, Faculty of Mech. Engineering, SloveniaImre Horvath, Delft University of Technology, NetherlandsJulius Kaplunov, Brunel University, West London, UKMilan Kljajin, J.J. Strossmayer University of Osijek, CroatiaJanez Kopač, UL, Faculty of Mech. Engineering, SloveniaFranc Kosel, UL, Faculty of Mech. Engineering, SloveniaThomas Lübben, University of Bremen, GermanyJanez Možina, UL, Faculty of Mech. Engineering, SloveniaMiroslav Plančak, University of Novi Sad, SerbiaBrian Prasad, California Institute of Technology, Pasadena, USABernd Sauer, University of Kaiserlautern, GermanyBrane Širok, UL, Faculty of Mech. Engineering, SloveniaLeopold Škerget, UM, Faculty of Mech. Engineering, SloveniaGeorge E. Totten, Portland State University, USANikos C. Tsourveloudis, Technical University of Crete, GreeceToma Udiljak, University of Zagreb, CroatiaArkady Voloshin, Lehigh University, Bethlehem, USA

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General informationStrojniški vestnik – Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue).Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax. Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. Legal title passes to the customer on dispatch by our distributor. Single issues from current and recent volumes are available at the current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all other information please visit: http://en.sv-jme.eu/.

You can advertise on the inner and outer side of the back cover of the magazine. The authors of the published papers are invited to send photos or pictures with short explanation for cover content.We would like to thank the reviewers who have taken part in the peer-review process.

Cover: The simulation of elastomeric insert elements for standard claw couplings under centrifugal and torque load requires not only the use of high-end simulation tools like nonlinear Finite Elements Analysis and Injection Moulding (see two images above) but also the determination of part specific mechanical properties with adequate material test devices (see two pictures at the right side). The verification of the simulation results always needs appropriate test benches like e.g. a laser beam supported distortion detection test stand (see bottom left-hand side). Image courtesy: Department of Engineering Design and CAD, University of Bayreuth

ISSN 0039-2480

Aim and ScopeThe international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis. The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue.The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s).

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8Contents

Contents

Strojniški vestnik - Journal of Mechanical Engineeringvolume 57, (2011), number 7-8Ljubljana, July-August 2011

ISSN 0039-2480

Published monthly

PapersReinhard Hackenschmidt, Bettina Alber-Laukant, Frank Rieg: Simulating Nonlinear Materials

under Centrifugal Forces by using Intelligent Cross-linked Simulations 531Gregor Čepon, Lionel Manin, Miha Boltežar: Validation of a Flexible Multibody Belt-Drive

Model 539Radouane Akrache, Jian Lu: Integrated Design for Fatigue Life Estimation of Structures 547Simon Kulovec, Leon Kos, Jožef Duhovnik: Mesh Smoothing with Global Optimization under

Constraints 555Chuangwen Xu, Ting Xu, Qi Zhu, Hongyan Zhang: Study of Adaptive Model Parameter

Estimation for Milling Tool Wear 568Srđan Podrug, Srečko Glodež, Damir Jelaska: Numerical Modelling of Crack Growth in a Gear

Tooth Root 579Viktor Jejčič, Tone Godeša, Marko Hočevar, Brane Širok, Aleš Malneršič, Andrej Štancar,

Mario Lešnik, Denis Stajnko: Design and Testing of an Ultrasound System for Targeted Spraying in Orchards 587

Nuša Fain, Mihael Kline, Jožef Duhovnik: Integrating R&D and Marketing in New Product Development 599

Vaclav Pistek, Pavel Novotny: Virtual Engine - A Tool for a Powertrain Dynamic Solution 610Mohammad Bagher Nazari, Mahmoud Shariati, Mohammad Reza Eslami, Behrooz Hassani:

Computation of Stress Intensity Factor in Functionally Graded Plates under Thermal Shock 622

Instructions for Authors 633

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8, 531-538 Paper received: 17.01.2011DOI:10.5545/sv-jme.2011.013 Paper accepted: 23.06.2011

*Corr. Author’s Address: University of Bayreuth, Department of Engineering Design and CAD, 95440 Bayreuth, Germany, [email protected] 531

Simulating Nonlinear Materials under Centrifugal Forces by using Intelligent Cross-Linked Simulations

Hackenschmidt, R. ‒ Alber-Laukant, B. ‒ Rieg, F.Reinhard Hackenschmidt* ‒ Bettina Alber-Laukant ‒ Frank Rieg

University of Bayreuth, Department of Engineering Design and CAD, Germany

Actual sophisticated development processes are conducted by the use of multiple computer-aided tools (CAx-tools) to accelerate product development. However, because of below optimal simulation strategies and procedure guidelines mainly for complex materials and loading the development process is constricted and hence sluggish. The main emphasis of the article is to show how Intelligent CROss-linked Simulations (ICROS) methodical approach can be used to handle complex processes supported by specific computer techniques employed. Development of an elastomer insert subassembly for a standard claw coupling is used as an example of such a complex process.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: product development, CAx, ICROS, FEA, simulation, workflow

0 INTRODUCTION

Classical claw couplings (Fig. 1) are flexible and designed for positive torque transmission. They are fail-safe. Operational vibrations and shocks are efficiently dampened and reduced with the use of an elastomeric insert element to be located between metal parts. The two congruent coupling halves with concave claws on the inside are peripherally offset in relation to one another by half a pitch.

Fig. 1. Standard Claw coupling

To broaden the clutches technical field of application for up to 40,000 rpm high-speed rotating drive-trains, the question of material distortion both under centrifugal / torque and compression load has to be investigated. To avoid costly hardware experiments, the development of

an effective simulation solution, also transferable to a wide range of couplings with different nominal torques had top priority.

As the use of a variety of different computer-aided tools (CAx-tools) e.g. for strength of material and manufacturing simulations is necessary for a useful outcome, the methodical approach based on Intelligent CROss-linked Simulations (ICROS) was chosen to optimize the virtual simulation process chain as presented in subsequent sections of this paper.

1 RELATED RESEARCH

Product development as a whole consists of many sub-processes that have to be performed in specific order. These processes are also iterative and linked to certain product-specific data. By a detailed analysis of these processes, their functionalities and complex interactions can be uncovered. There were many attempts to improve the product development processes in industry, from traditional phase-gate approach [1] to more efficient set-based concurrent engineering [2].

In order to achieve a better organisation and an efficient use of available product development, computer-aided tool, the Artificial Intelligence (AI), has been extensively applied [3] to [5], along with other multi-criteria analyses [6] and [7].

Despite all the proven benefits of modern engineering software, one of the main problems existing today in the development process is the

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8, 531-538

532 Hackenschmidt, R. ‒ Alber-Laukant, B. ‒ Rieg, F.

Babylonian-like system variety and complexity. On the one hand, as discussed in [8], the conflicts in-house use of multiple systems, programs and simulation tools may lead to coordination problems.

On the other hand, the complexity of global supplier structures with their own simulation systems also creates significant handling problems (Fig. 2).

When designing complex products, often various special analysis tools need to be applied [10]. Moreover, sometimes even different shape models representations are needed to perform the analysis [11]. In addition, the existing sequence of simulation tools does not adequately model fibre reinforced polymer parts [12].

Depending on their relations single sub-processes can be composed to complete process-chains up to adequate support during the post-

processing phase by the use of e.g. intelligent rule-based consultative system [13].

It can be concluded that the achievement of adequate coordination of multiple simulation programs still represents a bottleneck in the product development process.

2 ICROS

To ensure a reliable accomplishment of product development by using multiple simulation programs ICROS recommends to organize the procedural method following the widespread four step engineering design approach according to Pahl/Beitz [14] or the VDI 2221 [15]. This basic approach only has to be adapted from product design in a way that it can support process design [16]:

Fig. 2. Complex simulation tool environment [9]


533Simulating Nonlinear Materials under Centrifugal Forces by using Intelligent Cross-Linked Simulations

• First step: Clarification and specification of task and simulation needs.

• Second step: Conceptual design of the simulation needs.

• Third step: Design of the simulation scenario.• Fourth step: Development of a suitable

simulation environment.A detailed discussion about the application

of methods, processes and instruments is made in advance. This approach stimulates the use of adequate virtual design tools already in the early phase of the overall process.

In the same way, it also determines the criteria and information that has to be carried along the way through all the design and simulation steps. With qualified information about the simulations needed and the CAx-software available decisions about either reserving capacities in the in-house CAE-department or the necessity for contacting external service providers, is facilitated. This is fundamental for developing generic simulation process chains, and also for the outline of a project-based workflow and timeline.

Detailed decisions about programs, operating systems and adequate hardware have to be made under the viewpoint of necessary functionality and existing system environment. It is fundamental to know the detailed program capacity and coverage of internally available or even externally used programs. If, for example, a part out of a material with non-linear behaviour has to be developed, the simulation tool needs to be able to cope with inhomogeneous material.

The results of the examinations have to be fixed to all necessary details, in corresponding worksheets. This ranges from correct export- and import-formats, including corresponding settings, to detailed support in order to resolve interdependencies of results or design tasks. These should be provided on an effective level of granularity to take account of software- and user-specific circumstances. They can be combined to form a holistic environment, which is used in this specific development task. The abstraction to a generalized and certifiable process chain later on is easily possible.

This will lead to a dramatic improvement in coping with challenging tasks, especially in today’s multinational and complex relations between customers and tiers. The precise analysis

of the main tasks to be performed in this complex development process determines that especially the simulation phase itself has to be supported by documents that help the designer to choose the right simulation features or, if experienced designers are involved, represent special topics seldom used or critical (Fig. 3). In this way, also internal regulations or legal restrictions can be provided on the spot after a full ICROS-schema is developed.

Fig. 3. Required input data / generated output data for simulation processes

3 CLAW CLUTCH DEVELOPMENT USING ICROS

The design of a claw coupling with elastomeric damping elements is a challenging task, especially if high speed rotational frequencies are claimed for its application. Without doubt, the specification list according to Pahl/Beitz [14] is a basic prerequisite for the engineering task as here all the technical needs have to be defined.

The discussed clutch application assumes mainly correct dimensioning of the polymer part. Hence, there is a need for adequate computer-aided simulation tools to predict the material behaviour.

As polymers are widely non-linear in their characteristics, in the first ICROS step the variety of software to be considered has to be selected. Table 1 shows a representative list.

Table 1. Software selection list excerpt for polymer mechanical stability calculation

Program Linear /nonlinear Version

MSC.Marc y/y Marc 2010

Abaqus y/y Explicit or Implicit 6.10

ProMECHANICA y/n Wildfire 5Z88Aurora y/y V2... ... ....



The list has to be verified and completed by other necessary programs to meet all requirements in regard to all the simulation needs. In the second ICROS step the simulation program requirements for the entire simulation chain were discussed and fixed for all the necessities of the project:• centrifugal force load calculation,• mould injection behaviour,• displacement simulation,• die casting mould machining.

This leads to a well-defined list of programs (Table 2), which are of course adjustable and adaptable due to the companies’ standards and prerequisites.

Table 2. Overall software selection list excerpt

Task Program

Centrifugal Forces AbaqusMSC.Marc

Displacements Abaqus

Injection moulding Moldex3D Moldflow

Mould machining ProMECHANISM... ...

Fig. 4. Standard process workflow for polymer simulation processing

A typical simulation program flow suggestion for such an engineering design problem can be found in ICROS´standardized workflow diagrams and has to be adapted to the concrete task in the third ICROS step (Fig. 4).

The classical approach along the ICROS path with modelling the clutch in the 3D-CAD system followed by a linear FEM calculation under high rotation speed (28,000 rpm) plus torque load (60 Nm) of the charged insert-clutch-contact areas lead to fundamental results (Fig. 5).

Fig. 5. First simulation results

Firstly, due to the rotation load, the displacement areas show significant radial deformation of the elastomeric insert. Secondly, the torque burdened areas are partially disabled in their distortion; that is the reason why the appropriate regions differ from the others. These results represent the reality very well in principle, but unfortunately the absolute figures as seen in Table 3 are some order of magnitudes too high as compared with a physical high speed test on a specially developed high speed test bench.

Table 3. Simulation vs. experimental results

Linear Simulation

Non-linear Simulation Test

Displacement max [mm] 1.0 1.3 1.7

Here, it was a great challenge to measure the radial polymer deformation values at the clutch while rotating up to 40,000 rpm. It was realized by the use of a light beam in combination with a highly sensitive photo cell, delivering the strength



of current according to the real deformation peak of the elastomeric element. Not only maximum but also enduring distortion and time dependent creeping effects could be measured very precisely.

Fig. 6. High-speed test bench

To ensure reliable simulation results, it was found that the use of linear material parameters determined out of standard pulling tests as provided e.g. by the producer of elastomeric materials, do not fit the real material values. The explanation lies in the specific material behaviour: For reasons of expense, thermoplastic elastomers (TPE) are used. These materials are either copolymers or physically mixed polymers.

Compared to common thermoset elastomers with chemical bonding these special thermoplastic elastomer blends have a physically cross linking depending on their hard/soft segmentation of the blend components (see Figs. 7a and b). Therefore, by room temperature and moderate forces they act like real elastomers only with the help of semi crystalline agglomerations and the resulting van der Waals forces.

The properties lie between both materials thermoplastic and elastomers (see Fig. 7c).

In spite of elastomers the production of TPE is quite simple owing to the use of standard injection moulding processes (Fig. 8). Nevertheless, the most important difference between thermoset elastomers and thermoplastic elastomers is the type of the cross-linking bond in their structures. The cross-linking mechanism of TPE strongly depends on the fabrication process and differs substantially. The behaviour cannot be simulated in its complexity. To ensure that TPE´s

behaviour is neither linear elastic nor viscoelastic, an additional simulation with a hyperelastic material model was done which produced more realistic results but they did not fit the above pattern at all.

a)

b)

c)

Fig. 7. Conformation and properties of thermoplastic elastomers and thermoset

elastomers

Different material models like Mooney Rivlin, Neo Hooke, Yeoh, Ogden, Marlow or Arruda-Boyce are suitable to deal with the problem.

The chosen material model is a hyper elastic model of Ogden which depends on the principle stretch ratios λi.

UD

Ji

Ni

i i

N

iel

ii ii= + −

+ −( )+

= =∑ ∑

12 1 2 3

1

223 1 1

µα

λ λ λα α α ,

λ λi iJ=−

13 , (1)



and αi, μi, Di are to be determined from experimental test data [17].

Additionally, known hardening effects of elastomeric parts under pressure load [18] led to a conclusion that for the investigated clutch part, a specific determination of the material parameters is indispensable.

Fig. 8. Insert mould process simulation results

Hence, a part specific pulling rig was developed for the use on a standard Zwick testing machine (Fig. 9).

Fig. 9. Insert pulling rig

The resulting material parameters served as mapping basis for the FEM model in an adequate non-linear FEM tool. The comparison of the results shows that the simulation data are very close to the measured reality, leading to the

manufacturing approval of the mould forms and materials procurement. It should be stated that some additional improvement loops on behalf of the geometrical attributes of the clutch and insert geometry were also performed. Conducting thoroughly this fourth ICROS step results in the development of a detailed simulation workflow plan perfectly suitable for the task (Fig. 10).

Fig. 10. ICROS high-speed simulation workflow overview

The findings of this specific task according to the simulation tool needs and interactions are added to the general ICROS case database and can be used for related virtual development tasks.

Fig. 11. Combination of ICROS with AI for exceptional problems



To face these challenges, engineers should have direct contact to the best practices for their current simulation step [19]. Ideally, it is essential to provide them with the necessary information according to their respective design experience without constraining their creativity. This case sensitivity could be managed with the help of AI (Fig. 11).

4 RESULTS AND CONCLUSIONS

Due to the requirement of being able to handle centrifugal forces and distortions resulting from a very high rotating speed applied on nonlinear elastomer, the finding of an optimized virtual simulation tool dedication was investigated. It could be pointed out that material properties can be mapped and scaled to a computer model by a skilled combination of virtual product design and prototype testing using the ICROS method presented.

With the help of adequate methods like AI it should even be possible to come to an automatic case covering detection system to effectively support engineer in developing processes.

5 REFERENCES

[1] Morgan, J.M., Liker, J.K. (2006). The Toyota product development system: integrating people, process and technology. Productivity Press, New York.

[2] Raudberget, D. (2010). Practical applications of set-based concurrent engineering in industry. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 11, p. 685-695.

[3] McMahon, C., Lowe, A., Culley, S. (2004). Knowledge management in engineering design: Personalization and codification. Journal of Engineering Design, vol. 15, p. 307-325.

[4] Sancin, U., Dobravc, M., Dolšak, B. (2010). Human cognition as an intelligent decision support system for plastic products’ design. Expert Systems with Applications, vol. 37, p. 7227-7233.

[5] Dolšak, B. (2002). Finite element mesh design expert system. Knowledge-Based Systems, vol. 15, no. 5-6, p. 315-322.

[6] Kostanjevec, T., Polajnar, A., Kostanjevec, M. (2009). Product development simulation with multicriteria analysis. International Journal of Simulation Modelling, vol. 8, no. 1, p. 38-47.

[7] Fain, N., Moes, N., Duhovnik, J. (2010). The role of the user and the society in new product development. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 7-8, p. 521-530.

[8] Dolšak, B., Novak, M. (2011). Intelligent decision support for structural design analysis. Advanced Engineering Informatics, vol. 25, p. 330-340.

[9] Goering, J.U. (2007). Kopplung und prozess-orientierte Verknüpfung der Methoden und Werkzeuge. FORFLOW - Bayerischer Forschungsverbund für Prozess- und Workflowunterstützung zur Planung und Steuerung der Abläufe in der Produkt-entwicklung: 1. Ergebnisbericht, Erlangen, p. 87-98.

[10] Chen, D.C., Chen, W.J., Lin, J.Y., Jheng, M.W., Chen, J.M. (2010). Finite element analysis of superplastic blow-forming of Ti-6Al-4V sheet into closed ellip-cylindrical die. International Journal of Simulation Modelling, vol. 9, no. 1, p. 17-27.

[11] Hamri, O., Léon, J.C., Giannini, F., Falcidieno, B. (2010). Computer aided design and finite element simulation consistency. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 11, p. 728-743.

[12] Alber, B., Rieg, F., Hackenschmidt, R. (2007). Product design with high-tech-polymers ‒Practical use of CAE-tools with cross-linked simulations and experimental verification. Materialprüfung, vol. 49, no. 7-8, p. 402-407.

[13] Novak, M., Dolšak, B. (2008). Intelligent FEA-based design improvement. Engineering Application of Artificial Intelligence, vol. 21, no. 8, p. 1239-1254.

[14] Pahl, G., Beitz, W., Feldhusen, J., Grothe, K.-H. (2007). Konstruktionslehre - Grundlagen erfolgreicher Produkt-entwicklung- Methoden und Anwendung, Berlin.

[15] VDI 2221 (1993). Methodik zum Entwickeln und Konstruieren technischer Systeme und Produkte. VDI-Handbuch Konstruktion, Berlin - Düsseldorf.



[16] Hackenschmidt, R., Alber, B., Rieg, F. (2007). Intelligente Verknüpfung von Simulationsprogrammen. CAD-CAM Report, vol. 26, no. 4, p. 34-41.

[17] Dassault Systèmes (2009). ABAQUS Analysis User´s Manual. vol. 3, Vélizy-Villacoublay.

[18] Holden, G. (2000). Understanding Thermoplastic Elastomers. Hanser, München.

[19] Krehmer, H., Eckstein, R., Lauer, W., Roelofsen, J., Stöber, C., Troll, A., Zapf, J., Weber, N., Meerkamm, H., Henrich, A., Lindemann, U., Rieg, F., Wartzack, S. (2010). Das FORFLOW-Prozessmodell zur Unterstützung der multidisziplinären Produktentwicklung. Konstruktion, no. 10, p. 59-68.

http://www.konstruktionslehre.uni-bayreuth.de/deutsch/forschung/Forflow.pdf




*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, [email protected] 539

Validation of a Flexible Multibody Belt-Drive ModelČepon, G. ‒ Manin, L. ‒ Boltežar, M.

Gregor Čepon1 ‒ Lionel Manin2 ‒ Miha Boltežar1,*

1 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia 2 Université de Lyon, CNRS, INSA de Lyon, France

In the past decade the applicability of belt-drives has been extended significantly due to their increased reliability. With automotive engines it is now common to join a large number of belt-drives into a single, long belt-drive with several tensioner pulleys. However, these belt-drives can exhibit complex dynamic behaviors; therefore it is very important to predict the dynamics response of such systems using validated numerical models.

The aim of this paper is to perform the validation of a developed belt-drive model. The validation of this belt-drive model was performed using a two-pulley belt-drive. The numerically obtained results are compared with experimental data under various operational conditions. Finally, the applicability of the belt-drive model is presented by simulating a serpentine belt-drive, considering non-steady, belt-drive operational conditions. ©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: belt-drive, validation, ANCF, angular speed loss, serpentine belt-drive

0 INTRODUCTION

Belt drives are commonly used to transmit power in many engineering applications, such as automotive engines, industrial machines, etc. V-ribbed, belt-drive systems have become increasingly important to the automotive industry since their introduction in the late 1970s. Because of their simple installation and low maintenance, together with an ability to absorb shocks, they are frequently used instead of chain or geared transmission systems. However, they can exhibit complex dynamic behaviors, such as the transverse vibrations of the belt spans, tension fluctuations, sliding of the belt over the pulley, etc. It is therefore very important to predict the dynamic response of such systems using validated numerical models.

To ensure stable working conditions the dynamic response of such systems has been studied extensively. A review of the literature [1] identifies two well-defined groups of studies. The first group deals with the transverse belt span response [2] to [5] and the rotational response of the pulleys in the belt-drive [6] to [9]. The second group deals with describing the belt-pulley contact formulation [10] and [11]. As these two groups suffer an unsatisfactory connection to each other, Leamy and Wasfy [12] and [13] bridged this gap

by developing a general, dynamic finite-element model that includes frictional contact. Most recently, Čepon and Boltežar [14] presented an improved belt-drive model using the absolute nodal coordinate formulation (ANCF). The belt pulley contact forces were formulated as a linear complementarity problem (LCP), which enabled the incorporation of the discontinuous Coulomb friction law.

For any reliable simulations of belt-drives along with a validated numerical model, the proper material and contact parameters should be obtained. In [15], Čepon et al. presented methods for identifying the stiffness and damping for V-ribbed belts. Experimental studies of the contact between a grooved pulley and a V or V-ribbed belt are presented in [11] and [16]. In [16] the authors identified the contact parameters that are suitable for incorporation into the planar, multibody, belt-drive model that is presented in [14]. The procedure includes an experimental measurement of the contact-penalty parameters as well as a measurement of the friction coefficient.

The aim of this paper is to validate the belt-drive model developed by Čepon and Boltežar [14]. This validation involved using the two-pulley belt-drive. The numerically obtained results were compared with the experimental data under various operating conditions. The belt-drive


540 Čepon, G. ‒ Manin, L. ‒ Boltežar, M.

material and the contact parameters used in the numerical model were obtained from [15] and [16]. Finally, the applicability of the belt-drive mode is presented by simulating the dynamic response of the complex, serpentine belt-drive with tensioners, which are common in automotive engines.

This paper is organized as follows. In Section 1 the belt-drive model is briefly presented. The validation procedure of the belt-drive model is presented in Section 2. In Section 3 the dynamic simulation of the serpentine belt-drives is presented. Finally, the conclusions are drawn in Section 4.

1 NUMERICAL BELT-DRIVE MODEL

The numerical belt-drive model is based on multibody system dynamics together with the absolute nodal coordinate system (ANCF) [14]. An ANCF is proposed that can be used in large rotation and deformation analyses of flexible bodies that undergo arbitrary displacements. The belt is modeled as a collection of two-dimensional beam elements that are based on the element originally proposed by Berzeri and Shabana [17]. The authors in [15] additionally supplemented the above-mentioned beam element with a damping mechanism. The system of equations of motion, including all the beam elements and the constraint equations describing the connectivity constraints, can be written as:

M CC 0

e Q QQ

B B

B B

B

B

eT

e

f e

d

=

+

λλ, (1)

where MB is the constant mass matrix of the belt, CeB is the Jacobian of the constraint equations and λB is the vector of Lagrange multipliers. The vector QeB is the generalized force vector that includes external forces, Qf is the generalized force vector due to the stiffness and damping forces, and e includes the accelerations of generalized coordinates of all the belt elements.

Each belt element has five possible contact points, which are equally spaced along the length of the element, Fig. 1.

Fig. 1. Belt pulley contact formulation

In the tangential direction the discontinuous Coulomb friction law is used. In order to compute the possible sticking forces the contact problem in the tangential direction has to be formulated as a linear complementarity problem [14]. By using the discontinuous Coulomb friction law and linear complementarity problem it is possible to identify sticking and sliding contact. Moreover, events such as the transition from sticking to sliding or sliding to sticking are also possible. The equations of motion, including the contact forces between the belt and the pulley, can be written as:

q H W W hr F N N T T= + +( ) ,λλ λλ (2)

where λN and λT are the contact forces in the normal and tangential directions. Variable qr includes accelerations of generalized coordinates, HF matrix presents the system mass properties, WN is a kinematic matrix associated with normal contacts, WT is a kinematic matrix associated with tangential contacts and h is the vector of external forces [14]. Finally, the contact problem can be formulated in the form of a linear complementarity problem. As reported in [14], this formulation leads to an accurate prediction of the belt-pulley contact forces, even when non-steady, belt-drive operational conditions are considered. For a detailed description of the belt-drive model and the contact formulation between the belt and the pulley the interested reader is referred to [14] and [15].

2 VALIDATION OF THE BELT-DRIVE MODEL

2.1 Two-Pulley Belt-Drive Experimental Setup

The validation of the belt-drive model was made using a two-pulley belt-drive, as shown in


541Validation of a Flexible Multibody Belt-Drive Model

Fig. 2. A V-ribbed belt with five ribs and a K-rib section (5PK) was used.

Fig. 2. Two-pulley belt drive experimental setup

The material properties and contact parameters of the belt are given in [15] and [16] and presented in Table 1. The measured friction characteristics [16] are given in Fig. 3. The friction coefficient depends on the normal contact force and the sliding velocity in the contact.

Table 1.Two-pulley belt-drive parameters

Parameter Sym. ValueDriver and driven pulley R 0.05 m

Belt length LJ 1.2 mMass moment of inertia of the pulley JT 0.013 kgm2

Pulley central distance Lc 0.45 m

Density of the belt material ρ 0.096 kg/m

Axial stiffness EA 30400 N/ribViscoelastic damping factor cA 4.1 Ns/rib

Bending stiffness EI 5.2·10-3 Nm2/ribRayleigh parameter α 2.8 s-1

Rayleigh parameter β 1.8·10-3 s

In order to verify the numerical model the numerical results were compared with the experimentally obtained results. The driver pulley was rotated by DC motor and the torque on the driven pulley was achieved by a piston hydraulic pump. The angular velocity of driven and driver pulley was measured with HAIDENHAIN ERN1325 2048 precise optical encoders. The

initial tension of the belt spans was set by changing the mid-distance of the pulleys.

The torque on the driver and the driven shaft was measured with strain gages. Along with this measurement, the transverse displacements of the upper (tight) and lower (slack) spans were also measured using laser-displacement sensors. Based on the displacements we were able to deduce the natural frequencies of the belt spans for the given operational conditions.

2.2 Comparison between the Simulated and Experimental Results

The comparison between the numerically and experimentally obtained results was preformed with two different initial belt tensions and several angular velocities of the driver pulley.

The numerical two-pulley belt-drive model [14] is presented in Fig. 4 and the belt-drive parameters are given in Table 1.

Points A and B denote the measurement location of the transverse displacement of the upper and lower belt spans. The discretization of the belt involved using 48 beam elements. Three contact points were proposed in the contact between one beam element and the pulley.

As the beam elements have equal length, the contact points are equally spaced along the length of the belt. Thus, the periodic excitation due to the discretization is incorporated into the numerical model. This can be avoided by randomly changing the length of the beam elements, which also affects on the location of the contact points.

Friction coefficient μ

Slid

ing

velo

city

[m/s

]

Normal contact force [N]

Fig. 3. Friction coefficient versus the normal contact force and the relative tangential velocity



The random length of the beam elements was computed using the following equation:

L Ln

rand

Li

nL m

randi J

e

randie

J

= + ⋅

=∑ − ≤ ⋅ −

( . ),

,

1 0 12

11 10 4

(3)

where LJ is the length of the belt, Lrandi is the

ith length of the beam segment and rand is the random function that generates random numbers in the interval [-1,1].

2.3 Angular Speed Loss

The angular speed loss between the driver and the driven pulley has a significant effect on the efficiency of the power-transmission. Therefore, an accurate prediction of angular speed loss is of great importance, especially in the automotive industry. There are three contributions to consider when dealing with angular speed loss [11]: • the creep along belt,• the radial compliance,• the shear deflection.

Creep represents the belt stretching in the slip contact region between the belt and the pulley. Radial compliance represents the radial deformation as the rubber layer is subjected to a radial load when it is pressed against the pulley (Fig. 5).

Fig. 5. Radial compliance

For this reason the radius at the entry and exit regions of the belt-pulley contact are not equal, which then affects the angular speed loss. The shear deflection along the belt is caused by the frictional forces that are transferred from the belt-pulley contact though the rubber to the cord layer (Fig. 6).

Fig. 6. Shear deflection of the rubber layer

Usually, the analytical equation that estimates the angular speed loss is given as [10]:

∆ω ω= −− ++ +

1 2 2

2 20

01

T R M RkT R M Rk

, (4)

where T0 is the initial tension, R is the radius of the pulley, M is the torque on the pulley, k is the stiffness of the belt and ω1 is the angular velocity of the driver pulley. Eq. (4) only accounts for the creep theory and neglects all the other phenomena that impact the angular speed loss. However, in our numerical model, along with creep, the radial compliance is also taken into account.

In Fig. 7 the computed angular speed losses with the analytical Eq. (4) and the developed numerical model are compared with the experimentally obtained angular speed losses. The measured speed losses are much higher than those predicted by the analytical model or our numerical model. The grey region in Fig. 7 presents the difference between the results obtained with the numerical model of the belt-drive and the experimentally obtained results.

Fig. 4. Numerical belt-drive model



This difference is due to the tangential deformation of the belt-rubber layer, which is not accounted for in the numerical belt-drive model. It can be seen that the effect of the shear deformation becomes significant at higher torque values. The blue region presents the difference between the numerical model and the analytical model. This difference is the effect of the radial compliance, which is not accounted for in the analytical solution. In our numerical model this radial deformation is taken into account through the elastic component of the penalty contact force.

Fig. 7. Angular speed loss between the driver and the driven pulley (ω = 62.8 rad/s, T0= 310N)

Fig. 8. Angular speed loss between the driver and the driven pulley (ω = 22.6 rad/s, T0 = 310 N)

From the comparisons presented in Fig. 7 and Fig. 8 it is evident that the analytical model gives the poorest prediction of the angular speed loss. Moreover, the point of belt slippage is not correctly determined. However, our numerical model gives more reliable predictions of the angular speed loss, especially at low torques. In addition, the numerical model can quite accurately predict the point of the belt slippage. This accurate

prediction is the result of a well-identified friction coefficient and the rigidity of the belt bending [16] and [17]. At high values of torque, which occur near the slippage point, the axial force in the slack span results mainly due to the bending of the belt span. The belt bending stiffness forces the belt to bulk outwards, which generates additional axial forces in the belt. This acts as a tensioner, which supplies the minimal axial force in the slack span.

Fig. 9. Belt normal contact force versus wrapping angle

Fig. 10. Belt tangential contact force versus wrapping angle

The normal and frictional forces between the belt and the driven pulley obtained using the numerical model are presented in Figs. 9 and 10. It can be seen that the numerical model predicts the peaks of the normal and tangential forces at the entry and exit section of the belt, which was also reported in [14].

2.4 Belt Span Transverse Response

The transverse belt-span response was measured with two laser sensors positioned at the upper and lower belt spans. The experimentally obtained results were compared with the result obtained using the numerical belt-drive model.



The excitation of the belt span is caused by the roughness of the belt surface, the radial clearance, of the bearing, the wear of the belt grooves, etc.

a)

b)

Fig. 11. Magnitude spectra of the slack belt span response at point A versus the torque on the driven pulley; a) experiment, b) numerical

simulationa)

b)

Fig. 12. Magnitude spectra of the tight belt span response at point B versus the torque on the driven pulley; a) experiment, b) numerical

simulation

Due to the random nature of the excitation it is practically impossible to model all these phenomena in a numerical belt-drive model.

Thus, the time histories obtained from the experiment and the numerical model cannot be directly compared. However, we can compare the frequency contents of both signals.

In Figs. 11 and 12 the magnitude spectra of the tight and slack and belt spans versus the torque on the driven pulley are presented. The belt-span responses are obtained at a driver pulley angular velocity ω = 62.8 rad/s and initial tension of the belt T0 = 411 N. From the magnitude spectra the dependence of the belt-span natural frequencies on the drive-pulley torque can be obtained. This torque correlates directly with the value of the axial force in the slack and tight spans. The increase in the torque, when slack span is considered, causes a decrease in the belt’s axial force. This can be seen from Fig. 11a, where the dependence of the first natural frequency versus the torque can be identified. From Fig. 11b, which presents the results of the numerical simulation, even higher natural frequencies can be identified. As in the case of the experimentally obtained natural frequencies, the first natural frequency is the most pronounced. Moreover, the agreement between the experimentally identified natural frequencies and the frequency identified from the simulations is good. Similar conclusions can be drawn when a tight belt span is considered in Fig. 12. Here, the increase in the torque on the driven pulley causes an increase of the axial force of the belt. Thus, by increasing the torque the natural frequencies are increased. Also in this case, good agreement between the experiment and the numerical simulation was observed.

3 SERPENTINE BELT-DRIVE MODELING

In this section the applicability of the presented belt-drive model will be presented for modeling serpentine belt-drives with tensioners, which are common in automotive engines. The simulation will be performed for a serpentine belt-drive with three pulleys and two tensioners, Fig. 13.

Non-steady, belt-drive operational conditions are considered with the following angular velocity profile:



ωπ

=⋅ ≤ <

+ − ≥

600 3

0 0 3

60 10 2 40 0 3 0 3

t t

t t.

.

sin( ( . )) ..

s s

s (5)

Fig. 13. Serpentine belt-drive

The torque on the driven pulley is assumed to be constant and is equal to M = 45 Nm. The variables V1 and V2 denote the system of the spring and dashpot, which are connected in parallel.

In Fig. 14 the numerically obtained axial force in the tight (between pulleys P1-P2) and slack belt spans (between pulleys P3-P5) is presented. Due to the non-steady, belt-drive operational conditions, the axial forces in the belt are time dependent. The variation of the belt’s axial force is considerably smaller in the slack belt span, which is due to the use of tensioners.

a)

b)

Fig. 14. Force in the belt span; a) force in the belt span between pulleys P3-P5, b) force in

the belt span between pulleys P1-P2

In the process of the numerical simulation it is also possible to deduce the rotation of the tensioner arm, as shown in Fig. 15.

The angular velocities of the pulley in the belt-drive are presented in Fig. 16. It is evident that the angular-speed loss between the driver (P1) and the pulley (P2) is practically negligible. This is achieved with two tensioners, which supply sufficient axial tension and consequently friction, even at high torques.

Fig. 15. Rotation of tensioner arm T2

A dynamic simulation of belt-drives enables us to model the dynamic response of a complex serpentine belt. In this way, the belt-drive can be optimized from the view of the operational and shape parameters.

Fig. 16. Pulley angular velocities

4 CONCLUSION

In this paper a belt-drive model using the absolute nodal coordinate formulation is presented and a validation study is performed. A two-pulley experimental setup was proposed. Good agreement between the experimental and numerically obtained results was found. It was also shown that the numerical belt-drive model gives



a reliable prediction of the angular-speed loss, especially at low torques. Moreover, it accurately predicts the point of belt slippage. Considering the belt-span vibrations, the agreement between the experimentally identified natural frequencies and the frequency obtained from the simulation is good.

Finally, the applicability of the belt-drive model was presented by simulating a complex belt-drive with two tensioners.

In further work the parametric and sensitivity analysis should be performed in order to identify influential parameters. Moreover, the belt model should be improved by using higher order elements. This would lead to a reduction of element number and degrees of freedom and consequently, to computationally more efficient numerical algorithm.

REFERENCES

[1] Abrate, S. (1992). Vibrations of belts and belt-drives. Mechanism and Machine Theory, vol. 27, p. 645-659.

[2] Pramila, A., Laukanen, J., Pautamo, M. (1983). Vibration of axially moving material using the FEM. The ASME, paper no. 83-DET-96.

[3] Pellicano, F., Catellani, G., Fregolent, A. (2004). Parametric instability of belts: theory and experiments. Computers and Structures, vol. 82 p. 81-91.

[4] Čepon, G., Boltežar, M. (2007). Computing the dynamic response of an axially moving continuum. Journal of Sound and Vibration, vol. 300, p. 316-329.

[5] Qie, G., Dukkipati, R., Zhu, J., Qatu, M. (2008). Vibrations and instability of front-end accessory drive belt system. International Journal of Vehicle Noise and Vibration, vol. 4, p. 247-268.

[6] Hwang, S.J., Perkins, N.C., Ulsoy, A.G., Meckstroth, R.J. (1994). Rotational response and slip prediction of serpentine belt-drive systems. ASME Journal of Vibration and Acoustics, vol. 116, p. 71-78.

[7] Kraver, T.C., Fan, G.W., Shah, J.J. (1996). Complex modal analysis of a flat belt pulley system with belt damping and coulomb-

damped tensioner. ASME Journal of Mechanical Design, vol. 118, p. 306-311.

[8] Iwatsubo, T., Hasegawa, K., Arii, S., Shiohata, K. (1997). The formulation and dynamic analysis of a multiple belt system. Journal of Sound and Vibration, vol. 205, p. 293-307.

[9] Manin, L., Play, D., Soleilhac, P. (2000). Experimental validation of a dynamic numerical model for timing belt-drives behaviour simulation. ASME DETC, Baltimore.

[10] Bechtel, S.E., Vohra, S., Jacob, K.I., Carlson, C.D. (2000). The stretching and slipping of belts and fibers on pulleys. Journal of Applied Mechanics, vol. 67, p. 197-206.

[11] Gerbert, G. (1996). Belt slip ‒ a unified approach. Journal of Mechanical Design, vol. 118, p. 432-438.

[12] Leamy, M.J., Wasfy, T.M. (2002). Transient and steady-state dynamic finite element modeling of belt-drives. Journal of Dynamic Systems, Measurement, and Control, vol. 124, p. 575-581.

[13] Leamy, M.J., Wasfy, T.M. (2005). Time-accurate finite element modelling of the transient, steady state and frequency responses of serpentine and timing belt-drives. International Journal of Vehicle design, vol. 39, p. 272-297.

[14] Čepon, G., Boltežar, M. (2009). Dynamics of a belt-drive system using a linear complementarity problem for the belt-pulley contact description. Journal of Sound and Vibration, vol. 319, p. 1019-1035.

[15] Čepon, G., Manin, L., Boltežar, M. (2009). Introduction of damping into the flexible multibody belt-drive model: A numerical and experimental investigation. Journal of Sound and Vibration, vol. 324, 283-296.

[16] Čepon, G., Manin, L., Boltežar, M. (2010). Experimental identification of the contact parameters between a V-ribbed belt and pulley. Mechanism and Machine Theory, vol. 45, p. 1424-1433.

[17] Berzeri, M., Shabana, A.A. (2000). Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation. Journal of Sound and Vibration, vol. 235, p. 539-565.


*Corr. Author’s Address: Laboratoire d’Ingénierie des Systèmes de Versailles, Université de Versailles Saint-Quentin-en-Yvelines, 7, rue Jean Hoët - 78200 Mantes-la-Jolie, France, [email protected] 547

Integrated Design for Fatigue Life Estimation of StructuresAkrache, R. ‒ Lu, J.

Radouane Akrache1,* ‒ Jian Lu2

1Laboratoire d’Ingénierie des Systèmes de Versailles, Université de Versailles Saint-Quentin-en-Yvelines, France

2Laboratoire des Systèmes Mécanique et Ingénierie Simultanée, Université de Technologie de Troyes, France

The design of a product or a mechanical system involves several stages, starting with the development of product specifications and ending with its final destruction. The aim of our research is to develop appropriate tools by proposing new operating methodologies and new computer tools to link up material development process with the mechanical design. In the first part, we will outline the overall approach adopted, and describe an integrated design method for estimating the fatigue life of mechanical structures. In the second part, we will discuss prestressing processes and take them into account in our approach. The third part is devoted to developing a calculation code for determining the multiaxial fatigue life of 3D structures.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: multiaxial fatigue life, integrated design, finite element method, fatigue criteria

0 INTRODUCTION

To achieve the aim of integrated design of mechanical systems, research into integration problems of and on a more fundamental level, the development of modelling tools and experimental control techniques are indispensable. Several factors have been integrated, corresponding to the optimization of mechanical systems, modelling of non-linear problems, experimental measurements, surface treatment, and the study of new materials and new manufacturing processes. In the field of optimization, a special resolution method has been developed [1]. It shows that, based on several concepts, a design problem can be expressed as a problem of optimization. This, in turn, allows us to produce a calculation code for non-linear optimization with mixed variables. These concepts can also be used to optimize the geometry of a part according to criteria such as cost, endurance and lifetime. In currently available software, a mechanical system is represented as the sum total of the volumes of its different components. This type of representation does not enable the user to easily design a mechanical system. A certain number of fundamental notions have also been left aside in current CAD systems. We therefore, propose adding several modelling and optimization modules to these tools. Another module i.e. the calculation of fatigue life is also

integrated into this global approach as indicated in Fig. 1.

Fig. 1. Flow-chart of fatigue life evaluation during the design phase

1 TAKING RESIDUAL STRESS INTO ACCOUNT

1.1 Definition

Residual stress is generally defined as the stress that persists in a mechanical component which is not subjected to outside stress. Residual stress exists in practically all metal parts. It corresponds to the mechanical and metallurgic history of each point in the component and the component as a whole during the manufacturing


548 Akrache, R. ‒ Lu, J.

process. It generally exists on three levels depending on the scale on which it is observed: (i) macroscopic stress; (ii) stress due to the heterogeneity and anisotropy of each crystal or grain in a mechanical polycrystalline, and (iii) microscopic stress. In structural analysis, macroscopic residual stress is used and modelled.

1.2 Integration of Residual Stress into Fatigue Life Calculation

The integration of residual stress into a computable calculation must be gradual and can be separated into several phases. Currently, little direct consideration is given to the residual stress parameter in design. In specifications, requirements that are often closely linked to residual stress without specially mentioning it, are made . In the first phase of integration, the notion of semiquantitativity can be used to evaluate the increase in performance in terms of lifetime or limit of endurance. Several manufacturing processes and surface treatments develop residual stress, which tends to increase the fatigue life and the limit of endurance. These processes include shot-peening, cold rolling and nitriding. The second phase consists in developing analytic and numerical calculation methods integrating residual stress. The method which takes residual stress into account in our approach is indicated in Fig. 2.

Fig. 2. Taking residual stress into account

On an experimental level, recent developments have enabled residual stress profiles

induced by various industrial processes [2] to be obtained. It has been known for a long time that residual stress can be relaxed when components are subjected to cyclic loading. Using the 2D finite element method, we have modelled residual stress relaxation and the influence of the various factors involved. A criterion for determining the stability of the residual stress as a function of the cyclic characteristics of the materials [3] and [4] has been proposed. For a material with cyclic softening, there is gradual relaxation of residual stress whereas, for a material with cyclic hardening, the residual stress is stabilised after several fatigue cycles (Fig. 3).

Fig. 3. Influence of cyclic properties on the fatigue resistance of materials

Continuation of this research consists from developing methods for calculating the relaxation of residual stress in three-dimensional structures under complex thermomechanical loading. The major difficulties lies in introducing residual stress profiles measured on 3D structures. Recent studies have improved the possibility of carrying out this type of calculation [5].

If the different effects of residual stress on the appearance of fatigue in structures is known, then a quantitative estimatation of the fatigue life can be given. By limiting the estimation of the lifetime of a component to the initial appearance of fatigue cracking, the problem of predicting the lifetime of a mechanical component subjected to a high number of cycles (>5.104 cycles) can be analysed. To achieve this aim, a tool for predicting fatigue life must be developed. In the next section this calculation code that will integrate the residual stresses is presented.


