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Platnica SV-JME 57(2011)4_kor1.ai 1 6.4.2011 10:55:23Platnica SV-JME 57(2011)4_kor1.ai 1 6.4.2011 10:55:23

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

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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 – The 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/.

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We would like to thank the reviewers who have taken part in the peer-review process.

Cover: An independent wire rope core (IWRC) is composed by a simple straight strand as the core and six outer strands. Outer strands includes both single and nested helical wires. This figure is composed to show a right lang lay IWRC from different aspects. An IWRC is used as a core component to compose more complex wire ropes such as Seale and Warrington type.

Image courtesy: Cengiz Erdönmez

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)4Contents

Contents

Strojniški vestnik - Journal of Mechanical Engineeringvolume 57, (2011), number 4

Ljubljana, April 2011ISSN 0039-2480

Published monthly

Papers

Cengiz Erdönmez, Cevat Erdem İmrak: Modeling Techniques of Nested Helical Structure Based Geometry for Numerical Analysis 283

Jinpeng Chen, Marko Hočevar, Brane Širok: Melt Volume Flow Measurement in the Mineral-Wool Production Process 293

Milomir M. Gašić, Mile M. Savković, Radovan R. Bulatović: Optimization of Trapezoidal Cross Section of the Truck Crane Boom by Lagrange’s Multipliers and by Differential Evolution Algorithm (DE) 304

Gregor Škorc, Jure Čas, Simon Brezovnik, Riko Šafarič: Position Control with Parameter Adaptation for a Nano-Robotic Cell 313

Jacek Mucha: A Study of Quality Parameters and Behaviour of Self-Piercing Riveted Aluminium Sheets with Different Joining Conditions 323

Sebastjan Žagar, Janez Grum: Surface Integrity after Mechanical Hardening of Various Aluminium Alloys 334

Abdelhamid Saoudi, Mohamed Bouazara, Daniel Marceau: Fatigue Failure Study of the Lower Suspension Vehicle Arm Using a Multiaxial Criterion of the Strain Energy Density 345

Tatjana Šibalija, Vidosav Majstorović, Mirko Soković: Taguchi-Based and Intelligent Optimisation of a Multi-Response Process Using Historical Data 357

Instructions for Authors 366

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)4, 283-292 Paper received: 09.01.2009DOI:10.5545/sv-jme.2009.006 Paper accepted: 12.01.2011

*Corr. Author’s Address: Institute of Informatics, Computational Science and Engineering Program, Maslak, Istanbul, Turkey, [email protected] 283

Modeling Techniques of Nested Helical Structure Based Geometry for Numerical Analysis

Erdönmez, C. - İmrak, C.E.Cengiz Erdönmez1,* - Cevat Erdem İmrak2

1 Istanbul Technical University, Institute of Informatics, Turkey 2 Istanbul Technical University, Faculty of Mechanical Engineering, Turkey

The aim of this paper is to introduce a new methodology of defining and modeling the nested helical structure (NHS) for wire ropes, and to present an accurate wire rope 3D solid modeling, which can be used for finite element analysis. Both single and nested helical wire parametric equations are presented. Derivation of the Frenet-Serret frame for the helical structures is explained, which enables one to define a normal plane along the centerline of a single helical or nested helical curve in 3D space. Both single helical and nested helical solid structures are generated by sweeping a circle or a quadrilateral by using the moving trihedron along the centerline of the helical geometry. When the length of the NHS is increased, surface quality of the NHS diminishes rapidly and it is not possible to generate a good mesh by using the commercial CAD tools. However, the proposed method introduces a solution of modeling helical structures without length limitation with generating an accurate and valid mesh. Illustrative examples are presented to show the benefits of the proposed modeling procedure by using finite element analysis.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: nested helical structure, nested helix, single helix, double helix, Frenet-Serret frame

0 INTRODUCTION

Helix geometry is one of the interesting curves among the space curves in 3D spaces. Some structures such as screws, DNA molecules, and wire ropes have helical substructures. The general form of a helix can be referred to as a single helix. It is effortless to construct and model a single helical geometry using the commercial CAD software. Coiling a helix around another creates a new geometry, which can be called double helical or nested helical structure. The word double helix is not defined explicitly at the moment. Double helix is used mostly for the DNA molecules and structures in the literature [1] to [3]. A double helix typically consists of two similar helices with the same axis, differing by starting angle along the axis. Intertwined helices with different radii, i.e. successive layers vary in their radii to guarantee the maximum possible geometric distance in DNA molecules. For this reason, the complicated new type of helix which is nested over a single helix is called a nested helix (NH) throughout this paper so as to distinguish these two helical structures. The structures produced using NH are called nested helical structures (NHS). The use of helical wires can be seen widely in the construction of wire

ropes. Mechanical and structural compositions are analyzed analytically in a number of papers [4] to [6].

Meanwhile, it is difficult to construct a NHS by using commercial CAD tools. In this paper, first a general definition of the helix is discussed and then the parametric representation of the NH is presented. A normal plane perpendicular to a curve is defined using the Frenet-Serret frame [7], which is known as the moving triad. Modeling a solid wire using NHS, which enables the production a valid meshed solid model to use during finite element analysis (FEA) is introduced. The aim of this paper is to exhibit a new methodology to model NHS and remove the difficulties encountered during modeling and numerical analysis of wire ropes. Finally, a wire strand and an independent wire rope core (IWRC) are modeled and analyzed using the proposed method.

1 GENERAL DEFINITION OF HELICAL GEOMETRIES

Helix as a space curve in R3 is defined solely with the following Eq.:

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)4, 283-292

284 Erdönmez, C. - İmrak, C.E.

x ry r

z p

==

=

cos ,sin ,

,

θθ

θπ2

(1)

where θ, r, and p represents the turning angle and radius and pitch length of the helix, respectively. A general helix geometry is depicted in Fig. 1. The helix angle α is related with the pitch length of the helix p directly with tan α = p / (2πr). A helix with a length of L can be generated by computing the number of as ω = L / p along its length where p corresponds to the pitch length of the helix. The helix angle θ has to sweep an angle starting from θ = 0 to θ = ω·2π for producing a helical structure of length L. In this way, the desired helical curve is generated.

Fig. 1. General helix geometry

1.1 Nested Helical Geometry

Cartesian coordinate system (x, y, z) with the Cartesian frame {ex, ey, ez} is used to define the location of the centerline of a single outer helix by:

x ry rz r

s s s

s s s

s s s s

===

cos ,sin ,

tan .

θθ

θ α

(2)

The helix lies along the ez axis while the radius of the single helix and laying angle are defined as rs and αs respectively. Free angle θ defines the location of the wire around the rope axis ez relative to ex and the single helix phase angle is defined as θ0 = θ(z=0). Using the free angle

θ and the phase angle θ0, helix angle of the single helical wire is defined as θs = θ0 + θ. Angle θs is used to define both the single helical wire angle of strand 1 and the outer single helical wire angle of the strand 2 as depicted in Fig. 2a.

The outer nested helical wires on strand 2 are wound around the outer single helical wire by using the centerline of the single helical wire defined in Eq. (2) by using the angle of θd. Centerline of the nested helical geometry is depicted in Fig. 2a and defined by the following parametric Eq. [8]:

x x ry y r

d s d d s d s s

d s d d s

= + −= + +

(cos cos sin sin sin ),(cos sin s

θ θ θ θ αθ θ iin cos sin ),

sin cos ,θ θ α

θ αd s s

d s d d sz z r= −

(3)

where θd = m·θs + θd0 is the NH wrapping angle around the single helical wire centerline while m is the construction parameter, which is the ratio of the nested helical wire rotating angle to the single helical wire rotation angle, m = θd / θs , and θd0 is the wire phase angle. The distance rd is defined by the distance between the NH centerline and the single helix centerline as shown in Fig. 2a. In addition, the solid model of the nested helical wires around a single helical wire centerline is presented in Fig. 2b. According to Eq. (3) a right lay NH can be constructed. To construct a left lay NH, it is enough to negate one of the coordinate values of xd or yd which are defined in Eq. (3).

1.2 A Moving Trihedron and Plane Construction

Frenet-Serret expression describes the kinematic properties of a particle, which moves along a continuous, differentiable curve in 3D Euclidean space R3. Frenet-Serret frame [7] is used to construct a normal plane, which is perpendicular to the single helical or NHS to construct a 3D solid part.

Let I R⊂ be an interval and ψ : I → R3 be a parameterized space curve, assumed regular and free of inflection points. ψ(θ) is the trajectory of a particle moving through 3D space. The moving trihedron, known as the Frenet-Serret frame, corresponds to an orthonormal basis of three vectors; T(θ), N(θ) and B(θ). The unit tangent vector T(θ), the unit binormal vector B(θ) and the unit normal vector N(θ) can be defined respectively,


285Modeling Techniques of Nested Helical Structure Based Geometry for Numerical Analysis

T ( )( )

( ),θ

ψ θ

ψ θ=

′

′ (4)

B( )( ) ( )

( ) ( ),θ

ψ θ ψ θ

ψ θ ψ θ=

′ × ′′

′ × ′′ (5)

NB

B( )

( ) ( )

( ) ( ).θ

θ ψ θ

θ ψ θ=

× ′

× ′ (6)

The line ψ(θ) + tT(θ) is the tangent line at ψ(θ). Here t R∈ represents a parameter corresponding to create the tangent line in a given range. The binormal vector B(θ) is perpendicular to both ψ′(θ) and ψ″(θ) and hence perpendicular to the osculating plane. The line ψ(θ) + tB(θ) is the binormal line at ψ(θ). Finally, the normal vector is the vector perpendicular to both tangent and binormal vectors with its direction determined by the right-handed system. The line ψ(θ) + tN(θ) is the normal line at ψ(θ). Therefore, tangent vector T(θ), normal vector N(θ) and binormal vector B(θ) form a coordinate system with origin ψ(θ). The tangent line, normal line and binormal line are the three coordinate axes with positive directions given by the TNB vectors, respectively. These three vectors are usually referred to as the moving trihedron or triad at point ψ(θ).

The single helical curve for a strand can be written as in vector notation by ψ(θs),

ψ θ θ θ θ( ) ( cos , sin , ).s s s s s sr r h= (7)

Vector notation of the nested helical wire centerline can be written as in vector notation by ψ(θd),

ψ θ θ θ θ θ θ α

θ θ

( ) ( cos cos sin sin sin ,

cos sind x r r

y rs s d d s d d s s

s s d d

= + −

+ θθ θ θ α

θ αs d d s s

s d d s

r

z r

+

−

sin cos sin ,

sin cos ),

(8)

where θd = m·θs + θd0. The tangent, binormal and normal vectors for a single helical wire and NHS can be found by substituting Eqs. (7) and (8) into Frenet-Serret formulas given in Eqs. (4) to (6) respectively. The tangent line (ψ(θ) + tT(θ)), the normal line (ψ(θ) + tN(θ)) and the binormal line (ψ(θ) + tB(θ)) can be obtained with respect to θs for single and nested helical wires, respectively. Using the definition of tangent, binormal and normal lines, three points to construct a circle on a plane can be obtained, which is perpendicular to the single helix or NH centerline.

1.3 A Single Helical or NH Solid Part Construction

The idea of using single helical or NH wire centerline to construct a solid part is based on the difficulties experienced at the modeling and analysis stages. Single helical geometry design can be easily done using the well-known

Fig. 2. IWRC; a) single and nested helical wire centerlines, b) solid model of the nested helical wire



CAD packages while the NHS is not available as a simple tool to use. NHS can be seen mostly in rope constructions at first glance. To have a NHS, a strand is wrapped over another one in a helical manner as shown in Fig. 2a. To perform the numerical analysis over this kind of structure, a fully defined model of the problem should be prepared and converted into an acceptable form for numerical analysis. Problems have been encountered at the modeling and analysis stages in different areas;• Creating NHS is not possible by using CAD

tools directly for the moment,• Exporting NH geometry using CAD software

in acceptable format for FE analysis software destroys some portion of the solid structures,

• Meshing is not possible due to irregularities on the surfaces of NH geometries,

• It is impossible to export NH geometries properly to the FE code file format and meshing the solid geometries using the FE codes encounters difficulties.

To illustrate the aforementioned problems, a single helical and NH geometries are modeled with the lengths of 300 mm and 1000 mm by using SolidWorks® and transferred to finite element code Abaqus/CAE® using IGES and Parasolid file formats. It should be emphasized that the procedures mentioned in this paper are evaluated by using different modeling and analysis tools such as CATIA® and ANSYS® but similar results are found for the helical geometries.

Single helical parts can be generated by using the helix tool available in the library of SolidWorks and the produced single helical part can be meshed in Abaqus/CAE. Meanwhile, there is no available tool for modeling NHS in CAD packages. For this reason, NHS are modeled by using parametric equations via the explicitly written script codes for CAD packages, and then exported to FE analysis file format.

Figs. 3 and 4 have the same number of rows and columns. Column (a) represents helices created in SolidWork, columns (b) and (c) represent imported forms of IGES and Parasolid file formats in Abaqus/CAE respectively and, column (d) represents the helical geometry generated by using the parametric equations in HyperMesh®.

A new code is developed in Matlab to generate single helical/NH wire locations with the control nodes. These control nodes are exported to HyperMesh and using these control nodes, a spline is generated. Then, a normal plane perpendicular to this spline curve is generated by using the Frenet-Serret frame defined in Eqs. (4) to (6). A circle is created over this plane and swept along the single helical/NH curve centerline, which creates the meshed part in HyperMesh as shown in column (d) of Figs. 3 and 4. It has been concluded that the solid wire geometry is spoiled out when the number of control nodes and the length of wire are increased. This situation is demonstrated by comparing the cross sections of the columns (b) and (c) with item numbers (1) and (3) of Figs. 3 and 4 respectively. Comparing these figures, it can be seen that the solid structures are degenerated while the part lengths are increased from 300 mm to 1000 mm. As a result, comparisons of the solid and meshed parts quality scales are given at the last columns of Figs. 3 and 4. It can be seen that the NH mesh quality is better than that of the others. This is evaluated while using NH mesh generated by HyperMesh in FE analysis code.

While meshing the solid parts, errors occurred in FE software due to the complex geometry of the mesh region for sweep meshing. It has been reported that the meshed parts are in unusable quality in FE analysis, which is the main problem of meshing NHS. These problems do not occur while using the proposed modeling procedure using HyperMesh. To see the problematic meshed surfaces closely, the front view of item (4) – column (b) of Fig. 4 is presented in an enlarged form in Fig. 5.

The meshed surface is degenerated and it is unusable for FE analysis. Using the proposed modeling procedure, single helical and NH meshed structures are created with success by using HyperMesh as in Fig. 6. It can be clearly seen that the meshed parts are precisely defined. It has been concluded that the NH meshed parts generated using this method are error free and that this procedure is the effective choice for generating helical parts for the FE analysis purposes.



Fig. 4. NHS solid models created with SolidWorks and meshed with Abaqus/CAE, and NHS modeled and meshed with HyperMesh

Fig. 3. Single helix solid model created with SolidWorks and meshed using Abaqus/CAE, and model&mesh created with HyperMesh



Fig. 5. Zoomed front view of a NH wire

a) b)Fig. 6. a) single helical, b) NH meshed solid parts

in Abaqus/CAE

1.4 Construction of a Complex Single Helical and NH Wire Mesh

During the modeling issue, it was observed that finite element software needs smooth and precisely defined solid meshed surfaces. Meanwhile, the commercial CAD package is not suitable for the construction of NH geometry because of the irregularities that appeared at the meshing stage. FE analysis code needs precisely meshed solid models. Therefore, the idea of designing a meshed model of the single helical and NH wire is proposed as a solution. An algorithm to develop a meshed model of a single or NH wire is presented in Fig. 7. The algorithm includes mainly four stages:• geometry generation,• solid Part and Mesh generation,

• model generation,• analysis of the result processing.

In the geometry generation stage, a new code is developed to find the single helical or NH control nodes using Eq. (1) or Eqs. (2) and (3), respectively. To construct a solid geometry, a normal plane which is perpendicular to the single helical/NH spline curve is needed. Frenet-Serret frame is constructed over the single helix/NH curve using the Eqs. (4) to (6) by substituting Eqs. (7) and (8) respectively. Using the Frenet-Serret equations tangent, normal and binormal lines as depicted in Fig. 2a are defined and three points are generated to construct a plane perpendicular to the helical spline curve using these points. At the end of the geometry generation stage, the control nodes to construct single/NH wire and the nodes to build a plane perpendicular to the single helical/NH wire is output to a file in “*.inp” file extension as shown in Fig. 8.