549Integrated Design for Fatigue Life Estimation of Structures

2 DEVELOPMENT OF A FATIGUE LIFE CALCULATION CODE

2.1 Introduction

Predicting the fatigue life of three-dimensional structures is always a tricky problem, because it must assess the length of time during which man and machine are safe. Whenever new parts are developed in industry, their fatigue life has to be estimated to check the durability of the corresponding mechanism. To carry out this estimation, experiment-based criteria must be established.

2.2 Fatigue Criteria

The scientific literature includes several suggestions for fatigue criteria. Some were originally applied to particular loading conditions. In order to produce a fatigue design for structures under dynamic loading, the safety range limited by a threshold needs to be calculated. Above this threshold, the material will be damaged or cracks will appear. For high cycle fatigue, most of the criteria are stress-based formulae. In practice, the critical values for these parameters are calculated and checked that the loading case obtained is within the range of safety.

2.2.1 Crossland and Sines Criteria

The plasticity model used as a basis for these criteria is the Von Mises criterion which suggests that plasticity appears when the octahedral shear (shear relative to the facet leaning equally on the principal axes) reaches a certain limit. These two criteria are expressed by a linear relationship between the octahedral shear amplitude and the hydrostatic pressure (mean pressure during the cycle for the Sines criterion [6], maximum pressure for the Crossland criterion [7]). If fixed coordinate axes towards the material are chosen (x, y, z) the stress variation tensor ∆Σij( ) between two instants, t1 and t2, of the

cycles is written:

∆Σ Σ Σij ij ijt t t t( , ) ( ) ( ) .1 2 2 1 = − (1)

The second invariant J2 of this tensor is intrinsic: an intrinsic octahedral shear amplitude can be defined by:

∆ ∆τoct a J, ,=

12

23 2

12

(2)

where ΔJ2 is the largest possible value of the second invariant, obtained by double maximisation:

∆ ∆ΣJ J t tt t ij2 2 1 21 2

=

max max ( , ) . (3)

The limit for the Sines and the Crossland criteria will be: ∆τoct a mB P A, + ⋅ ≤ , (4)

∆τoct a B P A, max+ ⋅ ≤ . (5)

2.2.2 Dang Van Criterion

Dang Van [8] postulates that the basic mechanism of fatigue cracks is the maximum shear of the most unfavourably positioned crystallographic plane. The material is considered homogeneous and isotropic at the macroscopic scale and is composed of monocrystals (or grains) with uncertain positions. The unfavourably positioned grains can be represented by an elastoplastic insertion immersed in an elastic matrix. The first cycles produce plastic slip at the grain level, and are rapidly stabilized: there is local elastic shakedown of the material. The fatigue criterion is expressed as a linear combination of the local shear stress in these grains and the concomitant hydrostatic pressure:

τ α βn t P t, ( ) .( ) + ⋅ = (6)

The shear expression is obtained by using the Tresca criterion:

τ σ( ) ( ) .t tij= max Tresca (7)

The model is represented in the plane [τ(t), P(t)]; every couple [τ(t), P(t)] concerns a particular facet and is situated in the half-plane position τ(t). The constants α and β are determined from two tests under simple loading. At least two Wöhler curves are to calculate their constants can also be used. In this case, the Wöhler curves used have a 50% probability of rupture.



2.2.3 Lu Criterion

This criterion [9] is based on the amplitude of the octahedral shear stress (τoct) or the maximum shear stress (τmax), and the maximum pressure Pmax. For different materials, τoct or τmax is the critical plane. The basic criterion can therefore be expressed as follows:

τ τmax, , , , .a oct a m altor f AP BP C= ( ) (8)

An example can be given using the following formula:

τmax, ,a mD

altEA P B P C+ ( ) + ( ) ≤ (9)

where A, B, C, D and E are material constants.• If τa is taken in the maximum shear plane

(τmax,a), then D = E = 1 and A = B, which gives the Dang Van criterion.

• If τa is taken in the octahedral shear plane (τoct,a), when:

• D = E = 1, A = B ; we obtain the Crossland criterion,

• D = E = 1, B = 0 ; we obtain the Sines criterion,

• D = E = 1, A ≠ B; we obtain the Kakuno criterion [10].

This type of development can be continued to invent new criteria, but it only makes matters more complicated because more and more parameters have to be determined, since even with a Dang Van linear relationship, two Wöhler curves have to be determined to obtain at least the two points needed to construct the diagram. This criterion only becomes complex with particular loading and materials. As a result, it is the only fatigue criteria formula that can be used for a high number of cycles. However, the basic difference between this proposal and the other three criteria is obvious for non-proportional loading and in presence of stress concentration. In this case, the new criterion is proposed to make calculations at critical depths with stabilized states (elastic shakedown or plastic shakedown), and to take the combined out-of-phase stress effect into account using maximisation on all axes. For a combined torsion/bending out-of-phase stress, the Dang Van criterion can be written in the following form:

12

4

3

2 2σ ω τ ω ψ

σ σ ω

a a

m a

t t

A B t

sin sin

sin .

( )( ) + +( )( ) =

= + + ( )( ) (10)

Since this formula does not take the results during dephasing stress into account with sufficient precision [7], we suggest modifying it as follows: shear amplitude according to Tresca or Mises (τa, maximized on all the component axes and for all the terms of the loading sequence) = A + B·Pmax. For a combined torsion/bending out-of-phase stress using the Tresca criterion, this gives:

12

4

3

2 2σ τ

σ σ

a t a t

m a t

k

A B

,max ,max

,max ,

( ) ( )

( )

( ) + ( ) =

= + +( ) (11)

k is a so-called phase lag-sensitive coefficient. It depends on the nature of the material, the frequency, level and type of the stress. If there is no stress dephasing, then k = 1. The physical signifiance of this formula is as follows: when there is dephasing stress, the time needed by the material to react depends on the nature of the material and the loading level. The material remembers, as it were, the maximum previous stress along another stress axis. Therefore, the stress level to be taken into account is not the maximum stress along one axis and the instantaneous stress along the other axes, but the maximum stress τa1,max, τa2,max and τa3,max along all the axes. Where, for i = 1, 3:

τ τai t t t t ai t t,max , ,max max .1 2

1 21 2( ) ( )=

(12)

When the stress frequency is high, the time needed for the memory effect to occur is even lower still. When there is stress dephasing and if k is between 0 and 1, the errors are relatively small. Using k = 1 for high cycles fatigue limit when the loading frequency is higher than 15 Hz, a maximum underestimation of the fatigue resistance corresponding to 10% is observed. Thus, the general formula depends on the maximum stress along all the axes, and coefficient k:



τ τmax ,max , , .= ( )( )f kai t t1 2 (13)

2.3 Fatigue Life Prediction

We have developed a global approach to calculate the fatigue life of 3D structures [11]. The numerical results obtained by using a finite element method, together with the tests results, were introduced into a main program (Fig. 4). The results are shown by graphic representation of the fatigue life of the structure. The mechanical characteristics of the selected material, together with the fatigue data in the form of Wöhler curves, are recovered. In our case, the Wöhler curves we used have a 50% probability of rupture. For a criterion with two constants, such as that of Crossland, Sines or Dang Van, at least two Wöhler curves are needed to calculate their constants. In the case of simple or combined in-phase loadings, the Sines, Crossland or Dang Van criterion can be used. When there is combined out-of-phase loading, the Lu criterion is added to the list of possible criteria. Once the two constants have been calculated for the fatigue criterion chosen, the corresponding line on the diagram for this criterion can be plotted. This line will correspond to a particular number of cycles.

Fig. 4. Fatigue life calculation

Likewise, several lines can be plotted on the criterion diagram (each line corresponds to a specific number of cycles), the coefficients of which are calculated using the Wöhler curves (Fig.

5). This method is normally valid in the field of endurance, but we have extended the use of the fatigue criterion to include other field. An example of plotting of life contour is given for a notched specimen subjected to bending. The structure studied is modelled with CAD software to provide data in standardized form. The boundary conditions and the loading are assigned to the structure. With finite element software such as Abaqus or I-DEAS, an elastic or elastoplastic analysis can be carried out. The results of calculations based on the finite element method, in the form of stress tensors, are recovered and integrated into the fatigue life calculation module. As a result, the fatigue life in the diagram for the criterion used can be mapped. This means that, at any point on the criterion diagram, there is the corresponding fatigue life.

Fig. 5. Map of fatigue life in (τ,P) diagram

This approach is applied to simple loading (alternate tension, alternate bending, etc. or combined loading (bending-tension, torsion-tension, etc.) whether it is in-phase or out-of-phase. If it is out-of-phase, the method proposed by Lu is used to prove the applicability of the method and to take the out-of-phase effect into account.

An example of application of this method relates to two different notched specimens subjected to the same loading. The specimens have stress concentration coefficients corresponding to: kt1 = 1.3, and kt2 = 1.7. Tests were carried out



on FGS cast iron. The mechanical properties for this material are tensile strength of 750 MPa, a Young’s modulus of 162.2 GPa and a yield stress of 416 MPa. The bending fatigue strength is 294 MPa (R = -1), and the torsion fatigue strength is 218 MPa (R = -1). The fatigue life is calculated for the two specimens using the Crossland fatigue criterion. The computational results are illustrated for the initial specimen in the form of cartography (Fig. 6).

Fig. 6. Prediction of fatigue life for two different specimens; a) a coefficient of stress concentration kt1 = 1.3, b) a coefficient of stress concentration

kt2 = 1.7

These results show a clear difference in fatigue life prediction when the notch shape changes. Specimen with a coefficient of stress concentration equal to kt1 = 1.3 has a longer fatigue life than those coefficient of stress concentration is equal to kt2 = 1.7. An example is given of the predicted fatigue life in the case of a combined bending/torsion out-of-phase (phase angle 90°). In this case, the best fatigue life prediction results were obtained with a dephasing-sensitive coefficient k = 0.13 for Lu criterion. This criterion can therefore, be applied successfully in the case

of combined out-of-phase loading. The results obtained for the different criteria using the Wöhler curves are compared with the experimental results (Fig. 7).

Fig. 7. Prediction of Wöhler curves

2.4 Prediction of Admissible Residual Stress and the Safety Coefficient

In this approach [11], a calculation method for predicting the admissible residual stress and the safety coefficient for a particular fatigue life has been developed. It is thus possible to use this tool during the design phase to determine whether or not residual compressive stress should be introduced. The computer code also indicates the level of the residual stress and the zone in which it should be introduced.

Fig. 8. Calculation of safety coefficient in (τ,P) diagram

The purpose of the first method is to predict the safety coefficients of a structure for a particular fatigue life in order to know the performance to



be improved. The same notched specimens as for he prediction of the fatigue life were used. In this part, only the Crossland criteria will be used. The general principle of the calculation of the safety coefficient is illustrated in Fig. 8 with any fatigue criterion (Crossland, Sines, Haigh or Goodman). The simulation was carried out on FGS cast iron in bending. The targeted fatigue life for our specimen was 106 cycles. For this desired fatigue life, the representative point “L” of a tensile load is placed in the diagram of the Crossland criterion. We then calculate the value of the safety coefficient which is given by the following Eq.:

s OMOL= . (14)

Using the Wöhler curves of FGS cast iron, admissible residual stress are predicted for a particular fatigue life of 106 cycles represented by the line drawn in the diagram of the Crossland criterion (Fig. 9).

Fig. 9. Calculation of admissible residual stress (ARS) in (τ,P) diagram

For a load equivalent to the amplitude L1 or L3, the fatigue life is equal or greater than 106 cycles. It is not necessary, therefore, to introduce residual stresses in the structure.

When the load L2 is applied, it induces a short fatigue life. To achieve a fatigue life of 106 cycles, negative admissible residual stresses (ARS) in the structure can be introduced. The idea is to provide these constraints and also the different surface treatments applied to achieve the desired fatigue life.

In case applying the load L3, its fatigue life is greater than 106 cycles. Then residual stresses

will not need to be introduced, and consequently, no surface treatment.

Fig. 10. Prediction of admissible residual stress for a targeted lifetime of 106 cycles [MPa]

By mapping the safety coefficients for a particular fatigue life, the areas with the highest risk which must be modified accordingly during the design and manufacturing stage can also be predicted. It has been observed (Fig. 10) that fatigue life is minimal in zones with high stress concentration. In these same zones, residual compressive stress must be introduced in order to achieve the required fatigue resistance of the structure. The predicted safety coefficients in bending needed for the structure to resist fatigue up to 106 cycles (Fig. 11) was also mapped.

Fig. 11. Prediction of safety coefficient for a targeted life of 106 cycles

3 CONCLUSION

As part of a global approach to integrated mechanical design, a tool for calculating fatigue life, which is compatible with industrial software such as Abaqus and I-DEAS, has been developed. The tool allows no proportional multiaxial loading



and residual stress to be taken into account. By combining it with other tools developed in our laboratory, components and mechanical systems can be optimized. For a given lifetime of a particular material and loading, modelling can be used to indicate whether prestressed is necessary. The areas to be reinforced together with the prestressed conditions required can also be mapped. In this way, a genuine prestressed engineering strategy can be developed. Residual stress will no longer be considered the result of a manufacturing process, but a modifiable parameter. It can thus be optimised according to mechanical loading.

4 ACKNOWLEDGEMENTS

The authors would like to thank the Ministry of Research and Technology for the financial support thus enabling this research.

5 REFERENCES

[1] Lafon, P. (1994). Optimal design of mechanical system: optimization of variables mixed. PhD, INSA Toulouse. (in French)

[2] Lu, J. (ed.) (1996). Handbook of measurement of residual stresses. The Fairmont Press-Prentice Hall.

[3] Lu, J., Flavenot, J.F., Turbat, A. (1988). Prediction of residual stress relaxation during fatigue, Mechanical relaxation of residual stresses. ASTM STP993, p. 75-90.

[4] Lu, J., Flavenot, J.F., Turbat, A. (1988). Residual stress relaxation under cyclic loading: Influence of the mechanical properties and prediction by calculation,

Memory and scientific study, p. 615-626. (in French)

[5] Rouhaud, E., Milley, A., Lu, J. (1997). Introduction of residual stress fields in finite element three-dimensional structures. 5th Int. Conf. on Residual Stresses, ICRS, Linkoping

[6] Sines, G. (1981). Fatigue criteria under combined stress or strain. Transactions ASME, J. Eng. Mat. and Tech., vol. 13, p. 82-90.

[7] Crossland, B. (1956). Effect of large hydrostatic pressure on the torsional fatigue strength of an alloy steel. Int. Conf. on fatigue of metals, IME/ASME, p. 138-149.

[8] Dang Van, K., Cailletaud, G., Flavenot, J. F., Douaron, Lieurade, H.P. (1984). Fatigue initiation criterion to large numbers of cycles under multiaxial stress. J. Int. de Printemps: Amorçage des fissures sous sollicitations complexes, French Society of Metallurgy, p. 301-337.

[9] Lu, J., Flavenot, J.F., Diboine, A., Lasserre, S., Froustey, C., Bennebach C., Palin-Luc, T. (1996). Development of a general multiaxial fatigue criterion for high cycles of fatigue behaviour prediction. Multiaxial fatigue and design, Pineau, A., Cailletaud, G., Lindley, T. C. (eds.), The European Structural Integrity Society, ESIS 21, Mechanical Engineering Publications, p. 477-487.

[10] Kakuno, H., Kawada, Y. (1979). A new criterion of fatigue strength of a round bar subjected to combined static and repeated bending and torsion. Fatigue of Eng. Mat. and Structures, vol. 2, p. 229-236.

[11] Akrache, R. (1998). Prediction of fatigue life of 3D structures by the finite element method. PhD, UTT de Troyes. (in French)


*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, [email protected] 555

Mesh Smoothing with Global Optimization under ConstraintsKulovec, S. ‒ Kos, L. ‒ Duhovnik, J.

Simon Kulovec* ‒ Leon Kos ‒ Jožef DuhovnikUniversity of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Mesh (pre)processing remains an important issue for obtaining useful meshes used in mechanical engineering, especially for finite element calculations. An efficient and robust combination of constrained mesh smoothing together with global optimization based algorithm is presented. In contrast to other “popular” mesh smoothing algorithms that use only local diffusion approaches to smoothing we propose Lagrange-Newton Sequential Quadratic Optimization (LNO) with constraints that can satisfy local and global cost functions, respecting posed constraints. Local cost function is modeled with local average edge length, while global cost function includes barycenter and global average edge length.

Experiments with triangular, quadrilateral, and mixed meshes show flexibility of the proposed method to achieve near ideal elements for given input meshes. Convergence is presented for several 2D and 3D meshes. Various additional goals can be mixed over the area of interest with applied weights. In contrast to other methods, unconstrained meshes still preserve their global shape while improving local quality. ©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: smoothing, sequential quadratic optimization, SQO, mesh structure, geometry, vertex, cost function

0 INTRODUCTION

Mesh optimization methods are used in mechanical engineering applications areas such as solid and fluid dynamics, heat transfer, material science etc. The numerical investigation of these physical problems may require fine grained meshes over a single area of a physical model to resolve large solution variation. Even some commercial software still has problems with fine mesh generation, thus assuring effective and robust adaptive grid methods for such problems is still necessary. Currently, the majority of virtual reality applications use triangular meshes as their fundamental modeling and rendering is primitive. Such meshes can be the result of the modeling software, or may be an output of a scanning device. Their properties are often not considered as meshes with high quality. They have a non-ideal mesh elements and bad vertex connectivity. With mesh optimization one can systematically achieve improved mesh quality that will provide a reliable analysis. The purpose of this paper is to show effective mesh optimization technique that ensures better mesh structure and is applicable to general meshes. Improvements in mesh are obtained by just repositioning of vertices without changing connectivity. I.e., the position of the

mesh vertices is modified, but the mesh topology remains unchanged. While internal mesh vertices are freely movable, external vertices must often remain fixed on boundaries. Moving (or shifting) vertices can have a drastic effect on the quality of a mesh and it is more efficient than refinement and collapsing vertices especially when the translation amplitudes are small. Such mesh relaxation can be regarded as mesh smoothing as it results in a visually pleasing mesh that follows some local or global rules.

Our approach is based on the general theory of the Lagrange-Newton Optimization [1] (LNO) applied to the finite element meshing problems. The LNO method is one of the iterative quadratic methods. In these methods, each iteration step includes a solution of a quadratic optimization problem. LNO is a non-linear optimization and originates from Sequential Quadratic Optimization (SQO). Comparable smoothing methods are Laplacian [2], Lennard-Jones [3], and Plaint [4]. Our smoothing technique differs from the above mentioned in several notable ways: (a) it is not restricted to triangular meshes, (b) includes global and local optimization cost functions, (c) preserves boundaries and can assure various geometrical constraints, (d) can be applied to 2D and 3D meshes as well as non-


556 Kulovec, S. ‒ Kos, L. ‒ Duhovnik, J.

manifold ones, (e) cost function can be weighted and extended with additional functionals, (f) pre-calculates average edge lengths at every iteration step. This ensures very fast convergence and flexible vertex movement.

In practical implementation of general purpose LNO theory the input mesh structure is processed using .OBJ or .STL file format. The source code is written in the C++ programming language. For the mesh handling, we used an open-source library (Open Mesh).

The motivation of the work presented is to propose and analyze reasonable cost functions and to compare how they perform in “benign” situations and to identify the most promising ones for application on difficult problems. This paper considers only meshes in which the vertices are moved with a fixed connectivity with applied movement constraints on the boundary vertices.

The paper is organized as follows. Section 1 describes the basics of a constrained optimization, Sequential Quadratic Optimization, Lagrange Newton Optimization, and connections between these two methods for general meshes. Section 2 discusses cost functions followed by differences between global and local constraint optimizations. In Section 3 several complex meshing examples are presented to demonstrate the effectiveness and the effect of the proposed mesh optimization method. After discussion of the results, conclusions are given in Section 4.

1 BACKGROUND

In a general optimization, the aim is to obtain the best result under given circumstances. The ultimate goal of an engineer‘s decisions is to minimize the effort required or to maximize the desired benefit. An optimization can be defined as a process of finding the conditions that give the maximum or the minimum value of a function [10]. From Fig. 1 it can be seen that if the point x* corresponds to the minimum value of the function f(x), the same point also corresponds to the maximum value of the negative of the function.

Constrained optimization techniques can be classified into two main categories: the direct and the indirect methods. The constraints in the direct methods are handled in an explicit manner, whereas in most of the indirect methods,

the constraint problem is solved in a sequence of unconstrained minimization problems. Our mesh optimization problem is an indirect optimization technique using the method of sequential quadratic programming.

Fig. 1. The minimum of f(x) and the maximum of - f(x) are the same values of x*

1.1 Sequential Quadratic Optimization

The SQO is considered as one of the best iterative optimization techniques. The method can be divided into two theoretical bases: (i) a set of nonlinear equations is solved by using the Newton’s method, and (ii) a Lagrangian function formed with Kuhn-Tucker conditions. Find the solution of:

x f x

H x c xx H

n

* arg min ( ),

( ) .

=

= ∈ = ∈

0 (1)

Here ci is the ith component of a constrained function c n r: . Now the Lagrange’s func-tion can be written:

L(x,λ) = f(x)‒λT·c(x), (2)with the gradient

L xL x

L xf x J

c xx c

T'

'

'

',

( , )

( , ) ( ),λ

λ

λ

λ

λ

( ) =

= ( ) −

−

and the Jacobian matrix of the constraint c is:

Jcxxc ij

i

j( ) =

∂∂

( ).

At the stationary point xs is L'(xs, λs) = 0, which satisfies the constraints and Kuhn-Tucker conditions.


557Mesh Smoothing with Global Optimization under Constraints

Thus, a non-linear system of equations is obtained:

Find (x*, λ* ) to satisfied L’(xs, λs) = 0.To solve this problem, the Newton-

Raphson’s method can be used. In each iteration step, the next iterate solution is found as (x+h, λ+η). Each step is determined by L''(x,λ) [h η]T = ‒L′(x,λ), with:

LL L

L LW JJ

xx x

x

cT

c

'''' ''

'' '',=

=

−−

λ

λ λλ 0

where W L xxx= ( )'' ,λ and

L x f x c xxx ir

i i'' '' ''( , ) ( ) ( ).λ λ= − =Σ 0

When one Newton-Raphson step is solved by x=x+h, λ=λ+η, ,and elimination of η:

W JJ

h f xc x

cT

c

−−

= − −

0 λ

' ( )( )

. (3)

Eq. (3) gives the solution h and the corresponding Lagrange multiplier vector λ to the following problem:

Find h argmin q he= ∈ ( ) .

In the next step, a constant q h h Wh f x hT T( ) = ⋅ + ( )1 2/ ' is defined and con-straints lin n

ch |J h c x= ∈ + ( ) = 0 .

1.2 Lagrange Newton Optimization

LNO is a kind of Sequential Quadratic Optimization [1]. The name Lagrange-Newton comes from the two steps: in the first one, a Lagrangian function is optimized followed by the second, the Newton step when a new solution achieved. The first efficient implementations were developed by Han (1976) and Powell (1977) [1]. Currently, it is considered as the most efficient method.

The LNO method includes a soft line search with a special type of the penalty function. The description with an update method for the Hessian matrix can be concluded. This makes the method a Quasi-Newton [1] with a good final convergence without having to implement second derivates.

First, a quadratic model q of a cost func-tion in neighborhood of x is considered,

f x q

f x f x W xT T

+( ) ≈ ( ) == ( ) + ( ) + ( )

δ δ

δ δ δ' / ,1 2

then, a feasible region is defined,

Hd i rd i i r m

n i

i

= ∈= =≥ = +

δ

δδ

( ) , , ,( ) , , ,

....

...0 1

1

Corresponding to a linear model, the constraints: c x d c x J xc+( ) ≈ ( ) = ( ) + ( )δ δ δ .

First the step parameter α and matrix W(x) need to be calculated.

Next, the step length alpha must be calculated. If h turns out to be too large, the quadratic model may be a poor approximation of the true variation of the cost function. Therefore, a soft line search is made (a so-called exact penalty function) described in Fradsen [1]. For μi ≥ |λi| is:

π µ µ

µ

y f y c x

c y

i

r

i i

i r

m

i i

, ( )

min , ( ) .

( ) = ( ) + +

+

=

= +

∑

∑1

1

0

(4)

The choice of the penalty factor is divided into two parts: (i) the first iteration step μ ≥ |λ|, and (ii) the later iteration steps:

µ λ µ λi i i i= +( ) max , / .1 2 (5)

The linear approximation for ci(y)=ci(x+αh) is:

π α ψ α α

µ α

µ

( ) ≈ ( ) = ( ) + ( ) +

+ ( ) + +

+

=

= +

∑

∑

f x h f x

c x h c x

T

i

r

i iTi

i r

m

i

'

' ( )1

1

mmin , ( ) .'0 c x h c xiTi( ) +α

(6)

We accept the value of α that the point (α,π(α)) is below the dashed line indicated in Fig. 2. The slope of the coordinate between (0,ψ(0)) and (q,ψ(1)) is 10%.



∆ = ( ) − ( ) −

− ( )

=

= +

∑

∑

h f x c x

c x

T

i

r

i i

i r

m

i i

'

min , .

1

1

0

µ

µ

(7)

Fig. 2. Approximation ψ(α) of the line search function π(α)

To approximate π(t) on the interval [0, α] the second order polynomial P(t) = π(0) + Δt + (π(α) ‒ π(0) ‒ Δα) t2 ⁄ α2 is used. If the coefficient t2 > 0, then polynomial has a minimizer:

βπ α π α

α=

( ) − ( ) −−∆ 2

2 0( ).

∆ (8)

The iteration procedure calculation of α = min0.9α, maxβ, 0.1α is repeated until π(α) ≥ π(0) + 0.1Δα.

For the next iteration step, it is required to update W(x), which for the first iteration equals I. In the next iteration steps:

W x L xxx( ) = '' ( , ).λ (9)

The change in the gradient of Lagrange’s function is:

y L x L x

f x f x J x J x

x new x

new c new cT

= ( ) − ( ) =

= ( ) − ( ) − ( ) − ( )( )

' '

' '

, ,

,

λ λ

λ (10)

where xnew = x + αh. In each iteration, the curvature condition,

yT (xnew‒x) > 0 must be checked If the condition does not satisfy Wnew = W, then for u = Wh:

W Wh y

yyh u

uunew TT

TT= + −

1 1α

. (11)

The whole procedure of the Lagrange Newton method is repeated until the stop criterion is satisfied. For x = xprev + αh. the stop criterion is:

η α

λ

λx q h f x

c x c xi

i ii

i

, ( )

( ) min , ( ) ,

( ) = ( ) − +

+ + ∈ ∈∑ ∑L M

0 (12)

where is a set of active inequality and equality constraints, and is a set of inactive inequality constraints.

2 COST FUNCTIONS DEFINITION

First, a definition of two optimization cost functions with the constraints: (i) local and (ii) global is given. The cost functions will be formed from mesh vertices. In our case, the functions will ensure similarity of mesh elements (equal triangles, quads, etc. in one 2D mesh structure) on the (i) local and (ii) global level. The most important constraint is that the vertices are moved with a fixed connectivity. That means the vertices must be connected with the same edges even after optimization.

2.1 Local Cost Function

In the first step the equation of the local average length is defined:

l

v v

pi nav i

i j i jj

p

( , )

( , ) ( , )

, .=

+==

−

=∑ 1

0 1for to (13)

Let us begin with the vertex of the mesh structure vi,j. Operator || || is the Euclidian norm operator. Indices i and j define vertex position in the mesh structure. Index i represents the number in the mesh structure vertices (i = 1 to n) and index j represents any mesh element of the mesh structure ( j = 1 to m). xi,k (triangle, quad, etc.) are the edge lengths. The mesh elements in Fig. 3 are represented by indices i and k. Index k represents the kth edge of the local mesh element (k = 1 to p). There are three constant values for the input mesh structure: (i) number of all vertices n), (ii) number of all mesh elements m), and (iii) number of edges in one mesh element p).



Fig. 3. Triangular mesh elements presentation

In the second step the local cost function is defined:

f v v llocali

m

j

p

i j i j av i= − −( )=

−

=

−

+∑∑0

1

0

1

12

, , , . (14)

Eq. (13) presents the average local length of an input mesh element (triangle, quad, etc.). For variables introduced in Eq. (13) see Fig. 3.

2.2 Global Cost Function

In this cost function pre-calculated average edge lengths are used. The edge lengths are constant during iterations and can thus be considered as global. The lobal cost function is defined as:

f v v lglobali

m

j

p

i j i j av gl= − −( )=

−

=

−

+∑∑0

1

0

1

12

, , , , (15)

with the global average length (see Fig. 4):

lv v

m pav gli

m

j

pi i

,

, ,.=

−

+=

−

=

−+∑ ∑0

1

0

11 0 0

(16)

The set of nonlinear equations is solved using the Lagrange-Newton optimization method. The LNO method searches the design vector solution X = x x xn

T1 1, ,,... , which minimizes

f(x).The design vector x1 for i = 1 to n is a set

of optimized vertex coordinates.

Fig. 4. Quadrilateral mesh elements presentation

2.3 Smoothing Methods

The most common smoothing method is Laplacian [2], where each vertex is moved to the centroid of its neighbors. Laplacian smoothing defines the number of adjacent vertices to vertex i with ℵ = i j j i| shares an edge with averaged over number of vertices αi i= ℵ1/ , and the force between vertices f(d) = 1. Vertices thus always attract each other regardless of the distance.

The Lennard-Jones potential [3] from chemistry describes attraction/repulsion behavior. Its smoothing function is f(d) = d‒13 ‒ d‒4. This model suffers from numerical instabilities.

The Pliant method with re-triangulation [4] uses f(d) = (1‒d4) ·exp(‒d4). The goal of the method is to create meshes with normalized edge length of 1. Reasoning behind this smoothing function is that if two vertices are too close to each other (d < 1), they repel, and if they are too distant (d > 1), they attract each other.

In our mesh smoothing optimization local (LCF) and global (GCF) cost function (Sec. 2.1 and 2.2) optimization is proposed. The main advantage of our optimization method is global mesh structure optimization. That means that all the vertices in mesh structure are repositioned in one iterations step. Other methods use just one vertex (diffusion) repositioning per iteration step.

With the local cost function vertices of mesh structure are moved to ensure equal edge lengths of faces. In contrast to other smoothing methods our LCF method calculates average edge lengths in every iteration step for all faces. This ensures flexible vertices in the mesh structure.

For GCF we propose mesh smoothing with constant average edges lengths which



are calculated before smoothing begins. Our optimization algorithm can ensure approximately equal external form as the initial mesh structure even after optimization without boundary constraints.

3 RESULTS

At the beginning the results of this optimization method with two different cost functions applied to many different data sets, ranging from small sets sampled from simple mesh structures to complex models with many vertices, are showed. For the small samples, the final vertices positions are known.

a) b) c)Fig. 5. A simple triangular mesh structure; a)

initial, b) local optimized after 5 iterations, and c) global optimized after 4 iterations meshes

a) b)Fig. 6. Convergence of a) local after 5 and b)

global cost functions after 4 iterations

We began with a simple triangular mesh with fixed boundary mesh elements. Then, the center vertex was moved into some extreme position (see Fig. 5).

In the next step the LNO algorithm was applied. The expected result after LNO is to have a vertex in middle position of boundary area. In Fig. 3 results for two different cost functions and LNO results for local (see Fig. 5b) and global (see Fig. 5c) oriented cost functions are presented. In this case the results are equal. Using global iteration is favorable due to faster convergence.

The second “trivial” example for testing the LNO algorithm is quadrilateral mesh structure shown in Fig. 7.

a) b) c)Fig. 7. Simple quadrilateral mesh structure; a)

initial, b) local optimized after 4 iterations, and c) global optimized after 3 iterations meshes

a) b)Fig. 8. Convergence of a) local after 4 and b)


The result of the LNO method are four equal square elements in the input mesh structure for the local and global cost functions. A similar result for the vertex positions after application of the LNO algorithm is expected. The difference between the local (Fig. 6b) and the global (Fig. 6c) optimization result is usually within few iteration steps.

Fig. 9. Initial quadrilateral mesh structure with equidistant boundary mesh vertices

In Fig. 9 the “un”-optimized input mesh structure is presented. The mesh has 25 internal



vertices and 24 external (boundary) vertices that are fixed and equidistant. The LNO method for two different cost functions and the same con-straints (local and global cost functions) is done first. The results for the local cost function are presented in Fig. 10a. For the global cost function, see Fig. 10b. After optimization there are equal mesh elements (squares) in both optimization re-sults. Despite different cost functions, the same vertices positions are obtained after 30 iteration steps for the local and global cost function.

a) b)Fig. 10. a) Local; and b) global optimized mesh

structure after 30 iteration steps

For all simple examples tested the optimal vertices positions are known. In the first case, four equilateral triangles and for the second and the third example equilateral squares were expected. Initial examples show the accuracy of the LNO algorithm that is implemented in C++ language.

a) b)Fig. 11. Convergence of a) local; and b) global

cost functions after 30 iterations

3.1 Triangle Meshes

Let us begin with a more complex triangular mesh structure [5] optimization. In Fig. 12 a triangular mesh with several vertices is shown. The triangular mesh structure with two different cost functions and two different types

of constraints was optimized. For LNO local and global cost functions were used. Different constraints were also used: (i) variable and (ii) fixed boundary mesh vertices.

Fig. 12. Initial triangular mesh structure

For the mesh optimization, shown in Fig. 12, different combinations of constraints and cost functions were attempted. In the first combination the local cost function and a constraint with variable boundary mesh vertices were used. The first combination result is presented in Fig. 13a after 50 LNO iterations. The resulting mesh is not very useful because the boundary vertices are moved and the triangle mesh elements are not equal.

In Fig. 13b an optimized mesh structure for the combination of the global cost function and a constraint with variable boundary mesh elements is presented. The mesh result is shown after 50 LNO iteration steps. The second optimization result is better than the first one. In the second optimized mesh, there are equal triangle mesh elements but the boundary mesh vertices moved from the initial positions compared to the first optimized mesh case. These two meshes are theoretically and practically useless due to large deviations between the optimized and initial mesh structures. Nevertheless, they show the impact of local and global cost functions with unconstrained cases where most algorithms fail to preserve shape or volume. It can be concluded that local optimization is likely to fail if there are no boundaries or “features” to follow. The failure rate can be estimated with some “smoothness” measure that shows the difference between the initial and final mesh structure.



a) b)Fig. 13. a) Local, and b) global optimizations after 50 iteration steps with variable boundary

mesh vertices

a) b)Fig. 14. Convergence of a) local, and b) global


a) b)Fig. 15. a) Local, and b) global optimizations

after 30 iteration steps with fixed boundary mesh vertices

Large boundary vertices deviations in the previous optimizations are prevented with fixed boundary vertices in the following examples. Let us make combinations of the local and global cost functions inside fixed boundary vertices. With fixed boundaries, it is ensured that the initial boundary vertices remain fixed during optimization. In Fig. 15a the optimized mesh

structure with the local cost function is shown. The mesh structure was reached after 30 iteration steps. The optimized mesh structure is composed of almost the same triangles but still with some exceptions which cannot be fixed with this optimization algorithm. In Fig. 15b the optimized mesh structure with the global cost function is presented. The global cost function ensures that the initial average edge length during optimization is preserved. The mesh structure converged after 50 iterations.

Both mesh results are similar (see Fig. 15). The local cost function is faster because the variable edge length in a local optimization is more flexible.



The final conclusion for triangle mesh structures is that the constraints in such optimi-zations must be applied to prevent changes of the initial boundaries. Comparing the initial (see Fig. 12) and the optimized mesh structures (see Fig. 15a), it can be concluded that the mesh after optimization has a better distribution of the mesh triangle elements and almost equal mesh elements over the whole mesh structure.

3.2 Quad Meshes

In this section the LNO method is applied on a more complex quadrilateral mesh structure. Let us optimize the initial quadrilateral mesh structure shown in Fig. 12. The initial mesh structure was optimized with the local and global cost functions and two different constraints.

For mesh optimization, two different types of cost functions and constraints were used. The first type was a combination of the local cost function and variable boundary mesh vertices. In the unconstrained optimization there was no



control over the mesh structure result. This means it was not known whether the initial mesh would roughly keep the initial boundary shape. As there were no constraints, the convergence of the LNO algorithm could not be expected.

Fig. 17. Initial quadrilateral mesh structure

a) b)Fig. 18. a) Local, and b) global optimizations after 70 iteration steps with variable boundary

mesh vertices



The result of the unconstrained mesh optimization after 70 iteration steps is shown in Fig. 18. In both meshes the boundary vertices were moved. The edge lengths are equal all over the mesh structure in both cases. However, in the global optimization case the mesh elements are almost square.

Let us look at the mesh optimization results with constraints as shown in Fig. 20. The constraints were fixed boundary vertices. With

this constraint, the possibility that the optimization algorithm changed the initial boundary position is disabled. It can be concluded that the vertices positions in the mesh after the optimization algorithm in both cases are almost equal (all mesh elements are almost squares). The final result is reached faster (60 iteration steps) in the case of the local cost function optimization. With regard to the speed, the local optimization in this mesh structure performs better.

a) b)Fig. 20. a) Local after 60 iterations, and b)

global after 250 iterations optimizations with fixed boundary mesh vertices

a) b)Fig. 21. Convergence of a) local after 60, and b)


First of all it can said that the LNO algorithm is convergent for constrained and unconstrained quadrilateral meshes. Like in the case of the triangle mesh optimization, constrained optimization gives better results (more squares in the mesh structure) compared to the unconstrained optimization. Finally, it can be concluded that a quadrilateral mesh optimization with local and global cost functions can be used in practice (FEM, CFD, etc.).

3.3 Numerical Examples

The following example presents an optimization of quadrilateral 2D mesh. The effect



of optimization algorithm is shown in Figs. 22 to 26. The initial grid (see Fig. 22) consists of two blocks generated subgrids corresponding to a trapezoidal subdomain and its continuation to the annular region. Boundary vertices on the exterior boundary are fixed and other vertices are allowed to “slide” like in the Branets-Carey [6] numerical example.

a) b)Fig. 22. Quadrilateral mesh structure; a) initial and, b) combination of barycenter and local cost

functions

Fig. 23. Convergence of mesh structure for combination of barycenter and local cost

functions after 150 iterations

Fig. 22 presents the initial quadrilateral mesh, which is the same as in Branets-Carey [6]. For optimization external vertices in mesh structure are used. The cost function is a combination of local and barycenter cost functions with weights. Barycenter is cost function which tends to equal diagonal of quadrilateral element.

The weight for the local cost function is wl = 0.3 and the weight for barycenter is wb = 0.3. In Fig. 22 optimized initial quadrilateral mesh structure with a combination of local and barycenter cost functions after 150 iterations is also demonstrated.

Minimization of quadrilateral mesh (see Fig. 22) cost function as the function of the number of iterations is presented in Fig. 23.

a) b)Fig. 24. Combination of a) barycenter with

global, and b) local with barycenter cost functions of quadrilateral mesh structure

a) b)Fig. 25. Convergence of mesh structure for:

a) barycenter with global cost functions after 350, and b) local with barycenter cost functions after

200 iterations

The above examples (Fig. 24) demonstrate two optimized mesh structures. The left example is the optimized mesh structure with a combination of the global with weight wg = 0.3 and barycenter with weight wb = 0.7 cost functions after 200 iterations. The right example presents the optimized mesh after 350 iterations with a combination of local cost function using weight wl = 0.3 and barycenter with wb = 0.3.



In Fig. 25 convergence of global and local cost functions in combination with barycenter is shown. The convergence in graph (see Fig. 25a) is similar like the one in the graph depicted in Fig. 23. The main differences are cost function values. It can be noticed that the curve in Fig. 25b shows faster convergence in comparison with the other two graphs.

a) b)Fig. 26. Combination of a) global with

barycenter and; b) local with barycenter and global cost functions of quadrilateral mesh

structure

The last 2D mesh examples demonstrate mesh optimization combination of the global cost function with weight wg = 0.7 and barycenter with weight wb = 0.3 after 200 iterations. The final example presents the optimized mesh structure in combination of: global (wg = 0.3), local (wl = 0.3) and barycenter (wb = 0.3) cost functions after 70 iterations.

Fig. 27 presents convergences of cost functions for quadrilateral mesh structure optimization.

The goal is also to improve the quality of the 3D mixed mesh structure (see Fig. 28) optimized with global and local cost functions in combination with the barycenter cost function. There is the initial 3D mesh structure with main quad elements and some triangle elements on boundaries.

a) b)Fig. 27. Convergence of a) global with

barycenter cost functions after 200 and, b) local with barycenter and global cost functions after 70

iterations

Fig. 28. Initial mixed 3D mesh example

Fig. 29. Optimization of mixed mesh structure with local and barycenter cost functions

Fig. 30. Optimization of mixed mesh structure with global and barycenter cost functions



Fig. 29 demonstrates the smooth behavior of mixed 3D mesh using local (wl = 0.6) and barycenter (wb = 0.4) cost functions. After the applied optimization quadrilateral mesh elements with equal diagonals and equal length of triangle element sides are obtained.

The mesh structure shown in Fig. 30 is optimized with global (wg = 0.6) and local (wb = 0.4) cost functions. The main difference of previous mesh structure is in values of cost functions during iterations (see Fig. 31).

Fig. 31 presents the convergence of local and global cost functions in combination with barycenter after 30 iterations.

Fig. 31. Convergence of mixed mesh structure for: a) local with barycenter, and b) global with

barycenter cost functions after 30 iterations

3.4 Discussion

The examples show optimizations of triangular, quadrilateral and mixed mesh structures. For every mesh type our optimization algorithm shows improved mesh structure. This is important for triangular mesh structures which are currently used for majority applications.

For the optimization local and global cost functions are proposed. For the optimization of unconstrained mesh structure it is better to use global cost function, while the local cost function performs better on constrained mesh structures. The global based algorithm ensures mesh smoothing with respect to all mesh vertices in one iteration step.

For a comparison of optimization quality of quadrilateral mesh structure Branets-Carey [6] mesh example was taken. The last example is 3D mixed mesh structure. There is the 3D mesh example with the main quadrilateral mesh elements and triangle mesh elements in external edges. In both cases optimizations repaired the mesh structure and have had cost functions convergence. Within optimization quads with

equal diagonals and triangles with almost equal sides can be mixed.

Other popular mesh smoothing algorithms (Laplacian [2], Lennard-Jones [3], and Pliant [4]) are only local diffusion approaches. At the same time the optimization algorithm in question possesses fast convergence. In other algorithms mixed mesh optimization examples were not observed.

4 CONCLUSIONS

This paper has focused on the applicative use of the constraints in mesh optimization and defined cost functions to ensure mesh quality. For testing the Lagrange Newton Optimization algorithm, several examples were used. For these examples, the optimal vertices positions were known. The cost functions were stated in terms of vertices based geometric entities. The cost functions were implemented in a post-processing procedure and shown to be effective in achieving good element quality in several problems. The same cost functions that were effective on quadrilateral meshes were also effective on triangular ones. The speed and efficiency issues were not considered although it has been observed in practice that no significant time penalty applies to optimization with one cost function as compared to another.

To summarize briefly what was looked into regarding LNO. Firstly, the regularity of the LNO algorithm was demonstrated in examples with known results (see Figs. 5, 7 and 9). Triangular and quadrilateral meshes were tested. The tests have proven the regularity of the optimization algorithm. Secondly, the results of constrained and unconstrained mesh optimizations were compared. Examples are shown in Section 3.2 and 3.3. Unconstrained optimizations are useless in the fields of FEM, CFD, etc. External (boundary) vertices and initial shape after unconstrained optimization are broken. Another problem is that the LNO method for some unconstrained cases is not convergent. It is also possible that the unconstrained optimization algorithms have no logical solution. Lastly, it can be concluded that the LNO algorithm is useful for triangular and quadrilateral mesh structures.



The results for triangular meshes are achieved in a few iteration steps. In the quadrilateral mesh optimization, the priority of LNO is to ensure more equal mesh elements (almost all elements in the mesh structure were squares).

5 REFERENCES

[1] Madsen. K., Nielsen. H.B., Tingleff, O. (2004). Optimization with constraints, 2nd ed. IMM, Technical University of Denmark, Kgs. Lyngby.

[2] Field, D.A. (1988). Laplacian smoothing and Delaunay triangulations. Comm. Applied Numer. Meth., vol. 4, p. 709-712.

[3] Allen, M.P., Tildesley, D.J. (1987). Computer simulation of Liquids. Claredon Press, Oxford.