Solid part and mesh generation stages compose the main parts of wire strand/rope generation procedure. The “*.inp” file, which holds the helical geometry, is imported into the HyperMesh. A spline is constructed using the control nodes corresponding to the single/NH wire. The normal plane defined by Frenet-Serret formulae is used to create a circle, which is perpendicular to the helical wire centerline. The surface of this 2D circle geometry is divided by quadratic brick elements of type C3D8R, which are dragged along the helical wire path to construct a meshed single helical/NH wire model. The generated shape is constituted with meshes and evaluated as orphan mesh in Abaqus/CAE. At the end of this operation, meshed helical wire geometry is exported to finite element model structure with “*.inp” file format, which can be imported by Abaqus/CAE.

In the model generation stage the orphan mesh geometry is imported in Abaqus/CAE which is constructed by using HyperMesh as mentioned above. It can be concluded that the wires developed by using the proposed method are well defined without length limitation and free of surface irregularities. While defining the contacts between wires using the generated meshes in IGES/Parasolid file formats, errors are encountered because of the conflicts between the wires due to irregular meshed surfaces. The new



NH meshed model gets rids of such problems, defining precise surfaces. Analysis stage can be conducted with the produced mesh of the wire strand/rope model.

Fig. 8. Geometry definition in Abaqus/CAE file format

After the solid part and mesh generation stage, assembly of the simple straight strand is composed by wrapping six single helical wires around a straight wire. Then, a single outer helical wire and six NH wires surrounding it are imported.

This composes an outer strand of an IWRC, which is assembled around the center straight strand to compose the complete final wire rope model shown in Fig. 9. It can be clearly seen that the wire rope structure includes 36 NH wires, which makes the FE analysis complicated. The number of nodes and elements also exceeds 200,000. Boundary conditions, load definitions, material properties, and contact controls are defined in Abaqus/CAE and the created job is submitted for the analysis of the proposed problem. Finally, the FE analysis result file is processed to produce numerical results for the solved problem using Abaqus/CAE viewer.

2 FINITE ELEMENT ANALYSIS OF THE WIRE STRAND/ROPE MODEL

In this section, an axial wire strand/rope FE analysis stage is presented. Material properties are defined based on the previous study of Jiang [9].

Fig. 7. Generating the NHS model and analysis algorithm



Fig. 9. A left Lang lay meshed wire rope structure

During the FE analysis models 8 nodes quadratic brick elements of type C3D8R are used. One side of the model is constraint to be a fixed boundary condition, while the other side is constraint not to rotate only in z axis. A friction coefficient of µ = 0.115 is defined. An explicit analysis is conducted over the model. A 28.75 mm length (6+1) Wire Strand (WS) is analyzed first with R1 = 1.97 mm, R2 = 1.865 mm and pitch length is p2 = 115 mm. Surface to surface contact is defined between center and six helical wires and between individual helical wires by considering the frictional effects. An axial strain of ε = 0.03 is applied to the non-rotating end of the model. Finite element analysis results show that a helical line of contact occurs between the center wire and the outer helical wires, and between consecutive helical wires of the strand as shown in Fig. 10a. The numbers of 42,818 C3D8R type elements are used in Fig. 10a. The mesh is refined to 196,524 number of C3D8R type elements and a more smooth helical line of contact between wires are obtained as shown in Fig. 10b.

As a second example, 300 mm length 6 × 7 Right Lang Lay (RLL) Independent Wire Rope Core IWRC is modeled, using the proposed modeling procedure. Wire radiuses are defined as R1 = 1.97 mm, R2 = 1.865 mm, R3 = 1.6 mm, R4 = 1.5 mm, pitch lengths are defined as p2 = 70

mm, p4 = 193 mm and p2* = 70 mm. An axial strain of ε = 0.015 is applied to the non-rotating end of the model. Wire by wire based FE analysis results are presented in Fig. 11. Analysis shows that the core wire of the IWRC holds the most of the axial force among the wires within an IWRC. In addition, the core strand of the IWRC encounters the maximum amount of load distribution during the axial loading process. These illustrative examples show that the proposed modeling and analysis procedure give the desired information about the behavior of wires within a wire rope. The proposed modeling scheme can be developed to solve more difficult wire rope problems, such as wire rope bent over sheave. From this point of view, it would be worth improving the present study for further use.

3 CONCLUSIONS

A new methodology and algorithm of constructing single and nested helical geometries are described in this paper. The problems faced during the model generation and meshing stages of helical structures are described and the solution strategies are argued. Instead of modeling a single helical or NH solid structure and meshing, it is proposed to model them directly as an orphan mesh by using the parametric mathematical



definitions of the single helical and NHS. In this manner, problems encountered in the surfaces of the helical wires are discarded at the source of the modeling stage. The proposed procedure for modeling is presented and discussed with illustrative examples. This process removes the surface irregularities encountered over the complex helical structures and generates precise

geometries. Data losses are obstructed while transferring solid parts between CAD package and finite element software by this proposed modeling strategy and algorithm. At the same time, the length limitations are left behind. The proposed procedure creates precise geometries without length limitations at all. Finally, FE analysis examples are presented to show the benefits of

a) b)Fig. 10. a) contact force distribution over a simple straight strand, b) line of contact over the center wire

with a fine mesh

Fig. 11. A right Lang lay 6x7 IWRC 300 mm, axial force-strain FE analysis result



the proposed modeling scheme. A wire strand is analyzed using the axial loading problem. The results of FE analysis show that there is a helical line of contact between wires within a strand. Another example is solved on a 6 × 7 wire RLL IWRC. Wire by wire axial force distribution is graphed by using the results of the FE analysis, which gives detailed information about the behavior of the wires within an IWRC. These examples demonstrate the benefits of FE analysis using the proposed modeling scheme. Further studies can be conducted by using the proposed modeling procedure to obtain detailed information about helical structures. In addition, the present modeling technique can be developed and used for further studies.

4 REFERENCES

[1] Metzler, R., Dommersnes, P.G. (2004). Helical packaging of semiflexible polymers in bacteriophages. European Biophysics Journal, vol. 33, no. 6, p. 497-505.

[2] Meng, X., Li, J., Hou, H., Song, Y., Fan, Y., Zhu, Y. (2008). Double helix chain frameworks constructed from bis-benzotriazole building blocks: Syntheses, crystal structures and third-order nonlinear optical properties. Journal of Molecular Structure, vol. 891, no. 1-3 , p. 305-311.

[3] Luo, F., Che, Y., Zheng, J. (2006). Synthesis and description of the first helical chain of Cu–Pb bimetallic atoms and Cu(I)–Cu(II) mixed-valence. Inorganic Chemistry Communications, vol. 9, p. 848-851.

[4] Costello, G.A., Sinha, S.K. (1977). Static Behaviour of Wire Rope. Proceedings ASCE, Journal of Engineering Mechanical Division, vol. 103, no. EM6, p. 1011-1022.

[5] Velinsky, S.A. (1993). A stress based methodology for the design of wire rope systems. Transactions of ASME, Journal of Mechanical Design, vol. 115, p. 69-73.

[6] Velinsky, S.A. (1988). Design and mechanics of multi-lay wire strands. Transactions of ASME, Journal of Mechanics, Transmissions, and Automation in Design, vol. 110, p. 152-160.

[7] Frey, J.P., George, P.-L. (2000). Mesh Generation application to finite elements. Hermes Science Publishing, Oxford.

[8] Elata, D., Eshkenazy, R., Weiss, M.P. (2004). The mechanical behavior of a wire rope with an independent wire rope core. International Journal of Solids and Structures, vol. 41, p. 1157-1172.

[9] Jiang, W.G., Henshall, J.L. (1999). The analysis of termination effects in wire strand using finite element method. Journal of Strain Analysis, vol. 34, no. 1, p. 31-38.


*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, [email protected] 293

Melt Volume Flow Measurement in the Mineral-Wool Production Process

Chen, J. ‒ Hočevar, M. ‒ Širok, B.Jinpeng Chen1 - Marko Hočevar2,* - Brane Širok2

1 Lanzhou Polytechnical College, Faculty of Electrical Engineering, Kitajska 2 University of Ljubljana, Faculty of Mechanical Engineering, Slovenija

The quality of the end product in mineral wool production depends on the fiberisation process on the spinning machine. An important process variable is the fluctuation of melt volume flow from the melter. In this paper, a method for measuring melt volume flow, which is based on the measuring the diameter and flow velocity using machine vision, is presented. The velocity is measured by measuring the time of the travel of flow disturbances on two consecutive images using a correlation method. The flow disturbances are generated using a pneumatic system. The results of laboratory calibration using water as well as the results of field measurements in a mineral wool plant are presented. The field measurements were performed by comparison with the weight of the final product. The results of laboratory calibration show agreement with reference volume flow measurements with R2 = 0.96 for water. The agreement among field measured values and available comparison method is also very good.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: mineral wool, melt, volume flow measurement, machine vision

0 INTRODUCTION

Mineral-wool is a general name given to many inorganic insulation materials made of fibres. It is widely used in the industry owing to its excellent properties in sound- and thermal insulation. There are several production methods for mineral wool [1]. The most commonly used mineral-wool production process is the fiberisation process of molten rock, which melts in a cupola or tub furnace on quickly rotating spinning discs. Molten rock enters through a siphon neck into a homogenization reservoir. Over the weir and directing channel, the molten rock falls under gravity onto the rotating discs of the spinning machine. Fabrication of mineral wool occurs on the spinning machine, as the melt droplets separate from the rotating wheels and are fiberised by high-speed airflow around the wheels. Using high-speed airflow that is fed coaxially over the disc, fibres are transported away from the spinning machine and thrown into a forming chamber. After leaving it, mineral wool enters the secondary conveyor belt where it is thermally treated in the polymerization chamber and finalised/cut to selected density, thickness and size.

The continuous melt volume flow measurement is desired for the regulation of the melter operation and for the regulation of the velocity of mineral wool product line. Melt volume flow fluctuations directly affect the quality of the final product of mineral-wool. Continuous melt volume flow measurements enable the regulation of product line velocity, which is important for compensating the density variations in the final product due to variations of melt volume flow from the melter.

Measurements of melt volume flow using conventional methods are not possible due to very high temperature of the melt. Temperature of the melt usually ranges from 1380 to 1500 °C, and melt dynamic viscosity μ from 15 to 8 dPa·s, surface tension σ from 0.439 to 0.410 N/m, and range of volume flows from 3 to 5.5 t/h. Currently, no reliable measurement method capable of instantaneous measurements of melt volume flow from the melter, is available. The following methods are used with limited success: measurement of the current consumed by the spinning machine electric motors [2], volume flow measurement using radioactive isotopes, weighing of primary wool layer [3] and [4], and weighing of the final product. The current consumed by the spinning machine electric motors depends on


294 Chen, J. ‒ Hočevar, M. ‒ Širok, B.

the melt volume flow as well as on the melt flow impingement point position, vibrations of wheels, etc. Volume flow measurement by radioactive isotopes is not used anymore due to safety and environmental concerns. Weighing of primary wool layer has proved unreliable due to a very low ratio of weight of the primary wool layer and weighing device, deposition of dirt and vibrations. The measurement results of weighing the final product are only available several minutes later, which is not suitable for production line speed control.

In this paper, a new method for measuring the volume flow of the melt in front of the spinning machine (Fig. 1) in the process of mineral wool production is presented. The volume flow is calculated from the measured values of diameter and velocity of melt flow. Due to very high temperatures, these variables are measured by acquiring images with industrial camera and by image analysis. Diameter is measured by detecting the border of melt flow, while velocity is measured from the measurement of time of travel of flow disturbances on two consecutive images using correlation method.

The method of velocity measurements is similar to flow measurement methods based on correlation and particle image velocimetry (PIV) [5]. A review of the PIV method development is given in [5] and [6]. PIV method enables quantitative measurement of fluid velocity vectors at a very large number of points simultaneously. Research focuses on the correlation of two successive scalar gray intensity images for the purpose of measuring imaged fluid motions. Authors employ various techniques of image processing among which are locally correlates images for displacements, rotations, deformations, and higher-order displacement gradient fields [7]. For a high amount of details on images, particle image analysis method is preferred in relation to particle tracking method [8]. Application of PIV is broad, Cheng et al. [8] algorithm was based on computing the cross correlation of bubble images with multiple spatial resolutions for bubbles flow in the tank, Zosel et al. [9] used μPIV for measurement of flow in micro holes and Hann et al. [10] used PIV for the measurement of flow velocity and acoustic particle velocity in a standing wave tube. Among measurements of

jets, Patte-Rouland et al. [11] used PIV method with orthogonal decomposition of a jet in the recirculation region, Hui Hu et al. [12] studied the mixing process in a lobed jet flow, and Sakakibara et al. [13] performed measurements of the particle/fluid velocity correlation and the dissipation of turbulent kinetic energy by particles. Cross correlation techniques are also used for flow velocity and volume flow rates measurement with other measurement principles [14]. Among those, Carlson and Ing [15] used ultrasonic speckle correlation imaging for flow velocity measurement in a vertical pipe, and Takamoto et al. [16] used ultrasonic correlation technique for measurements for very low volume flow rates.

The disturbances are detected if they are already present in the flow or if they are generated using a pneumatic disturbance generation system. Disturbance is generated using an airflow nozzle, mounted on a movable pneumatic cylinder, which enables positioning near the melt flow at the time of disturbance generation. The airflow nozzle is opened by a electric valve for several short bursts at the selected time intervals. Disturbance generation should not be repeated too often, e.g. interval too short as this increases the possibility of spilling the melt and disturbing the production process. Diameter can be continuously measured during the production process, while the measurement of velocity using the disturbance method can only be performed when disturbance is triggered. For proper process control, however, continuous volume flow estimation including velocity measurement of flow is required. Therefore, a contraction method for estimating small changes in velocity in real time when the velocity measurement using disturbance method is not available has been introduced. The principle of the contraction method is the following: the higher the flow velocity, the less contraction in the flow jet there is, and the lower the flow velocity, the more contraction in the flow jet there is.

The calibration of the measurement method in the production process is difficult since there is no reliable comparison method. Most appropriate is the comparison with weighing the material in front of the polimerisation chamber. Losses of material on the spinning machine, which leave it as perls, and losses due to cutting the plates at the edge, greatly influence the calibration


295Melt Volume Flow Measurement in the Mineral-Wool Production Process

uncertainty. Therefore, laboratory calibration of the measurement method was performed, where simulation of real production process was attempted.

In the following, the laboratory calibration procedure, results of laboratory calibration with water and the results of measurements in the mineral wool production plant are presented.

1 DESCRIPTION OF LABORATORY CALIBRATION PROCEDURE

Laboratory calibration was performed prior to the installation of system in the mineral wool production plant. Water as a media was used instead of mineral wool melt. In the mineral wool production process, calibration is impossible. The

Fig. 1. Schematics of mineral wool production

Fig. 2. Laboratory calibration layout



laboratory experimental work was performed on the measurement system as shown in Fig. 2. It consisted of:• pump,• orifice and pressure transmitter for reference

volume flow Qcal measurement,• pneumatic system for disturbance generation,• camera and illumination,• signal conditioning system, data acquisition,

processing and storage.

The flow medium was pumped from the reservoir by a centrifugal pump through a reference flow measurement device. The reference flow measurement Qref was used for the purpose of calibration. The flow medium exited the pipe in a vertical position, which was similar to the real process where the melt flew out of the melter and directing channel. Camera observation, illumination and disturbance generation area was located 10 Dp downstream from the exit of the flow medium from the pipe. Dp was pipe inner diameter. The flow then passed into a reservoir and was pumped again in the process of experiment.

During the experiment it was ensured that no bubbles were present in the flow. The experiment with water as a flow medium was performed. Water was colored by a yellow dye, which made it opaque and reduced reflections when illuminated, enabling adequate border detection in the image analysis process.

1.1 Pump

The purpose of the pump was to generate the flow simulating the outflow from the cupola melter. The pump type was centrifugal with peak volume flow 3100 l/h and peak electric power 900 W. The pump rotational speed was varied by a voltage regulator. The shape of the pipe at the outflow was circular with inner diameter Dp = 17 mm. The flow in the camera observation region was therefore, also circular.

1.2 Orifice and Pressure Transmitter for Reference Volume Flow Qcal Measurement

The reference volume flow measurement was based on measuring the stagnation pressure with an orifice. It was located 20 Dp after the

exit from the pump. Pipe and orifice plate inner diameter were 27.3 and 20 mm, respectively.

Reference volume flow Qcal was measured by the pressure difference on the orifice:

Qd v

df d=⋅π 2

4,

here, Δp is the pressure difference on the orifice, ρ is density of flow medium, and k is the constant of the orifice, calculated according to standard [17]. Δp was measured with a pressure transmitter DELTBAR S PMD75 by Endress Hauser. The measurement range of the pressure transmitter was 0 to 100 mbar. Flow measurement uncertainty was largely due to flow instabilities and was estimated to 3% of the measured value.