[4] Pascal, J.F., Houman, B. (1998). Geometric surface mesh optimization. Comput Visual Sci, vol. 1, p. 113-121.

[5] Vukašinović, N., Korošec, M., Duhovnik, J. (2010). The influence of surface topology on the accuracy of laser triangulation scanning results. Strojniški vestnik - Journal of Mechanical Egineering, vol. 56, no. 1, p. 23-30.

[6] Branets, L., Carey, G.F. (2005). A local cell quality metric and variational grid smoothing algorithm. Engineering with Computers, vol. 21, p. 19-28.

[7] Madsen, K., Nielsen, H.B., Tingleff, O. (2004). Methods for non-linear least squares problems, 2nd edition. IMM, Technical University of Denmark, Kgs. Lyngby.

[8] Arora, J.S. (2004). Introduction to optimum design. Elsevier, Academic Press, San Diego.

[9] Mulmuley, K. (1994). Computational geometry: An introduction through randomized algorithms. Prentice Hall, Inc.

[10] Knupp, P.M. (2000). Achieving finite mesh quality via optimization of the Jacobian

matrix and associated quantities. Part I-a framework for surface mesh optimization, International Journal for Numerical Methods in Engineering, vol. 48, p. 401-420.

[11] Brackbill, J.U. (1993). An adaptive grid with directional control. Journal of Computational Physics, vol. 108, no. 1, p. 38-50.

[12] Buscaglia, G.C., Dari, E.A. (1997). Anisotropic mesh optimization and its application in adaptivity. Instituto Balseiro and Centro Atomico Bariloche.

[13] Hoppe, H., DeRose, T., Duchamp, T., Mcdonald, J., Stuetzle, W. (1991). Mesh optimization. University of Washington, Seattle.

[14] Schittkowski, K. (1981). The nonlinear programming method of Wilson, Han, and Powell. Part 1: Convergence analysis. Numerische Mathematik, vol. 38, no. 1, p. 83-114.

[15] Rao, S.S. (1996). Engineering Optimization. John Wiley, Inc.

[16] Bossen, F.J., Heckbert, P.S. (1996). A pliant method for anisotropic mesh generation. Computer Science Dept., Carnegie Mellon University, Pittsburgh.

[17] Canann, S.A., Tristano, J.R., Staten, M.L. (1998). An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes. ANSYS, Inc.

[18] Bey, M., Boudjouad, S., Bouzid, N.T. (2007). Tool-path generation for free-form surfaces with B-spline curves. Strojniški vestnik - Journal of Mechanical Engineering, vol. 53, no. 11, p. 733-741.

[19] Chen, L. (2004). Mesh smoothing schemes based on optimal Delaunay triangulations. Math Department, The Pennsylvania State University, Pennsylvania.


*Corr. Author’s Address: Lanzhou Polytechnic College, Qilihequ, Gongjiawan 1, Lanzhou, Gansu, China,730050, [email protected]

Study of Adaptive Model Parameter Estimation for Milling Tool Wear

Xu, C. ‒ Xu, T. ‒ Zhu, Q. ‒ Zhang, H.Chuangwen Xu1,* ‒ Ting Xu2‒ Qi Zhu1 ‒ Hongyan Zhang1

1 Lanzhou Polytechnic College, China 2 School of Electronic Engineering, Jilin University, China

In a modern machining system, tool wear monitoring systems are needed to get higher quality production. In precision machining processes, especially surface quality of the manufactured part can be related to tool wear. This increases industrial interest for in-process tool wear monitoring systems. For the modern unmanned manufacturing process, an integrated system composed of sensors, signal processing interface and intelligent decision making model are required. In this study, a new method for on-line tool wear monitoring is presented under varying cutting conditions. The proposed method uses wear feature extraction based on process modeling and parameter estimation. An adaptive estimation model of milling tool wear in variable cutting parameters is built based entirely on milling power. The adaptive model traces the properties of cutting process by combining process state signal, cutting conditions, power model. The tool wear feature is obtained from the estimated parameters of the model and carried on in the theoretical and experimental study. Experiment results have proved that changes of the parameters in the cutting power model significantly indicate tool wear independently of varying cutting conditions and it makes tool wear a recognized process with high precision.© 2011 Journal of Mechanical Engineering. All rights reserved. Keywords: milling power, adaptive estimation model, tool wear, model parameters, information fusion

0 INTRODUCTION

Metal-cutting tool wear directly affects the precision, efficiency and cost efficiency of machining, so the on-line monitoring tool wear is becoming increasinhgly important, and has become an important research topic of flexible manufacturing system engineering. With other mechanical processing methods, the milling mechanism is more complex, while condition diversity, cutting parameters variability, and tool breakage and wear is random and complex. Thus, the feature extraction of milling tool wear is the key in tool wear monitoring research. This can effectively resolve the problem directly related to the accuracy and reliablity of milling tool wear monitoring. Therefore, new monitoring theories and technologies have been developed to solve the feature extraction of tool wear. In the previous literature [1] to [5], the identification method regarding the milling tool wear conditions is to identify the main purpose of tool wear, which reached a stage, and then a different processing method is applied according to the different

phases. But in the automated production, the conditions of tool wear can be identified, and tool wear value must be also obtained to satisfy the machining accuracy through compensating the tool radius and optimizing the cutting parameters in time. In this study, the research method to obtain tool wear value is presented. In the tool wear process, tool wear occurs as a process concerned with time, which requires the monitoring system to identify current tool wear value at any time, so as to provide a basis for compensating tool wear.

At present, the methods to obtain cutting tool wear include a direct and indirect method. The former usually measures the cutting tool wear value directly by using the optimal sensor, such as CCD pick-up head because touching the tool shape cannot be reached in the cutting process [6]. However, it is highly difficult to measure its value on-line accurately in the cutting process. In the latter the wear value by measuring the cutting vibration signals [7] or acoustic emission (AE) signals [8] is calculated. It remains difficult to utilize the techniques in the real cutting process as due to the complexity of real-time power


569Study of Adaptive Model Parameter Estimation for Milling Tool Wear

source signals, it is not easy to extract the feature information of tool wear from complex signals in time-domain, frequency-domain. In addition, many past methods were developed to monitor tool wear by measuring spindle and feed motor power (current) and proved that the tool wear is very sensitive to the change of the cutting power [9] and [10]. In the cutting process, techniques for tool wear monitoring are being used widely using the spindle and feed motor power. It does not interfere with cutting process by measurement equipment and the machine tool was not formed by a reworking process. However, generation mechanisms of the milling tool wear are more complex and in the view of various factors that affect tool wear, it is difficult to build the exact practical analysis model. Therefore, it is necessary to use experimental data to ensure the analysis and model. In some general methods, an explicit model is built by using Multivariate Linear Regression analysis method [11] and [12] or an implicit model by using the Neural Network [13]. MLR method for monitoring tool wear by measuring spindle and feed motor power is to establish a mathematical model between milling cutting parameters and the classification by fuzzy pattern using MLR analysis. Then, tool wear model for spindle and feed motor power is established. Tool wear value is predicted by tool wear model. Tool wear model is adjusted using cutting parameters to give it better dynamic, fuzzy and real-time characteristics. Therefore, it will be effective to be used in the nonlinear predictive control systems. The NN method for monitoring tool wear by measuring spindle and feed motor power is to establish a Neural Network model which contains milling cutting parameters and cutting power. Then, tool wear network model is trained by using several experimental data of tool wear in different cutting process. Tool wear value is predicted by the Network model. Several problems exist with these methods; (1) It is diffcult to establish an exact practical analysis model between milling cutting parameters and tool wear. (2) The model based on spindle and feed motor power is used to recognize tool wear and can also cause larger error in a different cutting process by using the MLR method because tool wear model coefficients are fixed, that is, of low-precision and limiting applications. (3) The results of prediction are

usually unstable because it is difficult to overcome multicollinearity of variables using the MLR method. (4) NN is difficult to give a reasonable interpretation of the factors influencing tool wear model.

In flexible manufacturing systems, varying cutting conditions are a great challenge to reliable wear monitoring. Intelligent monitoring strategies currently dominate in research work. Intelligent monitoring includes machining processes, signal sensing, feature extraction, learning/recognition, decision making and control. The performance of the whole monitoring system is heavily dependent upon the effectiveness of the feature extraction. The strategies for wear feature extraction in developed monitoring systems may be summarized in two categories based on the techniques for signal processing and analysis. A pattern recognition method is employed to identify tool wear based on various features. The parametric method includes two stages. In stage one; an empirical model is developed by regression analysis of experimental data. In stage two, tool wear is estimated in real-time using the empirical model and measurements of the cutting state signal and conditions. The advantage of the parametric method is that cutting conditions are used as a model input, so that wear estimation is independent of variation in the cutting condition. In actual machining, the empirical model still has large errors in the estimated tool wear or errors in recognition [14].

An improved strategy is proposed in this study for tool wear monitoring to solve such problems faced in the nonparametric and the parametric methods.

1 TOOL WEAR SENSING BASED ON PROCESS MODELLING AND PARAMETER

ESTIMATION

1.1 Strategy

The improved strategy for reliable intelligent tool wear monitoring separates tool wear estimation into two steps. In step one, wear feature extraction, a process model is developed with the cutting power defined as a function of cutting conditions. The model is then used to estimate wear feature parameters.


570 Xu, C. ‒ Xu, T. ‒ Zhu, Q. ‒ Zhang, H.

During machining, tool wear will create an error between the measured signal and the model output. The model then adjusts its parameters to eliminate the error. Therefore, changes in model parameters indicate tool wear. The wear feature extraction method is independent of variations of the cutting conditions. In step two, tool wear recognition, variations of the features obtained in step one are used to estimate or classify the tool wear state. Several empirical models, which describe the quantitative relationship between the features and actual wear are developed for wear estimation. Some innovative models, in which the learning and classifying functions are performed simultaneously by self-learning, are also developed for tool wear classifications [14].

1.2 Process Modelling and Parameter Estimation Techniques

For processes with specified input and output variables, models can be expressed mathematically as static and dynamic. Static process models usually use nonlinear polynomials, while dynamic process models use differential equations. For processes with only output variables, such as vibrations in machining processes, an autoregressive moving averaging (ARMA) model is suitable. Time-varying models are used for tine-varying processes. A process model may be derived from either a theoretical analysis or from an empirical formula. The well-known least squares (LS) method is normally used for parameter estimation. With on-line monitoring, a recursive LS method should be adopted. The primary advantage of the parameter estimation method is for multiple fault detection.

1.3 LS Method

The least square method - a very popular technique - is used to compute estimations of parameters and to fit data. It is one of the oldest techniques of modern statistics as it was first published in 1805 by the French mathematician Legendre in a now classic memoir. But this method is even older because it turned out that, after the publication of Legendre’s memoir, Gauss, the famous German mathematician, published another memoir (in 1809) in which he mentioned that he

had previously discovered this method and used it as early as 1795. A somewhat bitter anteriority dispute followed (a little reminiscent of the Leibniz-Newton controversy about the invention of Calculus), which, however, did not diminish the popularity of this technique. Galton used it (in 1886) in his work on the heritability of size, which laid down the foundations of correlation and (also gave the name) regression analysis. Both, Pearson and Fisher, who did so much in the early development of statistics, used and developed it in different contexts (factor analysis for Pearson and experimental design for Fisher).

Functional fit example: regression. The oldest (and still most frequent) use of OLS was linear regression, which corresponds to the problem of finding a line (or curve) that best fits a set of data. In the standard formulation, a set of pairs of observations is used to find a function giving the value of the dependent variable from the values of an independent variable. With one variable and a linear function, the prediction is given by the following equation:

Y a bX = + . (1)

This equation involves two free parameters which specify the intercept (a) and the slope (b) of the regression line. The least square method defines the estimate of these parameters as the values which minimize the sum of the squares (hence the name least squares) between the measurements and the model (i.e., the predicted values). This amounts to minimizing the Eq:

ε = −( ) = − +( )∑∑ Y Y Y a bXi i i iii

2 2[ ] , (2)

(where ε stands for “error” which is the quantity to be minimized). This is achieved using standard techniques from calculus, namely the property that a quadratic (i.e., with a square) formula reaches its minimum value when its derivatives vanish. Taking the derivative of ε with respect to a and b and setting them to zero gives the following set of Eqs. (called the normal equations):

∂∂

= + − =∑∑εa

Na b X Yi i2 2 2 0, (3)

∂∂

= + − =∑∑∑εb

b X a X Y Xi i i i2 2 2 02 . (4)



Solving these two Eqs. gives the least square estimates of a and b as: a M bMY X= + , (5)

with MY and MX denoting the means of X and Y and:

bY M X M

X Mi Y i X

i X

=−( ) −( )

−( )∑∑ 2 . (6)

OLS can be extended to more than one independent variable (using matrix algebra) and to non-linear functions.

Multiple Regression Least Square Method. The term multiple regression originates from a multiple number of independent variables (control parameters), which means that the dependent variable is changed by more than one independent variable. The examples of fitting equations are as follows:• Two independent variable: Z=aA+bB+c

(where Z: dependent variable; A, B: independent variables; a, b, c: constants).

• Three independent variable: Z=aA+bB+cC+d (where Z: dependent variable; A, B, C: independent variables; a, b, c, d: constants).

Let us think about the multiple regression with two independent variables to simplify the situation. The least square error in multiple regression will be:

ε = − ( ) =

= − + +( )

=

=

∑

∑

Z f x y

Z a bx cy

i i ii

n

i i ii

n

,

.

2

1

2

1

(7)

The first derivatives of ε in terms of a and b will be (Eqs. 8 to 10):

∂∂

= − + +( ) ==∑ε

aZ a bx cyi i i

i

n

2 01

, (8)

∂∂

= − + +( ) ==∑ε

bx Z a bx cyi i i i

i

n

2 01

, (9)

∂∂

= − + +( ) ==∑ε

cy Z a bx cyi i i i

i

n

2 02

1

. (10)

The Eqs. expended from Eqs. (8) to (10) will be:

Z a b x c yii

n

i

n

ii

n

ii

n

= + +== = =∑∑ ∑ ∑1

11 1 1

, (11)

x Z a x b x c x yi ii

n

ii

n

ii

n

ii

n

i= + += = = =∑ ∑ ∑ ∑

1 1

2

1 1

, (12)

y Z a y b y c yi ii

n

ii

n

ii

n

ii

n

= + += = = =∑ ∑ ∑ ∑

1 1 1

2

1

. (13)

Computation of the unknown constants using A X X X Y =

−T T1

and matrices will be (Eq. (14)).

If you have a data set (x1,y1,Z1), (x2,y2,Z2), ..., (xn,yn,Zn), computations of unknowns (a,b,c) are computed using matrices.

2 PARAMETER ESTIMATION METHOD FOR TOOL WEAR

In the milling process, the cutting power P is of the relation with the cutting speed, the feed speed f, the cutting depth ap and the cutting tool wear VB. At the same time, the cutting power changes with the different conditions such as the part material, the tool material and so on.

abc

x y

x x x y

i

n

ii

n

ii

n

ii

n

ii

n

i ii

n

=

= = =

= = =

∑ ∑ ∑

∑ ∑ ∑

11 1 1

1

2

1 1

yy y y

x

ii

n

ii

n

ii

n

i

n

ii

n

= = =

= =

∑ ∑ ∑

∑

1 1

2

1

1 1

1T

∑∑ ∑

∑ ∑ ∑

∑ ∑ ∑

=

= = =

= = =

y

x x x y

y y y

ii

n

ii

n

ii

n

i ii

n

ii

n

ii

n

ii

n

1

1

2

1 1

1 1

2

1

−

= =∑

1

1 1

1i

n

ii

n

x∑∑ ∑

∑ ∑ ∑

∑ ∑ ∑

=

= = =

= = =

y

x x x y

y y y

ii

n

ii

n

ii

n

i ii

n

ii

n

ii

n

ii

n

1

1

2

1 1

1 1

2

1

=

=

=

∑

∑

∑

T

Z

x Z

y Z

ii

n

i ii

n

i ii

n

1

1

1

. (14)



According to the metal-cutting principle, the spindle cutting power and the feed power are defined as follows [15] and [16]:

P a v f asa a

pa= 1

2 3 4 , (15)

P b v f afb b

pb= 1

2 3 4 , (16)

where a1 and b1 are the coefficients determined by the cutting tool geometry dimension and performance of the material. a2, a3, a4 and b2, b3, b4 is the exponent of the cutting parameters.

As Eqs. (15) and (16) show, a corresponding power value is output under certain cutting conditions and the cutting tool wear states. Eqs. (15) and (16) are a static nonlinear. The Eqs. can be written in the form as:

ln ln ln ln ln ,P a a v a f a as p= + + +1 2 3 4 (17)

ln ln ln ln ln .P b b v b f b af p= + + +1 2 3 4 (18)

If S = lnPs, F = lnPf, then:

S a a v a f a ap= + + +1 2 3 4ln ln ln , (19)

F b b v b f b ap= + + +1 2 3 4ln ln ln . (20)

Where XT = [1, lnv, lnf, lnap], A = [a2, a2, a3, a4]T, B = [b2, b2, b3, b4]T. XT is parameter matrix, A and B is coefficient matrix.

A series of milling states in varying cutting conditions are measured as follows:

Y v f a S Fi i i pi i i= , , , , , (21)

Where Yi is corresponding processing states under different cutting conditions, Pi is spindle cutting power, vi is cutting speed, fi is feed speed and api is cutting depth.

For these process states, Eqs. (19) and (20) can be written as:

S i X i A e i( ) ( ) ( ),= +T (22)

F i X i B e i( ) ( ) ( ),= +T (23)

where e is the model error. The parameters estimated by the Least

Square Method (Eqs. (7) to (14)) are:

A a a a a = 1 2 3 4, , , ,

T (24)

B b b b b = 1 2 3 4, , , .

T (25)

In real-time tool wear monitoring, the parameter estimation is confirmed by the recursive least square method according to the model error function.

The wear feature extraction strategy using cutting power modeling and parameter estimation is shown in Fig. 1. The procedure is summarized as follows: a) Establish a process model which describes

the relationship between cutting conditions and cutting power, i.e. Eqs. (15) and (16).

b) Use sensors to measure the model inputs and outputs (e.g. speed and power).

c) Estimate the model parameters using the Least Square Method. Detect changes in the model parameters as tool wear increase. These changes are stored as the wear feature parameter.

d) Recognize tool wear by estimating or classifying tool wear based on the wear feature [14].

3 THE TIME-VARIANT CHARACTERISTIC OF PARAMETERS ON POWER MODEL

Experiments are conducted in a XKA714 using the strategy described above. The milling experimental condition is shown in Table 1. Cutting experiment is used in a new tool (VB = 0.05 mm), respectively, according to the first, second and third group of cutting parameters in Table 2, consisting of 48 cutting group parameters by orthogonal combination. At the same time, spindle power and feed power value are detected. Input and output data for 48 group model are obtained. Eqs. (22) and (23) are used to fit the experimental data by the least square method and the results are shown in Tables 3 and 4. A worn tool (VB = 0.25 mm) is used to repeat these experiments and the results are shown in Tables 5 and 6.

In the milling tool wear process, characteristics with changes on the width of flank wear land and the area of wear land are studied. The width of the flank wear is used as a measure of the degree of tool wear evaluation. The width of flank wear land was measured using Tool Makers Microscope.



From experimental data in Tables 3 to 6 it can be seen that in normal cutting circumstances (the new cutting tool), the fitting error for 16, 32 and 48 groups of experimental data is all less than 3.5%, and that model parameter estimation

on three batches of data is very similar. From model results of tool wear it follows that the three groups of estimated model parameters are very similar and model fitting error is less than 6.5. The model parameters have a relatively fixed value

Table 1. Cutting experiment condition

Cutting toolMaterial High-speed steelType End milling cutterDiameter [mm] 14-20

Equipment XKA714Milling method Climb milling

Workspace material Thermal refining 45 steelCutting speed [m/min] 8.792~26.376Feed speed [mm/min] 20~35Cutting depth [mm] 2~5

Fig. 1. The extraction method of the tool wear feature using the adaptive model parameter estimation



Table 2. The experimental groups of the cutting parameters (Notes: v [m·min-1], f [mm·r-1], ap [mm])

Level The first group The second group The third groupv F ap v F ap v F ap

1 8.792 3.0 5 9.671 3.0 4 13.19 3.0 42 9.671 2.5 4.5 11.43 2.5 3.75 15.38 2.5 3.753 11.43 2.0 3.5 13.19 2.0 3 21.96 2.0 34 13.19 3.0 3 15.38 3.0 2.75 26.376 3.0 2.75

Table 3. The parameter estimation results of the spindle cutting power model (VB = 0.05 mm)

a1 a 2 a3 a 4Fitting

error [%]The first group data estimation 7.1021 0.1056 0.1734 0.0786 2.46The first and second group data estimation 7.1471 0.1174 0.1637 0.0777 2.78First, second and third group data estimation 7.1802 0.1057 0.1745 0.0796 3.12

Table 4. The parameter estimation results of the feed power model (VB = 0.05 mm)

b1 b 2 b3 b 4Fitting


Table 5. The parameter estimation results of the spindle cutting power model (VB = 0.25 mm)

a1 a 2 a3 a 4Fitting


Table 6. The parameter estimation results of the feed power model (VB = 0.25 mm)

b1 b 2 b3 b 4Fitting


Table 7. Selection on cutting speed and feed speed

Cutting parameters Group number1 2 3 4 5 6 7 8 9

v [m·min-1] 8.792 13.2 17.584 21.98 24.178 26.276 28.574 30.772 32.97f [mm·r-1] 3 2.75 2.5 2.5 2 2 1.75 1.5 1

corresponding to tool wear, and this has laid a good foundation for looking for the adaptive of tool wear. Comparing two sets of the experiment, it can be seen that worn tool model parameters

compared with the normal model parameters have changed dramatically, so the parameter model based on cutting power is the time-varying parameter model.



4 THE FEATURE EXTRACTION OF TOOL WEAR

The experiment of tool wear is designed to the varying cutting condition according to round trip milling and multi-feed. The cutting depths during every feed are 3.5, 2, 1.5 and 1 mm. 9 groups of cutting parameters shown in Table 7 are selected as the cutting speed and feed speed.

The feature extraction method for tool wear is to detect the changes ΔA , ΔB of the model estimation parameters which has been wear and the new tool, and calculate the distance function which indirectly reflects changes in the amount of tool wear. Prio to the experiment, the model parameters for the new tool were stored as the base values. The model parameters were then estimated for various worn tools and changes in the parameters were obtained by subtracting the base values from the estimated parameters. The

parameter changes were evaluated using the Distance function.

D A A

a a a a

1 1 0

12

22

32

42

= − =

= + + +

( ) ( ) ( ) ( ) ,∆ ∆ ∆ ∆ (26)

D B B

b b b b

2 1 0

12

22

32

42

= −

= + + +

( ) ( ) ( ) ( ) ,∆ ∆ ∆ ∆ (27)

where D1 is the calculation distance of the model estimation parameters for spindle cutting power, and D2 is the calculation distance of the model estimation parameters for feed power.

Based on the same cutting depth, in accordance with the cutting parameters of group number in Table 7, the experiment is applied. Eqs. (26) and (27) can be used to calculate the distance. The relationship between distance and tool wear is shown in Figs. 2 and 3. The feature D1, D2 and the

Fig. 2. The relation between the feature and wear on the spindle cutting power



Table 8. The error statistics between the feature D1 and wear on the spindle cutting power [unit/mm]

Cutting depth Group number1 2 3 4 5 6 7 8 9

3.5 largest absolute error 0.030 0.020 0.020 0.020 0.030 0.025 0.030 0.025 0.026average error 0.013 0.015 0.012 0.012 0.014 0.016 0.013 0.013 0.012




Table 9. The error statistics between the feature D2 and wear on the feed cutting power [unit/mm]






Table 10. The error statistics between the distance and the tool wear [unit/mm]






error statistics of tool wear are shown in Tables 8 and 9.

From Table 8, feature and statistical error of tool wear for the spindle cutting power can be seen: in the whole tracking tool wear, the largest absolute error is below 0.03 mm, and the average error is equal to 0.017 mm; from Table 9, feature and statistical error of tool wear on the feed cutting power can be seen: in the whole tracking tool wear, the largest absolute error is below 0.025 mm, and the average error is equal to 0.015 mm. It can be seen: (1) identification method for adaptive

tool wear model parameter estimation is superior to fusion pattern recognition of a fixed model coefficient, reduction in error and improved accuracy of recognition; (2) distance function by the composition of adaptive tool wear model parameters can reflect changes in the amount of tool wear; (3) from identification results of the spindle cutting power and feed power, feed power identification is better than spindle power, and thus both in the tool wear identification showed some differences or sensitivity. In order to overcome the limitations of a single factor, taking into account



identification differences in tool wear of the spindle power and feed power, feature distance function is used in two types of fusion based on the cutting spindle power and feed power. The two weights respectively 0.4 and 0.6 are satisfactory according to the experiment results.

D A A B B

a a a a

= − + − =

= ( ) + ( ) + ( ) + ( )

0 4 0 6

0 4

1 0 1 0

12

22

32

4

. .

.

∆ ∆ ∆ ∆22

12

22

32

420 6

+

+ + + +. ( ) ( ) ( ) ( ) .∆ ∆ ∆ ∆b b b b

(28)

According to Table 7, the experiment is applied to the group number in the same depth. Table 10 can be used to calculate the error

statistics between the feature distance and the tool wear, and its result is shown in Table 10.

Compared to Table 10 and Table 8, Table 9, the fusion distance function of tool wear feature can track the changes of tool wear value well and accurately; average error is 0.014 mm and the largest absolute error is less than before during tool wear identification.

5 CONCLUSION

In the milling process, a feature extraction method for power adaptive model parameter estimation is studied. The method regards the tool wear process as time-varying system parameters. By detecting the processing state signal and

Fig. 3. The relation between the feature and wear on the feed cutting power



processing parameters, processing state is predicted by using power model and least squares estimate model parameters. Model parameters are corrected according to the forecast error, so that the model automatically adapts to track the properties of the cutting process and obtains the parameters of the model as tool wear feature to achieve tool wear monitoring. The experiment results have shown that the model coefficients can be processed with the adaptive changes of processing conditions, and wear value is accurately estimated by feature parameter. In the actual processing, in order to achieve the different types of intelligent tool wear monitoring, this study can be used for tool wear feature extraction methods of different types of processing cutting power model parameters of self-learning.

6 ACKNOWLEDGEMENT

This research was supported by the Natural Science Foundation of Gansu under the research grant 1010RYZA173. The authors thank Cheng Zhongwen from CAD/CAM for providing super alloy material, and also Zhao Youxin, Liu Xiaobin and Li Baodong for their support.

7 REFERENCES

[1] Xu, C.W. (2009). Condition monitoring of milling tool wear based on fractal dimension of vibration signals. Strojniški vestnik ‒ Journal of Mechanical Engineering, vol. 55, no. 1, p. 15-25.

[2] Xu, C.W. (2009). Milling tool wear forecast based on the partial least-squares regression analysis. Structural Engineering and Mechanics, vol. 31, no. 1, p. 1-19.

[3] Wang, Y.L. (2008). Detection of the tool wear condition based on the computer image processing. Journal of Key Engineering Materials, vol. 375, no. 1, p. 553-557.

[4] Al-Azmi, A. (2009). Rapid design of tool-wear condition monitoring systems for turning processes using novelty detection. Journal of Manufacturing Technology and Management, vol. 17, no. 3, p. 232-245.

[5] Cuneyt, A. (2009). Tool wear condition monitoring using a sensor fusion model based on fuzzy inference system.

Mechanical Systems and Signal Processing, vol. 23, no. 2, p. 539-546.

[6] Mannan, M.A., Kassim, A. (2000). Application of image and sound analysis techniques to monitor the condition of cutting tools. Journal of Pattern Recognition Letters, vol. 21, no. 11, p. 969-979.

[7] Dimla, D.E. (2002). The correlation of vibration signal features to cutting tool wear in a metal turning operation. Journal of Materials Processing Technology, vol. 19, no. 10, p. 705-713.

[8] Srinivasa, P. (2002). Acoustic emission analysis for tool wear monitoring in face milling. Journal of Production Research, vol. 40, no. 5, p. 1081-1093.

[9] Shao, H., Wang, H.L. (2004). A cutting power model for tool wear monitoring in milling. Journal of Machine Tools and Manufacture, vol. 44, no. 14, p. 1503-1509.

[10] Ertunc, M.H., Loparo, A.K. (2001). Tool wear condition monitoring in drilling operations using hidden Markov models (HMPs). Journal of Machine Tools and Manufacture, vol. 41, no. 9, p. 1363-1384.

[11] Chen, J.C. (2004). A multiple-regression model for monitoring tool wear with a dynamometer in milling operations. Journal of Technology Studies, vol. 30, no. 4, p. 71-77.

[12] Xu,C.G., Wang, X.Y. (2006). New approach on monitoring cutting tool states by motor current. Journal of Instrument Technique and Sensor, vol. 32, no. 4, p. 34-40.

[13] Palanisamy, P., Rajendran, I. (2007). Prediction of tool wear using regression and ANN models in end-milling operation. Journal of Advanced Manufacturing Technology, p. 1433-3015.

[14] Wan, J. (1996). Intelligent tool failure monitoring for machining processes. Tsinghua Science and Technology, vol. 1, no. 2, p. 172-175.

[15] Lu, J. (2005). Theory of metal cutting. China Machine Press, Beijing, p. 123-132.

[16] Shao, H. (1994). Monitoring research based on cutting power. Shanghai Jiaotong University, Shanghai, vol. 35, no. 2, p. 25-35.


*Corr. Author’s Address: University of Maribor, Faculty of Natural Science and Mathematics, Koroška 160, 2000 Maribor, Slovenia [email protected] 579

Numerical Modelling of Crack Growth in a Gear Tooth RootPodrug, S. ‒ Glodež, S. ‒ Jelaska, D.

Srđan Podrug1 ‒ Srečko Glodež2,* ‒ Damir Jelaska1

1 University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Croatia

2 University of Maribor, Faculty of Natural Science and Mathematics, Slovenia

A computational model for determination of crack growth in a gear tooth root is presented. Two loading conditions are taken into account: (i) normal pulsating force acting at the highest point of the single tooth contact and (ii) the moving load along the tooth flank. In numerical analysis it is assumed that the crack is initiated at the point of the largest stresses in a gear tooth root. The simple Paris equation is then used for a further simulation of the fatigue crack growth. The functional relationship between the the stress intensity factor and crack length K = f(a), which is needed for determining the required number of loading cycles N for a crack propagation from the initial to the critical length, is obtained using a displacement correlation method in the framework of the FEM-method considering the effect of crack closure. The model is used for determining fatigue crack growth in a real gear made from case carburised and ground steel 14CiNiMo13-4, where the required material parameters were determined previously by appropriate test specimens. The results of the numerical analysis show that the prediction of crack propagation live and crack path in a gear tooth root are significantly different for both loading conditions considered.© 2011 Journal of Mechanical Engineering. All rights reserved. Keywords: gears, fatigue, crack growth, numerical modelling

0 INTRODUCTION

Two kinds of teeth damage can occur on gears under repeated loading due to fatigue; the pitting of gear teeth flanks and tooth breakage in the tooth root [1]. In this paper only the tooth breakage is addressed and the developed computational model is used for the calculation of tooth bending strength, i.e. the service life of gear tooth root.

The standardised procedures according to ISO-standards [1] are usually used for an approximate determination of load capacity of gear tooth root. They are commonly based on the comparison of the maximum tooth-root stress with the permissible bending stress. Their determination depends on a number of different coefficients that allow for proper consideration of real working conditions (additional internal and external dynamic forces, contact area of engaging gears, gear material, surface roughness, etc.). The standardised procedures are exclusively based on the experimental testing of the reference gears and they consider only the final stage of the fatigue process in the gear tooth root, i.e. the occurrence of final failure.

However, the complete process of fatigue failure may be divided into the “crack initiation” and “crack propagation” period [2] and [3]. An exact definition of the transition from initiation to propagation period is usually not possible. However, the crack initiation period generally accounts for most of the service life, especially in high-cycle fatigue, see Fig. 1. The complete service life of mechanical elements N can than be determined from the number of stress cycles Ni required for the fatigue crack initiation and the number of stress cycles Np required for a crack to propagate from the initial to the critical crack length, when the final failure can be expected to occur:

N N N= +i p . (1)

The presented work is mainly restricted on the period of the fatigue crack growth, neglecting or merely with experimental determination of the fatigue crack initiation period. In most of recent investigations [3] to [8] a loading cycle of gear meshing is presumed as pulsating acting at the highest point of the single tooth contact. However, in actual gear operation, the magnitude as well as the position of the force, changes as the


580 Podrug, S. ‒ Glodež, S. ‒ Jelaska, D.

gear rotates. This fact can be taken into account performing a quasi static numerical simulation in which the gear tooth engagement is broken down into multiple load steps and analyzed separately. In such a way, a more realistic stress cycle in the gear tooth root is obtained resulting in significantly more exact assessment of the crack propagation life, and consequently in the entire fatigue life.

log N

Dσ

DσFL

Crack initiation period Ni

Crack propagation period Np

Fig. 1. Schematic representation of the service life N of mechanical elements

In this paper, a similar procedure to the one described in [8] for bevel gears, is used to analyse fatigue crack growth. However, it is appropriately modified and adopted for spur gears. An approach that accounts for fatigue crack closure effects is developed to propagate crack under non-proportional load.

1 CRACK INITIATION SIZE

In order to calculate the number of stress cycles required for a crack to propagate from the initial to the critical crack length it is necessary to determine fatigue crack initiation size. Although there have been many approaches to determine crack initiation size, there has so far been no perfect approach. One of the most convenient representation of determining the crack initiation size is the Kitagawa-Takahashi plot of applied stress range required for crack growth, Δσ, against crack length, a, using logarithmic scales, as shown in Fig. 2 [9]. As the transition point between crack initiation and crack propagation period the threshold crack length ath is selected, below which linear elastic fracture mechanics (LEFM) is

not valid. For engineering applications empirical formula for this transition point is proposed [10]:

aK

thth

FL≈

12

π σ∆∆

, (2)

where ΔσFL is the fatigue limit and DKth is the threshold stress intensity range. The threshold crack length ath thus defines the transition point between short and long cracks, i.e. the transition point between initiation and propagation period in engineering applications. However, a wider range of values has been selected for ath in the literature, usually between 0.05 and 1 mm for steels where high strength steels take the smallest values [10] and [11].

ath log a

log

Dσ

Fatigue limit DσFL

Short crack regime

Non propagating cracks

Long crack regime (LEFM)

Propagating cracks

DKth

Fig. 2. Kitagawa-Takahashi plot

2 FATIGUE CRACK PROPAGATION

The application of the linear elastic fracture mechanics (LEFM) to fatigue is based upon the assumption that the fatigue crack growth rate, da/dN, is a function of stress intensity range DK = Kmax-Kmin, where a is a crack length and N is a number of load cycles. In this study the simple Paris equation is used to describe the crack growth rate:

dd

( ) .aN

C K a m= [ ]∆ (3)

This equation indicates that the required number of loading cycles Np for a crack to propagate from the initial length ath to the critical crack length ac can be explicitly determined, if C, m and DK(a) are known. C and m are the material parameters and can be obtained experimentally,


581Numerical Modelling of Crack Growth in a Gear Tooth Root

usually by means of a three point bending test according to the standard procedure ASTM E 399-80 [12]. For simple cases the dependence between the stress intensity range and the crack length DK(a) can be determined analytically as described in [11] and [12]. For a more complicated geometry and loading cases it is necessary to use alternative methods. In this work the finite element method (FEM) in the framework of the program package FRANC2D [13], has been used for simulation of the fatigue crack growth, since the uniformly distributed load on the tooth flank is assumed, which enables the usage of two-dimensional finite element mesh.

A different method can be used to determine the equivalent stress intensity range DKeq under mixed mode loading as appears when load is moving on the gear tooth [14] to [22]. In presented work the following equation is used to determine the equivalent stress intensity range:

2 0 0 0eq I IIcos cos 3 sin ,

2 2 2K K K

θ θ θ D = D - D

(4)

where θ0 is the crack-propagation angle and DKI and DKII are the stress intensity ranges for mode I and mode II, respectively.

To analyse the fatigue crack growth under mix mode conditions the value DK in Eq. (3) has to be replaced with the value DKeq. The crack-propagation angle θ0 is in this work determined using maximum tensile stress criterion (MTS-criterion) as follows:

21 I I

0II II

12 tan 8 ,4

K KK K

θ - = ⋅ ± +

(5)

where KI and KII are the stress intensity factors for mode I and mode II, respectively. The complete computational procedure of the fatigue crack propagation under mixed mode loading conditions considering the crack closure effect is described in [3], [23] and [24].

3 COMPUTATIONAL MODEL

In the proposed computational model, the uniformly load distribution along gear width is assumed, which enables the usage of two-

dimensional finite element model. The model is manufactured with the aid of specifically developed software, which on the basis of geometrical parameters determines the rack-generated gear tooth geometry. In order to capture the correct boundary conditions, one tooth on each side is included in the model. Boundary conditions of the left and right hand edge portions are kept fixed, and since solid gears are explored also the hub portions are kept fixed (Fig. 3). The distance between the root circle and the hub is taken to be of equal tooth height, so that the influence of the fixed hub on tooth base rotation can be neglected.

Fig. 3. FE-model

Two gear models are being explored (Fig. 4): first in which gear tooth is loaded with normal pulsating force acting at the highest point of the single tooth contact (HPSTC), and second in which the fact that in actual gear operation the magnitude as well as the position of the force changes as the gear rotates through the mesh, is taken into account.

Fig. 4. Loading conditions; a) load acting at the HPSTC, b) moving load



The computational analyses are performed for two different gear rim thickness sR in relation to the high of the tooth h (see Fig. 5):(i) sR = 3.3×h,(ii) sR = 0.3×h.

Fig. 5. Different rim thickness of analysed gear; a) sR = 3.3×h, b) sR = 0.3×h

3.1 Load Acting at the HPSTC

In that case a loading cycle of meshing gears is presumed as pulsating force acting at the HPSTC (Fig. 4a). The initial crack of length ath calculated using Eq. (2) is placed at the critical plane, which is assumed to be perpendicular to the notch surface in a gear tooth root.

3.2 Moving Load Model

For a moving load model, a quasi static numerical simulation method is presented in which the gear tooth engagement is broken down into multiple load steps and analyzed separately. During the contact of the teeth pair the load moves along each tooth flank thus changing its direction and intensity. In order to investigate the influence of the moving load on the gear root stress amplitude, the analysis is divided, for example, in sixteen separated load cases (j = 0 to 15) (Fig. 4b). Four of them take the force act on the tooth ahead (0 to 3) and four of them take the force act on the tooth after (12 to 15) the analyzed tooth; in six cases the entire load acts on the analyzed tooth (5 to 10), and in two cases the load is distributed on the two teeth in contact (4 and 11). Force intensity for different load cases can be calculated using the following Eq.:

F F Xj HPSTC= ⋅ Γ . (6)

The load sharing factor XΓ which accounts for the load sharing between the various pairs of teeth in mesh along the path of contact for spur

gears and no tip relief has a distribution shown in Fig. 6 [1]. Γy is the parameter on the path of contact and can be calculated as follows [1]:

Γ yy

w

= −tantan

,αα

1 (7)

where αy is the pressure angle at the treated point Y and αw is the pressure angle at the pitch cylinder.

Fig. 6. Load sharing factor XΓ

By analyzing the stress cycle in the gear tooth root it is determined that stress has a maximal value whenever load is in the HPSTC. It follows that the critical plane of the initial crack is a plane perpendicular to the surface at the notch root. The moving load on the gear tooth is non-proportional since the ratio of KII to KI changes during the load cycle. Consequently, the MTS- criterion will predict a unique kink angle for each load increment, but in the crack’s trajectory is computed at the end of the load cycle. The procedure is fully described in [3].

4 PRACTICAL EXAMPLE

The crack propagation was analyzed on the gear wheel of the gear pair with basic data given in Table 1. The gear is made of high-strength alloy steel 14CiNiMo13-4 (0.1% C, 0.27% Si, 0.63% Mn, 1.21% Cr, 0.12% Mo, 0.13% Cu, 0.005% P, 0.005% S) with Young’s modulus E = 2.07×105 MPa, Poison’s ratio n = 0.3, ultimate tensile strength Rm = 1277 MPa and yield strength Re = 1104 MPa. The gear material is case carburised and ground. Material parameters for crack propagation are given in Table 2.

In numerical computations it has been assumed that the initial crack corresponds to the threshold crack length ath, see Section 1. Considering the material parameters in Table 2 the threshold crack length is equal to ath ≈ 0.02 mm.



Its orientation is assumed to be perpendicular to the tooth root surface (Fig. 7).

Table 1. Basic data of treated spur gear pair [3]

Magnitude ValueNumber of teeth for pinion z1 = 28Number of teeth for wheel z2 = 28Module mn = 3.175 mmAddendum modification coefficient for pinion

x1 = ‒0.05

Addendum modification coefficient for wheel

x2 = ‒0.05

Gear width for pinion b1 = 6.35 mmGear width for wheel b2 = 6.35 mmFlank angle of tool αn = 20°Radial clearance factor c* = 0.35Relative radius of curvature of tool tooth

ρf* = 0.35

Addendum of tool ha* = 1.05Dedendum of tool hf* = 1.35Tip diameter Standard clearance

Table 2. Material parameters for crack propagation [3]

Magnitude ValueThreshold stress intensity range ΔKth = 122 Nmm‒3/2

Fracture toughness KIc = 2954 Nmm‒3/2

Material parameter of Paris equation C = 3.128×10‒13

Material exponent of Paris equation m = 2.954

Fatigue limit ΔσFL = 450 MPa

Fig. 7. Initial crack orientation

Since crack increment size needs to be prescribed in advance, crack increment size is taken to be 0.005 mm up to the crack length a =

0.2 mm, and after this 0.1 mm to the critical crack length.

Fig. 8 shows the dependence between the equivalent stress intensity factor Keq and crack length a for two different gear rim thickness (sR = 3.3×h and sR = 0.3×h) if the force is acting at the highest point of the single tooth contact (HPSTC). The FEM-mesh and the crack path for the same cases are shown in Figs. 9 and 10. The similar results are also presented for moving contact loading (see Figs. 11 to 13).

Fig. 8. The diagram (Keq ‒ a) for HPSTC-loading

Fig. 9. The FEM-mesh and crack path for gear rim thickness sR = 3.3×h for HPSTC-loading

Fig. 10. The FEM-mesh and crack path for gear rim thickness sR = 0.3×h for HPSTC-loading

Fig. 14 shows the number of stress cycles Np required for a crack to propagate from the initial (ath) to the critical (ac) crack length for gear rim thickness sR = 3.3×h, where two loading conditions are taken into account: (i) normal pulsating force acting at the highest point of the



single tooth contact (HPSTC), and (ii) the load moves along the tooth flank. It is clear that the crack grows faster in the case of moving loading conditions. Similar results for gear rim thickness sR = 0.3×h are shown in Fig. 15.

Fig. 11. The diagram (Keq ‒ a) for moving contact loading

Fig. 12. The FEM-mesh and crack path for gear rim thickness sR = 3.3×h for moving contact

loading

Fig. 13. The FEM-mesh and crack path for gear rim thickness sR = 0.3×h for moving contact

loading

Fig. 16 shows the crack paths which have been determined numerically for different rim thicknesses and different loading conditions. The numerical determined crack paths are then compared with the experimental results taken from [7]. A reasonable agreement between numerical and experimental results for deeper rim thickness is observed. This is not the case for thinner rim thickness where the numerical determined crack path significantly differs from the experimental results especially for larger crack lengths.

Fig. 14. Crack propagation live for sR = 3.3×h

Fig. 15. Crack propagation live for sR = 0.3×h

Fig. 16. Crack paths for; a) sR = 3.3×h, b) sR=0.3×h (A = numerical for HPSTC loading,

B = numerical for moving loading, C = experimental)

5 CONCLUSIONS

The numerical model used to predict the fatigue crack growth in a gear tooth root is



presented in this paper. The fact that in an actual gear operation the magnitude as well as the position of the force change as the gear rotates through the mesh, is taken into account. In such a way, a more realistic stress cycle in gear tooth root is obtained. The effect of gear rim thickness on the fatigue crack propagation in a gear tooth root and formation of a crack path is also studied. In the numerical computations the crack closure effect is also taken into account, extending an analytical model for plasticity induced crack closure with the partial crack closure concept. In this way, two other closure mechanisms: roughness and oxide induced crack closure are not considered.