1.3 Pneumatic System for Disturbance Generation

In the real process during the mineral wool production, the existence of disturbances in the melt flow is subject to operating conditions of the cupola melter. In the laboratory experiment, the disturbance was generated by a pneumatic system. Here, flow control valve and gooseneck pipe with nozzle to produce air disturbance were used. The nozzle was circular and its diameter was 3 mm. In order to generate a disturbance of proper intensity to the flow, the direction of the nozzle and distance from the flow was adjusted by hand depending on the volume flow of the flow medium.

1.4 Camera and Illumination

Volume flow in the measurement region was observed by a black and white CCD camera, and an image acquisition board. SONY XC-HR50 camera with acquisition frequency fs = 60 Hz and image depth 10 bits was used. The resolution of the camera was 640 × 480 pixels. Camera exposure time was 1/10000 s. Camera pixels were square. The size of each pixel in both directions corresponded to 0.14375 mm. Images were digitized using the National Instruments NI-1410 frame grabber. Labview and Vision software from National Instruments was used for data acquisition.

The illumination in the camera measurement region was provided by a Vega



VELUM DC 150 light source and VEGA randomized light guide. The background of the observed region was colored black, thus the calibration experiment conditions for border detection for measurement of diameter and velocity were similar to the field process conditions.

1.5 Signal Conditioning System, Data Acquisition, Processing and Storage

Data acquisition of the measured volume flow pressure was synchronized with image acquisition. The pressure signal was led through the SCXI 1120 conditioning device and digitized with a NI 6013 16-bit A/D data-acquisition board from National Instruments. For pneumatic valve triggering for disturbance generation, the NI 6118 digital output board was used. Labview software from National Instruments was used for data acquisition and digital triggering.

The software sequence was executed every 30 s. First with an undisturbed flow, the diameter was measured, then a disturbance was generated and a sequence of 10 consecutive images were recorded for velocity calculation, followed by an acquisition of reference data from the flow measurement device. The algorithm for velocity calculation is described in greater detail below.

2 DESCRIPTION OF VOLUME FLOW ESTIMATION ALGORITHM

The procedure of volume flow rate estimation consists of two parts: (1) measurements in the moment before disturbance generation, and (2) continuous measurements.

Before the moment of disturbance, generation flow diameter ddf is measured, while the flow is not disturbed. Velocity vd of the melt jet is measured at the moment of disturbance generation. Flow diameter ddf and velocity vd of the melt jet are therefore, available about the time when disturbance is triggered. The triggering of disturbance should not be performed too often as this may change the impingement point of the melt.

For continuous measurements flow diameter ddf is measured continuously. Mineral wool producers require information about volume

flow continuously. For continuous velocity estimation the principle of contraction is used. When the melt flow velocity increases in regard to the time when the disturbance was triggered, less contraction in the flow jet is present. On the other hand, when the melt flow velocity decreases, the more contraction in the flow jet is present.

Volume flow Qd is estimated using image acquisition and analysis from flow diameter df and velocity vd of the melt jet. With index d measurement is denoted which is performed when the disturbance is triggered. The volume flow is measured under the assumption that the melt flow is circular (Eq. (1)):

Qd v

df d=⋅π 2

4. (1)

Velocity vd is measured when the disturbance is triggered, while diameter measurements are available continuously. The change of velocity in intervals between disturbance generations is estimated using the contraction method. When the melt flow velocity increases, less contraction in the flow jet is present. On the other hand, when the melt flow velocity decreases, the more contraction in the flow jet is present.

The contraction volume flow Qcontr is set to the same value as the volume flow Qd when the system measures the velocity of disturbance. The contraction volume flow, therefore, follows the reference volume flow when disturbance is created, while between disturbances the contraction volume flow changes continuously as the diameter and contraction of the melt flow change.

The contraction method for volume flow Qcontr estimation was performed by the Eq. (2):

QK e e v

vdd

Qcontr

C Cd

d fdd

df

=⋅ − +( )

. .2

2. (2)

In Eq. (2), K is calibration constant, dfd average melt diameter before the disturbance is triggered, d current melt diameter, and C and Cd are current and contraction coefficient before the disturbance is triggered. Changes in viscosity or surface tension were not considered because they change very slowly in the real process. The form of equation was selected so that stable behavior was achieved, while the selection of exponential function for estimation of velocity was based



on [18]. Ziabicki [18] presented a simple model of a steady isothermal liquid jet, where velocity of the jet is exponentially dependent on the distance from the outflow from the pipe, while the diameter of the jet decreases exponentially. Fitting the jet contour in the selected window of limited size according to [18] proved adequate in this case. Contraction coefficients C and Cd were thus calculated as damping coefficients of exponential functions fitted to the edges of current and volume flow before the triggering of disturbance. Contraction coefficients represent a measure of contraction of flow at generation of disturbance (Cd) and at the moment of estimation of (C) of volume flow. In the case of increase of the volume flow rate compared to the time when disturbance was triggered (C > Cd) the value in parentheses is positive, while in the case of reduction of volume flow rate (C < Cd) it is negative.

Constant K of value 0.1 was used. The extensive work has not been performed to justify the selection of the constant. It is assumed that the estimation of Qcontr using the above procedure is appropriate when the velocity of flow changes slowly as this is the case during the mineral wool production process. Laboratory calibration with water volume flow was constant during particular measurement.

2.1 Measurements of Melt Flow Diameter df

Melt flow diameter df was measured in an image window of approximate size 6 d × 3 d. In the window 300 horizontal intensity profiles were calculated. In each intensity profile, thresholding was performed, and the diameter was estimated based on the pixels above the threshold. Threshold value 500 was used for the 10-bit image. Diameter detection algorithm included sub-pixel accuracy. To calculate the diameter df of melt flow in the window, all 300 diameters in a single image were averaged. In addition, diameters in the last 10 consecutive images were averaged.

Here, measurement with only one camera was used for calibration and measurements in the plant. For calibration use of one camera is adequate as outflow pipe as seen in Fig. 2 has circular cross section. In the plant, situation is different, the melt flows from a channel, which is cooled with water. Due to solidified melt on the

cool edges, the melt flow regularly changes its cross section at the position of the channel. Melt flow does change cross section to circular for some length. Due to a non-circular cross section, additional measurement uncertainty appears. Use of two or more cameras could improve this. If we estimate, that melt flow cross section has an elliptical cross section, they should be mounted in both principal axes of the ellipse for the case of two cameras.

Further sources of melt flow diameter df measurements uncertainty are limited resolution and field depth of the camera. Camera resolution was selected with compromise to the frame rate to enable 60 Hz frame rate required for flow velocity measurement. For an estimation of diameter, sub pixel accuracy was used and measurement uncertainty was therefore, much reduced. Field depth during calibration did not contribute to measurement uncertainty because the flow did not move and was properly illuminated, while during experiments in the mineral wool production plant the cameras lens was fully closed due to very high light intensity of the melt flow. Therefore, the field of depth was much higher than the maximum movement of the melt flow.

2.2 Measurements of Melt Flow Velocity vd

Melt flow velocity vd was measured at the moment of triggering of melt volume flow disturbance. Velocity vd was estimated by observing propagation l of disturbance in two consecutive images recorded in time interval Δt, that is vd = l / Δt . Time interval Δt between two consecutive images was 1/60 s. A sequence of 10 image pairs was recorded after the disturbance was generated. The timing of disturbance generation and image acquisition was synchronized so that the acquired image pairs included the entire flow disturbance propagation.

In each consecutive image pair, intensity profile was measured in each line of each image, and corresponding image diameters were calculated using the same thresholding method as for melt flow diameter measurement. Thus, diameters x(i) for the first and y(i) for the second image in the image pair were calculated. i is the index of lines in diameter series.



Cross correlation method was used to calculate the propagation l of disturbance of every image pair. The cross correlation r(k) was calculated for every shift k between both diameter series as shown by Eq. (3):

r kx i y i k

x i y ii

i i

( )( ( ) ( ))

( ( )) ( ( ))=

⋅ −∑

∑ ∑2 2. (3)

For a certain value of shift k, where cross correlation r(k) is maximal, shift k between two consecutive images represents propagation l of disturbance. For propagation l of disturbance, averaging over all 10 acquired image pairs was used. By doing so, only one velocity filed vector per image pair was calculated. This is different from most of other PIV applications and a serious limitation of the measurement procedure. However, this is necessary due to a low amount of details with melt flow fully saturated, present on individual image pairs. One possibility to improve the method would be to split the melt flow in a series of vertical sections and calculate velocity, which might require the use of filters on the camera lens. This would also mean that better representation of velocity field inside the melt flow could be achieved, as section of the melt near the channel outflow may slower than in other sections.

3 DESCRIPTION OF MINERAL WOOL PRODUCTION PLANT MEASUREMENTS

Experimental work in a mineral wool production plant was based on comparing melt volume flow with the amount of produced mineral wool insulation material. In the field experiments, the manufactured insulation material on the production line was weighed after the collection chamber. The weakness of this method is that a part of melt is not transformed into fibres and leaves the spinning machine as perls. These perls fall down due to a high specific weight before they reach the collecting chamber and do not contribute to the weight of the insulation material. In addition, the panels are cut from side to the desired size and some of the insulation material is therefore not included in calibration. During the experiment no production parameters were changed, so it was

estimated that the amount of losses is constant. The measured weight of melt flow in the selected time interval before the spinning machine is, therefore, always higher than the weight of the insulation material after the collecting chamber. Volume flow of melt was measured using the procedure described in section 2. To calculate the mass flow Qm = r · Qv for density ρ of melt, the value provided by the manufacturer of mineral wool was used, calculated according to the algorithm by [1], which takes into consideration the temperature and chemical composition of raw materials.

In order to measure the weight of panels, a mechanical weighing device was used. Every 60 s, four panels of total size 2 × 1 m were removed from the production line and weighed.

4 RESULTS AND DISCUSSION

In this section, the results of laboratory calibration and measurement results in a mineral wool production plant are presented.

4.1 Laboratory Calibration

The description of laboratory calibration is presented in section 2. For the selection of volume flow, the rotational speed of the pump was regulated by changing the voltage of the electric motor. Fig. 3 show calibration diagrams for water. In each measurement point, 50 measurements were evaluated. Qcontr and Qcal are average values of Qcontr and Qcal measurements in each measurement point. The calibration diagram for water gives regression coefficients R2 = 0.99.

Throughout the paper the following definition of regression coefficient is used:

Rn x y x y

n x x n y y

i i i i

nnn

i i

nn

i i

n=

−

−

−

∑∑∑

∑∑ ∑

111

2

1

2

1

2

1

2

11

n

∑. (3)

However, the weakness of the measurement method is that single measurements of Qcontr have relatively high deviation around the average.

Correlations may change with experimental conditions; among them are intensity of disturbance generation, illumination,



diameter of the pipe and velocity of the flow in the observation window etc. In addition correlation may change if larger or smaller interval of volume flows is selected. Influence of experimental conditions change was not investigated, and the measurements were performed at pre-set values. Among influent parameters, only disturbance generation was adjusted. At single measurement point at selected volume flow, all experimental conditions were constant.

Fig. 3. Calibration diagram for water, error bars show standard deviation of measurements of

Qcontr

In the production process, melt flow velocities and volume flows depend on the pressure inside the melter, the height of the measurement position downstream, the melt flow and on the presence of hardened melt on the outflow from the directing channel. The disagreement between the measured volume flow Qcontr and the calibration volume flow Qcal arises from the unknown location of velocity measurement, interaction with the blowing compressed air for disturbance generation and a limited number of image pairs for correlation analysis.

The exact location of the measurement of velocity according to Eq. (1) is not known and can be anywhere in the image observation window. The correlation analysis technique (Eq. (3)) can only provide instantaneous velocity inside the correlation observation area. When disturbance is detected in the lower part of the observation window, the measured velocity is higher, while in the case when the disturbance is detected in the upper part of the observation window, the velocity is lower. For the diameter of melt flow, the measured average middle diameter was used.

One possible solution of this problem is to use a narrow correlation calculation window, however, it would be difficult to trigger the disturbance in two consecutive images. In addition, more image pairs and more disturbances would be required.

The second source of measuring uncertainty of reference volume flow is the change in the velocity of the parts of melt flow due to the interaction with the blowing compressed air. In this case, the direction of blowing with compressed air was perpendicular to melt flow in order to minimize this influence. In addition, as the smallest disturbance possible was used, which was still adequate for good velocity detection using correlation algorithm.

The third source of measurement uncertainty is the limited number of acquired image pairs for each disturbance generation. For this analysis, 10 image pairs were acquired. The selection of the number of acquired image pairs was, however, influenced by the limited time available for disturbance generation.

To a smaller degree, the instability of pump operation also increases measurement uncertainty of volume flows Qd and Qcontr.

Fluids with higher viscosity are less susceptible to pulsations with compressed air, and the spraying of parts of fluid is less probable. A distinctive feature of Fig. 3 is that fitted calibration lines do not cross the starting point of the diagram. Flow instabilities on the edge of the pipe add a certain amount to the diameter of the flow regardless of position.

Fig. 4 shows flow diameters df for experiments with water. Diameters df were calculated from images as mean diameters in the observation window. The measurements performed with water have regression coefficient R2 = 0.96. Results show that in the observation region the diameter df of the flow is linearly dependant on the volume flow. On the other hand, the diameter of the flow in laboratory calibration was limited by the diameter of outflow pipe. It therefore be supposes that linear relationship can only be expected at low volume flows. Some saturation can also be seen at volume flows above 1000 l/h in Fig. 4. The water jet at the exit from the pipe has fixed diameter, and in the position some diameters from the outlet downwards the flow is accelerated and thinned. Thus, the flow can not



have zero diameter and there is no requirement for plots to pass through origin of Fig. 3 maintaining linear behavior observed at higher volume flows. Diameter measurement is reasonable down to the limit diameter where the flow is not sustained anymore and droplets are formed because of surface tension.

Fig. 4. Flow diameter diagram for water

4.2 Production Process Measurements

Production process measurements were performed during the mineral wool production process. Fig. 5 shows image pairs acquired during field experiments. Two cases of melt flows are shown: with disturbance generated using pneumatic system (Fig. 5a) and without disturbance (Fig. 5b). Both cases show two images recorded at a time interval Δt = 1/60 s. The first acquired image is shown above. Images were taken in a real production process.

Fig. 6 shows the results of the field measurement of the weight of melt flow in the selected time interval and produced insulation material after the collecting chamber. The agreement between the two variables is very good.

The measurements using the melt flow measurement technique successfully follow low frequency variations of the weight of insulation panels. This is suitable for the regulation of the production line speed to ensure the optimal density of the product and for the regulation of melter. The measurement results regarding the weight of panels show less high frequency variations than measurements of melt flow.

During the measurement it was ensured by continuous and careful cleaning of the flow

channel that the flow channel from the melter was free of solidification remains. The melt solidifies on water-cooled walls of the channel. Thus, it was possible to maintain the cross-section of the melt flow in the measurement position as circular as possible. Measurements of melt flow without cleaning the flow channel had much higher measurement uncertainty (results not shown). Results show that use of one camera is adequate, if the flow channel is carefully cleaned.

a) b) Fig. 5. Propagation of disturbance;

a) disturbance generated by pneumatic system; b) no disturbance is present

Fig. 6. Results of field measurements, comparison of measurement results regarding the weight of

melt flow in the selected time interval and weight of produced insulation panels after the collecting

chamber

It is assumed that the results of melt flow measurement agree well with the results of panel weighing also because of the high viscosity of melt. High viscosity of melt enabled



the generation of adequate disturbances and prevented the spraying of melt. Thus, the results of field measurements are better than the results of calibration in the laboratory, however, the validation procedure for both cases was different.

5 CONCLUSIONS

A method for measuring melt volume flow for mineral wool production has been presented. The method for measuring melt volume flow by using a vision system and disturbance generation proved successful in a field experiment. During laboratory calibration the variations of individual measurements had high standard deviations, while the average values were very accurate. However, several problems should still be addressed; size of velocity estimation region, a change of flow velocity due to pneumatic disturbance generation, and the increase in measurement uncertainty due to solidification remains on the outflow directing channel.

6 REFERENCES

[1] Širok, B., Blagojević, B., Bullen, P. (2008). Mineral wool, production and properties, Woodhead Publishing in Materials, Cambridge.

[2] Improvements in or relating to the production of mats or the like of mineral wool, international patent GB822528 (1959). ROCKWOOL AB, application number: GB19570015575 19570516.

[3] Širok, B., Mihovec, B., Bradeško, F., Možina, P. (2005). Conveyor scale for controlling rock wool surface density European Patent Nr. EP 1 194754 B1: Bulletin 2005/35,European Patent Office, Munich.