Using the numerical procedure described above the predictions of crack propagation lives and crack paths in regard to the gear tooth root stresses are obtained. They are significantly different in comparison to some simplified models, which have been published previously.

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[6] Kato, M., Deng, G., Inoue, K., Takatsu, N. (1993). Evaluation of the strength of carburized spur gear teeth based on fracture mechanics. JSME International Journal, vol. 36, p. 233-240.

[7] Lewicki, D.G., Ballarini, R. (1997). Rim thickness effects on gear crack propagation life. International Journal of Fatigue, vol. 87, p. 59-86.

[8] Spievak, L.E., Wawrzynek, P.A., Ingraffea, A.R., Lewicki, D.G. (2001). Simulating fatigue crack growth in spiral bevel gears. Engineering Fracture Mechanics, vol. 68, p. 53-76.

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[11] Ewalds, H.L., Wanhill, R.J. (1989). Fracture Mechanics. Edward Arnold Publication, London.

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[13] FRANC2D (2000). User’s Guide, Version 2.7. Cornell University, Ithaca

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[22] Abdel Mageed, A.M., Pandey, R.K. (1992). Studies on cyclic crack path and the mixed-mode crack closure behaviour in Al alloy. International Journal of Fatigue, vol. 14, p. 21-29.

[23] Budiansky, B., Hutchinson, J.W. (1978). Analysis of closure in fatigue crack growth. Journal of Applied Mechanics, vol. 45, p. 267-276.

[24] Kujawski, D. (2001). Enhanced model of partial crack closure for correlation of R – ratio effects in aluminum alloys. International Journal of Fatigue, vol. 23, p. 95-102.


*Corr. Author’s Address: University of Maribor, Faculty of Agriculture and Life Sciences, Pivola 10, 2311 Hoče, Slovenia, [email protected] 587

Design and Testing of an Ultrasound System for Targeted Spraying in Orchards

Jejčič, V. ‒ Godeša, T. ‒ Hočevar, M. ‒ Širok, B. ‒ Malneršič, A. ‒ Štancar, A. ‒ Lešnik, M. ‒ Stajnko, D.Viktor Jejčič1 ‒ Tone Godeša1 ‒ Marko Hočevar2 ‒ Brane Širok2 ‒ Aleš Malneršič2 ‒ Andrej Štancar3 ‒

Mario Lešnik4 ‒ Denis Stajnko4,*1Agricultural Institute of Slovenia, Slovenia

2University of Ljubljana, Faculty of Mechanical Engineering, Slovenia 3University of Ljubljana, Faculty of Computer and Information Science, Slovenia

4University of Maribor, Faculty of Agriculture and Life Sciences, Slovenia

The research aims to demonstrate the basic system elements of a prototype automated orchard sprayer, which can deliver pesticide spray selectively with respect to the characteristics of the targets. The contour of the apple tree canopy was detected by ultra sound sensors Prowave 400EP14D and appropriate electronics. Ultra sound signal was processed by a personal computer and fed in real-time to spraying nozzles which open and close in relation to the canopy structure. The current project focuses on developing the system components for spraying an individual tree. The evaluation was performed in field experiments by detecting deposits on leaves and water sensitive papers (WSP). The demonstrated concept of precise application of pesticide sprays supports a decrease in the amount of delivered spray, thereby reducing both costs and environmental pollution by plant protection products.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: air-assisted sprayer, ultra sound, algorithm, spray distribution, orchard

0 INTRODUCTION

Apple fruit orchards are sprayed mainly with axial fan ‘mistblower’ orchard sprayers, because the fan is effective in a wide range of orchard types and under a wide range of conditions. These sprayers are simple, robust, reliable and of a comparatively low cost in terms of purchase and operation. Unfortunately, the large radial spray plume generated by axial fan orchard sprayers is prone to spray drift, thus large losses to the atmosphere and ground occur [1] and [2]. Possibilities of adapting the characteristics of air stream generated by axial fan sprayer to different tree canopies are quite limited.

A number of systems for adjusting the applied dose of plant protection products according to orchard structure have been developed in the past decades. One widely accepted is the Tree Row Volume (TRV) dosing system initiated by [3]. In this system, the dose applied to an orchard is varied by varying the spray volume at constant pesticide concentration in proportion to the TRV. The TRV (m3 ha-1) is the volume of the tree canopy per unit of ground area (= 10000 × crown height × crop width / row spacing). The TRV spray volume adjustment system has been

adapted and tested for low volume spraying in several European countries [4] to [6]. In contrast to the TRV model, [7] and [8] proposed the use of leaf area measurements to improve the correlation between deposits given by different types of spraying equipment and types of hedgerow vineyards. However, different shapes and sizes of tree canopies, even among the same variety in the orchard, require continual calculation of TRV and adjustment of the applied dose of pesticide to optimize the spray application efficiency [9].

It is for these reasons that in the last 10 years measurement of crop structure has been simplified by the development of a range of non-invasive optical and ultrasonic sampling techniques. In particular, the development of a compact, tractor-mounted light and range detection system (LIDAR) has made it possible to take quick and detailed readings of crop structure [10]. These are suitable for computational processing to calculate a wide range of summary parameters based on a probabilistic interpretation of light transmission and crop interception characteristics [11]. Such a system employs a pulse time-of-flight ranging method, with separate apertures (side-by-side) for an infrared laser diode transmitter and a matched diode light receiver.


588 Jejčič, V. ‒ Godeša, T. ‒ Hočevar, M. ‒ Širok, B. ‒ Malneršič, A. ‒ Štancar, A. ‒ Lešnik, M. ‒ Stajnko, D.

Contrary to the expensive radar system, [12] suggested the use of ultrasonic sensors and proportional electro-valves with the corresponding software and automation, which allowed real time modification of the sprayed flow rate adapted to the crop structure of the vineyard. In response to changes in the shape and size of the vines during the growing season, this system reduced the spray volume and the use of pesticides by up to 57%, while maintaining coverage and penetration rates similar to those from conventional spraying methods.

However, since the ultrasonic sensors were originally designed to measure distances in industrial environments, where objects are rigid, and the surface of rebound is perpendicular to the direction of the ultrasonic wave, their utility in orchard measuring might be negligible [5]. Some of the deficiencies of standard sensors can be overcome by modern sophisticated ultrasound signal processing algorithms.

The purpose of our research was to develop an automated orchard sprayer consisting of an axial fan with nozzles controlled by an ultrasound processing system. The results of experiments in the apple orchard and comparisons of spray coverage characteristics as well as the savings of spray between two working modes (with and without automated guidance) are presented in the following sections.

1 METHODOLOGY

1.1 General Experiment Information

The spray distribution and coverage measurements presented are the outcome of experiments carried out in the research orchard of Brdo pri Lukovici (46o10’N, 14o40’E), owned by the Agricultural Institute of Slovenia. Spraying without using ultrasound guidance (control spraying mode, CM) was compared with a novel spraying method using prototype ultrasound sprayer guidance (automated spraying mode, AM). The configuration of the sprayer is explained in full details in section 1.2.

The experiments were performed on spindle trained 4-year old ‘Gala’ apple trees, shown in Fig. 1a, which were grafted onto M9 rootstock and planted at 0.7 m inter tree spacing

and an inter row spacing of 3.2 m. The average height of the trees was 2.5 m. A continuous one- side spraying of trees along the tree row was performed from both sides of the row. Within trees in the sprayed row, five trees and three inter-tree spaces were selected for an analysis of spray coverage and deposit. Each tree (Figs. 1b, and 2) represented one statistical repetition of experimental measurements, with 9 positions (P1 to P9) analysed in the canopy and 3 positions (P10 to P12) between trees.

a)

b)

Fig. 1. a) A prototype sprayer during the experiment in the orchard; b) detail with

measuring positions on the tree

The positions on the tree were selected according to:


589Design and Testing of an Ultrasound System for Targeted Spraying in Orchards

Fig. 2. Measuring positions on the tree and between trees

a) depth: at distance of 10 cm from the exterior (P1, P4, P7), in the middle at 30 cm from the centre of the trunk (P2, P5, P8), and behind the tree trunk (P3, P6, P9);

b) position on the tree: P1 to P3 were placed in the lower part of the tree height (650 mm), P4 to P6 in the centre of the tree (1300 mm) and P7 to P9 in the top part of tree height (2500 mm).

Additional three positions (P10 to P12) for measuring deposits between tree positions were selected according to the height; lower P10 (650 mm above the ground), middle P11 (1300 mm above the ground) and the top P12 (2500 mm above the ground).

The experiment was arranged in a single row, from which a 63.76 m long part was selected to ensure constant guiding and meteorological conditions. Any passing to other tree rows would immediately cause additional variability. During the tests the following values for the meteorological conditions were recorded: temperature 16.9 to 21.2 °C, relative humidity 68.8 to 74.8%, wind speed 1.2 to 1.8 ms-1 and wind direction 18 to 40 deg deviation from perpendicular direction of the sprayer track.

1.2 Sprayer

The prototype sprayer was developed by modification-upgrading of a mounted air-assisted sprayer AGP 200 (Agromehanika Kranj, Slovenia), equipped with a piston pump and a 200 l tank, a pressure-limiting valve, a blower unit with an axial fan and a nozzle boom around the air outlet (Fig. 3).

Fig. 3. A prototype mounted air-assisted sprayer; 1) electro-hydraulic valves, 2) electricity box, 3) operating nozzle- left nozzles closed during the

experiment, 4) axial fan

The prototype was fully operative on one side. There were 3-nozzle sections with one electric valve mounted in each one. Three ultrasonic sensors were placed 280 cm in front of the nozzle plane in the direction of travel, at 60, 120 and 200 cm above the ground (Fig. 4).

Fig. 4. Position of a) ultra sound sensors with horns and b) RGB camera; c) electric box

contains tachometer unit with display and power electronics to control the valves



Each sensor commanded one electrovalve. At the same time a bypass valve in the sprayer manifold allowed the prototype to work as a conventional sprayer to be used as reference in the field tests.

To avoid spraying at too low pressures, an anti-drip device was mounted on each nozzle with an internal spring set to open at 1.5 bar. These devices also helped to shorten response times by keeping the pipes full, ready to spray when the pressure exceeded the one set with the springs.

The position of the spraying nozzles in both modes is presented in Fig. 3. As seen, the first bottom nozzle was set at a height of 60 cm, the middle one at 90 cm and the top one on 120 cm. Each nozzle sprays within 80 to 90° angle, therefore it covers a height of about 1 m of tree crown, if each nozzle is orientated perpendicularly to the tree green wall and the nozzles are positioned around 0.5 m from the edge of tree crown. In our case with three nozzles, this was enough to cover a 2.5 m high tree crown, when assuming that the lowest 40 cm zone was not sprayed and neighbouring sprays slightly overlap.

All three nozzles of the sprayer were opened in the CM all the time and none of the three sprayer sections were controlled by a guidance system, as it is the case with standard radial sprayers already in use. On the other hand, during the AM opening or closing of nozzles was controlled online by ultrasound acquisition and analysis system.

1.3 Operational Conditions of the Orchard Sprayer

The spraying was performed at forward speed of 0.83 ms-1 (3.00 km h-1) for both spraying modes. Characterization of the air stream was obtained with a vane anemometer Schiltknecht MiniAir20 with 22 mm vane. To ensure proper sampling, air velocities were measured for each of three air outlet zones separately in an axial horizontal direction, 500 mm apart from the outlets and the nozzles where the air jet was wider than the diameter of the anemometer sample volume (100 mm). For all tests, the PTO rotational speed was 540 min-1. This gave a mean air volumetric flow rate of 2.90 m3 s-1 and a mean air velocity of 10.8 ms-1. The sprayer was

equipped with three hollow cone nozzles (Lechler TR yellow) operating with a pressure drop of 10.0 bar, to give total spray flow rates of 4.35 l min-1. Thus, the maximum range of values for the applied spray volume per unit of ground area was 290 l ha-1, when all the nozzles were opened. The sprayer settings (Table 1) were the same for both operating modes.

The pump used was a four piston semi-hydraulic diaphragm pump model (BM 65/30, Agromehanika, Slovenia) with volume flow 60 l min-1 at a selected rotational speed 540 min-1.

1.4 Control System for Executing the Sensor Guidance of Nozzles

For the control of the sprayer in the AM the nozzles were opened and closed based on presence or absence of targets, sensed by ultrasonic transceivers. This procedure is explained in more detail below.

System operation included the triggering of ultrasonic transceivers, a calculation of distance using transceivers’ own electronics, processing and time delaying of data from transceivers, and turning on/off valves for pesticides dosage. Same transceivers were used for sending and receiving. The triggering of transceivers was used to prevent unwanted false detections that could arise from the signal being detected on the selected transceiver immediately after another transceiver produced a sound burst.

System control was provided by a control unit consisting of a personal computer (PC), two 16 bit multipurpose data acquisition boards with counter I/O, a colour industrial fire wire IEEE 1394 camera and appropriate software for data and image acquisition, processing and data storage on disk. Control system was protected and mounted to the electric box on the left side of the tractor behind the driver (Fig. 1a). The PC was an embedded fan less computer IEI ECK – 3692 G with Intel Core 2 Duo 1.66 GHz processor with SSD data storage drive. For transceiver triggering and data acquisition USB data acquisition units NI 6112 and NI 6110 were used, each with analogue and digital inputs and outputs and two independent 32 bit counters.



Table 1. Operational parameters during treatments

Operational parameters

Nozzle serial number Lechler TR 80-02Colour Yellow

No. of active nozzles per side 3

Pressure [bar] 10Spray flow rate per nozzle

[l min-1] 0–1.45

Spray flow rate all nozzles [l min-1] 0–4.35

Forward speed [km h-1] 3Working width [m] 3.0

Reference application rate [l ha-1] 290

PTO speed [rev min-1] 540Volumetric air flow rate

[m3 s-1] 2.90

Ultrasonic transceivers used were Prowave 400EP14D with SRM 400 sonar ranging module electronics. The sensors were equipped with a horn with 25 mm length and 22° angle (Fig. 4). For triggering digital outputs from the control system were used. When ultrasonic transducers received the trigger input, they output a 5 ms tone burst of ultrasound at 44 kHz with bandwidth of 1.5 kHz at -6dB. Amplification of output signal included band pass filtering with temperature compensation.

A short period after the tone burst was sent, the transceiver was inactive to allow transceivers' oscillation to damp out. Then, transceivers switched to listening mode. The received signal was band pass filtered and amplified with a fixed first stage amplifier and later with a second stage variable rate amplifier. The variable rate amplifier used 32 steps, where the first received signals were amplified less and later the received signals more. The variable amplifier compensated for the reduction of intensity of received signal, which attenuates with increased time elapsed from output tone burst, corresponding to larger distances. The transceivers’ electronics checked for a threshold in returned signal; if the amplified echo signal from the output of the band pass filter exceeded 0.35 V, the comparator output a low output pulse. In such case, for the time of duration of the low output

pulse, a pulse width modulation PWM type of output was generated. For PWM output, the time between the tone burst output and the threshold received signal is a measure of distance of object in the transceivers view, while the presence of PWM output also denotes the presence of the target. The sensors were configured in such a way that the operational range was from 25 to 150 cm. The frequency of the acquisition of distance of sensors from targets was 300 ms for three sensors. This time corresponded to 90 cm of tractor movement.

The duration of output PWM signal was measured using counters on data acquisition boards. PWM signals were accepted as valid to indicate presence of the plant canopy structures, if distance to the target was from 50 to 110 cm. With such an approach, the number of leaves and density of the canopy were not distinguished by different PWM signal characteristics. The measured duration of PWM signal was delayed to compensate for the required time that the sprayer and pesticide spray need to reach the target. Time delay was fixed; therefore sprayer velocity was maintained constant. This was done manually by the driver who had available information about the tractor velocity from an inductive sensor mounted on the wheel and connected to tachometer unit with display as seen in Fig. 4. The signal from the control unit required to turn on the valves for pesticide dosage was provided by digital outputs on data acquisition boards through mosfet output power transistors. For the control of spray flow through the nozzles, output was connected to direct-acting solenoid valves 2/2 NC 1/4 21A2KV25, coil code RBDA08024AS 8W 24V/50Hz (ODE, Italy).

For later analysis of spray savings, simultaneously with information from distance transceivers, images of the target were acquired. The images were used only to detect positions, on which spray deposit was measured and to check spray nozzles open/closed status on the same positions. Flea2 color camera from Pointgrey Research Camera with 5.6 mm C-mount megapixel lens (Fig. 4) was used. The camera was connected to the computer using the fire wire IEEE 1394 connection. The resolution was 1024×768 pixels. The images were acquired with 30 fps and stored on the disk simultaneously with ultrasonic



measurements. PWM signals from ultrasonic sensors and images were simultaneously recorded to the disk. After the measurements, information was retrieved from the ecorded data about open/closed status of each deposit measuring position.

1.5 Sprayer Flow Rate Calculation

The different components and the control system were tested and fine-tuned in the laboratory and on artificial trees; later, when the sprayer prototype was fully assembled, it was tested in the orchard. This process resulted in a real-time system for the continuous separate opening and closing of all three nozzles according to the tree canopy structure. The real-time flow rate of each electro-valve controlled nozzle of the sprayer prototype was computed according to Eq. (9) as follows:

q p a v VNr= ⋅

⋅ ⋅⋅

( ),600

(1)

where q is the real-time flow rate in l min-1 a is a constant that considers only one side of the sprayer working width in m; v is the speed in km h-1; Vr is the volume application rate for the orchard in l ha -1; N is the number of nozzles; and p is the reduction coefficient of the maximum flow rate given by the following Eq.:

pt

ti

= ∑∑

, (2)

where ∑ti is the sum of actual opening time for each nozzle, ∑t is the sum of maximum possible opening time for all nozzles.

1.6 Analysis of Deposit and Spray Coverage

To analyze the spray deposit two methods were used; Water Sensitive Papers (WSP) and composite leaf samples. WSP measures a number of spray droplets and the percentage of coverage, while leaves samples were used to measure quantity of spray deposit.

In order to quantify the spray deposit and coverage of the drops resulting from different spray modes, Water Sensitive Papers (75 x 26 mm, WSP, Novartis, Switzerland) were placed every time on the same places in each of five

trees and three inter-space positions immediately before each spraying as proposed by [1]. The WSP were held by clothespins at fixed positions and were collected approximately 10 min after they had completely dried.

Data presented are average values of the measurements from upper and lower side of WSP at each specific position. Images of each WSP were digitized using the Optomax Image Analysis system (Optomax, NH, USA), consisting of a CCD camera with a zoom lens, a monitor to control the picture being analyzed, and a PC with a Frame Grabber card. The area resolution of the system was 1/417600 per field of view (720 × 580 pixels), so the smallest spot size detected by 1 pixel was 8 μm and image depth was 256 grey levels [6]. By using this system, coverage (with stains covered area - % coverage) the number of impacts and the number of impacts per unit area were all analyzed. Canopy deposits were measured on composite leaf samples, taken from the 12 positions of selected trees in 5 replications so that each sample contained five leaves. The chosen leaves for deposit measurements were held in the same position with clothespins. This ensured exactly the same positions of leaves for both modes of spraying and reduced the variability caused by position of leaves at the points of deposit analysis. After each experiment the leaves were collected from clothespins and placed in plastic bags, taken to the laboratory and stored in a dark and cool place before processing. Tartrazine (Citronin yellow, ETOL, Slovenia), which is often used in spray deposition experiments, was used as a tracer. The concentration of the tracer in the applied spray was 20 g1-1. Leaf samples were washed with distilled water, shaken in the same plastic bag as collected and the samples of 2 ml were taken for determining the concentration of tartrazine by spectrophotometer Varian CARY 50 BIO. The experimental procedures of [11] followed. Nevertheless, previous tests were made in the laboratory to confirm the accuracy of the methodology, especially in relation to tracer recovery from apple leaf samples, whereby the theoretical and normalised deposit was calculated according to the procedure described by [8]. The tartrazine leaching efficiency was assumed to be 90%.



All data were transferred from Optomax and Varian to formatted computer spread-sheets (Microsoft Excel) before a statistical analysis of variance (2 treatments x 5 repetitions x 12 locations) using the Statgraphics Statistics Package Program.

2 RESULTS AND DISCUSSION

2.1 Reduction of Spray Delivered per Unit Area

The working time and real-time flow rate of each particular nozzle for a test track is shown in Table 2. The effective working time for each nozzle was calculated as the sum of all opening times from the stored data of the valves’ open/closed status during the driving along the track, while the real-time flow rate was calculated according to the driven path and time. The procedure of turning the nozzles on/off was explained in the section 1.4.

Given the average operating time on the 63.76 m long experimental field track of 53.56 s per nozzle in the CM, and 42.74 s with the AM, nozzles were closed on average for 10.82 s; thus calculated spray savings at an average of 20.2% were achieved for all three nozzles together. For that reason, a significant reduction of the average real-time flow rate per nozzle from l.45 l min-1 to 1.16 l min-1 was achieved in comparison with spraying when the sprayer operated in the CM.

The total open time for all three sensors is the same (10.82 s), which means that trees and interspaces were detected in all three heights at the same time. Although the trees were formed in a spindle form with conical shape, the differences in the ratio between dense green wall area and empty

space (canopy gaps), which is closely related to the tree height zone, did not affect the average opening time among upper, mid and lower zones, as expected. Thus, further research of other types of ultrasound sensors is planned.

[9] reported 28% spray saving in a high density pear plantation and 68% in an older olive plantation, while controlling the sprayer nozzles with ultrasound sensors. In our experiment the spray saving of 20.2% is good owing to two reasons. First, the canopies in the orchard were more uniformly spread than in olive plantation [9], second, the deposits on targets remained unchanged or they were even higher than in control mode. Thus, for future improvement better performance of ultrasonic transceiver is necessary.

2.2 Spray Coverage

The quality of spray distribution determined by the analysis of WSP samples was expressed as the percentage of coverage and the number of impacts per cm-2. As seen from Table 3 in the ‘control’ repetition the highest coverage (42.39%) was obtained on the P1 ‘upper’ followed by P3 and P4. In all tree positions there was no statistically significant difference between the control and automated spraying modes, which means that the reduction of nozzle output during the automated spraying did not significantly reduce the spray coverage. Between trees the highest coverage (52.81%) was obtained again on the ‘control’ P10 ‘upper’ followed by P11 and P12. The same pattern was measured on the automated spraying, which means that common drift between trees could not be prevented significantly by a prototype ultrasound sprayer.

Table 2. Average working time [s] and real-time flow rate [l min-1] for automated (AM) and control (CM) spray distribution

Nozzleposition

Automated (AM) Control (CM)

Open time[s]

Close time[s]

Real-time flow rate[l min-1]

Open time[s]

Close time[s]

Real-time flow rate[l min-1]

1st above 42.74 10.82 1.16 53.56 0.00 1.452nd middle 42.74 10.82 1.16 53.56 0.00 1.453rd bottom 42.74 10.82 1.16 53.56 0.00 1.45Average 42.74 10.82 1.16 53.56 0.00 1.45

Index A/C 0.798 0.202 - - - -



Table 3. Comparison between the coverage (%) in control and automated (AM) spray distribution*

Position Control AutomatedLower Upper Lower Upper

P1 27.30 c A 42.39 ef A 30.95 c A 41.93 c AP2 17.40 abc B 37.34 def A 9.56 ab A 35.62 c AP3 11.10 abc B 39.77 ef A 19.87 abc A 37.69 c AP4 12.40 abc A 34.23 cde B 17.27 abc A 24.51 bc AP5 12.63 abc A 26.59 bcde A 7.67 ab A 25.90 bc AP6 25.62 bc B 33.24 cde A 4.85 ab A 29.91 c AP7 17.20 abc A 10.41 ab A 22.45 abc A 9.32 ab AP8 5.79 ab A 20.54 abcd B 5.60 a A 9.60 ab AP9 8.75 ab B 7.28 a A 3.60 a A 5.00 a AP10 20.40 bc B 52.81 f B 7.55 ab A 42.00 c AP11 12.60 abc A 40.56 ef B 7.03 ab B 33.01 c AP12 13.67 abc B 16.68 abc B 1.40 a A 8.43 ab A

Lower part of tree 18.60 b A 39.83 b A 20.13 b A 38.40 c AMiddle part of tree 16.88 b A 31.35 b B 9.93 a B 26.70 b AUpper part of tree 10.59 a A 12.74 a B 10.55 a A 7.97 a A

All tree positions together 15.35 b A 27.97 a A 13.54 b A 24.39 a AAll positions between

trees together 15.56 a B 36.68 b B 5.32 a A 27.84 a A

All positions 15.41 A 30.15 A 11.48 A 25.25 A

Table 4. Comparison between the number of impacts in control and automated (AM) spray distribution*

Position Control AutomatedLower Upper Lower Upper

P1 69 abc A 103 abc B 75 abc A 89 ab AP2 72 abc A 123 bc A 66 abc A 123 b AP3 83 abc A 117 abc A 114 bc B 115 ab AP4 79 abc A 111 abc A 138 d B 102 ab AP5 83 abc A 146 c A 79 abcd A 110 ab AP6 74 abc A 127 bc A 94 abcd A 112 ab AP7 129 c A 112 abc A 117 bc A 109 ab AP8 64 ab B 132 c B 44 ab A 85 ab AP9 53 ab A 79 ab A 75 a B 68 a AP10 98 bc A 72 a A 83 abcd A 102 ab BP11 61 ab A 101 abc A 101 bcd B 122 b AP12 23 a A 77 ab A 82 abcd B 81 ab A

Lower part of tree 75 a A 114 a A 85 ab A 109 b AMiddle part of tree 79 a A 128 a A 104 b B 107 b AUpper part of tree 82 a B 107 a B 67 a A 87 a A

All tree positions together 78 b A 116 b A 85 a A 101 a AAll positions between

trees together 61 a A 83 a A 88 a B 102 a B

All positions 74 A 108 A 86 A 101 A

*Notes: abc … differences between positions on the tree (Tukey HSD test; a = 0.05), A, B difference between Control and Automated spraying mode (t-test; a = 0.05), A, B comparisons of positions inside the tree and between trees (t-test; a = 0.05)



However, in both modes there was significantly higher coverage in the upper than on the lower side of WSP in all positions, except in case of positions P7 and P12, which is commonly known spray pattern for the axial fan mistblower. Additional comparison of summarized data showed that the coverage was the lowest in the upper part of tree (12.7% control and 7.97% automated), which significantly differs from the middle (31.3% control and 26.7% automated), and lower part of the tree (39.8% control and 38.4% automated). The same distribution was detected in both spraying modes; however there was no statistically significant difference between them, which means that the newer technique assured the same quality of spray coverage as the standard one.

The number of impacts per cm-2 is presented in Table 4. It can be seen that the

highest number of impacts (146) was detected in the ‘control mode’ on the P5 followed by P8 (132) and P2 (123). In AM the highest number of impacts (123) was again detected in P2 followed by P3 (115) and P6 (112). However, a decrease of impact numbers was detected on the WSPs lower facing, which could be connected to the fast pulse opening and closing of nozzles leading to a reduction of the droplet size. Although the use of automated system reduced the determined number of droplet impacts in all from 108 to 101 (see Table 4), there was no significant difference of the coverage values when the sprayer was operated in AM.

2.3. Spray Deposition

The quality of spray distribution determined by spectrophotometric measurements

Table 5. Comparison between the tartrazine tracer deposit [µg/cm2] in control and automated (AM) spray distribution

Position

Control AutomatedMeasured

deposit [µg/cm2]

Normalised deposit*

Measured deposit

[µg/cm2]

Normalised deposit*

Corrected normalised deposit**

P1 5.15 bc A 0.70 A 5.14 cd A 0.69 A 0.86 AP2 4.11 abc A 0.56 A 3.38 abc A 0.46 A 0.58 AP3 6.01 c A 0.81 A 4.46 bcd A 0.60 A 0.75 AP4 3.79 abc A 0.51 A 3.60 abc A 0.49 A 0.61 AP5 3.71 abc A 0.50 A 3.17 abc A 0.43 A 0.54 AP6 3.55 abc A 0.48 A 3.54 abc A 0.48 A 0.60 AP7 1.59 a A 0.21 A 2.26 ab A 0.31 A 0.39 AP8 2.21 ab A 0.30 A 1.87 a A 0.25 A 0.31 AP9 2.03 a A 0.27 A 1.67 a A 0.23 A 0.29 AP10 6.35 c A 0.86 A 6.09 d A 0.82 A 1.03 AP11 5.16 bc A 0.70 A 5.23 cd A 0.71 A 0.89 AP12 1.85 a A 0.25 A 1.58 a A 0.21 A 0.26 A

Lower tree 5.09 a A 0.69 A 4.33 a A 0.59 A 0.74 AMiddle tree 3.68 a A 0.50 A 3.44 a A 0.46 A 0.58 AUpper tree 1.94 b A 0.26 A 1.93 b A 0.26 A 0.33 A

All on the tree 3.57 A A 0.48 A A 3.23 A A 0.44 A A 0.55 A AAll between trees 4.39 A A 0.59 A A 4.36 A B 0.59 A B 0.74 A B

All positions 3.77 A 0.51 A 3.52 A 0.48 A 0.60 ANotes: * 7.4 µg/cm2 = 1 = 100% of theoretical deposit 1, ** 5.9 µg/cm2 = 1 = 100% of theoretical deposit 2, Normalised deposit = measured deposit / theoretical deposit* , *Theoretical deposit 1 = (applied hectare tracer rate at control mode (g/m2) / orchard leaf area m2), *Theoretical deposit 2 = (applied hectare tracer rate at automated mode (g/m2) / orchard leaf area m2), abc … differences between positions on the tree (Tukey HSD test; a = 0.05), A, B difference between Control and Automated spraying mode (t-test; a = 0.05), A, B comparisons of positions inside the tree and between trees (t-test; a = 0.05)



of tartrazin deposits on the leaf samples was expressed in µg/cm2 as well as in form of normalized deposit, whereby the maximum theoretical deposit amounting 7.4 µg/cm2 is assumed as 1 (100%) in control mode and 5.9 µg/cm2 in AM. The difference in the theoretical starting-points of both modes is due to the 79.8% nozzles opening time during AM.

As seen from the Table 5 ‘control’ the highest deposit (6.35 µg/cm2) was detected on lower inter tree position P10 followed by P3 and P1. In all upper tree positions (P7 to P9) there was a significantly lower deposit measured than in the middle and lower positions, which means that a relevant loss of spray appeared in this part of trees.

In AM the highest deposit (6.09 µg/cm2) was again detected on lower inter tree position P10 (Fig. 5), the second highest position was

the middle inter tree position P11 (5.23 µg/cm2) and the lower outer position P1. Although the overall deposit reached 3.52 µg/cm2 of leaf area in AM, which is for about 10% lower than in case of control mode (3.77 µg/cm2), the corrected normalized deposit was in fact by 9% higher (see Table 5 automated). Despite the 20.2% spray savings, due to a lower amount of spray flow through the nozzles, only 10% less spray was deposited on the leaves and the differences between positions were lower). At the same time a higher normalised deposit was detected.

This can be seen in the position P10 (1.03), P11 (0.89) and P1 (0.86), where values of normalised deposit did not differ statistically from the CM. From these results it can be concluded that the spray deposition quality in the AM is totally comparable to the one of the CM.

Table 5. Comparison between the tartrazine tracer deposit [µg/cm2] in control and automated (AM) spray distribution

Position

Control AutomatedMeasured

deposit [µg/cm2]

Normalised deposit*

Measured deposit

[µg/cm2]

Normalised deposit*

Corrected normalised deposit**

P1 5.15 bc A 0.70 A 5.14 cd A 0.69 A 0.86 AP2 4.11 abc A 0.56 A 3.38 abc A 0.46 A 0.58 AP3 6.01 c A 0.81 A 4.46 bcd A 0.60 A 0.75 AP4 3.79 abc A 0.51 A 3.60 abc A 0.49 A 0.61 AP5 3.71 abc A 0.50 A 3.17 abc A 0.43 A 0.54 AP6 3.55 abc A 0.48 A 3.54 abc A 0.48 A 0.60 AP7 1.59 a A 0.21 A 2.26 ab A 0.31 A 0.39 AP8 2.21 ab A 0.30 A 1.87 a A 0.25 A 0.31 AP9 2.03 a A 0.27 A 1.67 a A 0.23 A 0.29 AP10 6.35 c A 0.86 A 6.09 d A 0.82 A 1.03 AP11 5.16 bc A 0.70 A 5.23 cd A 0.71 A 0.89 AP12 1.85 a A 0.25 A 1.58 a A 0.21 A 0.26 A

Lower tree 5.09 a A 0.69 A 4.33 a A 0.59 A 0.74 AMiddle tree 3.68 a A 0.50 A 3.44 a A 0.46 A 0.58 AUpper tree 1.94 b A 0.26 A 1.93 b A 0.26 A 0.33 A

All on the tree 3.57 A A 0.48 A A 3.23 A A 0.44 A A 0.55 A AAll between trees 4.39 A A 0.59 A A 4.36 A B 0.59 A B 0.74 A B

All positions 3.77 A 0.51 A 3.52 A 0.48 A 0.60 ANotes: * 7.4 µg/cm2 = 1 = 100% of theoretical deposit 1, ** 5.9 µg/cm2 = 1 = 100% of theoretical deposit 2, Normalised deposit = measured deposit / theoretical deposit*, *Theoretical deposit 1 = (applied hectare tracer rate at control mode (g/m2) / orchard leaf area m2), *Theoretical deposit 2 = (applied hectare tracer rate at automated mode (g/m2) / orchard leaf area m2), abc … differences between positions on the tree (Tukey HSD test; a = 0.05), A, B difference between Control and Automated spraying mode (t-test; a = 0.05), A, B comparisons of positions inside the tree and between trees (t-test; a = 0.05)



3 CONCLUSIONS

Assessment of ultrasonic electronic control system for proportional spray application showed a total of 20.2% saving of spray per nozzle and area unit (0.30 l min-1 flow rate reduction) when used in AM, in comparison to spraying in CM. This saving was achieved without significant reduction of spray coverage at any tree positions making the approach interesting for further developments. However, this is not enough to claim the same spray savings for diverse spraying applications in a number of orchards, planted with different fruit varieties with trees of varying training systems and size.

P1 P2 P3 P4 P5 P6 P7 P8 P9P100

1

2

3

4

5

6

7

Mea

sure

d de

posi

t (µg

/cm

2 )

Position in the tree

Control Automated

Fig. 5. Measured tartrazine tracer deposit on the different tree position

Three ultrasonic sensors and three nozzles were used in our experiments. In practice, it would be better to have more electro-valve controlled nozzles with a narrower working angle, because in that case the ability of adapting of the individual nozzle output to the characteristics of the tree canopy zones (ratio between green wall area and canopy gaps) would be better.

The novel design of automated sprayer with ultrasonic sensors can bring progress in spraying plantations with a number of orchards of different training systems and age. For instance, especially in the case of smaller trees in young plantations the upper nozzle can be switched off;

or in the varying tree structure the opening/closing of nozzles can be adapted automatically.

It is well known that in the present development stage ultrasonic sensors can not distinguish very small and dense structures of the canopy, orchard supports and broad less dense canopies. For this reason and for the reason that most of the ultrasonic echo is formed on the canopy outer layer, the ultra sound sprayer guidance system operated by standard ultrasonic sensors, unlike the radar guidance systems, is not able to provide the information about the tree structure deep inside the tree crown.

Sensors detection should be evaluated regarding the tree structure and canopy properties. Sensors used in this experiment, provided only information in the form of presence of the target and its distance. Small very dense targets performed similar to large less dense targets. There might exist an opportunity for a further upgrade of sensors electronics to distinguish between both mentioned cases. Potential further improvement of our prototype system can be achieved by modifying the ultrasonic sensors so they could detect the tree structure selectively according to the different reflection from the leaf density in the middle of the crown and give a better discrimination of tree crown and the background also in the lower section of trees.

4 ACKNOWLEDGEMENTS

This research was funded by ARRS No. 3211-10-000040 as part a of EUREKA project. The funding is gratefully acknowledged. The authors also acknowledge the vital contributions made by the following colleagues: Stanislav Vajs, who was responsible for the field measurements; technician and tractor driver, Toni Gjergek; and Roman Mauc, the head of the experimental orchard in Brdo pri Lukovici, who was always willing to help during the measurements in the orchard; and to Professor Michelle Gadpaille, for her editing of the manuscript.

5 REFERENCES

[1] Cross, J.V., Walklate, P.J., Murray, R.A., Richardson, G.M. (2001). Spray deposits and losses in different sized apple trees from



an axial fan orchard sprayer: 1. effects of spray liquid flow rate. Crop Protection, vol. 20, p. 13-30.

[2] Eberlinc, M., Dular, M., Širok, B., Lapanja, B. (2008). Influence of blade deformation on integral characteristic of axial flow fan. Strojniški vestnik - Journal of Mechanical Engineering, vol. 54, no. 3, p. 159-169.

[3] Byers, R.E., Hickey, K.D., Hill, C.H. (1971): Base Gallonage Per Acre. Virginia Fruit, vol. 60, p. 19-23.

[4] Heijne, B., Doruchowski, R., Hołownicki, Koch, H., Jaeken, P., Siegfried, W., Hollinger, E. Cross, J.V., Orts, R. (1997). Developments in spray application techniques in European pome fruit growing. IOBC/WPRS Bull., vol. 20, no. 9, p. 119-129.

[5] Sutton, T.B., Unrath, C.R. (1984). Evaluation of the tree-row-volume concept with density adjustments in relation to spray deposits in apple orchards. Plant Disease, vol. 68, p. 480-484.

[6] Sutton, T.B., Unrath, C.R. (1988). Evaluation of the tree-row-volume model for full-season pesticide application on apples. Plant Disease, vol. 72, p. 629-632.

[7] Pergher, G., Gubiani, R., Tonetto, G. (1997). Foliar deposition and pesticide losses from three air-assisted sprayers in a hedgerow vineyard. Crop Protection, vol. 16, p. 25-33.

[8] Pergher, G., Petris, R. (2008). Pesticide dose adjustment in vineyard spraying and potential for dose reduction. The Cigr Ejournal, 10, Manuscript Alnarp 08 011, vol. X.

[9] Solanelles, F., Escolà, A., Planas, S., Rosell, J.R., Camp, F., Gràcia, F. (2006). An Electronic control system for pesticide application proportional to the canopy width

of tree crops. Biosystems Engineering, vol. 95, p. 473-481.

[10] Wangler, R.J., Connell, R.E., Fowler, K.L., Olson, R.A. (1993). Application of smart submunition technology to agribusiness. J.A. Deshazer, Meyer, G.E. (eds.). Proc. Spie Optics In Agriculture And Forestry, vol. 1836, p. 261-272.

[11] Walklate, P.J., Cross, J.V., Richardson, G.M., Murray, R.A., Baker, D.E. (2002). Comparison of different spray volume deposition models using lidar measurements of apple orchards. Biosystems Engineering, vol. 82, p. 253-267.

[12] Gil, E., Escolà, A., Rosell, J.R., Planas, S., Val, L. (2007). Variable rate application of plant protection products in vineyard using ultrasonic sensors. Crop Protection, vol. 26, p. 1287-1297.

[13] Moltó, E., Martín, B., Gutiérrez, A. (2000). Design and testing of an automatic machine for spraying at a constant distance from the tree canopy. Journal of Agricultural Engineering Research, vol. 77, p. 379-384.

[14] Hołownicki, R., Doruchowski, G., Świechowski, W., Jaeken, P. (2002). Methods of evaluation of spray deposit and coverage on artificial targets. Electronic Journal of Polish Agricultural Universities, from: http://www.ejpau.media.pl/volume5/issue1/engineering/art-03.html, accessed on 2010-09-11.

[15] Moltó, E., Martín, B., Gutiérrez, A. (2000). Pesticide loss reduction by automatic adoption of spraying on globular trees. Journal of Agricultural Engineering Research, vol. 78, p. 35-41.

[16] Pergher, G. (2001). Recovery rate of the tracer days used for spray deposit assessment. Transactions of ASABE, vol. 44, no. 4, p. 787-794.

http://www.ejpau.media.pl/volume5/issue1/engineering/art-03.html

http://www.ejpau.media.pl/volume5/issue1/engineering/art-03.html


*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia; [email protected] 599

Integrating R&D and Marketing in New Product Development

Fain, N. ‒ Kline, M ‒ Duhovnik, J.Nuša Fain1,* ‒ Mihael Kline2 ‒ Jožef Duhovnik1

1 University of Ljubljana, Faculty of Mechanical Engineering, LECAD Laboratory, Slovenia 2 University of Ljubljana, Faculty of Social Sciences, Slovenia

R&D - marketing integration is considered to be a critical activity within New Product Development (NPD). A theoretical framework for the study of R&D - marketing integration levels developed by Gupta et al (1986) is one of the most widely cited R&D - marketing integration frameworks in scientific literature. It is based on the presumption that strategy, environmental, organizational and individual factors are those determining R&D - marketing integration levels and consequently NPD success. Several empirical studies have been conducted to test this framework, however most of them have dealt only with portions of Gupta et al (1986)'s model. This paper is an attempt to put forward and test an integrated research protocol for the study of R&D - marketing integration, based on this theoretical framework. Empirical evidence gained from a questionnaire survey and two company case studies show, that people active within the R&D - marketing interface perceive the studied constructs as relevant for R&D - marketing integration, thus giving confirmation to Gupta et al (1986)’s model. The presented research protocol can therefore be considered as a valid start into R&D - marketing integration research within an integrated framework. ©2011 Journal of Mechanical Engineering. All rights reserved.Keywords: marketing, R&D, integration, NPD, theoretical framework, empirical evidence

0 INTRODUCTION

The multifunctional process of new product development (NPD) includes several activities carried out by groups with different abilities, knowledge elements, resources, competences and cultures. A successful NPD process meets market demands and needs with an appropriate technical solution. Marketing supplies the voice of the customer, while research and development (R&D) uses the company’s assets and capabilities to create a product with a differential competitive advantage [1] to [3]. In today’s competitive environment, the companies that succeed will be those which develop products that satisfy customer needs better than the products of their competitors. Therefore, it is necessary that companies fully research such needs, and generate ideas and solutions that can best satisfy them. The more innovative the NPD projects are, the greater is the need to integrate marketing and R&D functions within the company. However, although the need for integration has been widely recognised, the levels of integration of R&D and marketing in practice have proven to be low.

Marketing researchers see R&D as a subordinate function and the R&D handles marketing as a static or even limited function. Integration gaps that hinder the NPD process exist [4].

Gupta et al. [4] have put forward a theoretical framework for the study of R&D - marketing integration (Fig. 1), based on determining the ideal and needed levels for R&D - marketing integration. This framework is the most widely used and cited framework for the study of R&D - marketing integration.

The study of literature has shown that ideal levels of integration between R&D and marketing have been defined ([4] to [6]) and used to analyse companies within different economies. Other authors ([1] and [7]) have defined different integrative mechanisms that should lead to higher levels of R&D - marketing integration and have tested them within different economies. However, according to our knowledge, none of these studies have dealt with these processes within the same framework. Only parts of [4]’s framework have been tested empirically. Therefore, an integrated empirical study is needed to address the R&D -


600 Fain, N. ‒ Kline, M ‒ Duhovnik, J.

marketing integration levels. This paper presents such an attempt.

The research presented is twofold. Firstly, the applicability of partial studies of R&D - marketing integration on different cultural backgrounds is tested as literature study has shown that although the studied research works interpret R&D - marketing interface within NPD, they do this within leading world economies. This makes the transfer to other economies without regarding national and cultural differences questionable. Therefore, testing the framework is needed for exploring R&D - marketing integration in NPD context regarding the cultural and national differences among the studied countries. The first objective of this paper is to respond to that need by developing and testing a framework to study the country specific R&D - marketing integration process within the NPD processes. We do so by studying the R&D - marketing integration level in Slovenia. Secondly, we put forward a research protocol for the study of R&D - marketing integration portions of [4]’s model that have been left out of these empirical studies. We test this protocol on two companies within the Slovenian business environment.

The paper is structured into several sections. First, the theoretical framework for our study is presented and put forward the hypotheses. Then, the research methodology is presented. In order to get insight into the R&D - marketing interface with the focus on culture/nation specific influences, a questionnaire survey within Slovenian SMEs was conducted. In addition, we were interested in how the actors involved within the R&D - marketing interface experience their NPD processes. In order to gain knowledge on that issue, we have conducted multiple case studies of Slovenian companies with different NPD characteristics. The whole research is set up as an instrumental case study, meaning its aim is to generalise findings and make them applicable to other NPD processes outside the studied companies. The final result of the proposed research strategy is a set of causalities relevant for R&D - marketing integration. At the end the research findings are compared to the theoretical framework and conclusions are given.