[4] Hočevar, M., Širok, B., Blagojević, B. (2005). Mineral wool production monitoring using neural networks. International Journal of Information Technology, vol. 11, p. 64-72.

[5] Raffel, M., Willert, C.E., Wereley, S.T., Kompenhans, J. (2007). Particle Image Velocimetry, A Practical Guide. Springer, Heidelberg.

[6] Adrian, R.J. (2005). Twenty years of particle image velocimetry. Experiments in Fluids, vol. 39, p. 159-169.

[7] Tokumaru, P.T., Dimotakis, P.E. (1995). Image correlation velocimetry. Experiments in Fluids, vol. 19, no. 1, p. 1-15.

[8] Cheng, W., Murai, Y., Sasaki, T., Yamamoto, F. (2005). Bubble velocity measurement with a recursive cross correlation PIV technique. Flow Measurement and Instrumentation, vol. 16, no. 1, p. 35-46.

[9] Zosel, J., Guth, U., Thies, A., Reents, B. (2003). Flow measurements in micro holes with electrochemical and optical methods. Electrochimica Acta, vol. 48, p. 3299-3305.

[10] Hann, D.B., Greated, C.A. (1997). The measurement of flow velocity and acoustic particle velocity using particle-image velocimetry. Measurement Science & Technology, vol. 8, p. 1517-1522.

[11] Patte-Rouland, B., Lalizel, G., Moreau, J., Rouland, E. (2001). Flow analysis of an annular jet by particle image velocimetry and proper orthogonal decomposition. Measurement Science & Technology, vol. 12, p. 1404-1412.

[12] Hu, H., Saga, T., Kobayashi, T., Taniguchi, N. (2002). Simultaneous measurements of all three components of velocity and vorticity vectors in a lobed jet flow by means of dual-plane stereoscopic particle image velocimetry. Physics of Fluids, vol. 14, p. 2128-2138.

[13] Sakakibara, J., Wicker, R.B., Eaton, J.K. (1996). Measurements of the particle-fluid velocity correlation and the extra dissipation in a round jet. International Journal of Multiphase Flow, vol. 22, p. 863-881.

[14] Beck, M.S., Plaskowski, A. (1987). Cross correlation flowmeters - their design and application. Adam Hilger, Bristol.

[15] Carlson, J., Ing, R.K. (2003). Ultrasonic speckle correlation imaging of 2D particle velocity profiles in multiphase flows. Flow Measurement and Instrumentation, vol. 14, no. 4-5, p. 193-200.

[16] Takamoto, M., Ishikawa, H., Shimizu, K., Monji, H., Matsui, G. (2001). New measurement method for very low liquid flow rates using ultrasound. Flow



Measurement and Instrumentation, vol. 12, no. 4, p. 267-273.

[17] ISO 5167 (2003). Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits

running full. International Organization for Standardization, Geneva.

[18] Ziabicki, A. (1976). Fundamentals of fibre formation. Wiley, New York.


*Corr. Author’s Address: University of Kragujevac, Faculty of Mechanical Engineering Kraljevo, Dositejeva 19, 36000 Kraljevo, Serbia, [email protected]

Optimization of Trapezoidal Cross Section of the Truck Crane Boom by Lagrange’s Multipliers and by Differential

Evolution Algorithm (DE) Gašić, M.M. ‒ Savković, M.M. ‒ Bulatović, R.R.

Milomir M. Gašić ‒ Mile M. Savković* ‒ Radovan R. Bulatović Faculty of Mechanical Engineering Kraljevo, University of Kragujevac, Serbia

The cross sections of truck crane booms are complex box-like cross sections, which should provide continuous stress allocation. It is difficult to analytically determine optimal relations among geometric parameters of such cross sections. The paper deals with the method for determining relations among geometric parameters in order to achieve the optimal shape of the cross section. The method is based on Lagrange’s multipliers used for determination of extreme values. The optimisation of geometric parameters has also been done with the method of differential evolution (DE). The optimisation of the cross section is based on the strength criterion. The results of the applied methods have been verified by means of numerical example for an existing solution. The comparative analysis of the results of both methods has also been done.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: trapezoidal cross section, truck crane, boom, Lagrange’s multipliers, differential evolution algorithm

0 INTRODUCTION

The world’s truck crane manufacturers have been giving significance to the design of the truck crane booms having box-like cross sections, which increase bending and torsion stiffness, and decrease the weight. Since the technology of box-like girders has been enhanced, the classic rectangular cross sections have been replaced with more complex polygonal ones [1] to [8].

The box-like girders are made of sheet metal of various thicknesses because of optimisation and material saving. Papers [1] and [9], which deal with the telescopic truck crane booms, have proved that there are some local peaks of stress at the areas where the members are in contact, so the cross sections must be made of thicker sheets at contact areas. These stress peaks are rather noticeable when the boom segments are on maximum reach [9]. Both local stresses and the stresses at the polygonal cross sections are smaller at the areas where external load is transmitted from one segment to another [1] and [9].

The research of the optimal parameters of trapezoidal cross section (Fig. 1) has been done by two methods. The results of the comparative analysis are also shown.

The first method for cross section optimisation is based on Lagrange’s multipliers [8] to [10]. This method provides optimal values of geometric parameters of the cross section in the explicit form and also their functional relations. The obtained relations of geometric parameters determine the minimal cross sectional area. The method is also suitable for forming the algorithms of the cross sectional area optimisation.

The second method for cross section optimisation is based on the algorithm of differential evolution (DE). DE algorithm is efficient for solving optimisation problems where the objective function does not need to be continual in an area and where the values of design parameters do not need to be close to the initial values.

Price and Storn [11] successfully applied DE algorithm during optimisation of certain well-known non-linear, non-differentiable and non-convex functions. The papers [12] to [16] give a detailed description of DE algorithm as well as its application to various optimisation problems.

This paper proves that DE algorithm can be successfully applied to optimise the cross-sectional areas of the elements of supporting structures.


305Optimization of Trapezoidal Cross Section of the Truck Crane Boom by Lagrange’s Multipliers and by Differential Evolution Algorithm (DE)

1 MATHEMATICAL FORMULATION OF OPTIMISATION PROBLEM

The aim of the research is to define the geometric parameters of the cross section, as well as their relations, which will provide the minimum cross sectional area of the boom for defined load. The weight minimisation corresponds to the volume minimisation, i.e. to the cross sectional area minimisation, and it is determined from the condition that the stress at the appropriate cross section is less than or equal to the allowable stress. The allowable stress criterion only has been taken as boundary function AS it is typical for boom cranes [8] to [10]. The cross sectional area depends on the section height and width, sheet metal thickness, and relations among the parameters. If there are many optimisation parameters and if the optimisation of all parameters cannot be done, the dominant parameters need to be chosen.

This is a general mathematical formulation of the above-defined optimisation problem:

minimize f(X), (1)

subject to: gj(X) < 0, j = 1, …, m, (2)

where: f(X) is the objective function, gj(X) ≤ 0 represents the constraints defined by the search space, m is the total number of constraints. X = {x1, …, xD}T is a design vector consisting of D design variables. The design variables are the values, which should be determined during the optimisation procedure. Each design variable is defined by its lower and upper boundaries.

2 OPTIMISATION DONE BY LAGRANGE’S MULTIPLIERS

Generally, the truck crane boom is loaded by the longitudinal force N, the bending moments Mx, My, and the torsion moment T [1] to [9].

In order to determine the optimal values of geometric parameters by Lagrange’s multipliers we started with the expression for cross-sectional area, which is selected for the objective function f(X).

Lagrange’s function is defined as:

Φ(X) = f(X) +λg(X), (3)

where λ is Lagrange’s multiplier.

The following conditions need to be satisfied so the objective function has its minimum or maximum:

∂ ( )∂

= =Φ X

xi D

i

0 1, ,..., . where (4)

Eq. (4) can be also written as:

∂ ( )∂

+∂ ( )∂

= =f X

xg X

xi D

i i

λ 0 1,..., . (5)

When the multiplier λ is eliminated the equations that define the optimal values of parameters are obtained.

2.1 Objective Function and Boundary Function

The optimisation of three parameters (H, B, b) is done for trapezoidal cross-section (Fig. 1). Other geometric parameters such as wall thicknesses t1, t2 and t3 are not treated in this method as optimisation parameters. Their values are taken according to manufacturers’ recommendations and references [2], [5], [7] and [9].

B

H S

t2

t3

b

t1 x

y

yc

Fig. 1. Trapezoidal cross section

Below are the defined parameters: N axial force acting on the centre of the cross

section,Mx and My bending moments for x and y axes,T torsion moment,σ0 allowable stress of the basic boom material.


306 Gašić, M.M. ‒ Savković, M.M. ‒ Bulatović, R.R.

The geometric parameters of the truck crane boom are: Wx and Wy resisting bending moments for x and

y axes, Wt polar moment of resistance.

The design parameters can be expressed in the form of design vector:

X = (k, d, H)T

where:

k bB

d HB

= =, . (6)

The boundary function corresponds to the sum of normal and tangential stresses at the cross section [2]:

g k d H N

AMW

MW

TW

x

x

y

y

t

1

2

2

024 0

, ,

.

( ) = + +

+

+ ⋅

− =σ

(7)

Since the analysis of this problem includes the ratios between the sheet metal thicknesses and height [1], [5], [7] and [9]:

δ δ δ11

22

33= = =

tH

tH

tH

, , , (8)

the objective function, which stands for cross-section area, is:

f k d H A

H kd d

kd

, ,

.

( ) = =

= + + +−

22

13

2

4 1δ

δδ

(9)

Tangential stresses are much smaller in comparison to normal stresses, so the member 4(T/Wt)2 of the boundary function, Eq. (7) can be ignored [3] to [10]:

g k d H NA

MW

MW

x

x

y

y

e

1

2

02

202 0

, ,

.

( ) = + +

− =

= − =

σ

σ σ

(10)

The parameter values (8) of the trapezoidal cross section (Fig. 1) are within the following limits [5], [7] and [9]:

δ1 = 0.02 ÷ 0.03, δ2 = 0.02 ÷ 0.027, (11) δ3 = 0.015 ÷ 0.02.

Conformably to the reference [17] the accepted values of these parameters are:

δ1 = 0.0273, δ2 = 0.0221, δ3 = 0.0175, (12)

so the values of their ratio are:

δδ

δδ

1

2

2

3

1 56 1 26= =. , . . (13)

The accepted boundaries of defined parameters do not decrease the generality of the optimisation of the parameters H, B, b.

The relation between the bending moments is defined in practice and references [2] to [9] as:

My = ψMx , (14)

where the value of ψ coefficient is within the limits [5], [7] and [9]: ψ = 0.4 to 0.75. The relation (14) can be expressed as:

M MMy

x= , (15)

so the value of M coefficient is within the following boundaries: 1.3 to 2.5. Since the allowable stress depends on the used material, an arbitrary value of σ0 = 100 MPa has been adopted, which does not affect the problem generality.

2.2 Optimisation of Geometric Parameters

The objective function Eq. (9) is transformed into the following form:

f k d H A B d k

k B R

, ,

,

( ) = = +−

+

+ + = [ ]

2 23

2

3

1 22 2

12

δ δ

δ δ

(16)

where:

R d k k[ ] = +−

+ +

23

2

3 1 221

2δ δ δ δ . (17)

The position of the centre of trapezoidal cross sectional area (Fig. 1) is expressed as:



y

H kd

kd

kd d

kd

c =

+ +−

+ + +−

δ δ

δ δ δ

2 32

2 13

2

24 1

4 1

. (18)

The values of the moments of resistance for appropriate axes are:

W k d H H

d yH

k yH

yH

xc

c

c

( , , ) =−

−

+

3

2

2

2

11

δ

δ +

−

+−

+

+ −

HyH

kd

yH

c

c

33

2

1 124 1

0 5

3

δ

δ . +

−

2 2

4 1 kd

(19)

W k d H H kd d

dk k

d

y ( , , ) = +

+

+ −( ) +−

33

22

12

3 2

6 6

241 4 1

δ δ

δ

+

+ +( ) +−

2

3 22

81 4 1δ

dk k

d.

The expressions for moments of resistance (19) are not suitable for the application of Lagrange’s multipliers. Thus, their approximation has been done providing that their accuracy is not reduced (the error at this approximation does not exceed the value of 5%). The simplified expression for the moment of resistance for x axis is:

W’x (k,d,H) = Ahα . (20)

The graphic interpretation of the approximation can be seen in Fig. 2. Approximation coefficient value of α = 0.44 has been calculated from condition that the deviation between the values of the moments of resistance, stated in the Eqs. (19) and (20), does not exceed 5%.

The expression for the moment of resistance for y axis can be also transformed into:

W k d H B k d

k

y' , ,( ) = +

+

+−

+

βα

δ

δ δ

32

3

2

3 1

14 2

12

++

=

+

[ ]δ β2

2 31

14

k B k S ,

(21)

where:

S d k k1

2

3

2

3 1 22

21

2

2 0 88

[ ] =

+

−

+ +

= =

αδ δ δ δ

β α

,

. .

(22)

Fig. 2. Relation between the moments of resistance for x axis

Considering the existing solutions of truck cranes, it has been noticed that the boom first segment height is not less than 300 mm.

According to the above approximation, the boundary function (10) is:

g NB R

MB d R

MB k S

x y1 2 3 3

10

21

0=[ ]

+[ ]

++ [ ]

− =α α

σ( )

. (23)

In order to apply Lagrange’s condition, it is necessary to differentiate the boundary function (23) and the objective function (16) with respect to the stated parameters, and then to find the following ratios:

∂∂∂∂

α

α

B B

g

fN

B RM

B d R

MB k S R

x

y

1

4 2 5 2

51

32

31

= −[ ]

−[ ]

−

−+ [ ][ ]( )

,



∂∂∂∂

δ

α δ

α

d d

3

g

fN

B R

M R d

B d R

M

B

x

y

1

4 2

23

5 3 2

3 5

2

2

2

= −[ ]

−[ ]+( )

[ ]−

−(( )

,1 1

2+ [ ]k S

(24)

∂∂∂∂

α

δ δ

k k

2

g

fN

B RM

B d R

M S k k

x

y

1

4 2 5 2

1 32 2 1 4

= −[ ]

−[ ]

−

−[ ]+ + −( ) (11

1 4 12 5 21

22 3

−[ ] + [ ] − −[ ]

k

B k S k k

)

( ) ( ).

α δ δ

Setting the first and second Eq. (24) equal to each other gives the following:

d M k k k32

1

3

2

3

21 12

= +−

+ +

( ) .δδ

δδ

(25)

The following transformation can be done for defined parameter limits (11) and for defined optimization area (Fig. 3):

F k k1

21

3

2

3

212

=−

+ + ⋅

δδ

δδ

, (26a)

F k243

1= +( ). (26b)

Fig. 3. Comparative values of F1 and F2

Fig. 3 shows that functions (26a) and (26b) have the same values within defined boundaries. Replacing Eqs. (26a) and (26b) into Eq. (25) and considering F1 = F2, the relation between parameters k and d is obtained:

d M k= +4

31 23 ( ) . (27)

If we equalize the first and third Eq. (24), by means of certain transformations, the following Eq. is obtained:

Rk k

k RS

S[ ]+ −( )

=+ [ ][ ]

+[ ]

4 118 82 3 1

1

δ δ ααδ

( ).

3

(28)

Having (27) and ignoring the members of a very small value, Eq. (28) can be solved numerically. The solution, which is within the defining range of parameter k, is shown in Fig. 4.

Fig. 4. Solution to Eq. (28) within the defining range

Fig. 4 shows solutions of Eq. (28) only for the real world values of parameter k. Other solutions (k → 0, k > 0.8) are not considered because they are not of practical significance. If k → 1, the trapezoidal cross section becomes rectangular. If k < 0.4, the solution cannot be realized in practice.

The trapeze height can be obtained from the boundary function (23) and relation (6), if the members of a very small value are ignored:

HM d d R M k S

M k S Rx=

[ ]+ + [ ]{ }+ [ ][ ]

21

1 0

32 1

1( )

( ).

α σ (29)

3 OPTIMISATION BY DE METHOD

3.1 Brief Description of DE Algorithm

The DE algorithm is briefly described here, and the control parameters of the algorithm



are also dealt with. A detailed description of DE algorithm can be seen in references [11] to [16].

DE is a simple, but still strong evolutionary algorithm used for realization of the global minimum in numerous real world optimisation problems. The DE algorithm has the following control parameters: the population size NP, the crossover constant CR and the mutation constant F. Coding of chromosomes with real numbers, i.e. presentation of chromosomes as vectors of real values, is used in numerical application of DE in optimisation processes.

Generation of the initial population is performed stochastically. The population size NP is commonly ten times bigger than the number of design variables. At the beginning, each design variable is a random value which is found within the defined upper and lower boundaries. While defining the boundaries, attention should be paid to ensure that the values of design variables are not out of range which is really acceptable.

The mutation constant in DE is a real parameter, which controls the increase of difference between two individuals in the search space. The difference between two randomly chosen vectors defines the magnitude and direction of mutation. When the difference is added to a randomly chosen vector, it becomes a mutant vector. The basic idea of DE is that mutation is self-adaptive in the search space and the current population. At the beginning of the optimisation process, the magnitude of mutation is large because the vectors in the population are far away from the search space. When the process starts to converge, the magnitude of mutation starts to decrease. The self-adaptive mutation in DE leads the solution of the optimisation process toward the global minimum [16].

There are some basic rules, which are defined in [14], for taking the best values for CR. High values are effective for all problems, but they are not always the fastest. The problems with heavy interaction between design variables generally require a high CR. However, if interaction between design variables is lower, a lower CR can be used, which results in obtaining a satisfactory solution with a smaller number of iterations (faster solution). According to reference [14], the values of control parameters are presented in Table 2.

3.2 Optimisation Done by DE Algorithm

Design parameters can be expressed in the form of design vector X = (k, d, δ1, δ2, δ3, H).

In addition to the variables k, d, H, which have been optimised by Lagrange’s multipliers, the variables δ1, δ2 and δ3, are also optimised.

The objective function is:

f k d H A

H kd d

kd

( , , , , , )δ δ δ

δδ

δ

1 2 3

22

13

2

4 1

= =

= + + +−

,,

(30)

with the following boundaries:

g k d H N

AMW

MW

h k d

x

x

y

y1 1 2 3

1 1 2

100 0( , , , , , ) ,

( , , ,

δ δ δ

δ δ

= + +

− ≤

,, , ) . ,( , , , , , ) . .

δ δ δδ δ δ δ δ

3 1 3

2 1 2 3 2 3

1 56 01 26 0

Hh k d H

= − == − =

(31)

The limit g1(k, d, δ1, δ2, δ3, H) results from (10) while the limits h1(k, d, δ1, δ2, δ3, H) and h2(k, d, δ1, δ2, δ3, H) result from (13).

The boundaries of design variables δ1, δ2, and δ3 are defined by Eq. (11) and the boundaries of k, d, H are accepted according to references [5], [7] and [9]. Their upper and lower boundaries are shown in Table 1. Reference [14] proposes the constraints directly in the DE algorithm, which allow the values of design variables to remain within the mentioned boundaries during the whole optimisation process.

The parameters related to DE algorithm are shown in Table 2.

In Table 3 there are some final design variables for various accepted values M and Mx. On the basis of the final design variables, the values B, b, σe have been calculated as well as the numerical value of the objective function, i.e. the minimal trapezoidal cross sectional area of the truck crane boom has been obtained.

Table 1. Initial values of design variables

Boundary k d δ1 δ2 δ3 H

[cm]Lower 0.4 1.2 0.02 0.02 0.015 60Upper 0.8 2.2 0.03 0.027 0.02 90



4 COMPARISON OF OBTAINED RESULTS

Using Eqs. (9) and (29) the relation between the area and height of trapezoidal cross section as the function of external load and parameter M is obtained. The load values correspond to the load values of the truck cranes TD-16 made by [17]: IMK 14. oktobar – Krusevac and ADH-16 made by ILR – Belgrade.

Using the data from Table 3, and the objective function (9), a comparative analysis of the obtained results of both methods (Fig. 5) can be made. However, the exact comparison of the methods is not possible because the number of considered parameters is different for the first and the second method.

Analysing the obtained results (Fig. 5), it can be concluded that the results from both methods are in agreement, except for the case with values k = 0.6; M ∈ 2 to 2.5 (Fig. 5c). In that case, the results obtained by DE method offer better solutions in terms of material saving.

Table 2. Parameters of DE algorithm

NP (initial population)

D(number of design

variables)

CR (crossover constant)

F(mutation constant)

itermax(maximum number

of iterations)60 6 0.5 0.5 1000

Table 3. Accepted, final and optimised values of design variables

Accepted valuesМ = 1.33 М = 1.7 М = 2.5 М = 2.5 М = 1.7 М = 2.5

Mx = 35000 [kNcm]

Mx = 40000 [kNcm]

Mx = 45000 [kNcm]

Mx = 35000 [kNcm]

Mx = 45000 [kNcm]

Mx = 40000 [kNcm]

Fina

l val

ues o

f de

sign

var

iabl

es

k 0.415 0.407 0.501 0.495 0.591 0.606d 1.722 1.453 2.158 1.708 1.580 1.667δ1 0.028 0.029 0.029 0.026 0.026 0.027δ2 0.023 0.022 0.023 0.022 0.022 0.022δ3 0.017 0.018 0.018 0.017 0.017 0.018

H [cm] 86.9 82.8 86.9 76.4 86.0 76.8Number of iterations 27 22 13 34 26 39

Cal

cula

ted

valu

es

B [cm] 50.5 57.0 40.3 44.8 54.4 46.1b [cm] 21.0 23.2 20.2 22.2 32.2 28.0

Amin [cm2] 428.3 425.2 412.9 352.1 441.1 356.0σe [kN/cm2] 9.70 9.53 9.86 9.77 9.08 9.59

5 CONCLUSION

Both optimisation methods can be successfully applied to determine the relation between the geometric parameters of trapezoidal cross sections of the truck crane booms.

The method of Lagrange’s multipliers has advantages in defining the analytical form of the objective function, which is suitable for practical application. The achieved relations can be very useful for engineers, especially in the first phase of designing when facing the problems of defining the initial dimensions of the structure cross-sections, which should be close to the optimal ones.

DE method does not provide dependence of the objective function in analytical form, but it does provide the use of a larger number of boundaries, a wider range of initial design variables and a larger number of solutions, which meet the boundaries defined.



Fig. 5. Comparative illustration of the results of both methods a) parameter value k=0.4 b) parameter value k=0.5 c) parameter value k=0.6

DE method gives discrete values of the relation between some parameters as well as the minimal value of the objective function for defined load values. Apart from that, DE method has been applied in order to be compared to the first method.

After comparing the results obtained by means of two considered methods, we can state that there is a significant agreement between them. However, better solutions can be obtained by DE method (Fig. 5), because six parameters have been considered, unlike the first method of Lagrange’s

multipliers by which three parameters have been considered within optimisation.

If DE method is applied, solutions that are more accurate are reached for defined parameters k = 0.6, M ∈ (2 to 2.5) (Fig. 5c).

For defined values M ∈ (1.33 to 2), k ∈ (0.4 to 0.5) the agreement between the results is very good (Figs. 5a and b). Due to the fact that these ranges of values match with the real world ones, the method of Lagrange’s multipliers can be successfully applied to the structure optimisation, especially in the first phase of design.



However, cross-sections obtained should be further verified using other design criteria such as deflection of the boom structure and local stability of the metal sheets forming the trapezoidal cross-section.

6 REFERENCES

[1] Andrienko, N.N., Hasilev, V.L. (1987). Bigger carrying capacity of auto cranes due to lower mass of the boom. Mechanical Engineering, vol. 5, p. 48-54. (in Russian)

[2] Balovnev, V.I., Savellev, A.G., Moiseev, G.D. (1990). Calculation of dimensions by minimizing mass of building and mining machines. Construction and Mining Machinery, Mechanical Engineering, vol. 3, p. 72-80. (in Russian)

[3] Savellev, A.G. (1998). Theoretical positioning by optimal calculation of support having thin wall and minimal mass. Interstojmeh 98, p. 162-165.

[4] Šelmić, R., Mijailović, R. (1998). Identification of dimensions of trapezoidal cross section in structures. Interstojmeh 98, p. 203-205.

[5] Šelmić, R., Mijajlović, R. (1998). Optimum dimensions of trapezium cross-section in structures. XV. ECPD International conference on material handling and warehousing, p. 3.49-3.54.

[6] Savković, M., Gašić, M., Ostrić, D. (1999). Optimization of geometry of pentagonal cross section of auto crane boom. The 3rd

International Conference, HM-99, p. 6.12-6.15. (in Russian)

[7] Mijajlović, R., Marinković, Z., Jovanović, M. (2000). Dynamics and optimisation of cranes. Faculty of Mechanical engineering Niš. (in Serbian)

[8] Gašić, M., Rajović, M., Savković, M. (2002). Contribution to the optimization of

the box cross sections of the boom of the mobile hydraulic crane. The 4th International Conference HM-2002, p. A.55-A.57.

[9] Gašić, M., Savković, M., Petković, Z. (2002). Contribution to determination of stress in the contact zone of segments of auto crane boom. XVII. ICMFMDI international conference on Material flow, machines and devices in industry, p. I.40-I.43.

[10] Šelmić, R., Cvetković, P., Mijajlović, R., Kastratović, G. (2006). Optimum dimensions of triangular cross-section in lattice structures. Meccanica, vol. 41, p. 391-406.

[11] Storn, R., Price, K. (1997). Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, vol. 11, no. 4, p. 341-359.

[12] Storn, R., Price, K. (1997). A simple evolution strategy for fast optimization. Dr. Dobb’s Journal, vol. 264, p. 18-24.

[13] Storn, R. (1996). On the usage of differential evolution for function optimization. Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS), p. 519-523.

[14] Price, K.V., Storn, R.M., Lampinen, J.A. (2005). Differential evolution – a practical approach to global optimization, Springer, Berlin Heidelberg.

[15] Lampinen, J.A. (2001). Bibliography of differential evolution algorithm. Lappeenranta University of Technology.

[16] Kukkonen, S., Lampinen, J. (2004). Comparison of generalized differential evolution to other multi-objective evolutionary algorithms, from http://www.imamod.ru/~serge/arc/conf/ECCOMAS_ 2004/ECCOMAS_V2/proceeding/pdf/716.pdf, accessed on 2004-07-24.

[17] Catalogues of Serbian truck crane manufacturers (1996). imk 14. Oct., ILR.

http://www.imamod.ru/~serge/arc/conf/ECCOMAS_2004/ECCOMAS_V2/proceeding/pdf/716.pdf





*Corr. Author’s Address: Resistec UPR d.o.o.& Co. k.d., Krška cesta 8, SI-8311 Kostanjevica na Krki, Slovenia, [email protected] 313

Position Control with Parameter Adaptation for a Nano-Robotic Cell

Škorc, G. - Čas, J. - Brezovnik, S. - Šafarič, R.Gregor Škorc1,* - Jure Čas2 - Simon Brezovnik3 - Riko Šafarič2

1Resistec UPR d.o.o. & Co. k.d., Slovenia 2University of Maribor, Faculty of Electrical Engineering and Computer Science, Slovenia

3University of Maribor, Faculty of Mechanical Engineering, Slovenia

This paper describes the development of a nano-assembly system, built up using linear piezo motors. The so-called nano-robotic cell is based on an X/Y manipulator, supported by three serving tables, movable within a Z axis, and a position controlled using two different types of a bang-bang control methods. The presented application has been developed as a stand-alone application with the LabVIEW Real Time software package, a PCI-7356 servo controller card and a TMCM-090 stepper driver. Our experiments focused on two major problems present during the construction of nano-robotic assembly cells. The first one is a nonlinear characteristic of a linear piezo motor, which makes the use of classical control methods very limited. The second problem appears when a nano-robotic cell needs a bigger working space and at the same time, production demands that the manipulator moves more often over longer distances. In order to position in nano-resolution, the motors have to run at higher resolutions with smaller speeds. Therefore, long distance moves slow down the entire production process. Experiments on this system have shown that positioning within the nano-scale is possible, using a simple control method such as the bang-bang control method. Although positioning using this method is possible, certain limitations and weaknesses exists, making this simple method useless in nano-scale if higher speeds and longer move distances are needed. Certain changes in the basic control algorithm are proposed, which will ensure that the bang-bang control method becomes useful within higher speeds and over longer distances. All recommendations are supported and backed- up by practical experimental results.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: nano-robot cell, nano-positioning, bang-bang controller, MEMS assembly, LabVIEW real time

0 INTRODUCTION

Engineers are constantly confronted with greater demands for achieving a higher level of miniaturization regarding their products. Today’s production systems have already reached micro-scale regarding production and a lot of work has already been done within this scale. The authors have presented a micro-movement principle in [1] and [2], which is similar to ours in nano-scale. Intelligent control techniques [3] have already been implemented on micro-manipulators [4]. It is clear that the world expects science, productions systems and products to take one step further and achieve nano-scale solutions. It is well known that for the production of products with nano-scale measurements, the profession will have to develop completely new tools and devices. Authors have presented a novel kinematic scheme that leads

to a compact, integrated multi-axis, translational flexure structure for producing a pure spatial (X/Y/Z) movement in [5]. In our case linear piezo motors, mounted within each axis, to ensure an X/Y/Z spatial movement have been used. It is assumed that the nano-scale production system will overtake the nature of today’s production systems, which are often arranged into chains of separate working cells, each one with its own production purpose (assembling, gluing, welding, etc.). This paper introduces a practical development of one working cell, from the whole chain of a nano-production system, with priority in assembling with nano-scale resolution.

Authors have presented a robotic solution for the use in medicine in [6], built on the modules presented in [7], where the same actuators have been used, as in the present case. The presented system is controlled using the bang-bang control


314 Škorc, G. - Čas, J. - Brezovnik, S. - Šafarič, R.

method, with the possibility of positioning with 100 µm accuracy. A solution for using the same control method (with some extensions) for positioning using nanometer accuracy is presented here.

A working cell is actuated with five linear motors, which are assembled so that two of them act as X/Y manipulator and the other three as serving tables within the Z axis. A special gripper, which is used for gripping the objects, is placed at the top of the Y axis. The basic model of a nano-robotic cell is shown in Fig. 1 [8].

Fig. 1. A model of the nano-robotic cell

Our experiments focused on two major problems present during the construction of nano-robotic assembly cells. The first one is a nonlinear characteristic of a linear piezo motor. The main reason for this nonlinearity is the nature of the motor, which is based on piezo actuators. The use of classical control methods is very limited, due to the wide hystereses which are well known regarding piezo actuators. The second problem appears when a nano-robotic cell has to have a bigger working space and at the same time, production demands that the manipulator moves more often over longer distances. If positioning in nano-resolution, the motors have to run at higher resolutions with smaller speeds. Therefore, long distance moves are slowing down the whole production process. A solution based on two separate controllers is presented in [9]. The results from our experiments show that it is possible to

solve this problem with just one controller. Our solution is presented in continuation.

Section 1 describes the system equipment which was used for the development and implementation of this nano-robotic controller. A detailed description, with the characteristics of the nano-robotic cell and all of the components included in it, are given in 2. Section 3 describes the tested control methods and results of the experiments. Section 4 shows the practical application for the developed assembly cell. Section 5 provides the conclusions from the work.

1 SYSTEM COMPONENTS

The control system can be divided into five main elements, as shown in Fig. 2. The development machine marked as number 1, is a common notebook, based on Windows XP platform, supported by LabView 8.5 and C++ software packages. It is used for developing control algorithms and user interfaces. This machine can also be used for the execution of the control algorithms, but the limited frequencies of the program routines scan cycles, which cannot achieve higher frequencies than 1 KHz must be taken into account. Control of real time and time critical applications at a frequency of 1 KHz is impossible. A better solution for real time control can be achieved if a separate computer is added into this system, which would only be used for the execution of control algorithms. Such a computer is presented in Fig. 2 and marked as no. 2. A RealTime Desktop Target based on a Labview Real Time (Fig. 2, no. 5), which is totally independent operating system, has been built. The execution times of the control algorithms are much shorter, and execution frequencies of up to 1 MHz can be achieved. A desktop PC with a built-in processor with two cores was used, which allowed an execution of separate control tasks between two independent processor cores. Our Real Time target is supported by a PCI motion controller card 7356 from NI [10]. This card is used as an interface between the control algorithm and the power drivers of the motors. According to signals from the position feedback inputs and control algorithm, it produces a separate reference signal for each axis of the controlled system. This card has been configured in such a way that it acts


315Position Control with Parameter Adaptation for a Nano-Robotic Cell

as a stepper driver, therefore, all axis outputs act as a STEP/DIRECTON outputs.

Position feedback is assured with encoders, through encoder inputs. An alternative configuration of this card, as a servo driver, is also possible.