1 THEORETICAL FRAMEWORK AND HYPOTHESES

The theoretical framework, presented in Fig. 1, has been presented in the work of [4] and widely used for determining the levels of R&D - marketing integration in different studies (i.e [1], [7] and [8]).

This work obtains its support from strategy-structure-environment paradigms of organisational design, the organisational context of innovation, and the socio-cultural differences between managers and technical specialists, i.e. marketing and R&D personnel. The rationale for this model is based on three main concepts [4]:

The degree of R&D - marketing integration required depends on company’s new product strategy and its perceived environmental uncertainty.

The company’s ability to achieve R&D - marketing integration is affected by its (1) organisational factors such as structure and reward systems and (2) socio-cultural differences between R&D and marketing managers.

The integration gap that results from the difference between the perceived need and achieved integration is expected to affect the NPD success of the company.

Fig. 1. Theoretical framework for the study of R&D - marketing interface [4]

Based on the presented framework a research protocol was developed in order to test these concepts. The degree of integration achieved was assessed by conducting a questionnaire survey presented in previous studies ([1] and [7]) within the growing economy of Slovenia. Earlier


601Integrating R&D and Marketing in New Product Development

studies of achieved R&D - marketing integration have been carried out in the Western countries, such as USA, Japan and New Zealand (i.e. [1], [8] and [9]), leaving a gap regarding the R&D - marketing integration in the growing economies. Some comparison of the Western model of achieved R&D - marketing integration that has been developed from those studies (i.e. [1] and [7]) has been done in reference to China. However, mostly the field of the achieved R&D - marketing integration in growing economies is still under-researched. Slovenia, as our unit of study, has just recently joined the European Union and is still strongly oriented towards collectivism and has high power distance and uncertainty avoidance levels within its culture [10]. These characteristics put it opposite to many of the Western countries where the orientation is individualist and the levels of power distance and uncertainty avoidance in company culture are low. These characteristics make Slovenia a valid example for study.

The questionnaire used to study the achieved R&D - marketing integration was adopted from work of [1] and [7], who studied R&D - marketing integration on Western economies. It covers the areas of integration mechanisms, integration gaps and NPD success and states that the success of NPD depends on the degree of the cross-functional integration gap between R&D and marketing. Furthermore, the model specifies that the integrative mechanisms (formalisation, centralisation, organisational climate) influence the cross-functional integration gap ([1]; [7]). To minimize the gap, and as such to enhance product success, the integration mechanisms should be influenced. The main hypothesis we derive from literature review of the achieved R&D - marketing integration is:

H1: Influences on the level of R&D - marketing integration achieved are culturally determined.

Based on the model we derive a number of sub-hypotheses, first with respect to the relation between the cross-functional integration gap and the integration mechanisms (SH1 to SH3) and further regarding the effect of the cross-functional integration gap on NPD success (SH4). The hypotheses are derived from an in-depth literature review of Western R&D - marketing interfaces.

SH1: A lower degree of formalisation in a company corresponds to a reduced gap between R&D and marketing.

SH2: A lower level of centralisation in a company corresponds to a reduced gap between R&D and marketing.

SH3: A higher level of organisational climate used in a company corresponds to a reduced gap between R&D and marketing.

SH4: A smaller R&D–marketing gap corresponds with a greater probability of NPD success.

The presumption behind the proposed framework is that if any of the hypotheses supported by the western model do not hold for Slovenian SMEs, then H1 that the influencing factors are culturally determined, can be confirmed.

The degree of R&D - marketing integration required, which is, according to [4]’s model dependent on the company’s new product strategy and environmental uncertainty has, according to our literature review, not been studied within the same framework; therefore, there is no research protocol to be tested. The second part of our research therefore aims at developing a research protocol that can be used in order to integrate empirical evidence within the same model. We base the proposed protocol on the knowledge presented in the framework of [4] and put forward the second hypothesis:

H2: NPD success is fostered by an optimized level of R&D - marketing integration.

Since the nature of the research is explorative, we decided to test the hypotheses with an explorative case study, backed up with a survey on a national level. The survey within Slovenian SMEs serves as a pilot study to get an insight into the situation regarding R&D - marketing integration within the studied economy. The following case studiy represents empirical evidence for an integrated [4] R&D - marketing integration framework.

2 RESEARCH METHODOLOGY

We have decided to use two interrelated research strategies to find answers to the presented issues – a questionnaire survey and a case study research.



2.1 Questionnaire Survey within Slovenian SMEs

A questionnaire survey has been developed in order to get an insight into culture specific influences on R&D - marketing interface within Slovenian SMEs. A survey provides a quantitative or numeric description of trends, attitudes, or opinions of a population, by studying a sample of that population [11]. We chose to study Slovenian SMEs for two main reasons. First, Slovenia is in the process of transition from the technology-push model, which prevailed in the Slovenian central planned economy in the past, towards the opened economy of the Western countries, therefore leaving the field of the R&D - marketing integration in Slovenian companies open. The second reason for this choice of the unit of analysis is the fact that most of the cited studies about R&D - marketing integration were conducted on R&D - marketing integration in large companies, leaving the field of small and medium sized enterprises (SMEs) open for further research. SMEs are often cited for being able to react quicker to a changing business environment, having greater internal flexibility, being more willing to take risks, being more efficient, having informal communication coupled with less bureaucracy and having an entrepreneurial spirit [12]. At the same time, the lack of personnel and financial resources for R&D, narrower market niches and the inability to attain economies of scale can limit their NPD success in comparison to larger companies [12]. The differences in the organisational structure and performance therefore exist between the SMEs and large companies that have not been taken into account within the R&D - marketing integration studies so far. In Slovenia small industry is well developed. More than 93% of Slovenian companies are classified as small and 4.7% as medium-sized [13]. Next, proportionally more small manufacturing enterprises with innovation activity are found in Slovenia compared to any other of the European growing economies [14].

We chose to conduct a mailed questionnaire survey for two purposes: (1) our budget for the execution of this part of research was limited, and (2) a mailed questionnaire survey gives the respondent the possibility of answering at their own leisure, therefore it is not as intrusive as other

types of surveys. The nature of the survey was cross-sectional, meaning that our intention was to collect data at one point in time. The population we wanted to study was the R&D, marketing and management people within Slovenian SMEs that conducted NPD processes. In a multistage procedure we identified organisations that fitted our criteria, and afterwards obtained names and addresses of individuals from marketing, R&D and management functions. 197 companies involved in NPD were contacted in order to complete the questionnaire. They were randomly chosen out of SMEs involved in NPD, with the help of statistical programs IPIS and iBON, that group data on Slovenian companies. The data collection was carried out in November 2007 when we sent out the first questionnaires. After two weeks, we did a follow up by sending e-mails and after another two weeks we telephoned the respondents to remind them of the questionnaire. The effective response rate was 26%.

All the items used for measuring the defined constructs in the questionnaire were measured on a 7-point Likert scale and were taken from well-established and validated scales (for details se [1], [7] and [15]).

2.2 Case Studies within Slovenian Companies

We were also interested in how the actors involved within the R&D - marketing interface experience their NPD processes. In order to gain knowledge on that issue, we decided to conduct multiple case studies of Slovenian companies with different NPD characteristics. To find suitable companies we employed some selection criteria, i.e. availability of the company, characteristics of the NPD process. In each company where there is an R&D function, a marketing function that markets the products developed by R&D should exist. However, this is not always the case; therefore companies that have distinct R&D and marketing functions should be determined. Also, the NPD function needs to exist within the company, since our unit of study is the R&D - marketing interface within NPD. After combining these criteria with the availability of the case criteria, two companies were selected. Both of them suite the above criteria and are part of the global business-to-business environment. They



differ with regard to the products they develop, the way NPD is carried out in the company, the levels of R&D - marketing integration and the structures of their R&D and marketing functions.

Case 1 is a company operating in the global market within the fields of development, production, and marketing of commutators. Because their core product has reached the mature phase of its life cycle, the company is extending its product program to electronics, soft ferrites, wound and plastic components.

The company studied in Case 2 develops solutions for steel buildings, roofs, façades, steel constructions, containers, as well as sound and insulation systems. Both of the studied companies work within the high-tech business environment, where innovation, and consequently R&D play a central role. Both companies have separate R&D functions that are responsible for innovation within the company. Their marketing sections differ according to their importance within the company, organisation and cooperation with other functions. With this in mind, the two cases satisfy the last two case selection criteria ‒ the ability to learn from the case and the level of variety between cases. Therefore, they represent valid cases for our research.

In order to get an insight into the company profiles, several internal documents of the companies were studied in depth and a literature review of the R&D - marketing interface was conducted. The questionnaire survey, explained in the previous part of this section, served as a pilot study, enabling us to refine the structure of the interview protocol, which was chosen to be the main data collection tool for the purposes of this section. The use of different data sources and sampling of various types of managers within the companies was employed in order to provide a rich context for investigating the research questions of interest. The structure of the interview was based on the theoretical framework of [2], thus it was divided into four sections. The first set of questions was to determine the strategy the company follows in NPD, therefore we asked the interviewees to elaborate on the company’s short-, mid- and long-term goals regarding NPD, about their opportunity search and development, as well as their price politics in product management. The next set of questions was predefined to gain

knowledge about the external environment. The questions we asked the interviewees within this part were about the dynamics of the market and competition, their influence on the company’s NPD, market trends and company’s reaction to all of them. The last influencing factors – the organisational structure and individual factors, were partly already represented in the questionnaire survey, but to get a deeper view on the processes within NPD, we also posed several questions about them in the interview. We were interested in the structure of marketing and R&D departments, their cooperation in NPD projects, the hierarchy within the company and the placement of both departments within the structure, the level of entrepreneurship of the company, the reward/sanctioning system and how informal events within the company are organised.

Prior to conducting the interviews with the chosen managers, the questionnaire survey was sent to all the employees of R&D, marketing and management functions within each company, so that comparisons to the national level results could be made. The interviews were carried out in 2008 and were recorded with the permission of the interviewees.

The first activity of data processing was to make transcripts of the interviews. This led to about 100 pages of text. We sorted these texts into uniform Word documents and changed them to rich text format (.rtf) in order to be able to do open coding within the Scientific Software for content analysis Atlas 5.0. After this formal reorganisation, the units of coding ‒ sentences or paragraphs that captured the ideas of our interviewees completely needed to be determined. The coding was done openly, without a predetermined codebook. The coding was performed by two independent judges on the basis of theoretical knowledge about each of the influencing factors, explained in the model of [4]. A peer-review of the retrieved codes resulted in approximately 300 codes within one case. Merging of synonym codes was performed, irrelevant codes were eliminated and finally the codes were arranged into a hierarchical model, by which the four influencing factors on R&D - marketing integration could be explained. Also, the organisation of R&D and marketing processes was coded, to gain an insight into how the company operates within NPD.



3 RESULTS

The section is divided into two sub-sections. Firstly, the results of the national questionnaire survey are presented. Secondly, we present the findings of a questionnaire survey and content analysis for both case studies.

3.1 Questionnaire Survey Results

Before testing our sub-hypotheses we analysed the degree to which the three integrative mechanisms (formalisation, centralisation and organisational climate) are independent concepts. The results of the factor analysis and the correlation analysis show that formalisation and organisational climate are to some degree correlated (.395). Despite the result we decided to calculate three separate measures. We calculated their aggregated scores and gained sufficient to good Cronbach alphas (Table 1).

According to our sub-hypothesis lower degrees of formalisation and centralisation will have a positive effect on the level of collaboration between marketing and R&D. Furthermore, we sub-hypothesised that a higher level of organisational climate has a positive effect on the level of collaboration. Our last sub-hypothesis indicated that the cross-functional integration gap will have a negative effect on the NPD success.

Table 1. Summary statistics for the assessment scales

Cronbach Alpha Mean Standard

deviationFormalisation .837 4.48 1.45Centralisation .733 3.84 1.39Organisational climate .674 4.83 .90

Cross-functional gap .906 1.17 1.38

NPD success .830 4.73 1.00

Due to the high correlation of the integrative mechanism constructs we decided to test our sub-hypotheses using Partial Least Squares (PLS) analysis. Rather than assume equal weights for all indicators of a scale, the PLS algorithm allows each indicator to vary in how much it contributes to the composite score of the latent variable. Thus,

indicators with weaker relationships to related indicators and the latent construct are given lower weightings. In this sense, PLS is preferable to techniques such as regression which assume error free measurement [16].

We tested the model by employing SmartPLS program [17] and the tested model was significant. The results are depicted in Fig. 2. The model explains .231 (R2) of the variance in NPD success and .235 (R2) of the variance in the Cross-functional gap. The numbers in the figure indicate path coefficients for the variables and their significance.

The effect of formalisation on the level of R&D - marketing integration was not significant, and our first sub-hypothesis could therefore not be confirmed. However, due to the cultural background of Slovenia, which according to [10] indicates a preference towards the establishment and following of formal rules and procedures, and due to the size of the analysed companies, we decided to also test the direct effect of formalisation on NPD success. The results show there is a moderate positive direct effect present. This positive significant direct effect indicates that NPD success is influenced by formalisation; when the companies are more formalised they report more NPD success.

* Significant at 5%, ** Significant at 1%

Fig. 2. Summary of path model analysis

Similarly, our second sub-hypothesis cannot be confirmed, as centralisation showed no



significant effect either on the cross-functional integration gap or the rate of success.

Sub-hypotheses 3 and 4 were supported. The results show that the organisational climate has a negative effect on the cross-functional integration gap, which confirms sub-hypothesis 3. Also, there is a significant negative correlation between the cross-functional integration gap and the rate of NPD success, which supports sub-hypothesis 4. The analysis also revealed that organisational climate has a positive direct effect on NPD success. This positive significant direct effect shows that companies with a better organisational climate are more successful.

3.2 Case Study Results

Before the analysis of the interviews, we analysed the answers to the questionnaire survey in order to get some indications of what factors influence the R&D - marketing integration and what integrative mechanisms influence the cross-functional gap and NPD success. By comparing the results to the national survey presented in the previous section, we also hope to get some answers to H1, whether the influences on R&D - marketing integration are culturally bound. The results of the survey are presented jointly for both cases in Table 2 and Fig. 3.

Table 2. Summary statistics for the assessment scales for both cases

CronbachAlpha Mean Standard

deviation

Formalisation .948.863

4.864.91

1.741.15

Centralisation .626.875

3.743.51

1.461.01

Organisational climate

.850

.8004.575.09

1.430.81

Cross-functional gap

.972

.9322.051.23

1.521.19

NPD success .947.923

4.204.78

1.55.89

Note: Summary statistics for Case 1 are depicted in Bold, for Case 2 in Italics

Surprisingly, for Case 1, we could not confirm SH4, as there were no significant effects of the cross-functional gap on NPD success

present. We found those effects in Case 2, but were not able to confirm SH3, as organizational climate had no significant effect on the cross-functional gap. Both cases therefore give different results as the proposed Western model, thus giving confirmation to our first hypothesis (H1) that R&D - marketing integration is culturally bound.

The interview transcripts for both cases were also coded separately and are summarized in Table 3. For each of the four sections studied, examples of answers are shown for both cases, to give insight into the differences.

Findings for Case 1 show that the company follows the analyser strategy, rather than being a prospector in the field. Moreover, the environment in which the company is present is quite stable, as competitors are mostly well known, the customer requirements mostly well specified and the processes guided by legislative restrictions. With regard to the organisational factors, the content analysis confirmed the company is formalised and rather centralised. Several other influencing factors, such as the reward system and the proximity of the functions have been considered by the company and will be implemented within the new R&D - marketing centre.

Normal text = Case 1 *Significant at 5% Italics = Case 2 ** Significant at 1%

Fig. 3. Summary of the two case path model analyses

The last studied set of influencing factors revealed that the company has an informal procedure of information exchange and yearly



Table 3. List of example answers to interview questions for both casesStudied

dimension Case Example answers

Org

anis

atio

nal s

trate

gy 1

Marketing: “Our strategic goal is to grow in sales from 250 to 350 million by 2012 and to 500 million in 2015. And for that we’ll have to do acquisitions.”Management: “Our wish is that the organic growth is 5%,” ... “we have made an ambitious goal to reach 500 million, which means that the organic growth is just a part of it,” ... “the rest is acquisitions.”R&D: “A wish for diversification exists on the strategic level. There are also other products in sight.”

2

Management: “The strategy of the company has always been to build a strong network with external partners and to have R&D managers that coordinate where the needed knowledge comes from.”Management: “I believe that at the moment we absolutely are the trendsetter.”R&D: “In the last 6-7 years we are the trendsetter, we set the trends in this field and consequently we control the dynamics of the market.”Marketing: “We are definitely the leader,” ... “we develop most of the products, the most new things.”

Envi

ronm

enta

l unc

erta

inty

1

Marketing: “When you have a mature market the competition is well known. We know everything, what competences one has, what they know, what they are good at.”R&D: “Things are well defined, however, you have to reorganise according to what the customers want, according to the developments within the project.”

2

Management: “People are much more conservative about new products. If you come to one of your business partners and say, good news, we have a new product and you’ll be the first one we’ll build it for, that isn’t necessary good news.”Marketing: “There are very personal relationships built. And when you have a known product, the customer knows what he is going to get, and the sales person knows what he is selling, there is a trust between them. With a new product, a problem arises.”

Org

anis

atio

nal f

acto

rs

1

Marketing: “When you have known products, they are developed according to a certain procedure and this is much formalised.”R&D: “All projects run according to certain standards. These standards determine the R&D process.”Management: “All marketing and R&D activities will be led from Slovenia.”Marketing: “For strategic projects the decision comes from top management. For small projects the management of the responsible function can decide.”

2

Marketing: “The NPD process from idea generation trough the whole process is described.Management: our top management consists of one member,” ... “on a completely strategic level she makes input into the R&D process in the sense of general goal definition.”R&D: “These are some pointers that are checked and then summarized, followed by an explanation,” ... “we also have measurable goals.”

Indi

vidu

al fa

ctor

s

1

R&D: “We have two key information systems, a business and technical information system,” ... “however, the information are not combined.”R&D: “There is no joint system. Within a certain jurisdiction one can access information on either of the systems.”

2

Management: “We are developing an open innovation management system, to enhance and expand cooperation with external partners.”Management: “People can also cooperate only on projects,” ... “this makes the range of possible experts bigger.”

informal events are the enablers of bonding between different functions.

Next to the influencing factors, the interviewees also explained the function and processes R&D and marketing do within the company. The main interest for the purposes of this paper was in what phases of the NPD process the two functions cooperate and when their actions are taken separately.

The main effort the two studied functions have to do jointly is maintaining customer relationships. However, there is no general scheme

providing a procedure that would define in what phases and how. Marketing is mostly involved in providing an offer to the customer, whereby R&D is responsible for all the next phases of NPD. Although the company has defined the R&D - marketing interface as being of strategic importance, no guidelines for the cooperation of functions were given. All cooperation is mostly done on informal levels, which can be confirmed also by the results of the questionnaire survey, where organisational climate is the only factor influencing R&D - marketing involvement gap.



Findings for Case 2 on the other hand show that the company is a prospector in its own industry. As described by the interviewees, the company is a trendsetter, facing several copying attempts by its competition. In addition, although the industry is conservative, the company is facing a dynamic business environment, where competition is also innovative and offers complete solutions with technical support to the customers. With regard to the organisational factors, the company is formalized in the sense that most of the processes are described in written documents, however, on the other hand, the informal levels of cooperation are also present within the company. The centralisation level is not high. The rewarding system and top management values are well integrated into the company culture. Also, the company has a well developed informal communication structure that goes up to the top management levels. In NPD the company focuses on solving problems for customers by providing complete solutions. Both, R&D and marketing are part of the NPD process, whereby the focous of marketing is related to building and maintaining relationships with customers and analysing market changes and trends. R&D, on the other hand, has to provide the product solution and technical support throughout the process of NPD as well as later on.

As can be seen from the questionnaire survey, the content analysis of the interviews and the company documents, all the processes are formally written down and access to these documents is given to the employees that operate within certain parts of the processes. This type of formalisation enables the company employees to have a good overview of the process, so all the relevant processes can run smoothly. Such notion can also be drawn from the questionnaire survey results, where high levels of formalisation are correlated to a smaller R&D - marketing gap. Since the processes are well defined, all functions have a clear knowledge on their tasks, so the cooperation can run smoothly. When looking at the greater picture of NPD success, however, two influencing factors need to be considered – good organisational climate and lower levels of formalisation. The analysis has shown that both have an influence on NPD success. If higher levels of formalisation enable the processes to

run smoothly, lower levels of formalisation and good organisational climate reinforce informal communication and cooperation of the functions, leading to even higher levels of NPD success.

4 DISCUSSION AND CONCLUSIONS

Research has shown that there are several factors influencing the R&D - marketing integration within NPD processes. By conducting a questionnaire survey on a national level within Slovenia we intended to show that there is a cultural effect present within R&D - marketing integration. Our focus on the R&D - marketing integration in Slovenia tested the validity of the so called Western model in another cultural and economical arena. We were able to partly confirm the application of the model to other non-western environments; however several interesting limitations with regard to the culture also arose in the analysis.

As formalisation has received mixed support in the previous studies, the lack of support for our first hypothesis was not very surprising. The lack of correlation between the level of formalisation and the size of the cross-functional integration gap might be due to the cultural background of the studied economy. Slovenia scored very high on the dimension of uncertainty avoidance in Hofstede’s [10] study of cultural differences between countries. Uncertainty avoidance refers to the preference towards structured processes opposite unstructured processes. High scores on uncertainty avoidance indicate a preference towards the establishment and following formal rules and procedures. In such cultural background, the top managers are involved in operations, precision and punctuality come naturally, flexible working hours are popular and expertise and specialists are highly valued [10]. These characteristics are consistent with a high mean score on the formalisation level of Slovenian SMEs in our study.

Centralisation was also found to be a controversial integration mechanism in previous studies on R&D - marketing integration. Some studies confirmed its positive effect on R&D - marketing integration, others a negative effect. Our results showed that centralisation has no significant effect on the R&D - marketing



integration or NPD success. Reasons for this might be found both in the fact that we studied a growing economy, as well as in the fact that the studied companies were SMEs. Slovenia also scored high on the power distance dimension in Hofstedes’ (2001) study. The power distance index measures the extent to which the less powerful members of organisations and institutions accept and expect that power is distributed unequally. A high level of power distance indicates that the members of an organisation expect and accept a high level of authority and centralisation as a predetermined condition, meaning it does not affect their work significantly. The size of the company and relations between the employees may also be the reasons for the lack of support for the proposed hypothesis. For example, the centralisation level might differ if the studied company is a family company or if it employs very few employees. Centralisation effects might be lower in the first example and more obvious in the second. Previous studies also showed that centralisation is usually not present in SMEs, because communication between employees is more direct and the actions of employees more immediate. The mean score for centralisation (=3.84) in our research supports this notion. The lack of centralised relations in the studied companies could therefore be the reason for our results.

Organisational climate has on the other hand proven to be an important factor, effecting the R&D - marketing integration, as well as the level of NPD success. These results put Slovenia in line with the proposed Western model of R&D - marketing integration, where a positive effect of organisational climate on R&D - marketing integration has been proven in several studies. In our study the effect of organisational climate has proven to be the most important integrative mechanism for SMEs, as it had a significant effect on the cross-functional gap and also directly on NPD success.

On the whole, the integration mechanisms considered in our study have proven to be moderately effective for achieving collaboration between the two functions we focused on. However, the theoretical model that we derived from the existing literature did not fit our data. Our results show that the relevance of two of the main construct in the model should be questioned

for the situation of SMEs in growing economies. If our arguments hold, the theoretical model would need to be redifined and less emphasis should be put on formalisation and centralisation and much more on organisational climate. It would also be interesting to study different industrial branches and their influence on the studied elements. Although our questionnaire included the definition of the industrial branch of the studied companies, the sample gained is too small to proceed with further study along these lines, so a greater amount of survey response is needed. We will proceed with this in our future research.

The aim of this paper was also to develop a research protocol for an integrated study of R&D - marketing integration according to Gupta et al [4] framework. Empirical evidence gained from the two case studies show that people active within the R&D - marketing interface perceive the studied constructs as relevant for R&D - marketing integration, thus giving confirmation to Gupta et al [4] model. The presented research protocol can therefore be considered as a valid start into R&D - marketing integration research within an integrated framework, however it needs further empirical tests.

With studying two companies within Slovenia, we also wanted to confirm that NPD success is influenced by the level of R&D - marketing integration. The two companies that were studied differ with regard to their strategy, environmental influences, organisational structure and also individual factors that influence NPD. When comparing the perceived integration gap of the two companies, the company of Case 2 seems to have a higher level of R&D - marketing integration, as the score for perceived cross-functional integration gap is closer to 0 than it is for Case 1. When comparing this result to the influencing factors, it seems to be consistent with the propositions made by Gupta et al [2] that claim that a prospector strategy, within a dynamic environment call for a greater need for integration. Since the company is successful in NPD as it can hold the position of a trendsetter within the target markets, we can conclude that strategy and environmental uncertainty are influencing factors that can foster or hinder R&D - marketing integration. On the other hand, the organisational and individual factors have brought



some contradicting results, compared to Gupta et al [4] and the proposed Western model of R&D - marketing cooperation. We find an explanation to this within the cultural aspects of NPD. These aspects will also be further studied in the future.

5 REFERENCES

[1] Song, M., Thieme, R.J. (2006). A cross-national investigation of the R&D - marketing interface in the product innovation process. Industrial Marketing Management, vol. 35, p. 308-322.

[2] Fain, N., Moes, N., Duhovnik, J. (2010). The role of the user and the society in new product development. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 7-8, p. 521-530.

[3] Zargi, U., Kusar, J., Berlec, T., Starbek, M. (2009). A company’s readiness for concurrent product and process development. Strojniški vestnik - Journal of Mechanical Engineering, vol. 55, no. 7-8, p. 427-473.

[4] Gupta, A.K., Raj, S.P., Wilemon, D. (1986). A Model for studying R&D - marketing interface in the product innovation process. Journal of Marketing, vol. 50, p. 7-17.

[5] Gupta, A.K., Wilemon, D. (1991). Improving R&D - marketing relations in technology-based companies: Marketing’s perspective. Journal of Marketing Management, vol. 7, p. 25-43.

[6] Griffin, A., Hauser, J.R. (1996). Integrating R&D and marketing: A review and analysis of the literature. Journal of Product Innovation Management, vol. 13, p. 191-215.

[7] Lu, I., Chang, T. (2002). A contingency model for studying R&D - marketing integration in NPD. International Journal of Technology Management, vol. 24, no. 2-3, p. 143-164.

[8] Parry, M.E., Song, M.X. (1993). Determinants of R&D - marketing integration in high-tech Japanese firms. Journal of Product Innovation Management, vol. 10, no. 1, p. 4-22.

[9] Garett, T.C., Buisson, D.H., Yap, C.M. (2006). National culture and R&D and marketing

integration mechanisms in new product development: A cross-cultural study between Singapore and New Zealand. Industrial Marketing Management, vol. 35, p. 293-307.

[10] Hofstede, G. (2001). Culture’s Consequences: Comparing Values, Behaviors, Institutions, and Organisations across Nations. 2nd Ed. Thousand Oaks, London, New Delhi: Sage Publications.

[11] Kleinsmann, M.S. (2006). Understanding Collaborative Design. PhD Thesis, Delft University of Technology, Faculty of Industrial Design Engineering, Delft.

[12] Bommer, M., Jalajas, D.S. (2004). Innovation sources of large and small technology-based firms. IEEE Transactions on Engineering Management, vol. 51, no. 1, p. 13-18.

[13] Sanyal, R.N., Guvenli, T. (2004). Perception of managerial characteristics and organisational performance: comparative evidence from Israel, Slovenia, and the USA. Cross Cultural Management, vol. 11, no. 2, p. 35-57.

[14] Eurostat (2003). SMEs in Europe – Candidate Countries. Office for Official Publications of the European Communities, Luxemburg. Available at: http://epp.eurostat.ec.europa.eu/cache/ITY_OFFPUB/KS-CJ-04-001/EN/KS-CJ-04-001-EN.PDF, accesed on 2008-09-05

[15] Fain, N. (2010). Integrating marketing and R&D during New Product Development, PhD thesis, University of Ljubljana, Faculty of Mechanical Engineering, Ljubljana.

[16] Chin, W.W., Marcolin, B.L., Newsted P.R. (1996). A partial least square latent variable modeling approach for measuring interaction effects: Results from a monte carlo simulation study and voice mail emotion/ adoption study. Proceedings of the 17th International Conference on Information Systems, , Cleveland, Ohio, from http://disc-nt.cba.uh.edu/chin/icis96.pdf, accesed on 2008-03-22, p. 21-41.

[17] Ringle, C., Wende, S., Will, A. (2005). SmartPLS Version 2.0 M3 from www.smartpls.de, accesed on 2007-05-14.

http://www.sciencedirect.com/science/journal/07376782

http://www.sciencedirect.com/science/journal/07376782

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http://disc-nt.cba.uh.edu/chin /icis96.pdf

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*Corr. Author’s Address: Institute of Automotive Engineering, Faculty of Mechanical Engineering, Brno University of Technology, Technicka 2, 61669, Brno, Czech Republic, [email protected]

Virtual Engine - A Tool for a Powertrain Dynamic SolutionPistek, V. ‒ Novotny, P.

Vaclav Pistek* ‒ Pavel NovotnyInstitute of Automotive Engineering, Faculty of Mechanical Engineering, Brno University of Technology,

Czech Republic

The paper presents computational and experimental approaches to a powertrain vibration analysis. A complex computational model of a powertrain - a virtual engine is a powerful tool for a solution of structural, thermal and fatigue problems. The virtual engine results should answer different questions, mainly those concerning the area of noise, vibrations and component fatigues. The paper also includes a description of fast algorithm for a hydrodynamic solution of a slide bearing incorporating pin tilting influences. The main contribution is the fact that all models, that is those of a cranktrain, a valvetrain, a gear timing mechanism and a fuel injection pump are solved simultaneously, using a complex computational model. Synchronous solutions can have a fundamental effect on results of powertrain dynamics solutions. Additionally, it might help to understand influences among powertrain parts. The virtual engine is assembled as well as numerically solved in Multi Body System. Virtual engine results are validated by measurements on Diesel in-line six-cylinder engine.© 2011 Journal of Mechanical Engineering. All rights reserved. Keywords: vibrations, noise, dynamics, powertrain, hydrodynamics

0 INTRODUCTION

Modern powertrains are complex thermo-mechanical systems improved by large and gradual development. Car producers still increase engine parameters like engine performance or torque together with a significant decrease of fuel consumption. Powertrains and cars supplied to European, US or Japanese markets have to be in compliance with national legislatives, which force the producers to significantly decrease noise, vibrations and emissions of every new powertrain. All these conditions have to be satisfied in very short developing periods.

Generally, the increase of engine performance often leads to an increase of powertrain noise and vibrations. Noise and vibration problems can be resolved by experimental or computational methods. Experimental methods are often very expensive which causes a fast development of modern computational methods. Modern computational methods can provide very exact results but only on condition that exact inputs are included. The inputs are often supplied by experimental methods. A portion of experimental methods continuously decreases, however, the experimental method still plays an important role in powertrain development.

All computational and measurement methods are applied to new turbocharged diesel inline six-cylinder engine. Some of the engine parameters are engine displacement 6.2 litres, peak power output 125 kW at engine speed 2200 rpm and compression ratio 17.8. The engine includes an OHV (Over Head Valve) valvetrain with two valves per cylinder and a camshaft located in a crankcase. The slide bearings are used for the bearing of the crankshaft as well as the camshaft. The valvetrain is driven by the front end of the crankshaft using helical gears. The engine incorporates a mechanically controlled fuel injection pump and other accessories like a piston compressor or an oil pump. The crankshaft includes a rubber torsional damper to decrease torsional vibrations. The design of the new engine originates from a turbocharged diesel inline four-cylinder engine.

1 THE STATE OF THE ART REVIEW

Historically, there have been many cranktrain computational models. Technical literature includes a large number of different computational models. The references [1] to [5] can be taken as examples of a wide variety of cranktrain computational models. The present state of the art in cranktrain simulations shows


611Virtual Engine - A Tool for a Powertrain Dynamic Solution

computational models being solved in time domain with high portions of flexible bodies. Other powertrain parts like a valvetrain, are included only as an additional mass or frequently, they are not included at all. Crankshaft and engine block interactions are solved using a hydrodynamics model of a slide bearing most often. A slide bearing model comes from a numerical solution of Reynolds equation, often without pin tilting influences [3] and [4] or with a simple pin tilting approximation [1]. Full elastohydrodynamic solution of Reynolds equation including shell and pin deformations is still not fully applied for powertrain dynamics with many slide bearings. The elastohydrodynamic solution of slide bearings of a separate connecting rod is often used for detailed slide bearing solutions. Theoretically, simultaneous full elastohydrodynamic solution of all cranktrain bearings can be used but numerical costs are high and there are no significant benefits for the cranktrain dynamics.

The present state of the art of rubber torsional damper computational models often includes a torsional spring and a torsional damper in a serial arrangement. This computational model does not describe rubber frequency behaviour for a solution in time domain correctly. For frequency dependencies it is necessary to use more complex models including Maxwell parts arranged in parallel. The rubber damper can sometimes influence axial crankshaft vibrations, therefore, axial properties have to also be incorporated Sometimes.

Valvetrain computational models have also been developed over a long period. First, discrete computational models of the valvetrain (still in use) included discrete point masses or springs. Springs have included only linear dependences of a force vs. a deformation. A tappet or a valve was excited by a lift function. With increasing Multi-Body Systems (MBS) the valvetrain computational models became more complex and incorporated rigid bodies and nonlinear contact forces. Later, some of the parts were replaced by spring-damper-mass bodies or beam bodies [6]. Camshaft angular irregularities on the basis of a separate cranktrain model solution were also incorporated. The present state of the art includes computational models with flexible parts. Spring models use flexible bodies with valve coil contacts enabling to understand

contacts between coils as well as spring stiffness changes [7] and [8]. The single valvetrain models are assembled to a complete valvetrain model [9]. However, drive timing mechanism or injection pump influences are not often included nor are influences of a compressor, an oil pump or other powertrain accessories.

So far each part of a powertrain has been solved separately. It has sometimes been extended by influences of other model results or measurement results but these results have been obtained from separate solutions. Valvetrain dynamic simulations can be taken as an example. A camshaft is driven by an angular velocity obtained from a separate cranktrain solution or from measurements. At present the need to solve all powertrain parts together continuously increases. This solution enables to include all interactions among parts. The results will show that, for example, valvetrain dynamics is highly influenced by a cranktrain but at the same time the cranktrain is slightly influenced by the valvetrain, both influenced by a timing drive or an injection pump.

2 COMPUTATIONAL METHODS

2.1 Virtual Engine

A complex computational model of the engine, in other words a virtual engine, is solved in time domain. This enables an incorporation of different physical problems including various nonlinearities. The virtual engine is assembled as well as numerically solved in MBS (Multi Body System) ADAMS.

ADAMS is a general code and enables an integration of user-defined models directly using ADAMS commands or using user written subroutines. The key features of the virtual model like the slide bearing model, the torsional damper model or gear timing drive model are incorporated into ADAMS model using Matlab program.

The virtual engine includes all the significant components necessary for NVH (Noise Vibrations and Harshness) or fatigue analyses. The included modules are: a cranktrain, a valvetrain, a gear timing drive with fuel injection pump and a rubber damper. Fig. 1 presents the virtual engine and its submodules.


612 Pistek, V. ‒ Novotny, P.

Fig. 1. Virtual engine including main subsystems

2.2 Flexible Parts

Flexible bodies represented by FE (Finite Element) models have a decisive importance on powertrain dynamics simulations. The FE models of each component should be created with special effort. In addition, a uniform FE mesh is often preferred.

In general, for a solution in time domain, FE models are very large and require a reduction. The discretization of a flexible component into a finite element model represents the infinite number of DOF (Degrees of Freedom) with a finite, but very large number of finite DOF. For the reduction of FE models, the Craig-Bampton method is used [10].

For the powertrain dynamic solution main components are treated as flexible models. A crankshaft model presents a fundamental component of the virtual engine. A reduced FE model is used for simulations of powertrain dynamics. The dynamics of powertrain moving parts are influenced by the stiffness of an engine block. Therefore, a reduced engine block FE model is also used for dynamics solutions. Reduced FE models of a camshaft, rockers and valve springs are used for a solution of valvetrain dynamics.

2.3 Torsional Rubber Damper Model

A torsional vibration damper is an important component of some cranktrains. It can significantly increase fatigue of engine parts together with a decrease of noise and vibrations. Different designs of torsional vibration dampers can be used. The rubber damper is chosen for the target engine.

Rubber mechanical properties can be characterized by very small compressibility and a high ability to reach large strains at small stresses without any plastic deformations. Maximal relative deformations of rubber can reach values of 800%. Force versus deformation rubber properties are strongly nonlinear. Therefore, Hook’s law cannot be used for stress-strain behaviour. Generally, every material is compressible, however, rubber can be treated as an uncompressible and isotropic material.

A phenomenological approach is used for the description of rubber mechanical properties. This approach does not originate from any molecular structure but comes from mathematical models. The Mooney-Rivlin two-parametric model is used for rubber structure modelling. This model introduces a hypothesis that strain energy W is a linear combination of two invariants of Finger tensor [11]:

W C I C IdJ= −( ) + −( ) + −( )10 1 01 2

23 3 1 1 , (1)

where I1 and I2 are the first and the second invariant of a deviatoric component of Finger tensor, J is the determinant of a deformation gradient (for incompressible materials J = 1) and C10, C01 and d are constants. More information about rubber material properties can be found in [11] and [12].

The Mooney-Rivlin material model parameters have to be determined using average damper operating temperatures. An average operating temperature can be roughly estimated from similar torsional rubber dampers running on similar engines. Temperatures of rubber central volume of similar torsional dampers vary between 60 and 80 °C. Additionally, the fact that the material properties of rubber in this temperature range are only slightly changed is very helpful. The average temperature of 70 °C can be used for temperature corrections of material properties.



Pilot cranktrain dynamic calculations show that the loading frequency range is from 100 to 200 Hz.

The Mooney-Rivlin two-parametric model used for calculations is able to correctly describe rubber behaviour up to 30% of tension deformations and up to 10% of compression deformations. Real deformations in rubber damper are significantly smaller than these limit deformations. Mooney-Rivlin coefficients used for FE calculations and including temperature corrections are C10 = 1.065, C01 = 0.263 a d = 0.016.

A final rubber damper MBS model includes only global properties like torsional stiffness or axial stiffness.

A rubber damper MBS computational model has to incorporate dependency of torsional stiffness as well as torsional damping on frequency. FE solution founds the static torsional stiffness, the value is kT = 56145 Nm/rad and incorporates no frequency dependencies. The frequency is incorporated using rubber frequency dependencies presented [11] and [12]. Torsional damping can be computed using frequency dependent torsional stiffness and relative damping as:

b kT

Tωω χω

( ) = ( ), (2)

where kT(ω) is frequency dependent torsional stiffness, χ is relative damping and ω is angular velocity.

Generally, the torsional damper can be described by parallelly arranged torsional stiffness and damper, however, the single arranged torsional stiffness and damping cannot be included as frequency dependent into MBS model.

Thus, a different approach has to be used for MBS simulations in time domain. A more complex MBS computational model of the torsional rubber damper has to be used. The model includes three serially connected Maxwell members (a spring and a damper). Two rigid parts (a damper ring and a damper flange) connected by a cylindrical joint and a serially arranged spring and damper in axial direction are also included in the model. The MBS model of the rubber damper is presented in Fig. 2.

The torsional stiffness of the complex rubber model can be calculated using Eq. (3) and the torsional damping using Eq. (4).

k

real k

k i b k i b k i b

M

T

T T T T T T

( )ω

ω ω ω

=

++

++

++

0

1 1 2 2 3 3

11 1

11 1

11 1

, (3)

b

imag k

k i b k i b k i b

M

T

T T T T T T

ω

ωω ω ω

( ) =

++

++

++

1 1

1 11

1 11

1 10

1 1 2 2 3 3

, (4)

where kM is torsional stiffness of the torsional damper, bM is torsional damping of the torsional damper, kTi is torsional stiffness of i-spring, for i=1,2,3 , bTi is torsional damping of i-damper and kT0 is parallel torsional spring stiffness.

Fig. 2. MBS computational model of the torsional rubber damper

The resulted torsional stiffness kM and damping bM are frequency dependent but each spring or damper includes frequency independent values.

Fig. 3. Development process of MBS rubber damper computational model

Coefficients kTi, bTi a kT0 are found by least squares method programmed in Matlab. The



frequency range is chosen from 50 to 300 Hz and covers all significant frequencies occuring in the torsional damper.

The global stiffness values originate from a detailed solution of the three dimensional FE model in combinations with Matlab calculations. The development process starts with rubber shape and hardness proposals. The rubber hardness of 70 Shore is proposed from simple results of cranktrain torsional vibration calculations using a discrete torsional model. Fig. 3 shows the complete process of MBS rubber damper model development.

Generally, poor knowledge of rubber material properties is one of the main problems for a computational modelling of a cranktrain equipped with a rubber damper. The proposed approach for the determination of torsional damper global properties comes from elementary mechanical properties of rubber with a consideration of rubber frequency and temperature behaviour. However, this approach cannot produce highly accurate data because accurate rubber properties often do not exist. In addition, a rubber aging process or rubber producer tolerances (sometimes the rubber hardness tolerance is ±5 Shore) has to be also considered.

2.4 Slide Bearing Model Incorporating Pin Tilting Influences

Present computational models enable a description of a slide bearing behaviour in great detail. These models are often very complicated and require long solution times even on condition that only one slide bearing model is being solved. The target engine includes tens of slide bearings, therefore, all model features of slide bearings have to be carefully considered.

The loading capacity of a slide bearing model included in the virtual engine is considered in a radial direction and also incorporates pin tiltings, which means that radial forces and moments are included in the solution. For the solution of powertrain part dynamics elastic deformations can be neglected because integral values of pressure (forces and moments) for HD (hydrodynamic) and EHD (elastohydrodynamic) solution are approximately the same. This presumption is very important and it enables

a simplified solution. On the other hand, the solution can not be used for a detailed description of the slide bearing. Solutions of tens of EHD slide bearing models simultaneously seem to be extremely difficult and do not provide any fundamental benefits for general dynamics. The virtual engine therefore incorporates a compromise solution using the HD solution with elastic bearing shells and can be named (E)HD approach.

A HD approach presumes that shapes of a pin and a bearing shell are ideal cylindrical parts. The pin and the bearing shell are rigid bodies without any deformations. An oil gap between the pin and the shell is filled up but the oil and gap proportions are small in comparison with pin or bearing shell proportions. Only hydrodynamic frictions occur, while lubricating oil is incompressible and oil flow is laminar.

Generally, oil temperature has a significant influence on slide bearing behaviour. Oil temperature is treated as a constant for the whole oil film of the bearing. This presumption enables an inclusion of temperature influences after the hydrodynamic solution according to temperatures determined from similar engines.

In general, if the equation of the motion and the Continuity equation [2] are transformed for cylindrical forms of bearing oil gap together with restrictive conditions [2], the behaviour of oil pressure can be described by the Reynolds differential Eq. (5). This frequently used equation is derived for a bearing oil gap [1] or [2] and can be written in the form:

∂∂

∂∂

+

∂∂

∂∂

=

∂∂

+∂∂

x

h px z

h pz

U hx

ht

3 3 6 2η , (5)

where p is pressure, h is oil film gap, η is dynamic viscosity of oil and U is an effective velocity. The oil film gap is defined as:

h R r e= − + cos( ),ϕ (6)

where R is a shell radius, r is a pin radius, e is a pin eccentricity and φ is an angle about pin axis.

The following relations can be defined as:

ϕ = =

xR

xD2 ,

Z Z

B=

2 ,



ψ = =−

≅−s

DR rR

R rr

, ε =−eR r

, (7) where D is a shell diameter, B is a width of the bearing, Z is a dimensionless co-ordinate in the bearing axis direction, s is a bearing clearance, ψ is an independent bearing clearance and ε is dimensionless eccentricity.