The reference signal mentioned above is then guided to the power driver of our system. The power driver marked as no. 3 and presented in Fig. 2, is assembled from five TMCM-090 power stepper units from Trinamic [11]. These power units are developed especially for the linear PiezoLEGS motors [12] assembled in our nano-robotic cell. They convert the STEP/DIRECTION reference signal at TTL level, into an appropriate waveform signal with an amplitude of 50 V. TMCM-090 allows us to set different waveform settings and different step resolutions. The changed waveform settings and step resolutions, result changed force of the motor and changed length of the separate motor step. From here on power and feedback cords are connected directly to the nano-robotic cell.

In addition to the already mentioned basic components, some other peripheral and power components, which are assembled in the nano-robotic controller were used. Fig. 3 shows all the components used in the controller.

Fig. 3. Nano-robotic controller

The controller is assembled on two platforms, constructed from acrylic glass. The placements of the components allow easy access in case of the potential need for changes due to experiments. On the upper platform there are five TMCM-090 cards, which are attached onto five BB035 basic boards from Trinamic [13]. They are used for an easier connection of power and signal cords. The basic boards are supplied with a DC voltage of 50 V from the switching power supply, mounted on the upper left corner of the same platform. At the upper right-hand corner of controller there is a cord connection box where all connections for power and signal lines were

Fig. 2. System components



established. The platform underneath consists of a switching card, temperature measuring card, and gripper power module. The switching card is made from TLP521-4 optocouplers. Half of the card’s capacity is used for automated selection of the waveform and resolution settings. These optocouplers are directly connected to BB035 selection jumpers. The reference signal from the encoders (also called Z channel or Index signal) is passed through the other half of the optocouplers. The encoder reference is directly connected through optocouplers to HOME input of PCI-7356 motion controller. These inputs are only used during the referencing phase of the robotic cell when the power supply is switched-on. After referencing has been completed, the home signals are no longer needed and they are switched off. A temperature measuring card was created with PT1000, and a source of constant current. We assume that the temperature influences positioning accuracy within nano-scale. This temperature card will give us another feedback signal, which will be included in our control algorithm of the near future. A gripper power module is used to supply the piezo actuator of the gripper, with voltage of ±100 V.

2 DESCRIPTION OF THE NANO-ROBOTIC CELL

The nano-robotic cell has five axes. Each axis is driven by a linear piezo motor produced by the PiezoMotor Upsala AB company. The so-called PiezoLEGS motor is based on four piezoceramic drive legs. Each drive leg consists of two piezo actuators, therefore, it can be considered as a piezoceramic bimorph. Using special electronic drive, each actuator can be activated separately and thus a rhombic working space of the tip of the drive leg is achieved. Fig. 4 shows four different states of leg movement. Each state in Fig. 4 is described using letters from a to d. The state marked with a represents the lowest point of drive leg movement if none of the piezo actuators is activated. State b shows the situation of a leg when voltage is applied to the right piezo actuator. Since the left piezo actuator is not supplied with voltage, the entire piezo leg bends to the left side. An extreme left position of the rhomb is achieved. Bending in the opposite direction is achieved

applying voltage to the left piezo actuator, while at the same time, the right actuator is not supplied. This situation is represented by letter d. The situation marked with the letter c shows the upper extreme of the working space, which is achieved when both piezo actuators are supplied.

Fig. 4. Four different states of leg movement

All four piezo legs are built in motor housing in such way that the working spaces of each leg corresponds with the drive rod of motor. The drive electronics activates two of four piezo legs at the same time with the same voltage waveform. Drive rod movement is achieved when one pair of the legs is bending while the second one is extended (pushes the drive rod). The bending of piezo legs in the X direction can be represented by Eq. (1), where x(t) represents the achieved bending point in the X direction, k1 a constant of variable parameters (influence of friction, load, drive conditions, etc.), and u1(t) with u2(t) voltages applied to each piezoelectric of one leg.

x(t) = k1 [u1(t) ‒ u2(t)] . (1)

Using almost the same Eq. (2) the extensions and contractions in the Z direction, where z(t) represents the achieved extension or contraction in the Z direction, and k2 a constant of variable parameters, can be described. Voltages



u1(t) and u2(t) have the same meaning as in Eq. (1).

z(t) = k2 [u1(t) + u2(t)] . (2)

If the cycles of bending and extending the piezo legs are continuously repeated, a linear movement is achieved in the form of little steps. According to the technical specification of the motor, movement in steps length from 2 nm to 8 µm can be achieved, with speeds up to 12.5 mm/s (with a factory delivered demo drive electronic). Standard motors are delivered with a drive rod of length 50 mm. A stroke up to 35 mm can be achieved with this length of rod [14].

Position feedbacks of the axes are achieved using linear encoders from NANOS instruments, which work on an electro-magnetic principle. Each encoder set consists of a magnetic scale and sensor electronics. The magnetic scale is standard delivered over a length of 50 mm, and has a division of 500 µm. Each increment of scale is interpolated with 13 Bits to achieve a maximal resolution of encoder system. The chosen system guaranties a resolution of 61 nm, with precision of ± 0.15% [15].

Fig. 5. Mechanism of the nano-robotic cell

Fig. 5 shows the basic mechanical assembly of the nano-robotic cell. All five motors together with linear encoders are attached to the metal base. Two motors at the top of the base form an X/Y manipulator. Both motors of the manipulator are mounted right-angled to each other using elastic joint. This elastic joint is used to reduce those forces, which are the result of big parallel tolerance between motors, the drive rod, and a

linear rail system. The Y motor of the manipulator is mounted on a special linear rail system and is therefore, movable. The other four motors are fixed mounted (one in the X direction and three in the Z direction). A special serving table is attached to each motor of the Z axis.

A gripping device is needed to form a positioning application. In this case a gripper developed by Fraunhofer-Institute of Reliability and Microintegration from Germany was used. This microgripper was fabricated by means of a UV-lithographic process and chemical wet etching technology from microstructurable photosensitive glass [16]. With little changes in the basic form of the gripper, gripper movement of approximately ±10 µm was achieved. The neutral opening of the gripper tip is 200 µm. By activating the piezo actuator in both directions (piezo actuator is used to move gripper tip), it is possible to grip objects of sizes from 190 to 210 µm. Fig. 6 shows the original basic form of the used gripper.

Fig. 6. Original form of the used gripper

3 RESULTS OF THE EXPERIMENTS

First in the series of our experiments was conducted with the bang-bang control technique. This technique is probably one of the first and simplest control techniques. The easiest way to demonstrate its functionality is a practical example of heating water. Electrical cookers use bimetal thermostats for switching a heater ON and OFF. Water temperature is constantly measured and compared with a set temperature. The heater is switched ON if the actual temperature has a lower value than set temperature and OFF if it is greater. Water temperature oscillates around



set temperature with a frequency dependent of the hysteresis of bimetal (big hysteresis causes small switching frequency and vice versa). This principle for position control, where motors were switched ON/OFF according to the result of the comparison between the actual and target position (positional error) was borrowed. In this case, the hysteresis was set to zero to achieve positioning as accurately as possible.

The goal of the first experiment was to discover any limitations of the classical bang-bang control method. Different step-lengths and different motor speeds were set manually. In the second part of this section the results concerning the extended bang-bang control method, when the motor step lengths and motor speeds were set automatically are presented. Each experiment is presented on the basis of position overshot. Position error was measured with the linear encoder system, which guaranties a resolution of 61 nm, with precision of ±0.15% [15]. The supplier had individually calibrated each encoder system to reach our needs. Functionality of the measuring system was tested and compared with the microscopic vision system in [17].

The results were recorded for one axis of the nano-robotic cell, where a longer distance move was repeated 10 times within each set point. Figs.7 and 8 present the dependences between the average overshot (calculated from 10 repetitions of experiment with same parameters) and motor speed. Motor step length in the first experiment was set at ~250 nm and in the second at ~3.9 nm. The target points for both experiments were set at 10000 increments away from the reference point, which means a move distance of 0.61 mm. The motor speed was changed from 1 to 3000 steps/s over 300 steps/s. The hysteresis of the bang-bang control method was set to 0. This meant that by reaching the target point, maximal acceleration of the motor in the opposite direction was set. Overshot is defined as the difference between the target point and the point where the top of the axis completely stops.

The results of the experiment with a 250 nm step length show that positioning with an accuracy of 100 µm is not possible if the motor speed is higher than approximately 1400 steps/s. Although a better measuring system than in [7] was used, system dynamics did not allow

us to achieve better resolutions over the whole speed range. Positioning within nanometer scale was very speed limited with this set-up. Motor speeds of up to 21 steps/s can be used for nano-positioning. The results of the experiments with a reduced step length of 3.9 nm show that a reduction in step length causes a reduction in the overshot. When the motor was set up to a maximal speed of 3000 steps/s, the size of the average overshoot was lower than 40 µm.

Fig. 7. The results of the experiment with 250 nm step length

Fig. 8. Results of experiment with 3.9 nm step length



The reduction of step length caused a drastic reduction in motor speed. In this case, positioning in the nanometer scale was possible with motor speeds of up to 289 steps/s. More hours are needed to achieve an experimentally given target point with nano-scale resolution. The presented results show that positioning with this system and classical bang-bang control method is possible although it is considerably speed-limited. These speed limitations render the presented method not useful for productions processes, where long distance moves are needed.

The conclusions from the first two experiments can help solve the problem of speed limitations within the presented method. Motor speeds and motor step lengths have been set up as fixed due to the whole positioning process. Better results can be achieved if this method is extended in such way that different step lengths and motor speeds are set automatically according to the travelling distance of the axis. The basic idea is to make the classical bang-bang control method adaptive in this way so that long distance moves are done using higher speeds and longer step lengths, while shorter distance moves are done using lower speeds and shorter step lengths. In order to improve the accuracy of longer distance moves, automatic control of motor speed and step length switches to lower speeds and shorter step lengths, as soon as the driven axis comes within the surroundings of the target point. In this way, the time needed to reach the target point is reduced, using the nano-scale resolution, by long distance moves. During the first two experiments a common bang-bang control method with one hysteresis was used. In this case, the basic hysteresis was extended to five different levels, where each level forms a new hysteresis. Hystereses 1 to 4 are used for speed reduction depending on the distance to the target point. The step length is set fixed to 250 nm due to all four hysteresis. As soon as hysteresis 5 is reached, the step length is reduced to 3.9 nm and the speed

increased. Hysteresis limits are determined using practical experiments on all five axes of the nano-robotic cell. Table 2 shows the limits, which guarantee stable positioning.

Table 2. Parameters of adaptive bang-bang regulationHysteresis

numberUpper lim. increments

Lower lim. increments

Speed [steps/s]

Step [nm]

1 ∞ 6000 3000 2502 5999 1000 1000 2503 999 300 500 2504 299 10 100 2505 10 0 1000 3.9

Fig. 9 shows the recommended control principle and the extended method. Fig. 10 shows a step response for adaptive bang-bang control. Travelling distance was set to 10000 increments, as in the first two examples. Speed and steep length was switched automatically according to Table 2. Three screenshots at different time moments were established. Each screenshot presents the dependence of position and time from different viewing aspects. The black line on graph A (Fig. 10) shows the step response of our system depending on the reference represented by red line. Graph B (Fig. 10) shows the difference between the actual and target positions from the time when the first overshoot appears. The graph marked with letter C (Fig. 10) shows oscillation around the target point, which is typical for the bang-bang control method (can also be seen on the second half of graph B – Fig. 10). The use of this method reduces the dependence on overshot regarding travel speed and move distance. Maximum averages (calculated from 10 repetitions of experiment) overshot when travelling a longer distance was in this case never bigger than 1586 nm. In the first experiment, a maximal average overshot of 358558 nm and in the second 38430 nm. The size of the maximal average oscillation around the target point was

Table 1. Numerical values of average overshotSpeed [steps/s] 1 300 600 900 1200 1500 1800 2100 2400 2700 3000

Overshot by 250 nm step [nm] 244 11407 24156 45323 73139 105835 141093 181841 242658 304512 358558

Overshot by 3.9 nm step [nm] 61 1037 3538 4453 8174 9333 15860 19459 27206 31781 38430



Fig. 9. Extended bang-bang control method

constant within one encoder increment or 61 nm. In the first two experiments this oscillation was always as big as the overshot. The time needed to accomplish longer distance moves is therefore, reduced drastically.

4 PRACTICAL USE OF THE NANO-ROBOTIC CELL

Temporarily the nano-robotic cell is still in the development phase. Final application for this project can be seen in MEMS assembly.

Fig. 11: Practical application with nano-robotic

Fig. 10: Step response of the adaptive bang-bang control method; a) step response of the adaptive

bang-bang control method, b) Difference between the actual and target positions, c) Oscillation

around the target point



A level that can be used for the positioning of micro-parts has been reached. An anti-dust chamber was assembled for these purposes. Complete application presented in Figs. 11 and 12 shows user interface developed for a simpler use of the application. The developed software supports the implementation of different fire-wire cameras, which can be added to anti-dust chamber. In this case, a special camera attachment system must be mounted onto the nano-robotic cell. In the upper right-hand corner of Fig. 12, a camera screenshot can be seen due to the process of positioning. For test purposes, a camera system was mounted so that it covered the middle serving table.

Fig. 10: User interface of the nano-robotic cell

5 CONCLUSION

In this paper the development of the nano-robotic cell which will in the near future be used for MEMS assembly, has been described. The entire application was built within LabVIEW Real Time and is therefore, very flexible. The developed platform has been created for the implementation of different control methods. We have presented the implementation of a classical bang-bang control method and on the basis of the experimental results, proposed certain changes to the basic method. These proposed changes reduce the limitations of the classical bang-bang control method to a minimum, which makes the extended bang-bang control method useful within MEMS production processes. We have proved that a simple bang-bang control method with certain extensions can be used for positioning within nano-scale. Although good results have already been achieved, our future work will focus on further investigations into control methods for

nano-positioning. Further implementations and experiments regarding different control methods for our system will provide us with an answer as to which method is more appropriate for MEMS assembly processes.

6 ACKNOWLEDGEMET

Operation part financed by the European Union, European Social Fund.

7 REFERENCES

[1] Juhas, L., Vujanic, A., Adamovic, N., Nagy, L., Borovac, B. (2000). Development of platform for micro-positioning actuated by piezo-legs. ICRA IEEE International Conference on Robotics and Automation, San Francisco, vol. 4, p. 3647-3653.

[2] Fahlbusch, S., Fatikow S. (2001). Implementation of self-sensing SPM cantilevers for nano-force measurement in microrobotics. Ultramicroscopy, vol. 86, no. 1, p. 181-190.

[3] Čas, J., Klobučar, R., Šafarič, R. (2008). Neural network based control of micro-manipulator. 10th International workshop on advanced motion control, Trento, AMC, IEEE proceedings, vol. 2, p. 444-449.

[4] Čas, J., Škorc, G., Šafarič, R., Milanovič, M. (2008). Planar manipulator for micro-sized object. International Electrotechnical and Computer Science Conference, ERK proceedings, Portorož, , vol. B, p. 207-210.

[5] Qing, Y., Jingyan, D., Ferreira, P.M. (2008). A novel parallel-kinematics mechanisms for integrated, multi-axis nanopositioning: Part 1, Kinematics and design for fabrication. Precision Engineering, vol. 32, no. 1, p. 7-19.

[6] Rea, M., McRobbie, D., Elhawary, H., Zion, T., Lamperth, M., Young, I. (2008). System for 3-D real-time tracking of MRI-compatible devices by image processing. IEEE/ASME Transactions on Mechatronics, vol. 13, no. 3, p. 379-382.

[7] Elhawary, H., Zivanovic, A., Rea, M., Davies, B.L., Besant, C., Young, I., Lamperth, M.U. (2008). A modular approach to MRI-compatible robotics. Engineering in



Medicine and Biology Magazine, IEEE, vol. 27, no. 3, p. 35-41.

[8] Škorc, G., Čas, J., Brezovnik, S., Šafarič, R. (2008). Simulation of nano robotic cell with support for 6D – HID. International Electrotechnical and Computer Science Conference, ERK Proceedings, Portorož, vol. A, p. 245-248.

[9] Perng, M.H., Wua, S.H. (2006). A fast control law for nano-positioning. International Journal of Machine Tools and Manufacture, vol. 46, no. 14, p. 1753-1763.

[10] National Instruments, Motion controller 7356 datasheet, from http://www.ni.com/pdf/products/us/735x.pdf, accessed on 2009-01-05.

[11] Trinamic, TMCM 090 manual, from http://www.trinamic.com/tmc/media/Downloads/modules/TMCM090/TMCM-090_manual.pdf, accessed on 2009-01-05

[12] PiezoMotor Upsala AB, PiezoLEGS, from http://www.piezomotor.se/pages/PLtechnology.html, accessed on 2009-01-05.

[13] Trinamic, BB-035 from http://www.trinamic.com/tmc/ media/Downloads/modules/Baseboards/BB-035_manual.pdf, accessed on 2009-01-05.