A definition of a dimensionless oil film gap H in dependence on angle can be used:

H *( ) cos .ϕ ε ϕ≅ +1 (8)

Additionally, the pressures in oil film can be replaced by dimensionless pressures [5].

ΠDDp=ψ

ηω

2 and ΠV Vp=

ψηε

2

. (9)

ΠD denotes dimensionless pressure for a tangential movement of the pin, ΠV is dimensionless pressure for a radial movement of the pin, ω is effective angular velocity and ε is a derivative of dimensionless eccentricity with respect of time.

Pin tilting angles can be introduced as:

γγγ

=tgtg

*

max* , (10)

δδδ

=tgtg

*

max* , (11)

where γ is a dimensionless pin tilting angle in narrowest oil film gap and δ is a dimensionless tilting angle in the plane perpendicular to the plane of narrowest oil film gap. γ* denotes a real tilting angle in a plane of the narrowest oil film gap and γmax* denotes a maximal possible tilting angle in the plane of the narrowest oil film gap for given eccentricity. δ* is a real tilting angle in the plane perpendicular to the plane of narrowest oil film gap and δmax* is a maximal real tilting angle in the plane perpendicular to the plane of narrowest oil film gap for given eccentricity.

Fig. 4 presents the definition of pin tilting angles and Fig. 5 presents the definition of general and maximal tilting angle in a plane of the narrowest oil film gap.

Fig. 4. Definition of tilting angles of pin

Fig. 5. Description of real tilting angles in plane of the narrowest oil film gap

The final definition of the dimensionless oil film gap depending on tilting angles is:

H H

H Z Z

= =

= − −

( , , , )

( cos sin ),*

ϕ ε γ δ

γ ϕ δ ϕ1 (12)

and includes a dependency on two tilting angles. If the dimensionless oil film gap is used

for the Reynolds equations for tangential and radial movements of the pin, then the Eq. (5) can be rewritten into two separate Eqs. [2] but with a modified definition of the dimensionless oil film gap.

∂∂

∂∂

+

∂∂

∂∂

=

∂∂ϕ ϕ ϕ

H DB Z

HZ

HD D32

23 6

Π Π, (13)

Likewise the dimensionless pressure is modified as follows [5]:

∂∂

∂∂

+

∂∂

∂∂

=ϕ ϕ

ϕH DB Z

HZ

V V32

23 12

Π Πcos . (14)



Π Π= H32 . (15)

If the Eqs. (10) to (12) are input into Eqs. (13) and (14), the final forms of Reynolds equations are:

∂

∂+

∂∂

+ =

=

2

2

2 2

2Π Π

ΠD DD

D

DB Z

a Z

b Zϕ

ϕ ε γ δ

ϕ ε γ δ

( , , , , )

( , , , , ),

(16)

∂∂

+

∂∂

+ =

=

2

2

2 2

2Π Π

ΠV VV

V

DB Z

a Z

b Zϕ

ϕ ε γ δ

ϕ ε γ δ

( , , , , )

( , , , , ). (17)

The equation term a(φ,ε,Z,γ,δ) is defined as:

a Z H HH H DB

Hz( , , , , )ϕ ε γ δ ϕϕ ϕ= − + +

−34

22 22

2 , (18)

and the equation terms bD(φ,ε,Z,γ,δ) and bV(φ,ε,Z,γ,δ) are defined as:

b Z H HV ( , , , , ) ,ϕ ε γ δ ϕ=−

632 (19)

b Z HD ( , , , , ) cos .ϕ ε γ δ ϕ=−

1232 (20)

Functions Hφ, HZ and Hφφ are partial derivatives of the oil film gap and can be written as:

∂∂

= + − −

− − =

H Z Z

Z Z Hϕ

εγ ϕ γ ε ϕ

δ ϕ εδ ϕ ϕ

sin ( )sin

cos cos ,

2

2 (21)

∂∂

= − − −

− − =

HZ

HZ

εγ ϕ γ ϕ

δ ϕ εδ ϕ

cos cos

sin sin ,

2

12

2 (22)

∂

∂= + − +

+ + =

HZ Z

Z Z H

ϕ

ϕϕ

ϕεγ ϕ γ ε ϕ

δ ϕ εδ ϕ

2 2

2 2

cos ( )cos

sin sin , (23)

∂∂

=HZZ 0. (24)

Eqs. (16) and (17) are solved numerically. The FDM (Finite Difference Method) is used for a numeric solution.

The FDM in basic form uses a constant integration step, however, this strategy can be disadvantageous because in casethe pin eccentricities are very high, the oil film pressure becomes concentrated in small areas so it is necessary to use a very small integration step. This leads to higher computational models. Therefore, FDM using variable integration step and multigrid strategies is developed.

The iterative solution starts using a very small computational grid. After a few iterations the results are approximated to a more dense grid and again a few iterations are solved. The new results are used for re-meshing the algorithm to generate new variable computational grid. The grid density is changed in dependency on the prescribed conditions (a pressure gradient). Three point integration scheme is chosen for the solution because for small integration steps it is very fast and the accuracy is similar to five-point integration scheme. Fig. 6 presents an example of computational grid for FDM with a variable integration step.

The resulted formula for iterative solution of dimensionless pressure at point i, j defines Eq. (29).

The formula for the numerical solution Eq. (29) is different for tangential and radial pin movement only in the term bD (for tangential pin movement) and bV (for radial pin movement) respectively.

Fig. 6. Computational grid for FDM with variable integration step

The solution approach with variable integration steps presumes sufficient density of a



solution grid according to pressure differentiations with respect to the bearing angle and bearing width. This strategy enables solving problematic pressure zones in acceptable solution time.

Eq. (29) is solved iteratively for the tangential pin movement as well as for the radial pin movement. Initial and boundary conditions are the same for both solutions. The first boundary condition describes: p

z B Z=±

=±( )= ⇒ =2

10 0Π . (25)

The only initial condition describes: p ϕ ϕ=( ) =( )= ⇒ =0 00 0Π , (26)

This initial condition is used only for the first iteration and after that it is replaced by the cyclic boundary condition: p pϕ ϕ π ϕ ϕ π=( ) =( ) =( ) =( )= ⇒ =0 2 0 2Π Π . (27)

The cavitation condition is included during the numerical solution. This condition resets negative pressures to zero values.

Eq. (33) describes real physical processes and does not allow negative pressures in liquids (a cavitation). p p= ∈ < ⇒ = ∈ <0 0 0 0Π Π . (28)

Fig. 7 presents solution results of modified Reynolds equation for tangential pin movement, relative eccentricity ε = 0.8, first pin tilting angle γ = 0.8 and second tilting angle δ = 0.

The computed pressure distributions have to be transferred to equivalent force systems for a solution in MBS. Pressure on an elementary surface can be imagined as an elementary force dF on this elementary surface dS. Integral values are dimensionless reaction forces F and reaction moments M and can be found by an integration of pressure across the whole bearing surface with coordinates φ and z.

Fig. 7. Solution results of modified Reynolds equation for tangential pin movement, relative

eccentricity is ε = 0.8, first pin tilting angle is γ = 0.8 and second tilting angle is δ = 0

Elementary forces and moments for axes ”1“ and ”2“ can be defined as follows:

dF p dSdF p dSdF p dS

D D

D D

V V

1

2

1

= −= −= −

cos ,sin ,cos ,

ϕ

ϕ (30)

dM p z dSdM p z dSdM p z dS

D D

D D

V V

1

2

1

= −= −= −

cos ,sin ,cos .

ϕ

ϕ (31)

Π

∆Π

∆Π

∆ ∆

∆Π

i j

ii j

ii j

j j

ji j

D V

DB

Z

,

, , ,

, =

+

++

++−

−

−

+1 1

2

1 11

11

1

2

2

1ϕ ϕ

ϕ ϕ∆∆

Π

∆ ∆

∆ ∆ ∆ ∆

ZZ Z

b

DB Z Z

a

ji j

j jD V

j j j j

−−

−

− −

+−

+ −

11

1

1

2

21

2 2

,

,

.

ϕ ϕ

(29)



The indexes 1 and 2 represent projections to axes „1“, „2“, index D means results for a tangential pin movement and index V means results for a radial pin movement.

The pressure distribution for radial pin movement is symmetrical, therefore, the forces F2V and moments M2V equal zero.

If all integration conditions are satisfied, the axis force components „1“ and „2“ can be found using equations:

F p dS p Rd dz

DB d d

D DS

DB

B

D

10

2

2

2

2 4

= − = − =

= −

∫∫ ∫∫−

cos cos

cos

ϕ ϕ ϕ

ηωψ

ϕ ϕ

π

Π ZZ DBD

0

2

1

1

2 14

πηωψ∫∫

−

= Φ ,

(32)

F p dS p Rd dz

DB d

V VS

VB

B

V

10

2

2

2

2 4

= − = − =

= −

∫∫ ∫∫−

cos cos

cos

ϕ ϕ ϕ

ηεψ

ϕ ϕ

π

Π ddZ DBV

0

2

1

1

2 14

πηεψ∫∫

−

=

Φ ,

(33)

F p dS p Rd dz

DB d d

D DS

DB

B

D

20

2

2

2

2 4

= − = − =

= −

∫∫ ∫∫−

sin sin

sin

ϕ ϕ ϕ

ηωψ

ϕ ϕ

π

Π ZZ DBD

0

2

1

1

2 24

πηωψ∫∫

−

= Φ ,

(34)

and components of moments for axes „1“ and „2“ can be found as:

M p z dS p z Rd dz

DB Z d

D DS

DB

B

D

10

2

2

2

2 4

= − = −

= −

∫∫ ∫∫−

cos cos

cos

ϕ ϕ ϕ

ηωψ

ϕ

π

Π ϕϕηωψ

π

dZ DBD

0

2

1

1

2 14∫∫−

= Θ ,

(35)

M p z dS p z Rd dz

DB Z

D DS

DB

B

D

20

2

2

2

2 4

= − = − =

= −

∫∫ ∫∫−

sin sin

sin

ϕ ϕ ϕ

ηωψ

ϕ

π

Π dd dZ DBDϕ

ηωψ

π

0

2

1

1

2 24∫∫−

= Θ ,

(36)

M p z dS p z Rd dz

DB Z

V VS

VB

B

V

10

2

2

2

2 4

= − = − =

= −

∫∫ ∫∫−

cos cos

cos

ϕ ϕ ϕ

ηεψ

π

Π ϕϕ ϕηεψ

π

d dZ DBV

0

2

1

1

2 14∫∫−

=

Θ .

(37)

The equivalent force system including the resulted force and moment can also be replaced by the force acting on an arm ξ.

Hydrodynamic databases include integral values Φ1D, Φ2D, Φ1V, Θ1D, Θ2D, Θ1V for chosen ratios D/B and pin tilting. The resulted forces and moments (F1D, F2D, F1V, M1D, M2D, M1V) inserted into MBS can be obtained by an inclusion of bearing sizes, bearing clearances, dynamic viscosity and pin kinematic values.

3 POWERTRAIN DYNAMIC SOLUTION RESULTS

3.1 Cranktrain Dynamic Solution Results

The determination of cranktrain torsional vibrations represents a fundamental step in powertrain development. Cranktrain torsional vibrations influence torsional vibrations of each powertrain rotating component. These vibrations can significantly influence forces in every single valvetrain or forces in a gear timing drive. Fatigue of powertrain components like a crankshaft or a camshaft is also affected. An experimental determination of torsional vibrations using, for example, laser vibration tools is an advance and it can help to validate computational models.

A summary of a cranktrain torsional behaviour can provide a harmonic analysis of torsional vibrations determined from a crankshaft pulley angular velocity. Fig. 8 shows computed and measured harmonic analysis results of cranktrain torsional vibrations of the powertrain with a rubber damper. The sixth harmonic order is the most dominant one and a resonance of this order occurs above the engine speed range. The rubber torsional damper causes system retuning, which means that amplitudes of dangerous harmonic orders are restricted mainly to the engine speed range. The sixth order resonance is forced out of the engine speed range. Brüel&Kjaer Rotational



Laser Vibrometer Type 2523 and POLYTEC 4000 Series Laser Vibrometer are used for torsional vibration measurements. These experimental tools enable measurements of angular velocities of arbitrary rotating parts.

Fig. 8. Harmonic analysis of crankshaft pulley torsional vibrations of an inline six-cylinder

engine with rubber torsional damper (a computation and a measurement)

Comparisons of computed and measured results show some differences. These differences are partially caused by different combustion pressures. The inline diesel four-cylinder engine was used for combustion pressure indications but these pressures are slightly different from the inline diesel six-cylinder engine used for torsional vibration measurements.

3.2 Valvetrain Dynamic Solution Results

The camshaft vibrations are influenced mainly by cranktrain torsional vibrations and also by all single valvetrain torques, a gear timing mechanism and an injection pump torque. Fig. 9 presents harmonic analyses of measured and computed angular velocities of a camshaft end near to the camshaft bearing No. 1. There are mainly harmonic orders known from cranktrain torsional vibrations.

The results which can be very efficiently used for valvetrain computational model

validations are strains and stresses in some component parts. In the case of the target engine, strain gauge measurements on a rocker and an outer valve spring have been used. Relative strains and stresses from the same places respectively are analysed by computational models of a rocker and a spring.

Fig. 9. Harmonic order analysis of camshaft end angular displacement (a computation and a

measurement)

Fig. 10. Computed and measured stresses of the first cylinder intake rocker for engine speed 2200

rpm

Deformations produce better results than forces found by previous calibration tests because these forces are of static values. However, the measured values are dynamic, which can



cause inaccuracies in results. Valve spring stress measurements can be taken as an example. The calibration test deforms the valve spring in the form of the first mode shape (static shape) but in reality higher mode shapes can also be excited. They cannot be found by strain gauge measurements because they can lie on vibration nodes. Therefore, the calibrated force does not show any additional force.

Fig. 11. Computed and measured stresses of the first cylinder inline valve spring for engine speed

2200 rpm

The comparison of computed and measured stresses on a rocker surface in a given direction for an engine speed 2200 rpm is presented in Fig. 10. Fig. 11 shows a comparison of computed and measured stresses on an outer valve spring surface in a given direction for an engine speed 2200 rpm.

3.3 Powertrain Surface Velocity Solution Results

In general, powertrain surface vibrations and radiated noise are coupled. The noise produced by a powertrain can be understood from crankcase surface velocities. Fig. 12 shows measured and calculated Campbell diagrams of crankcase surface velocities near the second cylinder and crankshaft axis. The value 5.10-8 ms-1 is used as a reference velocity. The measured results have been determined by POLYTEC Vibrometer OFV-5000.

The main area of the most significant velocity amplitudes is from 50 to 350 Hz. The first and second torsional frequencies (210 and 255 Hz) can be found in computed and in measured results. Engine attachments to the ground have a fundamental influence on surface velocities with frequencies up to 150 Hz. The computed and measured results show the movement of the whole engine (a rotation about a crankshaft axis direction) at natural frequency 66 Hz. The Campbell diagrams (Fig. 12) shows a resonance of this frequency at the engine speed 1300 rpm.

Fig. 12. Measured and calculated Campbell diagrams of crankcase surface velocities near the

second cylinder and crankshaft axis

4 CONCLUSION

The results enable providing recommendations for solutions of vibrations, noise or component fatigues of a powertrain: The solution of component fatigues: Independent subsystem models of the cranktrain or the valvetrain can be used. In the case of the cranktrain, the flexible engine block models have to be used. In the case of the valvetrain, the variable driving angular velocities have to be incorporated into the model. Highly detailed computational models can also be used for an independent solution of some



subsystems. A detailed analysis of a connecting rod using thermo-elastohydrodynamic (TEHD) models of the slide bearings can be taken as an example.

The solution of powertrain part dynamics: The crankshaft, the camshaft or other component vibrations can be partially solved using independent models, however, the complex computational models provide more accurate results. What is more, they help to understand interactions between powertrain subsystems.

The solution of powertrain noise, vibrations and harshness: The complex computational models of the powertrain incorporating the most significant powertrain subsystems have to be used. Engine block models using reduced FE bodies should include all parts like covers, caps and intake or exhaust manifolds. All significant noise sources like combustion pressure forces, meshing gear forces or injection pump torques have to also be included into the powertrain model.

The virtual engine results can help to understand the NVH behaviour of a new powertrain and enable to speed-up the development process together with reductions of expensive prototypes. The presented computational approach enables an analysis the NVH properties of a powertrain in the range of days. The contribution of different modifications on existing virtual engine (different crankshaft design, added ribs on a crankcase etc.) can be found in range of hours or days.

Therefore, the computational tools based on FEM, MBS, EHD or CFD principles together with experimental tests play an important role in modern powertrain design.

5 ACKNOWLEDGEMENTS

The above activities have been supported by the grant provided by the GAČR (Grant Agency of the Czech Republic) reg. No. 101/09/1225, named “Interaction of elastic structures through thin layers of viscoelastic fluid«. The authors would like to thank GAČR for the rendered assistance.

6 REFERENCES

[1] Rebbert, M. (2003). Simulation der Kurbewellendynamik unter Berücksichtigung

der hydrodynamischen Lagerung zur Lösung motorakusticher Fragen. Ph.D. dissertation, Rheinisch-Westfälischen Technischen Hochschule, Aachen.

[2] Butenschön, H.J. (1976). Das hydrodynamische, zylindrische Gleitlager endlicher Breite unter instationärer Belastung. Ph.D. dissertation, Universität Karlsruhe, Karlsruhe.

[3] Knoll, G., Schönen, R., Wilhelm, K. (2006). Full dynamic analysis of crankshaft and engine block with special respect to elastohydrodynamic bearing coupling. Universität Gesamthochschule, Kassel.

[4] Du, I. (1999). Simulation of flexible rotating crankshaft with flexible engine block and hydrodynamic bearing for a V6 engine. Noise and Vibration Conference, Michigan, p. 89-96.

[5] Kuchař, P. (2007). Strength solution of dynamically loaded parts of combustion engines. Ph.D. dissertation. Prague.

[6] Strowe, Ch., Chattenberg, S. (2008). Friction and CO2 reduction through an integrated approach of valvetrain components. ATZ Technology, vol. 8, no. 7, p. 256-261.

[7] Ortmann, Ch., Skovbjerg, H. (2000). ADAMS/Engine powered by FEV, Part 1: Valve Spring. International ADAMS Users Conference, p. 117-128.

[8] Du, I., Chen, J. (2000). Dynamic analysis of a 3D finger follower valve train system with flexible camshafts. SAE World Congress, p. 250-263.

[9] Knoll, G., Brands, Ch., Schönen, R. (2003). Elastohydrodynamic interaction of camshaft and bearings under consideration of valve train forces. MTZ Motortechnische Zeitschrift, vol. 64, no. 9, p. 724-734.

[10] Craig, R.R. (1981). Structural Dynamics. John Willey & Sons, New York.

[11] Paulstra, L. (2007). Modelling of automotive antivibration rubber parts. Fall 172nd Technical Meeting of the Rubber Division of the American Chemical Society, p. 523-530.

[12] Macosko, C.W. (1994). Rheology: principles, measurement and applications. VCH Publishers, New York.


*Corr. Author’s Address: Shahrood University of Technology, 7 tir Square, 3619995161 Shahrood, Iran, [email protected]

Computation of Stress Intensity Factor in Functionally Graded Plates under Thermal Shock

Nazari, M.B. ‒ Shariati, M. ‒ Eslami, M.R. ‒ Hassani, B. Mohammad Bagher Nazari1,* ‒ Mahmoud Shariati1 ‒ Mohammad Reza Eslami2 ‒ Behrooz Hassani1

1 Shahrood University of Technology, Iran 2 Amir-Kabir University of Technology, Iran

This paper addresses the implementation of the element-free Galerkin method, which is enriched intrinsically for fracture analysis of functionally graded materials under mode I steady-state and transient thermal loading. The stress intensity factors are evaluated by means of both equivalent domain integral and displacement correlation technique. Continuum functions and the micromechanical model are used to describe the distribution of material properties. For thermal shock analysis, the modal decomposition method, which is a semi-discretization approach, is implemented to obtain the transient temperature field. Also, few parametric analyses are performed to study the effect of material gradation on the stress intensity factors. The results imply that the magnitude of the stress intensity factor reaches its peak a short while after the thermal shock, indicating its significant role in the fracture failure.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: functionally graded materials, element-free Galerkin method, equivalent domain integral, displacement correlation technique, thermal stresses

0 INTRODUCTION

Functionally graded materials (FGMs) are a new type of advanced composites that are introduced for use in high temperature environments. The composition, microstructure and/or crystal structure of the FGMs change gradually, forming a non-homogeneous material with continuously varying thermomechanical properties. In recent years, FGMs have been used widely in other applications. According to the experimental studies of Kawasaki and Watanabe [1], when sudden cooling is applied to ceramic/metal FGMs, some edge cracks are created on the ceramic surface. Therefore, examining the surface crack problem in FGMs under thermal loading,especially thermal shock, is important in failure analysis of these materials.

Jin and Noda [2] derived the general form of the thermoelastic crack-tip fields in FGMs. They assumed that the material properties are continuous and piecewise differentiable function of spatial position and some of them are not zero at the crack-tip. According to their study, the variation of material properties does not affect the order of singularity of thermoelastic crack-tip fields. Kishimoto et al. [3] showed that in the presence of thermal loading, the path independency of original J-integral is lost. They

presented a path-independent form of J-integral included extra term to regard the thermal effect. Analytical approaches including the perturbation method and singular integral equations have been used to consider thermal fracture of FGMs [4] and [5]. It is important to know that using analytical approaches is limited to some simple problems or especial conditions. For example, Noda and Guo [5] have studied the edge crack problem in FGMs under thermal shock using the perturbation method. For the sake of simplification, they assumed that the Poisson’s ratio is constant. Yildirim [6] and Dag [7] developed an equivalent domain integral to compute the mode-I stress intensity factor (SIF) under steady-state and transient thermal loading in isotropic and orthotropic FGMs, respectively. These analyses were performed by using very fine meshes of regular elements in HEAT2D and FRAC2D software. KC and Kim [8] and [9] used the interaction integral to evaluate the mixed-mode SIFs under steady-state thermal loading. Chen [10] used the interaction integral in conjunction with element-free Galerkin (EFG) method to compute SIFs for an interface crack in orthotropic functionally graded coating under steady-state thermal loading. These results were obtained by using first-order polynomial basis functions, which lead to a fine node arrangement. Also, Chen reported the value of J-integral was


623Computation of Stress Intensity Factor in Functionally Graded Plates under Thermal Shock

not completely path-independent and results were unreliable for small integral domain size.

The EFG method provides an efficient and robust framework of analyzing fracture mechanics problems. This method has been implemented for fracture analysis of cracks in FGMs under mechanical loading e.g. [11] or steady-state thermal stresses [10]. In this paper, the EFG method is applied in both steady-state and transient thermal fracture of FGMs. The transient thermal loading is imposed in the form of thermal shock.

This paper is organized as follows. Section 1 presents the thermoelastic governing equations. Section 2 provides the EFG discretization form of governing equations. Section 3 explains the use of the equivalent domain integral for thermal fracture of FGMs. Section 4 describes the modal decomposition technique to obtain the transient temperature field. Section 5 presents the obtained numerical results of thermal SIF as well as parametric analyses and the relevant aspects of the results are discussed. Finally, in Section 6 conclusions are drawn.

1 GOVERNING EQUATIONS

A body occupying a space Ω surrounded by a surface Γ under external actions, body forces and prescribed thermal boundary conditions has been considered. The governing equations for static linear thermoelasticity in the domain Ω are:

∇⋅ + =σ b 0, (1a)

−∇ + =∂∂

q Q c Tt

ρ . (1b)

Also, the heat flux is obtained based on the Fourier law: q I= − ∇k T . (2)

The constitutive equation is defined as:

σσ εε εε= −C : ( )th , (3)

where, εε = ∇su, (4a)

εε th T T= −α ( ) .0 I (4b)

Here, the material properties are the forth-order Hooke tensor C , isotropic conductivity k, expansion coefficient α, density ρ and specific heat

c. The field variables are displacement u, strain tensor ε, stress tensor σ, and thermal strain εth and the imposed values are heat source Q and body force b. Moreover, I is the identity second-order tensor and ∇s is the symmetric gradient operator on a vector field. The boundary conditions are as follows:

T T T= on Γ , (5a)

k T qI n q∇ ⋅ = on Γ , (5b)

k T h T T cI n q∇ ⋅ + − =∞( ) ,on Γ (5c)

u u= on Γu , (5d)

σ ⋅ =n t on Γt , (5e)

where h is the convection coefficient and n is the outward unit vector which is normal to Γ.

2 ELEMENT-FREE GALERKIN METHOD IN THERMOELASTICITY

We implement the EFG method to solve governing partial differential equations (PDEs) of 2D thermoelastic problems. This method needs only a set of nodes to construct the discretized model. In EFG, using moving least square (MLS) approximation leads stability in function approximation and applying the Galerkin procedure leads to a stable and well-behaved system of discretized equations. Here, the EFG discretization in the space dimension only is used and the Kantorovitch semi-discretization process is followed. According to the EFG method, the final discrete equations can be obtained as:

C T K K T F Fth th th th th + +( ) = +γ γ , (6a)

K K U F F+( ) = +γ γ , (6b)

where the dot (.) denotes differentiation with respect to time and:

Cijth

i jc d= ∫ ρ φ φ ΩΩ

, (7a)

K B Bijth

ithT

jth

i jk d h dc

= +∫ ∫Ω ΓΩ Γ

φ φ , (7b)

Fith

i i iQ d q d h dq c

= + +∫ ∫ ∫ ∞φ φ θ φΩ Γ ΓΩ Γ Γ

, (7c)

Fγ γ θφith

idT

= ∫ ΓΓ

, (7d)


624 Nazari, M.B. ‒ Shariati, M. ‒ Eslami, M.R. ‒ Hassani, B.

where:

Bith i

i

xx

=∂ ∂∂ ∂

φφ

1

2, (7e)

and

K DB Bij iT

jd= ∫ ΩΩ

, (8a)

K SijT

jiu

dγ γ= ∫ ϕϕ ϕϕ ΓΓ

, (8b)

F b ti iT

iTd d

t

= +∫ ∫ϕϕ ϕϕΩ ΓΩ Γ

, (8c)

F Si iu du

γ γ= ∫ ϕϕ ΓΓ

, (8d)

where

S =

=

SS

Suui

i u

i u

1

2

00

10

, ,if given on

if not given onΓΓ

(8e)

Bii

i

i i

xx

x x=

∂ ∂∂ ∂

∂ ∂ ∂ ∂

φφ

φ φ

1

2

2 1

00 , (8f)

ϕϕii

i=

ϕϕ0

0. (8g)

In the enriched EFG method, the singularity problems due to the presence of a crack is alleviated by enrichment functions. In the intrinsic enrichment, the standard basis (usually polynomials) vector is enriched by including the near-tip asymptotic displacement field [12]:

p xTx x r r

r r( )

, , , cos , sin ,

sin sin , cos sin=

1

2 2

2 2

1 2θ θ

θθ

θθ

, (9)

where r and θ are the usual crack-tip polar coordinates.

3 EQUIVALENT DOMAIN INTEGRAL FOR THERMAL FRACTURE

The J-integral is an energy-based method which is widely used to calculate SIFs. The J-integral originally was derived in the form of a contour integral [13]:

J W u n dj ij i j AA

= −∫ ( ) ,,δ σ1 1 ΓΓ

(10)

where ΓA is an arbitrary contour enclosing the crack-tip and nj is the jth component of the

outward unit vector normal to ΓA. For the sake of simplyfying the calculation, it is suitable to convert this contour form into an equivalent domain integral. Defining a smooth weight function q and applying the divergence theorem, the equivalent domain form of the J-integral is derived as [7]:

J q dA qdAij i j jA A= − +∫ ∫( u ) ( ) ,, , ,σ δ1 1 1W W expl (11)

where A is the area inside the contour ΓA. The first integral contains W,1, i.e., the partial derivatives of W with respect to x1. It should be noted that in FGMs the temperature field and material properties are dependent on spatial coordinates. In linear elastic fracture mechanics, J-integral is equal to the energy release rate and the relationship between the energy release rate and the mode I SIF is given by:

J K EI tip= 2 * , (12)

where E Etip tip* = for plane stress and Etip tip( )1 2−ν

for plane strain. Etip and νtip are Young's modulus and Poisson's ratio, respectively, evaluated at the crack-tip.

4 TRANSIENT HEAT CONDUCTION PROBLEM

To obtain the temperature field, the first-order matrix differential equation (6a) should be solved. Among many methods, the modal decomposition technique [14] was chosen. Modal decomposition is an analytical approach to solve systems of ordinary differential equations (ODEs) without the introduction of additional approximations. Based on the modal decomposition procedure, a coupled system of ODEs is turned into uncoupled equations by using eigenvectors. The complete solution of Eq. (6a) can be expressed as a linear combination of all eigenvectors of the system T(t) = [T1, T2, ..., TN]ψ(t) = Mψ(t), where M is an N×N square matrix whose columns are the eigenvectors. Substituting the above definition into Eq. (6a) and premultiplying it by MT, the uncoupled system of equation is obtained,

C K M F Fth th T th th* * ( ),ψψ ψψ+ = + γ (13)



where Kth* = MT · Kth · M, (14a)

Cth* = MT · Cth · M. (14b)

The system of Eq. (13) contains N uncoupled equations,

ψ ψi i ii

iis i N+ = =

ΛΛ

C* , ( , ,..., ),1 2 (15)

where si iith

iith= K C* */ and Λ = MT (Fth + Fγth).

The initial condition ψ (0) can be obtained from T(0) = M · ψ(0). Depending on the complexity of the right-hand side of Eq. (15), it is solved either analytically or numerically.

5 NUMERICAL RESULTS AND DISSCUSSION

In this section, the calculation of the mode I SIF for an edge crack in functionally graded plate (FGP) under thermal stresses is considered. In addition, a few parametric analyses are performed to study the effect of the gradation of material properties on the stress intensity factor. The distribution of material properties is determined by means of continuum functions e.g., exponential function or micromechanics models e.g., self-consistent model. Examples are presented here:• An edge cracked plate: exponential gradation.• FGP with an edge crack: power law gradation.• Edge crack in an FGP: micromechanics

model.The FGP of length W and height H with

a crack of length a, as depicted in Fig. 1a, is considered. The thickness (in the x3 direction) of the plate is assumed to be quite thin for plane stress analysis and large enough for plane strain analysis. The crack is aligned parallel to the direction of material property gradation. Initially, the FGP is at a uniform stress-free temperature T0. Temperatures of x1 = 0 and x1 = W faces are decreased to constant temperatures T1 and T2, respectively. All other faces, including the crack surfaces, are assumed to be insulated, which results in a dimensional heat conduction problem in the x1 direction. In all cases, the calculated SIFs will be normalized by dividing to:

K E T a0 00 0 1 0= −( ) ( ) ( ( )).α π ν (16)

5.1. An Edge Cracked Plate with Exponentially Gradation

Fig. 1a shows an unconstrained FGP with an edge crack of length a, Fig. 1b presents the complete node arrangement of the FGP which consists of 1695 regular nodes and 40 crack-tip nodes, with a total of 1735. Fig. 1c shows the crack-tip node arrangement. In this case, two different types of functionally graded materials are considered with exponentially varying thermomechanical properties (E, ν, α, k, ρc), in the x1 direction, e.g.:

E x E P xE( ) ( ) exp( ),1 10= (17)

where the nonhomogeniety parameters are defined e.g., as:

PW

E WEE =

10

ln ( )( )

. (18)

Fig. 1. An FGM plate with an edge crack; a) geometry, b) complete node arrangement, c)

crack-tip node arrangement

The values of the nonhomogeneity parameters for the first material are selected arbitrarily (academic materials) as they follow to provide conditions for which the references solutions are available.

E(0) = k(0) = α(0) = ρc(0) = 1.0, ν(0) = 0.3.

For the second case, the ceramic/metal FGM ZrO2/Ti-6Al-4V material with properties of Table 1 is assumed.



For the sake of comparison, two different cases of the thermal boundary conditions are considered in the steady-state analysis. In the third case, a transient analysis is also carried out for different temperatures at the left and right sides of the plate.

In order to verify the implementation of DCT and EDI approaches in the framework of EFG method, comparisons of the calculated SIFs and the available reference solutions are first presented. In this case, the temperature of x1 = 0 and x1 = W faces are decreased from T0 to T1 and T2, respectively. Table 2 compares the normalized SIFs with the results provided by Erdogan and Wu [4], KC and Kim [8] and Yildirim [6]. The obtained solutions are in good agreement with the references. It is interesting to note that our model is comprised of 1735 nodes, while the 2D mesh discretization in KC and Kim [8] consists of 966 elements and 2937 nodes in the framework of the finite element method.

Since the surface crack is usually created during cooling, the FGP problem subjected to a cooling shock is considered here. To consider the thermal shock, it is assumed that the FGP is initially at a uniform stress-free temperature T0 and suddenly cooled down to constant temperatures

T1 = 0.2 T0 and T2 = 0.5 T0 at the left and right hand side faces, respectively. The obtained results for the transient temperature distribution in the ZrO2/Ti-6Al-4V FGM versus normalized time τ, as defined in Eq. (19), is depicted in Fig. 2.

τρ

=k c

Wt( ) ( ) ( ) .0 0 0

2 (19)

According to these results, the temperature gradient near the plate edges is considerably large at the early times after imposing the thermal shock.

Figs. 3 and 4 present normalized SIFs in the ZrO2/Ti-6Al-4V plate resulting from the transient temperature field versus the normalized time τ and the normalized crack length a/W for plane strain and plane stress cases, respectively. As shown in these figures, the SIF quickly increases to a peak value that is drastically larger than the steady value and then decreases rapidly to the corresponding steady value for all crack lengths. In addition, the magnitude of SIF decreases as the normalized crack length a/W becomes larger in both transient and steady states that are in agreement with the results that have recently been reported by Noda and Guo [5].

Table 1. Material properties of ZrO2 and Ti-6Al-4V

MaterialsYoung's modulus

[GPa]

Poisson's ratio

Coefficient of thermal expansion [10-6 /K]

Thermal conductivity [W/(m K)]

Mass density [kg/m3]

Specific heat [J/(kg K)]

ZrO2 151.0 0.33 10.0 2.09 5331 456.7Ti-6Al-4V 116.7 0.33 9.5 7.5 4420 537.0

Table 2. Normalized mode I SIF in FGP under steady-state thermal loading

Material parameters Load Analysis

type

Normalized SIFPresent Erdogan

and Wu [4]KC and Kim [8]

Yildirim [6]EDI DCT

WPE=ln(5) WPα=ln(2)

T1 = 0.5 T0T2 = 0.5 T0

Plane strain 0.0124 0.0126 0.0125 0.0128 0.0128Plane stress 0.0090 0.0088 - 0.0090 0.0090

T1 = 0.05 T0T2 = 0.05 T0

Plane strain 0.0246 0.0240 0.0245 0.244 -

WPE=ln(5) WPα=ln(2)WPk=ln(10)

T1 = 0.2 T0T2 = 0.5 T0

Plane strain 0.0334 0.0343 0.0335 0.0334 0.034Plane stress 0.0234 0.0239 - 0.0235 0.024

T1 = 0.05 T0T2 = 0.5 T0

Plane strain 0.0405 0.0411 0.0410 0.0406 -



Fig. 2. Transient temperature distribution in the FGP (ZrO2/Ti-6Al-4V) for various normalized

times with T1/ T0 = 0.2 and T2/ T0 = 0.5

Fig. 3. Normalized KI in the ZrO2/Ti-6Al-4V plate versus normalized time and different crack

lengths in plane strain condition

As the final point, the magnitude of SIF for the plane strain is larger than plane stress. Noda et al. [14] have derived thermal stresses analytically for a homogeneous isotropic strip under one-dimensional transient temperature distribution. These results indicate that the thermal stresses for the plane strain case are equal to those of the plane stress multiplied by a factor of 1/(1-ν). Regarding the fact 0 < ν < 0.5, this factor is greater than one, which implies a larger SIF for the plane strain in comparison to the plane stress problem, which can be noticed from Figs. 2 and 3.

5.2. FGP with an Edge Crack with Power Law Gradation

A Ni/TiC plate with the configuration of the first example is considered here and a power-law function is assumed to describe the material properties in the x1-direction e.g., as follows.

E x E E W E x W p( ) ( ) ( ( ) ( ))( / ) .1 10 0= + − (20)

The exponent p is a positive constant used as an adjusting parameter to obtain certain distribution for material properties. As the exponent p can be chosen independently from the comprised materials, this function is significantly flexible and hence widely used in practice for the analysis of the FGMs. In the proportional material properties, the exponent p is assumed the same value for all material properties while it can be selected differently for non-proportional materials.

Fig. 4. Normalized KI in the ZrO2/Ti-6Al-4V plate versus normalized time for different crack lengths

in plane stress condition

Moreover, here different thermal boundary conditions are imposed on the uncracked face of FGP. To apply a thermal shock, the cracked face is assumed to be quenched to a constant temperature of T1 = 0 while having the free convection at the other face with a convection coefficient of h=10 W/(m2K) and the ambient temperature is assumed T0. The transient temperature distribution in the Ni/TiC plate is presented in Fig. 5 for the proportional case with p = 5. The effect of the convection boundary condition at the x1 = W face on the temperature distribution is more apparent at the steady-state. Figs. 6 and 7 show the transient thermal SIF versus crack lengths for the proportional case with p = 5 and p = 0.2, respectively. As can be seen, the variation of the thermal SIF is completely different for these cases. In the ceramic-riched case (p = 5), at the beginning of the thermal shock the SIF increases to a peak value and declines to its minimum quickly and then increase gradually to a steady-state value.

However, in the metal-riched case (p = 0.2) the SIF increases quickly to a peak value and then decreases rapidly until the crack is closed. The



corresponding time of the crack closure increases as the crack length is increased. In this example, the crack closure occurred in steady-state for all crack lengths.

Fig. 5. Transient temperature distribution in the FGP (Ni/TiC) for various normalized times with

T1 = 0 and h = 10

Fig. 6. Normalized KI in the Ni/TiC plate versus normalized time and different crack lengths in

plane strain condition and p = 5

The effect of the thermal boundary condition applied on the uncracked face for the linear proportional material i.e., p = 1, is illustrated in the Fig. 8. Here, the h = 0 corresponds to the insulated thermal boundary condition and h = ∞ corresponds to a known temperature boundary

condition. According to these results, while the value of the SIF is independent of the type of the thermal boundary condition applied on the uncracked face, the steady-state value is completely dependent. Moreover, a greater value for the steady-state SIF is obtained for the case of constant temperature at both faces.

Fig. 7. Normalized KI in the Ni/TiC plate versus normalized time for different crack lengths in

plane strain condition and p = 0.2

Fig. 8. The effect of thermal boundary condition at x1 = W on the variation of normalized KI

Now, the effect of the material gradation is studied and some parametric analyses are carried out to assess their effect on the SIFs. In all cases, it is assumed that the exponent p gets different values for the special property and

Table 3. Material properties of Ni and TiC

MaterialsYoung’s modulus

[GPa]

Poisson’s ratio

Coefficient of thermal expansion[10-6 /K]

Thermal conductivity[W/(m K)]

Mass density[kg/m3]

Specific heat[J/(kg K)]

TiC 320 0.195 7.4 25.1 4940 134Ni 206 0.312 13.3 90.5 8890 439.5



p = 0.2 for other material properties. Figs. 9 and 10 present the effect of variation in FGP elastic properties, i.e. Young’s modulus and Poisson’s ratio, on the SIF for the crack length a/W = 0.3 and the plane strain problem. According to Fig. 9, the magnitude of SIF, especially its peak value, increases significantly as the parameter pE is increased. These results indicate that for all values of pE, the peak and the crack closure time occur roughly simultaneously. This can be explained by the fact that the transient temperature distribution is independent of the variations of the parameter pE. We believe that the effect of Young’s modulus is responsible for the slight difference between the peak time and the steady time.

The influence of Poisson’s ratio gradation on the SIF is shown in Fig. 10. It can be seen that, by a decrease in pν, i.e. for metal-riched whose greater Poisson’s ratio, the magnitude of SIF and the crack closure time increase.

The analytical solutions for thermal stress distribution in an uncracked FGP under one-dimensional temperature distribution for the plane strain and plane stress cases are given as [4]:

σν

α νx xth E x C x C x T x t

2 2

12 1 1 2 1 11

1=−

+ − +( )( )( )( ) ( , ) ,∆ (21a)

and

σ αx xth E x C x C x T x t

2 2 1 1 1 2 1 1= + −( )( ) ( ) ( , ) ,∆ (21b)

respectively, where C1 and C2 are unknown coefficients determined from the force and moment boundary conditions in the x2 direction. From Eq. (21), it is observed that the thermal stresses are an increasing function of Young’s modulus.

Fig. 9. Normalized KI versus normalized time for different pE; plane strain with a/W = 0.3, p = 0.2

for other material properties

The effects of the gradation of the thermal properties on the SIF during the shock period are shown in Figs. 11, 12 and 13. Fig. 11 depicts the normalized SIF versus normalized time for various values of the exponent p for the thermal expansion coefficient, i.e., pα. According to this figure, the peak value of SIF for the case p = 0.2 is significantly greater than others. Also, depending on the pα value, the trend of SIF might be completely different. For example, the crack is closed for the pα = 0.2 and pα = 1 cases, while the SIF for pα = 5 increases gradually to a steady-state value after it peaks and reduces to a local minimum.

Fig. 10. Normalized KI versus normalized time for different pν; plane strain with a/W = 0.3,

p = 0.2 for other material properties

Fig. 11. Normalized KI versus normalized time for different pα values; plane strain with

a/W = 0.3, p = 0.2 for other material properties

Fig. 12 illustrates the SIF variation in terms of time for various values of conductivity parameter pk. It can be seen that an increase of the parameter pk causes a delay in the occurrence of the peak value of SIF and steady-state. This delay is not surprising since the diffusivity k/ρc is an increasing function of the conductivity and the pk = 0.2 correspond to metal-riched composition



with greater conductivity, Moreover, for ceramic-riched case (pk = 5) the peak value of SIF and the crack closure time is greater than the metal-riched case. The variation of SIF with the normalized time and the nonhomogeniety parameter of ρc is presented in Fig. 13. These results indicate that the peak value of SIF is almost independent from pρc. The peak time and the crack closure time increase for the ceramic-riched case (pρc = 5).

Fig. 12. Normalized KI versus normalized time for different pk. Plane strain with a/W = 0.3,

p = 0.2 for other material properties

Fig. 13. Normalized KI versus normalized time for different pρc values; plane strain with

a/W = 0.3, p = 0.2 for other material properties

5.3 Edge Crack in an FGP with Micromechanics Model

Prediction of the effective macroscopic properties is one of the basic issues in composite material theory. For FGMs, as the graded composites, some micromechanics models of composites have been developed. Among many micromechanics models extended for FGMs, self-consistent method (SCM) was used. Zuiker [16] has pointed out that the SCM provides a simple and initial estimate of effective properties which is

a benefit for relate optimal property distributions. Moreover, in this method the properties are determined independently of the phase of the inclusion and the matrix. This is significant for FGMs in which the volume fraction of the constituent phases varies in a wide range. For two-phase FGMs, the volume fraction of the ceramic is assumed in the form of a power function, i.e. Vc = 1‒(x1/L)p, in which L is the material gradation length and the exponent p is known as the gradient index. Here x1 = 0 corresponds to pure matrix phase (ceramic) and x1 = L to pure inclusion material (metal). For a two-phase composite, the effective materials are determined from [16],

14 3 4 3 4 3κ µ κ µ κ µ+

=+

++/ / /

,V Vc

c

m

m (22a)

V V

V V

c c

c

m m

m

c m

m

m c

c

κκ µ

κκ µ

µµ µ

µµ µ

++

+

+

+−

+−

+ =

4 3 4 3

5 2

/ /

00, (22b)

α αα α κ κ

κ κ= +

− −−m

c m m

c m

( )( / / )( / / )

,1 1

1 1 (22c)

V k kk k

V k kk k

m m

m

c c

c

( ) ( ).

−+

+−

+=

2 20 (22d)

We consider an edge crack in an unconstrained FGP of length W and height H = 8 W. To consider the thermal shock, it is assumed that only the cracked face of the FGP is suddenly cooled down to constant temperature T1 = 0 from the stress-free temperature T0. Fig. 14 presents the transient temperature distribution in the FGP. Here, it is assumed that ΔT = T(x1,t) ‒ T0.

Fig. 14. Transient temperature distribution in the FGP for various normalized times with T1 =0



Fig. 15. Normalized mode I stress intensity factor in the FGP versus normalized time and different

crack lengths in plane strain condition

Fig. 15 depicts the transient thermal SIF versus normalized crack lengths a/W for plane strain case. Although the steady value of SIF is greater for longer cracks, the peak value of SIF is significantly large for short cracks.

6 CONCLUSION

In this paper, the domain form of J-integral (EDI) and displacement correlation technique (DCT) in conjunction with element-free Galerkin method are implemented to evaluate the mode I stress intensity factor in FGMs under steady-state and transient temperature fields. The present study points out that: 1. In the enriched EFG framework a relatively

coarse mesh in compared with FEM and common XFEM is sufficient for analysis of cracks in FGMs under thermal loading.

2. A short while after the thermal shock, SIF increases to a large peak value, which is significantly greater than the corresponding steady value and then decreases rapidly to a steady value. Moreover, although the crack is closed at steady state for some cases, the value of SIF might reach to a large positive value during the thermal shock period. These imply that in thermal fracture analysis of FGMs, the SIF at the beginning of thermal loading might be the main factor in fracture failure analysis.

3. Parametric analyses indicate that the variation in the thermomechanical properties, especially thermal characteristics, has a significantly influence on the fracture behaviour of FGMs.

4. Comparison of the obtained numerical results with the reference solutions indicates that both energy-based EDI and direct approach DCT methods, in the framework of enriched EFG, are efficient tools to analyze the thermal fracture of FGMs.

7 REFERENCES

[1] Kawasaki, A., Watanabe, R. (2002). Thermal fracture behavior of metal/ceramic functionally graded materials. Engineering Fracture Mechanics, vol. 69, p. 1713-1728.

[2] Jin, Z-H., Noda, N. (1994). Crack-tip singular fields in nonhomogeneous materials. Journal of Applied Mechanics, Transactions ASME, vol. 61, p. 738-740.

[3] Kishimoto, K., Aoki, S., Sakata, M. (1980). On the path independent J-integral. Engineering Fracture Mechanics, vol. 13, p. 841-850.

[4] Erdogan, F., Wu, B.H. (1996). Crack problems in FGM layers under thermal stresses. Journal of Thermal Stresses, vol. 19, p. 237-265.

[5] Noda, N., Guo, L.C. (2008). Thermal shock analysis for a functionally graded plate with a surface crack. Acta Mechanica, vol. 195, p. 157-166.

[6] Yildirim, B. (2006). An equivalent domain integral method for fracture analysis of functionally graded materials under thermal stresses. Journal of Thermal Stresses, vol. 29, p. 371-397.

[7] Dag, S. (2006). Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach. Engineering Fracture Mechanics, vol. 73, p. 2802-2828.

[8] KC, A., Kim, J.H. (2008). Interaction integrals for thermal fracture of functionally graded materials. Engineering Fracture Mechanics, vol. 75, p. 2542-2565.

[9] Kim, J.H., KC, A. (2008). A Generalized interaction integral method for the evaluation of the T-stress in orthotropic functionally graded materials under thermal loading. Journal of Applied Mechanics, vol. 75, p. 1-11.



[10] Chen, J. (2005). Determination of thermal stress intensity factors for an interface crack in a graded orthotropic coating-substrate structure. International Journal of Fracture, vol. 133, p. 303-328.

[11] Rao, B.N., Rahman, S. (2003). Mesh-free analysis of cracks in isotropic functionally graded materials. Engineering Fracture Mechanics, vol. 70, p. 1-27.

[12] Fleming, M., Chu, Y.A., Moran, B., Belytschko, T. (1997). Enriched element-free galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering, vol. 40, p. 1483-1504.

[13] Rice, J.R. (1968). A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics, vol. 35, p. 379-386.

[14] Zienkiewics, O.C., Taylor, R.L. (2000). The Finite Element Method. Butterworth-Heinemann, Oxford.

[15] Noda, N., Hetnarski, R.B., Tanigawa, Y. (2003). Thermal Stresses. Taylor and Francis, New York.

[16] Zuiker, J.R. (1995). Functionally graded materials: choice of micromechanics model and limitations in property variation. Composites Engineering, vol. 5, p. 807-819.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8, 633-634Instructions for Authors

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J. (2009). Function and functionality in the conceptual design process. Strojniški vestnik - Journal of Mechanical Engineering, vol. 55, no. 7-8, p. 455-471.

Journal titles should not be abbreviated. Note that journal title is set in italics.Books:Surname 1, Initials, Surname 2, Initials (year). Title. Publisher, place of publication.[2] Groover, M.P. (2007). Fundamentals of Modern

Manufacturing. John Wiley & Sons, Hoboken.Note that the title of the book is italicized. Chapters in Books:Surname 1, Initials, Surname 2, Initials (year). Chapter title. Editor(s) of book, book title. Publisher, place of publication, pages.[3] Carbone, G., Ceccarelli, M. (2005). Legged

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8Vsebina

Vsebina

Strojniški vestnik - Journal of Mechanical Engineeringletnik 57, (2011), številka 7-8Ljubljana, julij-avgust 2011

ISSN 0039-2480

Izhaja mesečno

Povzetki člankovReinhard Hackenschmidt, Bettina Alber-Laukant, Frank Rieg: Simuliranje nelinearnih

materialov pod vplivom centrifugalnih sil s pametnimi navzkrižno povezanimi simulacijami SI 103

Gregor Čepon, Lionel Manin, Miha Boltežar: Validacija modela jermenskega gonila na osnovi sistema prožnih teles SI 104

Radouane Akrache, Jian Lu: Integrirano snovanje za ocenjevanje utrujenostne trajnostne dobe konstrukcij SI 105

Simon Kulovec, Leon Kos, Jožef Duhovnik: Glajenje mrež z globalno optimizacijo pod omejitvami SI 106

Chuangwen Xu, Ting Xu, Qi Zhu, Hongyan Zhang: Študija možnosti adaptivnega ocenjevanja parametrov modelov obrabe rezkalnega orodja SI 107

Srđan Podrug, Srečko Glodež, Damir Jelaska: Numerično modeliranje širjenja razpoke v korenu zoba zobnika SI 108

Viktor Jejčič, Tone Godeša, Marko Hočevar, Brane Širok, Aleš Malneršič, Andrej Štrancar, Mario Lešnik, Denis Stajnko: Načrtovanje in preskušanje ultrazvočnega sistema za ciljno pršenje sadovnjakov SI 109

Nuša Fain, Mihael Kline, Jožef Duhovnik: Integracija marketinga in razvoja v procesu osvajanja izdelka SI 110

Vaclav Pistek, Pavel Novotny: Navidezni mehanizem – orodje za reševanje dinamike pogonskih sestavov SI 111

Mohammad Bagher Nazari, Mahmoud Shariati, Mohammad Reza Eslami, Behrooz Hassani: Izračun faktorja intenzivnosti napetosti v funkcionalno gradientnih ploščah za stanje toplotnega šoka SI 112

Navodila avtorjem SI 113

Osebne vestiDoktorati, magisteriji, specializacije in diplome SI 115

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8, SI 103 Prejeto: 17.01.2011 Sprejeto: 23.06.2011

*Naslov avtorja za dopisovanje: Univerza v Bayreuthu, Oddelek za inženirsko oblikovanje in CAD, 95440 Bayreuth, Nemčija, [email protected] SI 103

Simuliranje nelinearnih materialov pod vplivom centrifugalnih sil s pametnimi navzkrižno povezanimi

simulacijami

Reinhard Hackenschmidt* ‒ Bettina Alber-Laukant ‒ Frank RiegUniverza v Bayreuthu, Oddelek za inženirsko oblikovanje in CAD, Nemčija

Razvoj izdelkov se v praksi izvaja s pomočjo različnih orodij za računalniško podporo (orodij CAx). Razvojni proces pa je zaradi neoptimalnih simulacijskih strategij in postopkov pogosto omejen in zato tudi počasen.

Da bi lahko tehnično področje uporabe standardnih parkljastih sklopk razširili tudi na pogonske sklope, ki obratujejo z vrtilnimi frekvencami do 40.000 vrt./min., je treba preučiti vprašanje deformacij materiala pod centrifugalnimi / torzijskimi in tlačnimi obremenitvami. Zaradi dragih fizičnih eksperimentov je najvišjo prioriteto dobil razvoj učinkovite simulacijske rešitve z različnimi računalniško podprtimi orodji.

Za zanesljivo dokončanje razvoja izdelka v okolju različnih simulacijskih programov je bila izbrana metoda ICROS (pametne navzkrižno povezane simulacije), ki predlaga štiri korake:

• Prvič: analiza in specifikacija naloge in potreb po simulacijah• Drugič: konceptualna zasnova potreb po simulacijah• Tretjič: zasnova scenarija izvedbe simulacij• Četrtič: razvoj primernega simulacijskega okoljaZa modeliranje materiala je bil izbran hiperelastični model po Ogdenu, ki sloni na razmerjih

glavnih raztezkov. Glavne parametre je bilo treba ugotoviti eksperimentalno.Za pridobivanje potrebnih podatkov za simulacijo je bila razvita visokohitrostna preizkusna miza.

Meritve vrednosti radialnih deformacij polimernega materiala sklopke pri vrtilnih frekvencah do 40.000 vrt./min. so zahtevna naloga in so bile opravljene s pomočjo svetlobnega žarka in zelo občutljive fotocelice.

Klasična pot metode ICROS daje fundamentalne rezultate in vključuje trodimenzionalno CAD-modeliranje sklopke, ki ji sledijo linearni preračuni po metodi končnih elementov za visoke vrtilne hitrosti s torzijsko obremenitvijo. Diagrami odmikov kažejo signifikantne radialne deformacije elastomernega vložka zaradi rotacijskih obremenitev. Drugič pa so deformacije torzijsko obremenjenih območij delno onemogočene. Ti rezultati se načeloma zelo dobro ujemajo z realnostjo, absolutne številke pa so v primerjavi s fizičnim preizkusom pri visokih hitrostih bistveno previsoke.

Ugotovljeno je bilo, da se linearni parametri materiala, ki so določeni s standardnimi nateznimi preizkusi, ne ujemajo z realnimi materialnimi vrednostmi zaradi uporabe stroškovno ugodnih termoplastičnih elastomerov (TPE). Ti materiali so bodisi kopolimeri bodisi fizikalno mešani polimeri.

Ti posebni termoplastični elastomerni blendi so za razliko od običajnih kemično vezanih duroplastičnih elastomerov fizikalno zamreženi, in sicer odvisno od sestave trdih in mehkih komponent blenda. Pri sobni temperaturi in zmernih silah se zato vedejo kot pravi elastomeri samo zaradi polkristalnih aglomeracij in posledičnih van der Waalsovih sil. Dejanske lastnosti so nekje med vrednostmi za oba materiala. Mehanizmov zamreženja TPE je veliko in so močno odvisni od izdelovalnega procesa, njihovega kompleksnega vedenja pa ni mogoče v celoti simulirati.

Zato je bil razvit vlečni mehanizem, posebej prilagojen za ta izdelek, ki daje realistične parametre na običajnem stroju za preizkušanje Zwick. Pridobljene vrednosti materiala so bile uporabljene kot osnova za preslikavo pri modelu MKE v ustreznem nelinearnem orodju za MKE. Primerjava rezultatov kaže, da so podatki iz simulacije zelo blizu izmerjeni realnosti.

Plod skrbne izvedbe štirih korakov ICROS je podroben načrt poteka dela priprave in izvedbe simulacij, ki je lahko močna podpora sofisticiranim procesom razvoja izdelkov. ©2011 Strojniški vestnik. Vse pravice pridržane.Ključne besede: razvoj izdelkov, CAx, ICROS, FEA, simulacija, potek dela


*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, [email protected] 104

Validacija modela jermenskega gonila na osnovi sistema prožnih teles

Gregor Čepon1 ‒ Lionel Manin2 ‒ Miha Boltežar1,*

1 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija 2 Univerza v Lyonu, CNRS, INSA de Lyon, Francija

Zaradi vse večje zanesljivosti jermenskih gonil se je njihova uporaba v zadnjih nekaj desetletjih zelo razširila. Po zaslugi nizkih stroškov inštalacije in vzdrževanja, možnosti blaženja šokov in dobrih obratovalnih karakteristik že vrsto let nadomeščajo verižna in zobniška gonila kjerkoli je to mogoče. Zlasti v avtomobilski industriji, ki predstavlja velik delež tržnega gospodarstva, je v zadnjem času značilno, da se več jermenskih gonil združuje v eno samo daljše jermensko gonilo. Ta jermenska gonila izkazujejo kompleksno dinamsko obnašanje, zaradi česar je potrebno okarakterizirati dinamski odziv tovrstnih sistemov z uporabo validiranih numeričnih modelov. Na osnovi teh modelov lahko določimo optimalne obratovalne, oblikovne in materialne parametre gonila.

V tem prispevku je prikazan postopek validacije razvitega numeričnega modela jermenskega gonila. Model jermenskega gonila je zasnovan na osnovi metode absolutnih vozliščnih koordinat, ki omogoča simulacije jermenskih gonil ob uporabi bistveno manjšega števila elementov in s tem prostostnih stopenj. Za popis stika med jermenom in jermenico smo uporabili pristop, ki temelji na preoblikovanju kontaktnega problema v linearni komplementarni problem. Tak pristop mogoča realen popis kontaktnih sil tudi pri neenakomernem obratovanju jermenskih gonil.

Za validacijo numeričnega modela jermenskega gonila je uporabljeno jermensko gonilo z dvema jermenicama. V okviru izvedenih meritev smo sočasno merili kotno hitrost pogonske in gnane jermenice, moment na pogonski in gnani gredi ter pomika spodnje in zgornje veje jermena. Pri različnih obratovalnih parametrih smo eksperimentalno dobljene rezultate primerjali z rezultati numeričnih simulacij. V sklopu teh primerjav so bili identificirani poglavitni mehanizmi, ki privedejo do zmanjšanja kotne hitrosti gnane jermenice. Zmanjšanje kotne hitrosti gnane jermenice ima namreč velik vpliv na učinkovitost prenosa moči jermenskega gonila. Na osnovi izvedenih primerjalnih analiz je mogoče ugotoviti, da z enostavnim analitičnim modelom zdrsa jermena po jermenici napovemo premajhno zmanjšanje kotne hitrosti. Zanesljivejše vrednosti zmanjšanja kotne hitrosti dobimo s predstavljenim numeričnim modelom jermenskega gonila. Predvsem pri nizkih vrednostih navora na gnani jermenici je ujemanje med napovedjo numeričnega modela in izmerjeno vrednostjo zmanjšanja kotne hitrosti odlično. Pri višjih vrednostih navora je razkorak med rezultati meritev in numeričnim modelom večji, kar je rezultat neupoštevanja strižnih deformacij torne plasti v modelu jermena. Numerični model nam poleg tega omogoča tudi natančno identifikacijo navora, ki vodi do zdrsa jermena po celotni kontaktni dolžini med jermenom in jermenico. To je predvsem rezultat natančnih meritev koeficienta trenja med jermenom in jermenico ter upogibne togosti jermena.

Z dvema laserskima merilnikoma smo merili tudi pomik jalove in delovne veje jermena. Izmerjene pomike vej jermena smo primerjali s pomiki, dobljenimi z numerično simulacijo. Ker so vzbujevalni mehanizmi jermenskega gonila do neke mere naključne narave (hrapavost jermena, zračnost v ležajih, itd.), jih je praktično nemogoče natančno vključiti v numerični model. Eksperimentalno in numerično pridobljeni odziv sistema je bilo tako mogoče primerjati le z vidika frekvenčne vsebine. Na podlagi prikazanih rezultatov lahko ugotovimo dobro ujemanje med resonančnimi frekvencami, dobljenimi na osnovi simuliranega in izmerjenega signala. Zmogljivost numeričnega modela jermenskega gonila smo prikazali pri simuliranju kompleksnega serpentinskega jermenskega gonila z več jermenicami in dvema napenjalnima jermenicama. Razviti numerični model omogoča izvedbo parametričnih občutljivostnih analiz, s katerimi lahko določimo vplivne parametre, ki imajo največji vpliv na hrup jermenskega gonila. ©2011 Strojniški vestnik. Vse pravice pridržane.Ključne besede: jermensko gonilo, validacija, absolutni vozliščni koordinatni sistem, serpentinsko jermensko gonilo, zmanjšanje kotne hitrosti


*Naslov avtorja za dopisovanje: Univerza v Versaillesu Saint-Quentin-en-Yvelines, 7, rue Jean Hoët - 78200 Mantes-la-Jolie, Francija, [email protected] SI 105

Integrirano snovanje za ocenjevanje utrujenostne trajnostne dobe konstrukcij

Radouane Akrache ‒ Jian LuLaboratorij za inženirstvo, Univerza v Versaillesu, Francija

Snovanje izdelka ali mehanskega sistema je sestavljeno iz več faz, ki se začnejo z izdelavo produktnih specifikacij in končajo z njegovim dokončnim uničenjem. Cilj raziskave je razvoj ustreznih orodij oz. predstavitev predlogov novih delovnih metodologij in računalniških orodij za povezovanje procesa razvoja materialov z mehanskim konstruiranjem. Razvili smo računsko metodo za napovedovanje večosne utrujenostne trajnostne dobe konstrukcij po metodi končnih elementov (MKE), in drugo metodo za napovedovanje porazdelitve dovoljenih preostalih napetosti in porazdelitve varnostnega koeficienta za zahtevano življenjsko dobo. Razvili smo globalen pristop k računanju utrujenostne trajnostne dobe 3D-konstrukcij. Numerične rezultate, ki smo jih pridobili po MKE, smo skupaj z rezultati preizkusov vstavili v glavni program. Rezultati so podani v obliki grafičnega prikaza utrujenostne trajnostne dobe konstrukcije. Wöhlerjeve krivulje v našem primeru napovedujejo 50 % verjetnost loma. Pri kriteriju z dvema konstantama, kot ga predlagajo Crossland, Sines ali Dang Van, sta za izračun konstant potrebni vsaj dve Wöhlerjevi krivulji. Pri enostavnih ali kombiniranih fazno usklajenih obremenitvah je mogoče uporabiti kriterij Sinesa, Crosslanda ali Dang Vana. Pri kombinirani fazno neusklajeni obremenitvi se na seznam možnih kriterijev doda še Lujev kriterij. Ko sta izračunani obe konstanti za izbrani kriterij utrujanja, je mogoče izrisati ustrezno linijo za ta kriterij na diagramu. Ta linija ustreza določenemu številu ciklov.

Pristop je uporaben za enostavne in za kombinirane obremenitve (upogib in nateg, torzija in nateg), bodisi fazno usklajene ali neusklajene. Če je obremenitev fazno neusklajena, se uporabi Lujeva metoda za dokaz uporabnosti metode in upoštevanje vpliva fazno neusklajene obremenitve. Integracija preostalih napetosti v izračun mora biti postopna in jo je mogoče razdeliti na več faz. Z dvodimenzionalno MKE smo modelirali popuščanje preostalih napetosti in vpliv različnih dejavnikov. Podan je predlog kriterija za ugotavljanje stabilnosti preostalih napetosti kot funkcije cikličnih značilnosti materiala. Namen druge metode je napovedovanje varnostnih koeficientov konstrukcije za določeno utrujenostno trajnostno dobo za namene izboljšanja zmogljivosti. Uporabili smo enake preizkušance z zarezo kot pri napovedovanju utrujenostne trajnostne dobe. V tem delu je uporabljen samo Crosslandov kriterij. V kombinaciji z drugimi orodji, ki smo jih razvili, lahko optimiziramo komponente in mehanske sisteme. Za dano življenjsko dobo določenega materiala pri določenih obremenitvah lahko z modeliranjem ugotavljamo, ali so potrebne predobremenitve. S kartiranjem varnostnih koeficientov za določeno utrujenostno trajnostno dobo lahko napovemo območja z največjim tveganjem, ki jih je treba ustrezno spremeniti v fazi snovanja in proizvodnje. Ugotovili smo (Sl. 10), da je utrujenostna trajnostna doba najmanjša v področjih z visoko koncentracijo napetosti. Integriranih je bilo več dejavnikov, ki obsegajo optimizacijo mehanskih sistemov, modeliranje nelinearnih sistemov, eksperimentalne meritve, obdelavo površin ter raziskave novih materialov in novih proizvodnih procesov. Razvita je bila posebna metoda reševanja, zasnovana na več konceptih, ki kaže, da je konstrukcijski problem možno izraziti kot problem optimizacije. Na ta način je mogoče ustvariti računsko kodo za nelinearno optimizacijo z mešanimi spremenljivkami. Te koncepte je mogoče uporabiti za optimizacijo geometrije dela po kriterijih kot so stroški, vzdržljivost in življenjska doba. Mehanski sistemi so v trenutno razpoložljivi programski opremi predstavljeni kot vsota njihovih posameznih komponent. Takšna predstavitev pa uporabnikom ne omogoča enostavnega snovanja mehanskih sistemov. V trenutnih sistemih za CAD so izpuščeni tudi nekateri osnovni pojmi. Zato predlagamo, da se tem orodjem doda več modulov za modeliranje in optimizacijo.©2011 Strojniški vestnik. Vse pravice pridržane.Ključne besede: večosna utrujenostna trajnostna doba, integrirano snovanje, metoda končnih elementov, kriteriji utrujanja, dovoljene preostale napetosti, varnostni koeficient

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8, 555-567 Prejeto: 12.05.2010 Sprejeto: 01.06.2011

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, [email protected] 106

Glajenje mrež z globalno optimizacijo pod omejitvami

Simon Kulovec* ‒ Leon Kos ‒ Jožef DuhovnikUniverza v Ljubljani, Fakulteta za strojništvo, Slovenija

Optimizacija mrežnih struktur je zelo pomembna v strojniških področjih kot so dinamika, prenos toplote in materiali. Če želimo izvajati numerične analize problemov iz omenjenih področij, moramo fizični model pomrežiti. Obstajajo tudi mreže, ki jih potrebujemo za izdelavo »freeform« konstrukcij na omenjenih in drugih področjih. Manjši in enakomerno razporejeni elementi (trikotniki, štirikotniki) mreže nam omogočajo natančnejše rezultate, vendar pa analiza traja dlje časa. Pojavljajo se komercialni programski paketi, kjer konstantno mreženje fizičnih modelov ni dobro rešeno. Opravili smo analizo in izdelali algoritem, ki bi omenjene težave odpravil. Trenutno se za osnovne modele in renderje, predvsem pri aplikacijah navidezne resničnosti, uporabljajo trikotniške mrežne strukture. Omenjene mrežne strukture dobimo s pomočjo pomreževalnikov v modelirnikih ali kot rezultat posnemovalnika površin. Razen trikotniških mrežnih struktur se, zlasti pri večjih »gradbenih« jeklenih konstrukcijah, za sestavne elemente konstrukcije uporabljajo tudi štirikotniki. Mreže, ki jih dobimo, običajno niso visoke kakovosti in optimizirane. Sestavljene so iz neidealnih mrežnih elementov in imajo slabo povezljivost med vozlišči. Zato smo se odločili za izdelavo optimizacijskega algoritma, ki zna optimizirati in izdelovati učinkovite in robustne mreže. Za razliko od obstoječih algoritmov za gladko mreženje, ki delujejo predvsem na ravni lokalnega glajenja, smo se pri glajenju mrež odločili za uporabo Lagrange-Newtonove metode sekvenčno-kvadratičnega optimiziranja z omejitvami, ki omogoča globalno reševanje problema negladkih mrež. Optimizacija se izdela za nepravilne n-kotniške mrežne strukture. Izbrana optimizacija je predvsem geometrijske narave. Cenilna funkcija za optimizacijo je funkcija posameznih stranic vhodne mrežne strukture. Vstopna mreža je nepravilna, zato se jo skuša z optimizacijo popraviti tako, da bo sestavljena iz čimbolj enakih elementov. Najprej določimo dve cenilni funkciji: (i) lokalno in (ii) globalno.

Predstavljen je primer uporabe optimizacije z omejitvami. Omejitev predstavljajo fiksna ali variabilna vozlišča poljubno izbrane mrežne strukture. Za lokalno optimizacijo določimo lokalno cenilno funkcijo. V nadaljevanju je obravnavana optimizacija mrežnih struktur z globalno optimizacijo. Za izračun globalne optimizacije in cenilne funkcije se uporabijo vnaprej izračunane povprečne dolžine robov, ki se med iteracijami ne spreminjajo.

Pri obravnavanih tipih mrežnih struktur s predvidenim optimizacijskim algoritmom izboljšamo mrežo. To je pomembno za trikotne mrežne strukture. Za optimizacijo uporabimo kombinacije lokalne in globalne cenilne funkcije. V primeru optimizacije brez omejitev dobimo boljše rezultate z uporabo globalne cenilne funkcije. Na drugi strani pa dobimo v primerih z omejenimi robnimi elementi začetne mrežne strukture boljše rezultate z uporabo lokalne cenilne funkcije, in sicer predvsem z ozirom na število iteracij, potrebnih za dosego podobnega rezultata. Za preizkus kakovosti optimizacije štirikotnih mrežnih struktur z uporabo našega algoritma je uporabljen mrežni primer, ki je obravnavan v članku Branets-Carey. Skupne cenilne funkcije konvergirajo v vseh primerih optimizacije z uporabo različnih kombinacij cenilnih funkcij in uteži. Kot rezultat optimizacije dobimo mrežno strukturo z enakimi diagonalami štirikotnih elementov in z enakimi dolžinami robov trikotnih elementov. V vseh primerih optimizacije se upošteva, da so vozlišča med celotnim procesom povezana z enakimi robnimi elementi. Obstajajo tudi drugi t.i. algoritmi za glajenje mrežnih struktur (Laplacian, Lennard-Jones in Pliant), vendar se osredotočajo predvsem na lokalna območja in ne na celotno mrežo. Kljub temu pa naš algoritem vsebuje lastnost hitre konvergence. V ostalih algoritmih nismo opazili optimizacije kombiniranih mrežnih struktur.© 2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: glajenje, sekvenčna kvadratična optimizacija, mrežna struktura, geometrija, vozlišče, cenilna funkcija


*Naslov avtorja za dopisovanje: Politehnika Lanzhou, Qilihequ, Gongjiawan 1, Lanzhou, Gansu, Kitajska,730050,[email protected] SI 107

Študija možnosti adaptivnega ocenjevanja parametrov modelov obrabe rezkalnega orodja

Chuangwen Xu ‒ Ting Xu ‒ Qi Zhu ‒ Hongyan ZhangPolitehnika Lanzhou, Kitajska

Obraba orodij za obdelavo kovin z odrezavanjem neposredno vpliva na natančnost, učinkovitost in stroške obdelave, zato je sprotni nadzor obrabe orodij deležen vse večje pozornosti in postaja pomembna raziskovalna tema pri razvoju fleksibilnih proizvodnih sistemov. Mehanizem rezkanja je v primerjavi z drugimi postopki strojne obdelave bolj kompleksen, pogoji so bolj raznovrstni, rezalni parametri bolj spremenljivi, obraba in lom orodja pa sta naključna in kompleksna.

Ugotavljanje značilnosti obrabe rezkalnega orodja je zato ključnega pomena za raziskovanje nadzora obrabe orodij. Uporaba značilnosti omogoča potrebno natančnost in zanesljivost nadzora obrabe orodij. Obraba orodja je proces, ki se odvija v času, zato je potreben nadzorni sistem, ki lahko določi vrednost obrabe orodja v vsakem trenutku kot osnovo za kompenzacijo obrabe orodja. Vrednosti obrabe orodja se uporabljajo za kompenzacijo polmerov orodij in za optimizacijo rezalnih parametrov v času. Zato se razvijajo novi postopki in tehnologije za nadzor in ugotavljanje značilnosti obrabe orodja. V tej študiji je predstavljena metoda za pridobivanje vrednosti obrabe orodja.

Spreminjajoči se pogoji pri odrezavanju predstavljajo velik izziv za zanesljivost nadzora obrabe. V raziskovalnem delu trenutno prevladujejo strategije pametnega nadzora. Pametni nadzor vključuje obdelovalni proces, zajem signalov, ugotavljanje značilnosti, učenje/prepoznavanje, odločanje in krmiljenje. Zmogljivost celotnega nadzornega sistema je močno odvisna od učinkovitosti ugotavljanja značilnosti. Strategije za ugotavljanje značilnosti obrabe v nadzornih sistemih lahko razdelimo v dve kategoriji glede na tehnike obdelave in analize signalov.

Predstavljena je nova metoda za sprotni nadzor obrabe orodij v spreminjajočih se pogojih odrezavanja. Predlagana metoda uporablja ugotavljanje značilnosti obrabe na osnovi modela procesa in ocenjevanja parametrov. Model adaptivnega ocenjevanja obrabe rezkalnega orodja v spreminjajočih se pogojih je v celoti zgrajen na moči, ki se rabi pri rezkanju. Adaptivni model sledi lastnostim procesa odrezavanja tako, da kombinira signal stanja procesa, pogoje odrezavanja, model moči in metodo najmanjših kvadratov. Značilnosti obrabe orodja se določajo iz ocenjenih parametrov modela in so bile določene s teoretično in eksperimentalno študijo.

Eksperimenti kažejo, da spremembe parametrov modela moči pri odrezavanju signifikantno odražajo obrabo orodja ne glede na spremembe pogojev pri odrezavanju, proces prepoznavanja obrabe orodja pa je z njimi zelo natančen. Ta študija je praktično uporabna za različne vrste pametnega nadzora obrabe orodja in jo je mogoče uporabiti za določanje značilnosti obrabe orodja pri različnih samoučečih modelih moči, ki se rabi pri odrezavanju.

Ta projekt lahko izboljša mednarodni položaj in konkurenčnost kitajskih proizvajalcev opreme, hkrati pa promovira znanstveno-tehnološko inovativnost v proizvodnji. Ustvari lahko visoko raven usposobljenosti v industriji in raziskovalnih sferah. Razvite izboljšave teorije obdelave informacij in tehnološkega sistema so lahko podlaga za izboljšave v proizvodnem sektorju ter za promocijo raziskav natančnih meritev in nadzora obrabe rezkalnih orodij.© 2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: moč pri rezkanju, model adaptivnega ocenjevanja, obraba orodja, parametri modela, združevanje informacij


*Naslov avtorja za dopisovanje: Univerza v Mariboru, Fakulteta za naravoslovje in matematiko, Koroška 160, 2000 Maribor, Slovenija [email protected] 108

Numerično modeliranje širjenja razpoke v korenu zoba zobnika

Srđan Podrug1 ‒ Srečko Glodež2,* ‒ Damir Jelaska1

1 Univerza v Splitu, Fakulteta za elektrotehniko, strojništvo in ladjedelništvo, Hrvaška 2 Univerza v Mariboru, Fakulteta za naravoslovje in matematiko, Slovenija

Namen prispevka je analizirati vpliv mesta delovanja sile na širjenje razpoke v korenu zoba zobnika. Analizirana sta dva primera, in sicer:• utripnasilavzunanjitočkienojnegaubiranja,• spreminjajočasesilavzdolžzobnegaboka.

Razentegajevprispevkuprikazanvplivdebelinezobnegavencanaširjenjerazpokevkorenuzobazobnika.

Za izvedbo omenjenih analiz je v numeričnem modelu predpostavljena začetna utrujenostnarazpokanamestunajvečjenapetostivkorenuzoba.Velikostzačetnerazpokejedoločenaizkustvenonapodlagipragaširjenjarazpokeintrajnedinamičnetrdnostigradivazobnika.Zaanalizoširjenjarazpokeje uporabljenaParisova enačba, kjer je faktor intenzivnosti napetosti določennumeričnopoMKE.Zadoločitev smeri širjenja razpoke je uporabljen kriterijMTS.Upoštevan je tudi učinek zaprtja razpoke,in sicer po principu plastifikacije materiala. Študija je izvedena na realni zobniški dvojici iz jekla14CrNiMo13-4,zakaterosoznanitudinekaterieksperimentalnirezultati.

Rezultatipredstavljeneraziskavekažejonanaslednjeugotovitve:• Zaboljnatančnoanalizoširjenjarazpokeinposledičnodoločitevživljenjskedobezobniškedvojiceje

trebaupoštevatidejansko(tojespreminjajočo)obremenitevvzdolžzobnegaboka.• Vprimeruzobnikovzzobnimvencemjetrebaupoštevatidebelinozobnegavenca,sajle-tavplivatako

naživljenjskodobokottudinasmerširjenjarazpokevkorenuzobazobnika.V prispevku je izvedena 2D-numerična analiza širjenja razpoke v korenu zoba zobnika ob

upoštevanjuprejnaštetihvplivov.Zanatančnejšoanalizobibilo treba izvesti3D-numeričnoanalizo, skatero bi lahko zajeli tudi vpliv neenakomerne porazdelitve sile po širini zoba. Prav tako bi bilo smiselno izvesti ustrezne lastnepreskuse, saj so vpredloženemdelu eksperimentalni rezultati povzeti iz ustreznestrokovneliterature.Zaanalizoširjenjarazpokebibilosmiselnouporabitišedrugekriterijeinmedsebojprimerjati dobljene rezultate.

Izvirnostprispevkajepredvsemvupoštevanjuspreminjajočeseobremenitvevzdolžzobnegabokanaširjenjeutrujenostnerazpokevkorenuzobazobnikatervupoštevanjuvplivadebelinezobnegavencanasmerširjenjaterazpoke.Izsledkipredloženegaprispevkasonamenjenipredvsemraziskovalcem,kiseukvarjajosproblematikodoločanjaživljenjskedobezobniškihdvojic zvključevanjem teoretičnihosnovmehanike loma.© 2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: strojni elementi, zobniki, utrujanje, širjenje razpoke, doba trajanja, numerično modeliranje


*Naslov avtorja za dopisovanje: Univerza v Mariboru, Fakulteta za kmetijstvo in biosistemske vede, Pivola 10, 2311 Hoče, Slovenija, [email protected] SI 109

Načrtovanje in preizkušanje ultrazvočnega sistema za ciljno pršenje sadovnjakov

Viktor Jejčič1 ‒ Tone Godeša1 ‒ Marko Hočevar2 ‒ Brane Širok2 ‒ Aleš Malneršič2 ‒ Andrej Štrancar3 ‒

Mario Lešnik4 ‒ Denis Stajnko4*1Kmetijski inštitut Slovenije, Slovenija

2Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija 3Univerza v Ljubljani, Fakulteta za računalništvo in informatiko, Slovenija

4Univerza v Mariboru, Fakulteta za kmetijstvo in biosistemske vede, Slovenija

Od začetka sistematičnega pridelovanja gojenih rastlin v sadovnjakih se ljudje spoprijemajo z rastlinskimi boleznimi in škodljivci. Pršilniki so stroji za nanašanje fitofarmacevtskih sredstev (FFS) v obliki drobnih kapljic na ciljno površino s pomočjo ventilatorja za usmerjeno ustvarjanje zračnega toka. Ta način je povezan z velikimi izgubami (drifti) v ozračje in tla, ki se jih skuša zmanjšati s prilagajanjem količine škropiva volumnu rastlin (TRV). Zelo uspešen način krmiljenja nanašanja FFS je laserski sistem (LIDAR), ki pa je drag in zato se ga skuša nadomestiti s cenejšim, a funkcionalno podobnim ultrazvočnim sistemom, ki se je obnesel pri citrusih in oljkah. Namen članka je predstavitev in testiranje pršilnika z ultrazvočnimi senzorji v slovenskih sadovnjakih jabolk.

Meritve smo izvajali z istim pršilnikom v kontrolnem (CM) in avtomatskem načinu (AM) pršenja, z dodatkom markerja tartrazin v štiriletnem jablanovem nasadu. Na petih drevesih in treh meddrevesnih prostorih je bilo izbranih 12 položajev za merjenje učinka ultrazvočnega krmiljenja. Šobe so se avtomatsko odpirale in zapirale glede na prisotnost ali odsotnost ciljev, zaznanih z ultrazvočnimi senzorji. Senzorji so bili uporabljeni za pošiljanje in prejemanje ultrazvočnih signalov. Delovanje sistema je bilo vključeno samodejno s proženjem ultrazvočnih senzorjev in izračunom oddaljenosti za preprečevanje morebitnih neželenih lažnih zaznav. Za kakovostno in kvantitativno določanje smo uporabili dve svetovno priznani metodi. Na lističih WSP smo z napravo za optično analizo Optomax Image Analyser šteli število kapljic, ki so jih zadele. Druga metoda je spektrofotometrično določanje depozita tartrazina na vzorcih jablanovih listov, s katerim določimo dejanske izgube škropiva zaradi drifta.

Zmanjšanje nanosa škropiva na enoto površine v načinu AM je bilo 20,2%. Največja pokritost s škropivom, 27,3%, je bila v načinu CM na položaju P1 na spodnji strani listov. Najmanjša pokritost je bila na spodnji strani lističev na položaju P8 (5,79%). Odnašanja škropiva med drevesi s prototipom ni bilo mogoče bistveno preprečiti. Število kapljic je največje v načinu CM na položaju P5, in sicer 146. Uporaba avtomatiziranega sistema je zmanjšala število kapljic iz 108 na 101, vendar ni signifikantnih razlik v pokritosti pri uporabi pršilnika v načinu AM. Največji nanos tartrazina 6,35 µg/cm2 je v načinu CM na položaju P10, v načinu AM pa tudi na položaju P10, in sicer 6,09 µg/cm2. Kljub 20,2-odstotnemu prihranku škropiva zaradi manjšega pretoka škropiva skozi šobe je bilo na liste nanesenega le 10 % manj škropiva, kakovost pršenja v načinu AM pa je popolnoma primerljiva s kakovostjo v kontrolnem načinu.

V našem poskusu so bili uporabljeni trije ultrazvočni senzorji in tri šobe. V praksi bi bilo bolje imeti več z elektroventili krmiljenih šob z ožjim kotom delovanja, ker bi bila v tem primeru sposobnost prilagajanja izhoda posamezne šobe še boljša. Raba ultrazvočno-elektronskega sistema na pršilnikih izboljšuje tretiranje v trajnih jablanovih nasadih tako z ekonomskega kot z okoljskega vidika, hkrati pa tudi razbremenjuje voznika, zato je pri delu manj napak in nesreč.

V prispevku smo prikazali izviren način pršenja nasadov jablan s sistemom ultrazvočnih senzorjev za nadzorovanje odpiranja/zapiranja šob in lastno razvitim krmilnim algoritmom. Predstavljeni prototip zmanjšuje porabo FFS vsaj za 20,2 % ob enakem biotičnem učinku in tako pomembno zmanjšujejo obremenjenost okolja.© 2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: pršilnik, ultrazvok, algoritem, razporeditev škropiva, sadovnjak


*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija; [email protected] 110

Integracija marketinga in razvoja v procesu osvajanja izdelka

Nuša Fain1,* ‒ Mihael Kline2 ‒ Jože Duhovnik1

1 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija 2 Univerza v Ljubljani, Fakulteta za družbene vede, Slovenija

Eden ključnih dejavnikov uspešnosti razvoja novih izdelkov je raven integracije marketinga in razvoja v procesu osvajanja novih izdelkov. Številne študije so se s to problematiko ukvarjale podrobneje (Griffin in Hauser 1996; Gupta in Willemon 1991; Lu in Chang 2002; Song in Thieme 2006; Garnett et al. 2006) in skušale identificirati različne integracijske mehanizme in merila določanja stopnje integracije med različnimi funkcijami v podjetju. Vendar pa je bila večina znotraj funkcijskih integracijskih mehanizmov obravnavana neodvisno od meril integracijskih vrzeli med posameznimi funkcijami, hkrati pa se nobena od študij ni podrobneje ukvarjala z različnimi pristopi k integraciji marketinga in razvoja v odnosu do kulturnih razlik med vzhodom in zahodom. Gupta et al. (1986) so predstavili teoretični model integracije marketinga in razvoja, ki temelji na vplivu strategije, zunanjega okolja ter individualnih in organizacijskih dejavnikov na sam proces integracije. Njihov model je največkrat citiran in analiziran model na tem področju, vendar pa ne obstaja metodološki pristop, ki bi model testiral celovito in upoštevaje vse dejavnike, relevantne za učinkovito integracijo. Pričujoči prispevek predstavlja raziskovalni protokol, ki temelji na modelu Gupte et al. (1986) in obravnava vse relevantne dejavnike za proces integracije marketinga in razvoja v procesu osvajanja izdelka.

Struktura raziskovalnega protokola, ki je predstavljen v prispevku, temelji na integraciji kakovostnega in kvantitativnega raziskovanja. Da bi pridobili poglobljeno znanje o integraciji marketinga in razvoja v procesu osvajanja izdelka z vidika kulturnih razlik, smo se odločili za izvedbo kvantitativne raziskave med malimi in srednje velikimi slovenskimi podjetji. Vprašalnik, ki smo ga razvili za potrebe raziskave, temelji na delih Songa in Thiemea (2006) ter Luja in Changa (2002), ki so raziskovali integracijske procese v razvitih gospodarstvih. Vprašalnik pokriva področja integracijskih mehanizmov, medfunkcijskih vrzeli in vplivov na uspešnost procesa osvajanja izdelka.

Ker nas je hkrati zanimalo, kako procese povezovanja funkcij doživljajo akterji teh funkcij, smo se odločili še za izvedbo študij primerov v slovenskih podjetjih, ki se med seboj razlikujejo glede na značilnosti procesa osvajanja izdelka. Celoten raziskovalni načrt smo zastavili tako, da lahko pridobljene rezultate posplošimo in omogočimo njihovo aplikacijo tudi v procesih zunaj obravnavanih podjetij. Z analizo notranjih dokumentov podjetij in izvedbo intervjujev z akterji marketinških, razvojnih in managerskih funkcij v podjetjih smo pridobili relevantne kakovostne podatke, ki smo jih nato analizirali s programom za analizo vsebine. Končni rezultat študij primerov je bil skupek relevantnih vzročno-posledičnih odnosov, vezanih na integracijo marketinga in razvoja v procesu osvajanja izdelka. Rezultati kažejo, da akterji, udeleženi v procesu osvajanja izdelka, doživljajo dejavnike, ki jih v modelu izpostavljajo Gupta et al. (1986), kot bistvene za učinkovito integracijo marketinga in razvoja, kar potrjuje analizirani teoretični model. Vendar pa se predvsem pri analizi organizacijskih in individualnih dejavnikov pojavljajo nekateri kontradiktorni rezultati, za katere iščemo argumente v kulturnih vidikih procesa osvajanja izdelka. Te dejavnike bodo avtorji poglobljeno obravnavali v prihodnosti.© 2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: marketing, razvoj, proces osvajanja izdelka, teoretični okvir integracije, empirični dokazi


*Naslov avtorja za dopisovanje: Tehnična univerza v Brnu, Fakulteta za strojništvo, Institut za avtomobilsko tehniko, Technicka 2, 61669, Brno, Češka republika, [email protected] SI 111

Navidezni mehanizem – orodje za reševanje dinamike pogonskih sestavov

Vaclav Pistek ‒ Pavel NovotnyTehnična univerza v Brnu, Fakulteta za strojništvo, Institut za avtomobilsko tehniko, Češka republika

Cilj tega dela je razvoj primernih računskih modelov za učinkovito reševanje dinamike pogonskih sestavov. Rezultati morajo odgovoriti na različna vprašanja, zlasti na tista v zvezi s hrupom, vibracijami in utrujanjem komponent.

Glavni prispevek je v tem, da se vsi modeli rešujejo sočasno s pomočjo zahtevnega računskega modela, t. i. navideznega mehanizma. Sinhrone rešitve imajo lahko temeljni vpliv na rezultate reševanja dinamike pogonskih sestavov, pomagajo pa lahko tudi pri razumevanju medsebojnih vplivov med deli pogonskega sestava.

V primeru obravnavanega pogonskega sestava, ki je vrstni dizelski šestvaljni motor, je računski model mogoče razdeliti na sestav ročične gredi s torzijskim blažilnikom, sestav ventilov, zobniški pogon za krmiljenje odmične gredi in vbrizgalno črpalko za gorivo.

Pristop k reševanju vključuje dobro znani metodi MKE (metoda končnih elementov), MBS (metode več teles) in nove numerične pristope za reševanje hidrodinamičnih drsnih ležajev in gumijastih torzijskih blažilnikov.