[14] Piezomotor Upsala AB: PiezoLEGS data and user instructions, (2003). 3rd ed., p. 3-15, retrieved on 05.01.2009 from nanos instruments web page: http://www.nanos-instruments.de/.

[15] Keoschkerjan R., Wurmus, H. (2002). A novel microgripper with parallel movement of gripping arms. Actuator, 8th International Conference on New Actuators, Bremen, p. 321-324.

[16] Čas, J., Škorc, G., Šafarič R. (2009). Micro positioning of planar mechanism – position measuring with submicron resolution, International Electrotechnical and Computer Science Conference, ERK 2009 proceedings, Portorož, vol. B, p. 217-220.


*Corr. Author’s Address: Rzeszow University of Technology, Faculty of Mechanical Engineering and Aeronautics, W. Pola 2, 35-959 Rzeszów, Poland, [email protected] 323

A Study of Quality Parameters and Behaviour of Self-Piercing Riveted Aluminium Sheets with Different Joining Conditions

Mucha, J.Jacek Mucha*

*Rzeszow University of Technology, Faculty of Mechanical Engineering and Aeronautics, Poland

This paper presents research progress in the assembly dimensional prediction area, using finite element analysis results. A case study of the SPR of two sheets of the aluminium alloy using a steel rivet was investigated. The riveting analysis has been performed for joined sheets using finite element method (FEM) with MSC Marc Mentat software.

Thus, a simulated analysis was adopted in this study to improve industrial productivity. The comparison analysis has been performed within the numerical experiment range to cover the effect of various riveting process parameters on the rivet deformation. Proper selection of corresponding rivet material features, i.e. its yield point and strain hardening, enables significant changing of the sheet joining process and specific finished joint parameters. The finite element simulation is effective in determining the optimal conditions.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: joint formation, rivetion load, mechanical properties, finite element modelling

0 INTRODUCTION

Welding demands localized heating of the material, which may lead to changes in the mechanical properties of the materials. When searching for new solutions to replace the spot welding process, well-known press joining technology (for example: clinching, self-piercing riveting, cold pressure welding) capabilities have been recognized.

Cold pressure welding is a special welding method that has been used in applications such as assembly of various parts at an increasing rate in recent years. Cold pressure welding takes place due to the breakdown of the surface layers caused by bulk plastic deformation [1].

Self-piercing riveted (SPR) joints gain even larger share in the thin-walled structure assembly process in the metal industry, especially in the automotive industry so [2] and [3]. The latter one demands for the modern solutions for both the car design and the car production technology. As an example, the self-piercing riveting is used by Audi [4] and Jaguar [5] for joining car body pieces. Modern joining by forming technologies such as Self-Piercing Riveting are increasingly used in sheet metal processing industries owing to their many advantages. Moreover, these technologies are often interesting joining alternatives of new

developed products with multi-material design and so on [6] to [9].

This is a submethod of pressed joints [10], and its basic benefit (in addition to the most important one – no bore drilling) is that various materials of different coating may joined, from painted and galvanized sheet metal, to plastic ones [11].

This method is used mostly for joining two or more thin sheets, which is acknowledged by the works of Han et al. [12]. The joint forming process is affected by several factors, which may be divided into relevant groups: geometrical factors, material factors, and technological factors [13].

The initial joined sheet hardening has a great meaning for the joining process and its quality indexes, which has been confirmed by Han et al. experimental research [14]. The work of Di Lorenzo and Landolfo [7] is also of great importance, where the analysis of joints made by various methods and strength tested was presented. When forming the joint, some joint execution correctness factors must be observed, as emphasized by Abe et al. [15] and Mori et al. [16]. Over the last few years, a rapid growth of the numerical computing methods based among the others on the finite element method (FEM) enabled analyzing a lot of issues related to such joint type


324 Mucha, J.

designing and performing. The application of modern research tools like professional computing FEM based software enables analyzing the virtual forming [17] to [22].

1 EXAMPLE JOINING OF ALUMINIUM SHEETS

During the SPR process, the self piercing rivet is pressed by a punch into two sheets, which are maintained between a blankholder and a lower tool.

The self-piercing riveting process can be described by the following four steps (Fig. 1):• clamping (step I), the blank holder presses the

two sheets against the die, and now the rivet is gradually pressed into aluminum sheets;

• piercing (step II), the punch pushes the rivet into the top plate;

• flaring (step III), the material of the lower sheet flows into the die and the rivet shank begins to flare outward, forming a mechanical interlock between the upper and lower substrates;

• release of the punch (IV step), finally, once the punch is retracted, the finished joint is achieved with the fastener properly seated in the sheets.

Fig. 1. Schematic representation of the SPR process

In particular, joint strength is determined by rivet flare into the locking sheet (reverse joint sheet), the dimensions of which are dependent on the profile. A typical internal die profile is shown in Fig. 2.

The use of the rivet, which indicates that the rivet has the characteristic shown in Fig. 3. The joint execution correctness may be assessed based on its appearance (Figs. 4b and c) and its cross section (Fig. 4d). The rivet is made of boron steel, and the sheets are aluminium alloy. The

mechanical properties of the rivet (material model 1) and sheets are shown in Table 1. Sheet joining has been performed for selected sheet thickness arrangement (1.5/2 mm).

a) b)

Fig. 2. Used die as an alternative I; a) real appearance of a basic die by Böllhoff,

b) its geometry

a) b)Fig. 3. Used rivet; a) real appearance,

b) major dimensions

Table 1. Mechanical properties of the rivet and sheets

Mat

eria

l Young’s Modulus

E [GPa]

Yield stressσ0.2

[MPa] Mat

eria

l m

odel

Flow stress [MPa]

C n

Riv

etB

oron

stee

l

188

1520 1 26271176 2 1970 0.088980 3 16421520 4 1659 0.014

Shee

tsA

l. al

loy

75 135 - 505 0.191

The flow stress of the rivet (material model 1) and sheets are obtained from the uniaxial compression and tensile tests, respectively, and the flow stress is used in the simulation. The material hardening effect has been described by the σ = f(ε) relationship, using the equation:

σ ε= C n( ) . (1)


325A Study of Quality Parameters and Behaviour of Self-Piercing Riveted Aluminium Sheets with Different Joining Conditions

The C factor in this equation is called the strain hardening curve coefficient (material constant), and n is the strain hardening curve exponent.

a)

b) c)

d)

Fig. 4. Example of final joint view; a) from the side, b) from the bottom, c) from the top, d) cross

section

Tests were carried out on two levels: • material tests on the base material and on the

rivet material were used to obtain the material properties used in the numerical models,

• riveting process tests using the new upsetting die.

Fig. 5. The characteristic parameters of SPR joint geometry

2 JOINT ASSESSMENT PARAMETERS

SPR is designed for thin sheet joining and particular attention must be paid to essential indexes, which may affect the load carrying capacity for tangent and normal loads. The essential parameters for joint execution

correctness assessment are presented on the cross section of a joint, see Fig. 5.

The final value of t2 depends on the rivet spreading course, and also its interference in the lower sheet. The rivet response to specified boundary conditions of the process is e.g. its spreading course, which may be characterized by the course of its corresponding diameter ratio:

SDDDr

r

r

= max

min

. (2)

Detailed recognition of the joining process enables optimal tooling selection based on e.g. riveting force value and the deformation of the pieces being joined.

3 THE NUMERICAL SIMULATION

Using the FEM simulation of the riveting process for specified parameters of the pieces being joined, the joining process and the join validity may be predicted. It will be possible to establish how and how much selected factors – geometrical, material and technological – affect the joining process. One of the objectives of the present paper is to simulate, utilizing the finite element method, the influence of changes in the riveting die and geometry on the material flow and consequent values parameter ti SPR joints, which directly affect the joint strength.

3.1 Model of Simulation

The numerical computations have been performed in MSC Marc Mentat 2005 software, where an additional procedure enabling the material separation has been applied.

This procedure is based on the body mesh part separation effect in a location, where the part dimensions have gained the specified minimum value. When the upper sheet thickness reaches a user defined value the sheet is divided into two parts. This procedure allows the rivet to penetrate into the bottom sheet.

The upper sheet material thickness, where the mesh elements were split at their contact boundary, was set as 0.02 mm. At the end of each computation step the routine checks whether the distance between two nodes on the boundary of


326 Mucha, J.

selected material is not lower than the user defined distance. If the condition is met, two adjacent elements, for which the critical distance was observed, are split along the common edge.

A mesh size of 0.15 × 0.15 mm was used for the parts that were adaptively remeshed as well as for the remaining parts in order to reduce contact problems. Such defined parameters of mesh reconstruction enabled a stable solution of the issue in each computation step [21].

Due to a form of the joint itself and the course of forming, the self piercing riveting process may be considered using the two-dimensional axisymmetric model – the axisymmetric state of stress and strains [22]. The boundary conditions have been defined based on the SPR riveting (Fig. 1).

The sheets have been joined and the rivet has been modeled using the elastic-plastic material model with an isotropic hardening, using the quadrilateral axisymmetric element of type 10. As the problem is axisymmetric, the four node 2D axisymmetric elements have been used, with four Gauss points [23].

3.2 Conditions for Simulation

For purposes of detailed analysis of fastener strain course during the riveting, it has been decided to determine the characteristic points I and II (Fig. 5), nodes of the rivet mesh elements, which enable tracking the change of a diameter of a tubular part of the fastener, respectively for Drmin

and Drmax (Fig. 5). Rivet spread ratio is measured for samples of each condition.

The rivet has enough hardness to piece the sheets, whereas the rivet is plastically deformed and the tubular leg of the rivet spreads. The joining process simulation has been performed for four rivet material models and one sheet material – see Table 1. It has been decided to perform the joining process simulation for other rivet material models (material model 2 to 4), Fig. 6.

The joined sheet and rivet yield point ratio significantly influences the joint creation process:

sr

sσσσ

= 02

02

, (3)

so this relationship has been additionally designated as Sσ. For the examined material models 1, 2, 3, 4, the Sσ value has been respectively: 11.26 (1), 8.71 (2), 7.26 (3) and 11.26 (4). Note that the difference of yield stresses for upper and lower sheet also affects the joint part behaviour when pressing the rivet. Note that the difference of yield stresses for upper and lower sheet also affects the joint part behaviour when pressing the rivet.

Due to a large number of variables in the form of input data, only one rivet geometry alternative has been used in the experiment. For all contact surfaces, the Coulomb friction model with the coefficient of friction µ = 0.05 has been adopted. In order to determine the coefficient friction effect on the joint forming process and riveting forces, the coefficient of friction µ = 0.1;

a) b) c) d)

Fig. 7. The general assumptions of die geometry with modified impression (var. II-V)



0.15; 0.20; 0.25 has also been defined for the contact surface of the rivet and sheets.

Fig. 6. The strain hardening curves for various rivet models

In order to analyze the effect of die impression form to the strain of joint pieces and riveting force levels, die models of various profiles (five) have been created and designated as follows:• I, as a basic profile with the cone offset from

the die bearing surface by 0.5 mm (see Fig. 2b),

• II, where the cone apex is located on the bearing surface level (same depth as in profile I), see Fig. 7a,

• III, with a bigger height of the bearing surface relative to the cone apex by 0.5 mm (see Fig. 7b),

• IV, for h = H and eliminating the intermediate line between radius R 1.250 and R 2.810, and with increasing dimension w of the impression bottom by 0.37 (see Fig. 7c),

• V, where the truncated cone has been used (see Fig. 7d).

The numerical experiment has been limited to the sheets of identical material: Al/Al. In order to demonstrate the effect of the joined sheet thickness on the riveting process course and the joint quality indexes ti, some determined arrangements have been used for the analysis. Based on a simple relationship, the upper to lower sheet thickness ratio index has been determined for the purposes of analysis:

δ tst

sb

tt

= , (4)

and its values have been tabulated in Table 2. The remaining geometrical parameters, i.e. the die and rivet parameters have not been changed.

Table 2. The joined sheet thickness ratio index

Parameter Valueδt 0.5 0.6 0.7 0.8 0.9 1

tsb [mm] 2


The author has decided to present the selected simulation results using 3D model, which has been achieved by expanding 2D axisymmetric joint model, achieved as a result of computations. The purpose was a better visualization of SPR joint form. Due to a large amount of information that may result from numerical computations, it has been decided to present the most important simulation results for:• five alternatives of die impression,• five different coefficient friction values

between the rivet and sheets,• six combinations of upper to lower sheet

thickness ratio index,• four models of rivet material for the same

material model of joined sheets.When analyzing the riveting force

characteristics vs. punch displacement (Fig. 8) it can be said that the die impression III is the best solution due to the riveting force value. Let us look at the plastic strain distribution and joined element deformations (Fig. 9). For the die impression III, the finished joint has the highest number of imperfections, namely in areas 4, 5, and 6 (Fig. 9a) free spaces between individual joint elements may be observed, and those spaces may reduce the joint rigidity and load carrying capacity. The joint made with the die impression II has the lowest number of imperfections. The force required to make such a joint is higher by approx. 13500 N comparing to profile alternative III, however, it is also lower by approx. 15000 N than in profile alternative I.

Using the die with an alternative IV and V when joining, has no significant effect on the riveting, force curve and its maximum value. The profile V and I features the same maximum riveting force, but for the profile IV the maximum


328 Mucha, J.

riveting force was 48500 N. It has been decided not to place them on any chart for clarity purposes.

Fig. 8. A comparison of riveting force curve for three profiles (rivet mat. 1, μ = 0.05, δt = 0.5)

It is significant to note that by using the dies with various impressions it is possible to change the form and size of the joint itself. Fig. 10 presents the characteristics of the finished joint diameter change Dj vs. used die alternative.

For the die impression III, the lowest riveting force has been achieved (Fig. 8) at reduced Dj size (Fig. 10), however at the burden of joint height growth on the side of a flash. For all die impression form cases as referred to the above, the value of material shrinking (t3) in an area 1 (Fig. 9a) was on a similar level. Its values and relations between the remaining indexes have been presented in Fig. 11. The local minimum for considered die alternatives may be observed on this chart. Due to a value of some indexes, the die impression profile IV seems to be the most

a) variant I variant II variant III variant IV variant V

b)

Fig. 9. The view of the joint made with the die of five impression alternatives: a) joint cross section, b) plastic strain distribution in the rivet (rivet mat. 1, μ = 0.05, δt = 0.5)

Fig. 10. The outer diameter of the finished joint Dj (flash) vs. used die impression for joining

(rivet mat. 1, μ = 0.05, δt = 0.5)

Fig. 11. The ti parameters for the joint made with die impression profile: I, II, III, IV, V (rivet mat. 1,

μ = 0.05, δt = 0.5)



effective for their highest values, as this has a significant meaning.

When riveting with the die impression profile III the lowest riveting force has been achieved (Fig. 8), but also the lowest caving t2 of the rivet in the lower sheet (Fig. 11) and its spreading (Fig. 12). The value of caving significantly influences the finished joint strength properties.

In this way, the application of such a die impression is not a favourable solution in that case. In turn, for the die impression alternative IV the highest values of the rivet caving in the lower sheet t2 and the second sheet shrank on the die cone t1. The value of the rivet spread index for die impression alternative II, IV, V is basically on the same level (Fig. 12). From the high value ti parameters preservation point of view, using the die impression form IV and V gives the best results for aluminum sheet joining.

Fig. 12. The effect of die impression form on the rivet spreading index in the finished joint (rivet

mat. 1, μ = 0.05, δt = 0.5)

The riveting force courses presented on Fig. 13 were determined based on the analysis of five models with different coefficients friction between the rivet and sheets. The friction between the rivet and the sheets has an influence on the results of the simulation, especially the friction between the rivet and the top sheet. The higher the value of the friction, the higher is the force needed to push the rivet though the sheet.

The final shape of the rivet shank and the part of the top sheet in contact with the tip of the rivet shank is influenced by friction. Such a

defined coefficient friction in the model does not significantly affect the maximum riveting force and the die impression filling. This is a factor, which significantly affects the value and the range of plastic strains in joined sheets and joint element deformation, see Fig. 14. The higher value the coefficient of friction, the higher are joint element deformations and material separation delay. This may be explained by the fact that at higher coefficient friction values, the material displacement resistance on the body contact boundary increases.

Fig. 13. The riveting force course vs. punch displacement for different coefficients friction between the rivet and joined sheets (die var. I,

rivet mat. 4, δt = 0.5)

a) b)Fig. 14. The comparison of the equivalent plastic strain distribution and joint element deformation

at the same punch path for the model with μ between rivet and sheets; a) 0.05,

b) 0.25 (die var. I, rivet mat. 4, δt = 0.5)

For different combinations of sheet thickness ratio tst/tsb, the fastener (with specified material properties) sooner or later expands in


330 Mucha, J.

the created joint. The simulation results in form of individual index values and their courses for corresponding joint alternatives was placed in the charts, see Figs. 15 and 16. The higher the upper to lower sheet thickness ratio dt, the higher are the values of parameter t3, both for the rivet material model 1 and 3. The remaining parameters, i.e. t1, t2, t4 decrease while the upper sheet increases for each presented rivet material model.