Drsni ležaj in njegov računski model imata ključen vpliv na rezultate dinamike pogonskega sestava. V obravnavanem motorju je na desetine drsnih ležajev, zato mora biti model numerično zelo hiter, vseeno pa dovolj natančen. Naslednji cilj je razvoj ustreznega modela drsnega ležaja, ki vključuje tako reakcijske sile v oljnem filmu kot reakcijske momente. Reakcijski momenti so še posebej pomembni tudi za drsne ležaje ročične gredi. Problemi hidrodinamike drsnih ležajev se učinkovito rešujejo ločeno od strukturnih problemov z metodo končnih razlik. Reševanje se izvaja iterativno na večkratnih in spremenljivih mrežah. Uporabljeni so tudi modeli kavitacije.

Naslednji pomemben del pogonskega sestava je torzijski blažilnik. Pri obravnavanem motorju je uporabljen gumijasti torzijski blažilnik in cilj tega dela je tudi računski model gumijastega blažilnika. V prispevku je predlagana tudi toplotna verifikacija gumijastega dela blažilnika. Za natančnejše reševanje torzijskih vibracij sestava ročične gredi v pogonskem sestavu z velikim razponom hitrosti motorja so uporabljeni modeli torzijskih blažilnikov z več Maxwellovimi členi. Za pravilno osno vedenje nekaterih gumijastih torzijskih blažilnikov so v računske modele vključene tudi osne lastnosti blažilnika. Za preverjanje maksimalnih temperatur so uporabljeni strukturni in toplotni računski modeli gumijastega dela, ki upoštevajo nastajanje toplote v odvisnosti od lokalnih relativnih deformacij gumijastih delov.

Rezultati dela kažejo, da so za najnatančnejše računske modele za reševanje vprašanj hrupa, vibracij in utrujanja komponent najprimernejši kompleksni modeli pogonskega sestava. Ti modeli omogočajo razumevanje interakcij med podsistemi pogonskega sestava, njihova prednost pa je tudi v dejstvu, da so vsi rezultati izračunani z enim samim računskim modelom in shranjeni v eni sami datoteki.

Največja slabost takšnega pristopa je visoka raven zahtevnosti modela. Kompleksni računski modeli zahtevajo vnos velikega števila parametrov, ki jih je pogosto le težko določiti. Slabost pa je tudi v dolgem času numeričnega reševanja modelov in v količini prostora, potrebnega za shranjevanje izračunanih rezultatov.

Razlog za razvoj kompleksnega modela je tudi pomoč pri razvoju nove serije vrstnih dizelskih šestvaljnih motorjev. Navidezni mehanizem naj bi inženirjem pomagal zmanjšati hrup in vibracije ter povečati utrujanje komponent v krajšem razvojnem času, s tem pa bi se znižali tudi skupni stroški razvoja novega motorja.© 2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: vibracije, hrup, dinamika, pogonski sestav, hidrodinamika


*Naslov avtorja za dopisovanje: Tehnična univerza Shahrood, 7 tir Square, 3619995161 Shahrood, Iran, [email protected] 112

Izračun faktorja intenzivnosti napetosti v funkcionalno gradientnih ploščah za stanje toplotnega šoka

Mohammad Bagher Nazari1,* ‒ Mahmoud Shariati1 ‒ Mohammad Reza Eslami2 ‒ Behrooz Hassani11 Tehnična univerza Shahrood, Iran

2 Tehnična univerza Amir-Kabir, Iran

Analiza toplotnih napetosti je eno najpomembnejših vprašanj v tehniki, saj so mnoge konstrukcije izpostavljene povišanim temperaturam. Lom zaradi toplotnih napetosti je po mnogih študijah zelo razširjen in zahteven način odpovedi konstrukcij. Eksperimentalne raziskave poleg tega odkrivajo, da se ob nenadni ohladitvi keramičnih/kovinskih funkcionalnih gradientnih materialov (FGM) na keramičnih površinah pojavijo robne razpoke. Preiskava problema površinskih razpok pri materialih FGM pod toplotno obremenitvijo, zlasti pri toplotnem šoku, je zato pomembna za analizo odpovedi teh materialov.

Članek obravnava implementacijo Galerkinove metode brez elementov, ki je prirejena za analizo loma funkcionalno gradientnih materialov v stanju stacionarnih toplotnih obremenitev zvrsti I in prehodnih toplotnih obremenitev. Faktorji intenzivnosti napetosti se računajo s tehnikama integrala ekvivalentne domene in korelacije odmikov. Dodatek vrha razpok omogoča ugotavljanje singularnosti pri vrhu razpok za termoelastična polja.

V pogojih vodilnih enačb linearne termoelastičnosti je za pridobivanje porazdelitve temperature prehodnega pojava uporabljena polanalitična metoda modalne dekompozicije kot prikladna tehnika za analizo toplotnih šokov. Profili značilnosti materiala so določeni z zveznimi funkcijami kot je eksponentna funkcija in z mikromehanskimi modeli. Opravljenih je bilo tudi nekaj parametričnih analiz za preučitev vpliva lastnosti materiala na faktor intenzivnosti toplotnih napetosti.

Rezultati kažejo, da se faktor SIF za kratek čas po toplotnem šoku poveča na visoko vršno vrednost, ki je znatno višja od ustrezne stacionarne vrednosti, nato pa se hitro zmanjša na stacionarno vrednost. Čeprav je razpoka v nekaterih primerih v stacionarnem stanju zaprta, lahko vrednost SIF doseže visoko pozitivno vrednost v času toplotnega šoka. To pomeni, da bi lahko bila vrednost faktorja SIF ob začetku toplotne obremenitve glavni dejavnik analize odpovedi z lomom pri funkcionalnih gradientnih materialih. Parametrična analiza tudi kaže, da ima spreminjanje termomehanskih lastnosti, zlasti toplotnih lastnosti, pomemben vpliv na lomne lastnosti materialov FGM. Primerjava pridobljenih numeričnih rezultatov z referenčnimi rešitvami kaže, da sta lahko metoda EDI na osnovi energije in metoda neposrednega pristopa DCT v okviru razširjene metode EFG učinkovito orodje za analizo toplotnega loma materialov FGM.© 2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: funkcijski gradientni materiali, Galerkinova metoda brez elementov, integral ekvivalentne domene, tehnika korelacije odmikov, toplotne napetosti

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8, SI 113-114Navodila avtojem

SI 113

Navodila avtorjem

Članke pošljite na naslov:Strojniški vestnik -Journal of Mechanical EngineeringAškerčeva 6, 1000 Ljubljana, SlovenijaTel.: 00386 1 4771 137Faks: 00386 1 2518 567E-mail: [email protected] [email protected]

Članki morajo biti napisani v angleškem jeziku. Strani morajo biti zaporedno označene. Prispevki so lahko dolgi največ 10 strani. Daljši članki so lahko v objavo sprejeti iz posebnih razlogov, katere morate navesti v spremnem dopisu. Kratki članki naj ne bodo daljši od štirih strani.

Navodila so v celoti na voljo v rubriki “Informacija za avtorje” na spletni strani revije: http://en.sv-jme.eu/

Prosimo vas, da članku priložite spremno pismo, ki naj vsebuje:1. naslov članka, seznam avtorjev ter podatke

avtorjev;2. opredelitev članka v eno izmed tipologij; izvirni

znanstveni (1.01), pregledni znanstveni (1.02) ali kratki znanstveni članek (1.03);

3. izjavo, da članek ni objavljen oziroma poslan v presojo za objavo drugam;

4. zaželeno je, da avtorji v spremnem pismu opredelijo ključni doprinos članka;

5. predlog dveh potencialnih recenzentov, ter kontaktne podatke recenzentov. Navedete lahko tudi razloge, zaradi katerih ne želite, da bi določen recenzent recenziral vaš članek.

OBLIKA ČLANKA

Članek naj bo napisan v naslednji obliki:- Naslov, ki primerno opisuje vsebino članka.- Povzetek, ki naj bo skrajšana oblika članka

in naj ne presega 250 besed. Povzetek mora vsebovati osnove, jedro in cilje raziskave, uporabljeno metodologijo dela, povzetek rezultatov in osnovne sklepe.

- Uvod, v katerem naj bo pregled novejšega stanja in zadostne informacije za razumevanje ter pregled rezultatov dela, predstavljenih v članku.

- Teorija.

- Eksperimentalni del, ki naj vsebuje podatke o postavitvi preskusa in metode, uporabljene pri pridobitvi rezultatov.

- Rezultati, ki naj bodo jasno prikazani, po potrebi v obliki slik in preglednic.

- Razprava, v kateri naj bodo prikazane povezave in posplošitve, uporabljene za pridobitev rezultatov. Prikazana naj bo tudi pomembnost rezultatov in primerjava s poprej objavljenimi deli. (Zaradi narave posameznih raziskav so lahko rezultati in razprava, za jasnost in preprostejše bralčevo razumevanje, združeni v eno poglavje.)

- Sklepi, v katerih naj bo prikazan en ali več sklepov, ki izhajajo iz rezultatov in razprave.

- Literatura, ki mora biti v besedilu oštevilčena zaporedno in označena z oglatimi oklepaji [1] ter na koncu članka zbrana v seznamu literature.

Enote - uporabljajte standardne SI simbole in okrajšave. Simboli za fizične veličine naj bodo v ležečem tisku (npr. v, T, n itd.). Simboli za enote, ki vsebujejo črke, naj bodo v navadnem tisku (npr. ms-1, K, min, mm itd.)

Okrajšave naj bodo, ko se prvič pojavijo v besedilu, izpisane v celoti, npr. časovno spremenljiva geometrija (ČSG).

Pomen simbolov in pripadajočih enot mora biti vedno razložen ali naveden v posebni tabeli na koncu članka pred referencami.

Slike morajo biti zaporedno oštevilčene in označene, v besedilu in podnaslovu, kot sl. 1, sl. 2 itn. Posnete naj bodo v ločljivosti, primerni za tisk, v kateremkoli od razširjenih formatov, npr. BMP, JPG, GIF. Diagrami in risbe morajo biti pripravljeni v vektorskem formatu, npr. CDR, AI.

Vse slike morajo biti pripravljene v črno-beli tehniki, brez obrob okoli slik in na beli podlagi. Ločeno pošljite vse slike v izvirni obliki Pri označevanju osi v diagramih, kadar je le mogoče, uporabite označbe veličin (npr. t, v, m itn.). V diagramih z več krivuljami, mora biti vsaka krivulja označena. Pomen oznake mora biti pojasnjen v podnapisu slike.

Tabele naj imajo svoj naslov in naj bodo zaporedno oštevilčene in tudi v besedilu poimenovane kot Tabela 1, Tabela 2 itd.. Poleg fizikalne veličine, npr t (v ležečem tisku), mora biti v oglatih oklepajih navedena tudi enota. V tabelah naj se ne podvajajo podatki, ki se nahajajo v besedilu.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8, SI 113-114

SI 114

Potrditev sodelovanja ali pomoči pri pripravi članka je lahko navedena pred referencami. Navedite vir finančne podpore za raziskavo.

REFERENCE

Seznam referenc MORA biti vključen v članek, oblikovan pa mora biti v skladu s sledečimi navodili. Navedene reference morajo biti citirane v besedilu. Vsaka navedena referenca je v besedilu oštevilčena s številko v oglatem oklepaju (npr. [3] ali [2] do [6] za več referenc). Sklicevanje na avtorja ni potrebno.

Reference morajo biti oštevilčene in razvrščene glede na to, kdaj se prvič pojavijo v članku in ne po abecednem vrstnem redu. Reference morajo biti popolne in točne. Vse neangleške oz. nenemške naslove je potrebno prevesti v angleški jezik z dodano opombo (in Slovene) na koncu Navajamo primere:Članki iz revij:Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Ime revije, letnik, številka, strani.[1] Zadnik, Ž., Karakašič, M., Kljajin, M.,

Duhovnik, J. (2009). Function and Functionality in the Conceptual Design Process. Strojniški vestnik – Journal of Mechanical Engineering, vol. 55, no. 7-8, p. 455-471.

Ime revije ne sme biti okrajšano. Ime revije je zapisano v ležečem tisku. Knjige:Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Izdajatelj, kraj izdaje[2] Groover, M. P. (2007). Fundamentals of Modern

Manufacturing. John Wiley & Sons, Hoboken.Ime knjige je zapisano v ležečem tisku. Poglavja iz knjig:Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov poglavja. Urednik(i) knjige, naslov knjige. Izdajatelj, kraj izdaje, strani. [3] Carbone, G., Ceccarelli, M. (2005). Legged

robotic systems. Kordić, V., Lazinica, A., Merdan, M. (Eds.), Cutting Edge Robotics. Pro literatur Verlag, Mammendorf, p. 553-576.

Članki s konferenc:Priimek 1, začetnica imena, priimek 2, začetnica imena (leto). Naslov. Naziv konference, strani.[4] Štefanić, N., Martinčević-Mikić, S., Tošanović,

N. (2009). Applied Lean System in Process Industry. MOTSP 2009 Conference Proceedings, p. 422-427.

Standardi:Standard (leto). Naslov. Ustanova. Kraj.[5] ISO/DIS 16000-6.2:2002. Indoor Air – Part 6:

Determination of Volatile Organic Compounds in Indoor and Chamber Air by Active Sampling on TENAX TA Sorbent, Thermal Desorption and Gas Chromatography using MSD/FID. International Organization for Standardization. Geneva.

Spletne strani:Priimek, Začetnice imena podjetja. Naslov, z naslova http://naslov, datum dostopa.[6] Rockwell Automation. Arena, from http://www.

arenasimulation.com, accessed on 2009-09-27.

RAZŠIRJENI POVZETEK

Ko je članek sprejet v objavo, avtorji pošljejo razširjeni povzetek na eni strani A4 (približno 3.000 - 3.500 znakov). Navodila za pripravo razširjenega povzetka so objavljeni na spletni strani http://sl.sv-jme.eu/informacije-za-avtorje/.

AVTORSKE PRAVICE

Avtorji v uredništvo predložijo članek ob predpostavki, da članek prej ni bil nikjer objavljen, ni v postopku sprejema v objavo drugje in je bil prebran in potrjen s strani vseh avtorjev. Predložitev članka pomeni, da se avtorji avtomatično strinjajo s prenosom avtorskih pravic SV-JME, ko je članek sprejet v objavo. Vsem sprejetim člankom mora biti priloženo soglasje za prenos avtorskih pravic, katerega avtorji pošljejo uredniku. Članek mora biti izvirno delo avtorjev in brez pisnega dovoljenja izdajatelja ne sme biti v katerem koli jeziku objavljeno drugje.

Avtorju bo v potrditev poslana zadnja verzija članka. Morebitni popravki morajo biti minimalni in poslani v kratkem času. Zato je pomembno, da so članki že ob predložitvi napisani natančno.

Avtorji lahko stanje svojih sprejetih člankov spremljajo na http://en.sv-jme.eu/.

PLAČILO OBJAVE

Domači avtorji vseh sprejetih prispevkov morajo za objavo plačati prispevek, le v primeru, da članek presega dovoljenih 10 strani oziroma za objavo barvnih strani v članku, in sicer za vsako dodatno stran 20 EUR ter dodatni strošek za barvni tisk, ki znaša 90,00 EUR na stran.

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)7-8, SI 115-120Osebne objave

SI 115

Doktorati, magisteriji, specialistična dela in diplome

DOKTORAT ZNANOSTI

Na Fakulteti za strojništvo Univerze v Ljubljani so z uspehom obranili svojo doktorsko disertacijo:

dne 28. junija 2011 Boris VIDRIH z naslovom: »Vpliv globalnih podnebnih sprememb in urbanizacije na lokalne klimatske razmere v mestih« (mentor: prof. dr. Sašo Medved);

V delu predstavljamo raziskave vpliva geometrijskih, snovnih in toplotnih lastnosti gradnikov mestnega okolja in regionalnih scenarijev globalnih podnebnih sprememb na lokalne klimatske razmere v mestih. Razviti so bili modeli toplotnega odziva naravnih in grajenih gradnikov mestnega okolja, s katerimi smo oblikovali dinamične robne temperaturne pogoje. Predstavljena je metoda njihovega vključevanja v orodje za računsko dinamiko tekočin. Za izbrane mestne četrti v obliki naravnih jeder in stavbnih sosesk so bili raziskani tokovni režimi in izdelani več-parametrični polinomi za določitev dnevnih minimalnih in maksimalnih jakosti toplotnih otokov. Razvita je metoda zaporednega združevanja mestnih četrti, ki omogoča napoved lokalnih meteoroloških razmer v mestnem okolju in analizo ukrepov blaženja mestnih toplotnih otokov s prilagajanjem velikosti in lastnosti gradnikov. Učinek ukrepov preverjamo s integralnim kazalnikom toplotnega ugodja v zunanjem okolju. Razvita je bila metoda oblikovanja baz korigiranih testnih referenčnih let, ki vključujejo tako regionalne globalne scenarije, kot specifične lastnosti naravnih in grajenih gradnikov mestnega okolja. Baze so prilagojene uporabi v numeričnih orodjih s katerimi vrednotimo toplotni odziv in rabo energije v stavbah;

dne 1. julija 2011 Barbara ZUPANČIČ z naslovom: »Behaviour of time-dependent materials under periodical mechanical loading conditions (Vedenje časovno odvisnih materialov pri periodični mehanski obremenitvi)« (mentor: prof. dr. Igor Emri);

V doktorskem delu je predstavljena vzpostavljena metodologija, ki na osnovi poznavanja časovno odvisnih materialnih lastnosti omogoča napovedovanje trajnosti časovno odvisnih materialov, izpostavljenih periodični mehanski obremenitvi. Vzrok za porušitev

polimernih materialov pod vplivom periodične obremenitve sta dva različna mehanizma, ki sta oba rezultat njihovega časovno odvisnega vedenja; bodisi pride do lokalnega pregrevanja, kar ima za posledico drastično spremembo mehanskih lastnosti materiala in posledično njegovo porušitev, bodisi se zaradi časovno odvisnega vedenja materiala pojavi akumulacija deformacijskega stanja, ki prav tako lahko vodi do pojava razpoke in porušitve;

dne 11. julija 2011 Jože STROPNIK z naslovom: »Vezani termomehanski problem konzole v elasto-plastičnem območju« (mentor: prof. dr. Franc Kosel);

Zaradi dinamičnega obremenjevanja konzole v elasto-plastičnem območju se v njej generira toplota, kar povzroča časovno in krajevno spreminjanje temperature. Generirana toplota je odvisna od mehansko fizikalnih lastnosti in reološkega modela materiala ter od načina, frekvence in amplitude obremenitve. Sprememba temperature konzole je odvisna od načina vpetja in stopnje toplotne izolacije. V delu je izpeljan postopek za izračun količine generirane toplote. Za eksperimentalno preverjanje rezultatov je bila konstruirana in izdelana posebna naprava. Prikazana je primerjava časovnega in krajevnega poteka temperature v torzijsko obremenjeni konzoli med izračunanimi in eksperimentalno dobljenimi vrednostmi;

dne 12. julija 2011 Klemen OBLAK z naslovom: »Večparametrska geometrijska optimizacija elementov turbopuhala« (mentor: prof. dr. Franc Kosel);

Osrednja ideja doktorske disertacije bazira na večparametrski geometrijski optimizaciji z uporabo umetne inteligence, oziroma evolucijskih algoritmov na realnih industrijskih aplikacijah, v tem primeru na elementih radialnega ter aksialnega turbopuhala. Z eksploatacijo sodobnih programskih orodij in večprocesorskih računalnikov je bila izvedena optimizacija togosti ohišja na radialni napravi ter optimizacija tako radialnega kot tudi aksialnega turbinskega kolesa z ozirom na aerodinamični izkoristek. V nalogi je razložen princip parametričnega programiranja geometrije posameznih kompo¬nent in koncept metode končnih elementov ter končnih volumnov za numerično reševanje. Dalje je podano fizikalno ozadje problema vključno z diferencialnimi


SI 116

enačbami elastomehanike, če gre za ohišje, oziroma enačbami aerodinamike, če gre za turbinski kolesi. Rezultati meritev izdelanih prototipov pričajo o uspešnosti uporabljene metode;

dne 13. julija 2011 Mitja MUHIČ z naslovom: »Termomehanski popis razpok na orodjih za tlačno litje zaradi utrujanja« (mentor: prof. dr. Franc Kosel, somentor: prof. dr. Janez Tušek);

Orodja za tlačno litje so izpostavljena velikim dinamičnim termomehanskim obremenitvam in neugodnim kemičnim pogojem. Termomehanske obremenitve povzročajo velike koncentracije lokalnih napetosti in posledično nastanek površinskih razpok. Naloga predstavlja nov pristop popisovanja velikosti in rasti poškodb –razpok zaradi temperaturnega utrujanja na orodjih za tlačno litje z opazovanjem in merjenjem posledičnih napak – poškodb na ulitkih iz aluminijeve zlitine v dejanskem procesu proizvodnje tlačnega litja. Raziskava je pokazala, da so poškodbe – razpoke večje in se pojavijo prej, če je orodje izdelano iz materiala z nižjo trdoto. Razpoke na orodjih so pogostejše in večje bližje dolivku zaradi višjih temperatur in večjega pretoka taline ter na mestih spremembe geometrije (ostri prehodi z majhnimi radiji), kjer so prisotne velike koncentracije lokalnih napetosti, ki presegajo mejo plastičnosti in povzročajo akumulacijo plastičnih deformacij. Predstavljena je analiza materiala, iz katerega je izdelano orodje za tlačno litje in popis temperaturnega in napetostnega polja na orodju z numeričnimi simulacijami.

*

Na Fakulteti za strojništvo Univerze v Mariboru so z uspehom obranili svojo doktorsko disertacijo:

dne 8. julija 2011 Manja KUREČIČ z naslovom: »Sinteza nanokompozitnih hidrogelov v porah PP membrane« (mentorica: prof. dr. Majda Sfiligoj Smole);

Cilj naloge »Sinteza nanokompozitnih hidrogelov v porah PP membrane« je bil sintetizirati nanokompozitni hidrogel z vključenimi nanodelci mineralov glin v porah PP membrane s sposobnostjo razbarvanja tekstilnih odpadnih vod. V raziskavi smo uporabili organsko modificirane montmorilonit delce (O-MMT), katerih poglavitna lastnost je velika aktivna

površina, ki jo dosežemo ob interkalaciji oz. eksfoliaciji silikatnih plasti delcev v hidrogelni matrici. Raziskava je bila razdeljena v tri sklope; Prvi del je zajemal študij lastnosti hidrofobnih delcev dispergiranih v vodi z namenom doseganja stabilne vodne disperzije. Pri tem smo uporabili neionski polisaharidni površinsko aktivni sistem na bazi inulina, za izboljšanje omakalnih sposobnosti delcev glin in izboljšanje njihove sposobnosti dispergiranja v vodnih sistemih. Disperzijam O-MMT različnih koncentracij površinsko aktivnega sredstva smo določali elektrokinetične lastnosti, velikosti delcev in stabilnost disperzije. O-MMT delcem obdelanim s površinsko aktivnim sredstvom smo določali hidrofilno-hidrofoben značaj in strukturo z medoto malokotnega rentgenskega sipanja. V drugem delu smo UV polimerizirali nanokompozitni hidrogel s vključenimi O-MMT nanodelci, pri čemer smo uporabili N-isopropilakrilamid kot monomer ter N,N-metilenbisakrilamid kot zamreževalec. Pri tem smo spremljali vpliv deleža zamreževalca in vključenih nanodelcev v nanokompozitu na stopnjo zamreženja in na stopnjo nabrekanja nanokompozitnega hidrogela. S pomočjo FT-IR spektroskopije smo določili mehanizem polimerizacije in zamreženja hidrogela in z metodo malokotnega rentgenskega sipanja interkalirano/eksfoliirano strukturo delcev v nanokompozitu. Učinkovitost nanokompozitnega hidrogela smo določili s stopnjo adsorbcije kislega barvila C.I. Acid Orange 33 s pomočjo UV/VIS spektroskopije. Proučili smo vpliv pH barvne raztopine, konc. barvila, časa, in deleža O-MMT delcev v nanokompozitu na stopnjo adsorbcije barvila. V tretjem, zadnjem delu smo in-situ polimerizirali nanokompozitni hidrogel v porah hidrofobne polipropilenske (PP) membrane. Za doseganje popolne prekritosti por PP membrane s polimeriziranim nanokompozitnim hidrogelom smo raziskali vpliv različnih postopkov omakanja na delež gela v membrani in hidrofilno/hidrofobni značaj membrane. Sposobnost sintetizirane nanokompozitne PP membrane za razbarvanje raztopine kislega barvila C.I. Acid Orange 33 smo določali z ultrafiltracijo. Raziskave so pokazale, da ima koncentracija PAS velik vpliv na pripravo stabilne vodne disperzije O-MMT delcev. Z uporabo stabilne disperzije O-MMT delcev dobimo razplasteno strukturo nanokompozitnega hidrogela, ki je sposoben adsorbiranja kislega barvila Acid Orange 33. Z višanjem koncentracije delcev v nanokompozitnem hidrogelu se viša


SI 117

različni dejavniki, vsekakor pa sta to tako ergonomija kot tudi dojemanje oblike izdelka, njegove lepote, to je estetika izdelka. To je področje, ki ga obravnava pričujoča doktorska disertacija. Izsledki raziskav so namenjeni snovalcem novih izdelkov, ki bodo ob uporabi predlaganega modela inteligentne podpore v obliki izdelka lažje zajeli tako fiziološke karakteristike uporabnika, kot tudi njegove čustvene preference. Ob teoretičnem delu raziskav, katerih rezultat je zbrano in evidentirano znanje s problemskih področij, predložena doktorska disertacija obravnavna še sistematizacijo, formalizacijo in strukturiranje v obliki ontologije, katere osnovni model je bil razvit. Na osnovi zbranega znanja, pa je v jedru predstavljen model inteligentne podpore pri ergonomskem in estetskem razvoju izdelkov, katerega uporabnost je potrjena s praktičnimi testiranji. V zaključku strjene misli kratko povzemajo namen in pomen raziskovalnega dela, hkrati pa odpirajo nova vprašanja, ki nakazujejo nadaljnje znanstveno-raziskovalno delo na tem področju in obetajo izboljšanje že doseženih rezultatov;

dne 12. julija 2011 Blaž ŠAMEC z naslovom: »Življenjska doba zavornih diskov tirnih vozil pri termomehanskem obremenjevanju« (mentor: prof. dr. Iztok Potrč);

V predloženi doktorski disertaciji je razvit model za določitev življenjske dobe zavornih diskov tirnih vozil. Model temelji na predpostavki, da natančno poznamo hitrostni in višinski profil proge, na kateri bodo le-ti obratovali. Posledično to omogoča napovedovanje ciklov termomehanskega obremenjevanja, ki so vhodni podatek za določitev življenjske dobe zavornih diskov. Na osnovi zahtev računskih modelov za izračun življenjske dobe po deformacijski metodi je bila v sklopu doktorske naloge opravljena podrobna analiza materialnih lastnosti nodularne litine EN-GJS-500-7. Trdnostne lastnosti litine so bile analizirane z nateznimi preskusi pri sobni temperaturi (ST), 300, 350 in 400 °C. Malo-ciklični preskusi utrujanja so bili izvedeni pri ST, 300 in 400 °C, za te temperature so bili določeni malo-ciklični parametri, ki so potrebni za izračun življenjske dobe, in izrisane deformacijske krivulje zdržljivosti. Ugotovljeno je bilo, da povišana temperatura močno vpliva na življenjsko dobo analizirane nodularne litine. S pomočjo numerične analize po metodi končnih elementov so bila analizirana napetostna in deformacijska polja, ki nastanejo med zaviranjem na dejanskem

stopnja adsorpcije barvila. Z in-situ polimerizacijo smo uspešno pripravili nanokompozitno membrano s vključenimi O-MMT delci razplastenimi v hidrogelni matrici, kar izboljša filtracijsko sposobnost PP membrane za 80%;

dne 8. julija 2011 Boštjan GREGORC z naslovom: »Vpliv trdno-kapljevitih zmesi na obratovalne karakteristike hidravličnih strojev« (mentor: prof. dr. Andrej Predin);

Doktorska disertacija obravnava vpliv delcev na obratovalne karakteristike hidravličnih strojev. Zastavljen problem je določiti vpliv delcev na razvoj kavitacije in hrupa, ter zapisati matematično fizikalni model vključitve disperzne faze delcev na razvoj kavitacije v programskem okolju CFD. V delu je izdelana podrobnejša analiza disperznih delcev v rečni vodi, ter njihov vpliv na obratovanje treh različnih hidroelektrarn. V eksperimentalnih raziskavah je bila največja pozornost namenjena določitvi odvisnosti masne koncentracije delcev na razvoj kavitacije in hrupa. Poglobljene raziskave so potekale na določitvi vpliva delcev na začetno kavitacijsko število. Eksperimentalne meritve so nam bile vodilo za potrditev rezultatov numeričnega modeliranja. V CFD smo kapljevito in parno fazo zajeli kot zvezdno fazo. Delce v večfaznem toku smo opredelili kot disperzno fazo. Numerično modeliranje kapljevite, parne in disperzne faze je potekalo z Euler-Euler pristopom, na osnovi Navier Stokesovih enačb. Uporabili smo kavitacijski model zasnovan na podlagi Rayleigh-Plessetove enačbe. Zapisali smo fizikalno matematični model vpliva delcev na razvoj kavitacije, v katerega smo vključili disperzno fazo. Posebej smo se osredotočili na strižno viskoznost trdnine. S parametričnim pristopom smo definirali in zapisali empirični nastavek, v odvisnosti od masne koncentracije delcev. Rezultate numeričnega modeliranja večfaznega toka, smo primerjali z eksperimentalnimi rezultati;

dne 11. julija 2011 Jasmin KALJUN z naslovom: »Model inteligentne podpore pri ergonomskem in estetskem razvoju izdelkov« (mentor: izr. prof. dr. Bojan Dolšak);

Vsak izdelek, ki ga neko podjetje ponudi na trgu, mora zadovoljiti neko potrebo. Izdelek opravlja svojo glavno funkcijo v tehničnem smislu, hkrati pa mora zagotavljati tako uporabo, ki bo uporabniku nudila ugodje. V nasprotnem primeru, izdelek na trgu ne bo uspešen, kar so pokazale številne raziskave, nekatere omenjene tudi v tem delu. Na ugodje uporabnika vplivajo


SI 118

zavornem disku ter določeno kritično mesto konstrukcije le-tega. Na podlagi numeričnih rezultatov je bila z deformacijsko metodo izračunana življenjska doba zavornega diska v različnih obremenitvenih primerih za nov in obrabljen disk, pri čemer so bile ugotovljene dokaj velike razlike med posameznimi hipotezami, ki upoštevajo večosno napetostno stanje. Na koncu je podana še metodologija določitve življenjske dobe zavornih diskov pri vožnji na določeni progi oziroma hitrostnem sistemu.

MAGISTERIJ ZNANOSTI

Na Fakulteti za strojništvo Univerze v Mariboru je z uspehom zagovarjal svoje magistrsko delo:

dne 10. junija 2011 Janez POLANC z naslovom: »Lesni in gozdni sečni ostanki kot gorivo« (mentor: prof. dr. Niko Samec).

SPECIALISTIČNO DELO

Na Fakulteti za strojništvo Univerze v Mariboru so z uspehom zagovarjali svoje specialistično delo:

dne 13. junija 2011 Janez FERENC z naslovom: »Modifikacija avtobusa s sistemom za zagotavljanje varnostne razdalje« (mentor: izr. prof. dr. Stanislav Pehan);

dne 13. junija 2011 Andrej VAUPOTIČ z naslovom: »Analiza zmogljivosti proizvodnega procesa z metodo pretoka« (mentor: izr. prof. dr. Borut Buchmeister);

dne 13. junija 2011 Gregor KRANČAN z naslovom: »Konstruiranje pritrdilnega sklopa orodij za toplotno stiskanje jeklenih prahov« (mentor: izr. prof. dr. Bojan Dolšak);

dne 14. junija 2011 Damjan POŽUN z naslovom: »Vzpostavitev in obvladovanje proizvodnje, obratovanja in vzdrževanja v družbi hidroelektrarne na spodnji Savi« (mentor: prof. dr. Andrej Polajnar);

dne 16. junija 2011 Slavko FUJS z naslovom: »Analiza dobe trajanja aluminijastega tečaja hladilnega aparata« (mentor: prof. dr. Zoran Ren).

DIPLOMIRALI SO

Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva:

dne 22. junija 2011:Blaž LIKOVIČ z naslovom: »Računalniška

simulacija nezgodnega primera na jedrski eksperimentalni napravi« (mentor: izr. prof. dr. Mihael Sekavčnik);

Andrej ŽAGAR z naslovom: »Postopek preverjanja in overjanja adsorpcijskih sušilnikov zraka« (mentor: prof. dr. Vincenc Butala, somentor: doc. dr. Boris Jerman);

dne 27. junija 2011:Dominik GERDEJ z naslovom: »Študija

izvedljivosti sistema daljinskega ogrevanja na lesno biomaso« (mentor: prof. dr. Alojz Poredoš);

Matej GERKMAN z naslovom: »Modeliranje in idejna zasnova hidravličnega digitalnega ventila« (mentor: izr. prof. dr. Niko Herakovič);

Matija HRIBERŠEK z naslovom: »Obvladovanje procesov preoblikovanja folije z brizganjem poliuretana« (mentor: prof. dr. Karl Kuzman);

Urban TOMC z naslovom: »Poseben način transporta toplote v aktivnem magnetnem regeneratorju« (mentor: prof. dr. Alojz Poredoš, somentor: doc. dr. Andrej Kitanovski);

dne 28. junija 2011:Dominik MIKUŽ z naslovom: »Razvoj

konvencionalnega vložnega vodnega 4/3 potnega ventila NV4« (mentor: doc. dr. Jožef Pezdirnik);

Damir MOHORIČ z naslovom: »Razvoj visokotlačne vodne črpalke z ročičnim mehanizmom« (mentor: doc. dr. Jožef Pezdirnik);

Eneja OSTERMAN z naslovom: »Energetsko vrednotenje soproizvodnje toplote in električne energije v sistemu daljinskega ogrevanja« (mentor: prof. dr. Sašo Medved);

Tomaž ŠUKLJE z naslovom: »Računalniško orodje za vrednotenje energetskih kazalnikov stavb« (mentor: prof. dr. Sašo Medved).

*

Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva:

dne 30. junija 2011:Janko HRAŠAR z naslovom: »Vpliv

modulnih transportnih pripomočkov na proizvodnjo vgradnih kuhalnih plošč v Gorenju, d.d.« (mentor: prof. dr. Iztok Potrč, somentor: doc. dr. Tone Lerher);


SI 119

Rok JAMŠEK z naslovom: »Razvoj kombiniranega zalogovnika vode za toplotne črpalke« (mentor: doc. dr. Marjan Leber, somentor: doc. dr. Iztok Palčič);

Marko JENUŠ z naslovom: »Quadriga - stilsko oblikovanje karoserije avtomobila« (mentor: izr. prof. Vojmir Pogačar);

Boris KOZJAN z naslovom: »Uvajanje sistema vodenja kakovosti v malo proizvodno podjetje« (mentor: izr. prof. dr. Bojan Ačko, somentor: izr. prof. dr. Borut Buchmeister);

Mira ŠTUCL z naslovom: »Racionalizacija proizvodnje v podjetju Carrera Optyl« (mentor: doc. dr. Marjan Leber);

Dejan TAJNIKAR z naslovom: »Nadgradnja zavornega sistema tovornega priklopnega vozila« (mentor: doc. dr. Uroš Župerl, izr. prof. dr. Aleš Hace, somentor: doc. dr. Edvard Detiček);

Jure VIDMAR z naslovom: »Optimiranje konstrukcije jarma vozička za premikanje aluminijastih drogov« (mentor: prof. dr. Zoran Ren, somentor: asist. dr. Matej Borovinšek);

Martin VRBANČIČ z naslovom: »Analiza stroja za stiskanje panelov« (mentor: izr. prof. dr. Bojan Dolšak, Somentor: asist. mag. Jasmin Kaljun);

dne 5. julija 2011:Klemen LONČARIČ z naslovom:

»Uvajanje novega profilnega sistema v proizvodnjo podjetja Almont d.o.o.« (mentor: izr. prof. dr. Borut Buchmeister, Somentor: doc. dr. Marjan Leber).

*

Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva:

dne 08. junija 2011:Vincencij MARN z naslovom: »Raziskava

možnosti uvedbe robotizirane strege plošč kamene volne v procesu izdelave lahkih gradbenih plošč« (mentor: izr. prof. dr. Niko Herakovič);

Iztok PANTAR z naslovom: »Lasersko podprta izdelava oljnega sesalnega filtra« (mentor: prof. dr. Janez Možina, somentor: prof. dr. Janez Tušek);

Klemen Jože URBANC z naslovom: »Zasnova mehanskih sklopov stroja za dinamično preskušanje« (mentor: prof. dr. Marko Nagode);

Miha BERNIK z naslovom: »Varnost pri padalskih skokih s stališča mesebojnih

oddaljenosti« (mentor: pred. Miha Šorn, somentor: izr. prof. dr. Tadej Kosel);

Matej CEGLAR z naslovom: »Primerjava različnih programov osnovnega šolanja pilotov v Sloveniji« (mentor: pred. Miha Šorn, somentor: izr. prof. dr. Tadej Kosel);

Lijan PETROVČIČ z naslovom: »Hidravlična naprava mobilnega rezalno-cepilnega stroja« (mentor: doc. dr. Jožef Pezdirnik);

Sandi STAREŠINIČ z naslovom: »Konstrukcija in trdnostna kontrola nadgradnje šasije tovornega vozila ACTROS 4146« (mentor: viš. pred. mag. Jože Stropnik);

Matjaž ŠAJN z naslovom: »Simulacija letalnih lastnosti in program preizkušanja amatersko izdelanega zrakoplova Rand Robinson KR-1« (mentor: izr. prof. dr. Tadej Kosel, somentor: pred. Miha Šorn).

dne 9. junija 2011:Miran BOGATAJ z naslovom:

»Načrtovanje orodja za zabrizgavanje drsnega obroča« (mentor: izr. prof. dr. Zlatko Kampuš);

Klemen CERAR z naslovom: »Korekcija geometrijsko popačene slike pri merjenju izdelkov s kamero« (mentor: doc. dr. Henri Orbanić, somentor: prof. dr. Mihael Junkar);

Rok HOSTNIK z naslovom: »Vzletni vitel za jadralne padalce« (mentor: doc. dr. Joško Valentinčič, somentor: doc. dr. Samo Zupan);

Tomaž MAROLT z naslovom: »Vpliv parametrov okolja v kabini vozila na prometne nesreče« (mentor: prof. dr. Vincenc Butala);

dne 23. junija 2011:Tine LIKON z naslovom: »Kovičeni spoji

tankih pločevin sovprežnih nosilnih konstrukcij« (mentor: doc. dr. Boris Jerman);

Tomaž MRAK z naslovom: »Priprava tehnologije varjenja zaščitne cevke temperaturnega zaznavala« (mentor: prof. dr. Janez Tušek);

Dunja SEME z naslovom: »Razvoj nosilne konstrukcije in pogona sončnega sledilnika za foto-napetostne module« (mentor: prof. dr. Matija Fajdiga, somentor: prof. dr. Sašo Medved);

Erik ŠKRJANEC z naslovom: »Lasersko rezanje različnih vrst jeklenih pločevin« (mentor: prof. dr. Janez Tušek);

dne 24. junija 2011:Anže DERLINK z naslovom: »Pristanek

letala ob odpovedi motorja« (mentor: pred. mag. Borut Horvat, somentor: izr. prof. dr. Tadej Kosel);

Matic GOMBOC z naslovom: »Program šolanja in operativne omejitve uporabe očal za


SI 120

nočno gledanje v Letalski šoli Slovenske vojske« (mentor: pred. mag. Borut Horvat, somentor: izr. prof. dr. Tadej Kosel);

Darijo MARKOČIČ z naslovom: »Izbor turbinskega agregata HE Kneža« (mentor: prof. dr. Branko Širok);

David ŠKET z naslovom: »Biogoriva tretje generacije v Sloveniji« (mentor: izr. prof. dr. Andrej Senegačnik);

dne 27. junija 2011:Boštjan PIRC z naslovom: »Uporaba in

analiza škropilnih gasilnih sistemov« (mentor: izr. prof. dr. Kazimir Jurij Modic);

Klemen RUPNIK z naslovom: »Načrtovanje orodja za namenski stroj za izdelavo kontaktnega obroča« (mentor: izr. prof. dr. Zlatko Kampuš);

Luka ŠEMOLE z naslovom: »Posebnosti tehnologij in orodij za večkomponentno brizganje termoplastičnih polimerov« (mentor: prof. dr. Karl Kuzman);

Jure VERDERBER z naslovom: »Trirazsežno tiskanje za hitro izdelavo prototipov in končnih izdelkov« (mentor: prof. dr. Janez Kopač, somentor: izr. prof. dr. Slavko Dolinšek);

Samo ZORMAN z naslovom: »Primerjava zanesljivosti delovanja sistemov za dovod goriva na letalih CRJ-200 in CRJ-900« (mentor: doc. dr. Tomaž Katrašnik);

dne 28. junija 2011:Robert ADAMIČ z naslovom:

»Optimizacija hlajenja tankih jeder na sodobnem 4-gnezdnem orodju za tlačno litje aluminijevih zlitin« (mentor: prof. dr. Janez Kopač, somentor: doc. dr. Franci Pušavec);

Gregor KAVČIČ z naslovom: »Sprememba orodja pri prehodu tehnologije litja rotorjev iz vertikalnih na horizontalne stroje« (mentor: prof. dr. Janez Kopač, somentor: doc. dr. Davorin Kramar);

Aleksander MORAVEC z naslovom: »Izboljšave na orodju za brizganje hladilnika reflektorja« (mentor: prof. dr. Janez Kopač, somentor: doc. dr. Davorin Kramar);

Marko PEČNIK z naslovom: »Nova izvedba tesnjenja sušilnega stroja« (mentor: prof. dr. Mirko Soković);

Franc TOMC z naslovom: »Zagotavljanje kakovosti pri obračunavanju storitev in dobav« (mentor: prof. dr. Mirko Soković);

dne 30. junija 2011:Romana BEGOVIĆ z naslovom: »Izračun

zmogljivosti letala z vertikalnim vzletom in pristankom« (mentor: prof. dr. Franc Kosel, somentor: doc. dr. Viktor Šajn);

Jure NOWAK z naslovom: »Analiza obstoječega športnega letališča z možnostjo nadgradnje instrumentalnega postopka vodenja letal na pristanek ob upoštevanju vplivov hrupa« (mentor: pred. Miha Šorn, somentor: izr. prof. dr. Tadej Kosel);

Tadej TROJNER z naslovom: »Optimiranje hitrosti planiranja pri preletu jadralnega letala« (mentor: prof. dr. Franc Kosel, somentor: doc. dr. Viktor Šajn);

*

Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva:

dne 24. junija 2011:Milan DEUČMAN z naslovom: »Zasnova,

montaža in strega CNC-obdelovalnega stroja« (mentor: izr. prof. dr. Miran Brezočnik, somentor: doc. dr. Mirko Ficko);

dne 30. junija 2011:Luka ČOKL z naslovom: »Računalniško

podprto konstruiranje in modeliranje roke za rotacijski nanos zaščitne obloge« (mentor: izr. prof. dr. Bojan Dolšak, somentor: viš. pred. dr. Marina Novak);

Jure GRAJNER z naslovom: »Priprava podjetja na recertifikacijo sistema vodenja« (mentor: izr. prof. dr. Bojan Ačko, somentor: prof. dr. Nenad Gubeljak);

Aleksander STANOJEVIĆ z naslovom: »Sodobni postopki preoblikovanja pločevine za maloserijsko proizvodnjo« (mentor: izr. prof. dr. Ivan Pahole, somentor: izr. prof. dr. Borut Buchmeister);

Tilen STRAŠEK z naslovom: »Preračun mostnega žerjava v podjetju Satler d.o.o« (mentor: red. prof. dr. Iztok Potrč, somentor: izr. prof. dr. Miran Brezočnik , doc. dr. Tone Lerher);

Aljoša URNAUT z naslovom: »Določitev postopkov obdelave za ventil K400« (mentor: prof. dr. Franci Čuš).

Vojko VOLAVŠEK z naslovom: »Uvedba črtne kode v podjetju Eurel, d.o.o.« (Mentor: prof. dr. Iztok Potrč, Somentor: doc. dr. Tone Lerher, izr. prof. dr. Miran Brezočnik).

journal of mechanical engineering 2011 7-8

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