Specific rivet material properties, e.g. the yield point and the hardening curve course, significantly affect the value of ti parameters during the joining process.

Fig. 15. The effect of joined sheet thickness ratio index δt during the riveting on final parameters ti

(die var., I, rivet mat., 3, μ = 0.05)

Fig. 16. The effect of joined sheet thickness ratio index δt during the riveting on final parameters ti

(die var. I, rivet mat. 1, μ = 0.05)

The relations between specific parameters ti and their course are presented in Fig. 17, where some regularity may be observed. The parameter t2 increases and t3 decreases while the resistance of the rivet material to plastic strain increases. This is due the increased rivet rigidity, which is responsible for specific sheet material flow in the die impression.

Fig. 17. The effect of sheet and rivet yield point index to ti parameter variations for joined

aluminum sheet (rivet mat. 1-3, die var. – I, μ = 0.05)

Fig. 18. The effect of sheet and rivet yield point index to the rivet expansion index in the finished

joint (rivet mat. 1 to 4, die var., I, μ = 0.05, δt = 0.5)

The rivet material response during its pressing is its hardening due to corresponding plastic strains. With a diversified rivet material hardening characteristics different behavior of rivet material may be found during the joining process (Fig. 18). The higher yield point ratio index Sσ,



the higher rivet spread index values are achieved in the joint. The selection of corresponding rivet material features, i.e. plastifying strain and its hardening curve course significantly affects the joint forming process and the final result in form of parameters ti, SDr, which finally is reflected in the load carrying capacity. In addition to the yield point the material hardening curve course should also be accounted for when selecting the rivet material for the specified combination of joined sheet mechanical properties.The difference of yield stresses for upper and lower sheet also affects the joint part behaviour when pressing the rivet. However, this requires a separate analysis.

5 CONCLUSIONS

The numerical FEM simulation results may be used when designing those modern joints both for other arrangements of joined sheet mechanical properties and the technology used to create them. Once the analysis has been performed, detailed conclusions were achieved and the most important conclusions are presented as follows:• One of the significant factors affecting the

finished joint form is the die impression geometry. Proper selection of die impression enables riveting force reduction and achievement of the smallest flash diameter of the finished joint. Lowering the conical part of die impression (i.e. making it flush with a die face) and decreasing the impression depth resulted in the highest value of most ti indicators;

• Proper selection of corresponding rivet material features, i.e. its yield point and strain hardening, enables a significant change of the sheet joining process and specific finished joint parameters;

• The energy consumption for the rivet strain depends, among else, on the strain hardening curve. The final joint parameters (ti) and the energy needed to the rivet material strain should be considered when selecting the rivet material (see Fig. 6).

The total forming energy dissipation rate in this case is obtained by summing-up all the energy dissipation rates, which are caused by the internal plastic deformation, shear at the velocity

discontinuities and due to friction at the tool-material interfaces, i.e. E E E ET i s f= + + , (5)

where:Ei is the internal energy dissipation rates due to

plastic deformation,Es is the energy dissipation rates along the

velocity discontinuity surfaces,E f is the frictional energy dissipation rates.

The internal energy dissipation rates due to plastic deformation are defined as:

E dVi ij ijV

= ∫σ ε , (6)

where:σij stress tensor,ε ij strain-rate tensor,V the volume.

Shear energy dissipation rates can be obtained using the following equation:

E k dAsA

= ∫ ∆ν , (7)

where k,│Δν│andA are the yield shear stress, the change of velocity at the velocity discontinuity surface and the area of the surface, respectively. The value of k =σ / 3 .

The frictional energy dissipation rates at the tool material interfaces may be determined using the basic equation:

E v dA mk v dAfA A

= =∫ ∫τ ∆ ∆ , (8)

where τ and m are the shear stress at the frictional surface and the friction shear factor which is assumed to be a constant over the surface, irrespective of the pressure between them and the velocity between the tool and the material, and this may be taken as τ = m·k,with0≤m ≤l.

The external energy rate of deformation is forming load:

F V Er p t= , (9)

where:Fr the riveting force,Vp velocity punch.


332 Mucha, J.

Hence,

FEVr

t

p

=

. (10)

The enclave of the plastic region, the deformed geometry, the punch load, and the value of parameters ti can be predicted by the finite element model. This information can be used to improve the manufacturing process and the design of tools. In the future, more precise optimization of the components will be possible by transferring data from previous stages of sheet forming and joining to the structural computation code.

6 REFERENCES

[1] Ozel, K., Sahin, M., Akdogan, A. (2008). Mechanical and metallurgical properties of aluminium and copper sheets joined by cold pressure welding. Strojniški vestnik - Journal of Mechanical Engineering, vol. 54, no. 11, p. 796-806.

[2] Barnes, T.A., Pashby, I.R. (2000). Joining techniques for aluminium spaceframes used in automobiles, Part 2 – Adhesive bonding and mechanical fasteners. Journal of Materials Processing Technology, vol. 99, no. 1-3, p. 72-79.

[3] Mucha, J. (2007). Modern mechanical on press joinability techniques for sheet metal elements. Proceedings of the International Scientific Conference Progressive Technologies and Materials in Engineering, Pro-Tech-Ma`07, p. 43-44.

[4] Kochan, A. (2000). Audi moves forward with all aluminium cars. Assembly Automation, vol. 20, no. 2, p. 132-135.

[5] Mortimer, J. (2001). Jaguar uses X350 car to pioneer use of self-piercing rivets. Industrial Robot: An International Journal, vol. 28, no. 3, p. 192-198.

[6] Carle, D., Blount, G. (1999). The suitability of aluminium as an alternative material for car bodies. Materials and Design, vol. 20, no. 5, p. 267-272.

[7] Di Lorenzo, G., Landolfo, R. (2004). Shear experimental response of new connecting systems for cold-formed structures, Journal of Constructional Steel Research, vol. 60, no. 3-5, p. 561-579.

[8] Varis, J. (2006). Economics of clinched joint compared to riveted joint and example of applying calculations to a volume product. Journal of Materials Processing Technology, vol. 172, no. 1, p. 130-138.

[9] Mucha, J. (2007). History of the riveted joint technique (Self Piercing Riveting – SPR). Mechanik, vol. 80, no. 5-6, p. 454-460.

[10] Mucha, J. (2007). Classification and characteristic of the riveted joints without making holes. Technologia i Automatyzacja Montażu, vol. 58, no. 4, p. 7-10.

[11] Pickin, C.G., Young, K., (2007). Tuersley I. Joining of lightweight sandwich sheets to aluminium using self-pierce riveting. Materials and Design, vol. 28, no. 8, p. 2361-2365.

[12] Han, L., Chrysanthou, A., Young, K.W. (2007). Mechanical behaviour of self-piercing riveted multilayer joints under different specimen configurations. Materials and Design, vol. 28, no. 7, p. 2024-2033.

[13] Mucha, J. (2008). The influence of shape of tool die and blankholder on effect of deformation joint elements and rivetion load values. Acta Mechanica Slovaca, vol. 12, no. 3, p. 279-286.

[14] Han, L., Young, K.W., Chrysanthou, A., O’Sullivan, J.M. (2006). The effect of pre-straining on the mechanical behaviour of self-piercing riveted aluminium alloy sheets. Materials and Design, vol. 27, no. 10, p. 1108-1113.

[15] Abe, Y., Kato, T., Mori, K. (2006). Joinability of aluminium alloy and mild steel sheets by self piercing rivet. Journal of Materials Processing Technology, vol. 177, no. 1-3, p. 417-421.

[16] Mori, K., Kato, T., Abe, Y., Ravshanbek, Y. (2006). Plastic joining of ultra high strength steel and aluminium alloy sheets by self piercing rivet. CIRP Annals – Manufacturing Technology, vol. 55, no. 1, p. 283-286.

[17] Porcaro, R., Hanssen, A.G., Langseth, M., Aalberg, A. (2006). Self-piercing riveting process: An experimental and numerical investigation. Journal of Materials Processing Technology, vol. 171, no. 1, p. 10-20.



[18] De Paula, A.A., Aguilar, M.T.P., Pertence, A.E.M., Cetlin, P.R. (2007). Finite element simulations of the clinch joining of metallic sheets. Journal of Materials Processing Technology, vol. 182, no. 1-3, p. 352-357.

[19] Mucha, J. (2009). Numeric study of the phenomena occurring in the self piercing riveting process, Mechanik, vol. 82, no. 4, p. 286-291.

[20] Mucha, J. (2009). Some aspects of designing process self piercing riveting. Archives of Mechanical Technology and Automation, vol. 29, no. 4, p. 91-101.

[21] Bouchard, P.O., Laurent, T., Tollier, L. (2008). Numerical modeling of self-pierce

riveting – From riveting process modeling down to structural analysis. Journal of Materials Processing Technology, vol. 202, no. 1-3, p. 290-300.

[22] Atzeni, E., Ippolito, R., Settineri, L. (2009). Experimental and numerical appraisal of self-piercing riveting. CIRP Annals –Manufacturing Technology, vol. 58, no. 1, p. 17-20.

[23] MSC (2005). SuperForm, User`s Guide.[24] MSC (2005). Marc, Theory and user

information, Volume A.[25] MSC (2005). Marc, Element library, Volume

B.


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

Surface Integrity after Mechanical Hardening of Various Aluminium Alloys

Žagar, S. – Grum, J.Sebastjan Žagar - Janez Grum*

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

The paper presents two types of aluminium alloys, EN AW 2007 and EN AW 6082, treated by shot peening in which the surfaces of the metals were subjected to cold deformation under different treatment conditions. For this purpose, S170 steel particles with a diameter of 0.5 mm and a hardness of 56 HRC were used with different air pressures and mass flows, providing Almen intensity levels between 10A and 28A. The treated surfaces were studied in terms of surface integrity at macro- and microscopic levels, and the surface roughness, microhardness profiles, and residual stresses of each treated surface layer were recorded. Research results reveal significant differences between the properties recorded in the surface integrity examination, which are based on the selected shot peening parameters. This means that these parameters substantially impact the surface conditions and the surface layer. The microscopic analysis confirmed that the sharpest treatment conditions result in surface deformations which may cause cracks and subsequently lead to the mechanical part’s collapse.©2011 Journal of Mechanical Engineering. All rights reserved. Keywords: shot peening, surface integrity, surface roughness, residual stresses, microhardness

0 INTRODUCTION

Due to numerous set-up parameters, shot peening is a very complicated process. By changing the parameters, a comparison of various treatment effects can be made based on Almen intensity measurements. The effects of the shot peening process can be influenced by modifying the following properties:• Peening medium type,• Available amount of the peening medium

energy,• Mass flow determining surface coverage,• Angle of incidence of the peening medium,• Nozzle distance, • Shot peening exposure time.

The quality of the shot-peened surface strongly depends on the material type and properties, the type of previously performed treatments, and the depth of the hardened layer [1] to [4]. For practical reasons, the industry compares the efficacy of various shot peening conditions to Almen intensity, which classifies these conditions according to hardness level. This, however, does not allow a direct comparison of microstructural changes nor a comparison of microhardness profiles and residual stresses of the mechanical part [5]. Moreover, shot peening also

affects surface microgeometry which is modified depending on the impact intensity of individual particles. Shot-peened surfaces are described in terms of standard surface roughness parameters [6] and [7].

Cold plastic deformation of the material's surface layer increases the density of dislocations, which in turn enhances the hardness of the material and causes residual stresses in the thin surface layer. Peening conditions that ensure a quality surface and an adequate fatigue strength of the material by using the particles' kinetic energy must, therefore, be selected. If shot peening parameters are too sharp, surface defects which undermine longterm hardness of materials in dynamic loading despite their enhanced hardness and greater residual stresses [8] and [9] may occur.

Herzog et al. [10] investigated the correlation between the material type, diameter, shot peening speed, and mass flow of the particles and hardness profiles and residual stresses in the surface layer of the 7020 aluminium alloy. As shot peening research parameters were modified, shot peening effects were determined by using Almen intensity. The results revealed that the size and profiles of the surface layer residual stresses influence the longevity of the material's dynamic hardness, i.e. fatigue strength. Additionally, this


335Surface Integrity after Mechanical Hardening of Various Aluminium Alloys

proved that in order to predict the desired residual stress profiles, a comparison between the shot peening parameters and Almen intensity will not suffice, as all parameters relevant to the process must always be included.

Guagliano [11] established a correlation between Almen intensity and different particle sizes and speeds for various materials under the same shot peening conditions. The induced residual stress profiles of the specimen surface layer after the shot peening process were determined by using the end elements method and were then compared with the experimental results. The research proved that by using the end elements method the residual stress profiles of the specimen surface layer can be very successfully predicted, with minor deviation, for different particle diameters (0.5 mm) and constant Almen intensity (12 A). The aim of the research was to offer users adequate guidance in selecting optimal shot peening conditions that guarantee the desired or required residual stress profiles.

Hong et al. [12] also used the end elements method to analyze the influence of individual shot peening parameters on the achieved residual stress profiles, such as the selection of various particle diameters and speeds while considering different angles of incidence. It was found that the particles reach the highest residual stress values at the angles of incidence between 90 and 75°. With the angles of incidence smaller than 75°, the same depths of the hardened layer are achieved with different residual stress profiles.

Kek et al. [13] present the research of a laser surface hardening process applied to the C45E steel with graphite absorber coating on specimen surfaces. The evaluation of the laser surface hardening process was performed by measuring the IR radiation from the interaction spot. The results confirmed a strong correlation between the IR radiation voltage signal and the dimensions of microstructural changes occuring in the laser surface hardening steel.

Trdan et al. [14] also investigated the optimum laser shock processing parameters for aluminium specimens in order to obtain the desired residual stress variation and improved corrosion resistance. The conducted experiments confirmed a characteristic influence of the first factor representing different pulse densities.

Potentiodynamic corrosion testing confirmed that the higher pulse density resulted in a stronger shift of pitting potential, which provided higher corrosion resistance.

Zupanc et al. [15] investigated the effect of surface hardening by shot peening on fatigue properties of high-strength aluminium alloy 7075-T651. The obtained results show a favourable influence of SP treatment on fatigue properties as induced compressive residual stresses and hardened surface layer retarded the initiation of fatigue cracks.

1 EXPERIMENTAL PART

1.1 Materials

Shot peening experiments using hard particles were conducted on the 2007-T351 and 6082-T651 aluminium alloys with the aim of comparing different shot peening parameters that influence surface integrity.

The specimens were obtained by cutting a 40-millimeter diameter rod into 8-millimeter thick disks. The cutting was performed with a cutting wheel used in the preparation of metallographic specimens under mild conditions and by using a coolant.

The 2007-T351 aluminium alloy was first subjected to homogenization annealing at 495 ºC and then hardened by natural ageing at room temperature. The chemical compositions of both alloys are given in Table 1. Apart from aluminium, the 2007 alloy also includes 3.3% to 4.6% copper, forming the first secondary phase Al2Cu, and magnesium and silicon, forming the second secondary phase Mg2Si. Both phases contribute to improving the alloy's mechanical properties.

The other aluminium alloy, 6082 - T651, was first treated by the homogenization annealing process at 540 ºC and subsequently hardened by artificial ageing at 160 ºC for 10 hours. The amount of copper in the 6082 alloy is very low, but the secondary phase Mg2Si, formed by magnesium and silicon, enhances the solid solution after ageing. The standard-based mechanical properties of both aluminium alloys are given in Table 2. The 2007 alloy with the separate phases Al2Cu and Mg2Si has greater


336 Žagar, S. – Grum, J.

tensile strength and hardness than the 6082 alloy which yields a single separate phase, i.e. Mg2Si.

1.2 Specimen Preparation

Only the S170 steel balls with a diameter of 0.5 mm were used in shot peening surface treatment on all specimens. The process was performed on a number of specimens with different mass flows ( m ), which was achieved by selecting various working air pressures (p) determining particle travel speed and kinetic energy. These different air pressure values were also used to obtain different mass flows of the steel balls. Upon impact, the particles' kinetic energy causes plastic deformation of the specimen surface. The level of plastic deformation is determined through surface hardness modifications and the hardness profile of the thin surface layer. The changes in the hardness profile and residual stresses of the shot-peened layer depend on dislocation density after surface treatment. The treatment utilizing the particles' kinetic energy guarantees longer life cycle of

mechanical parts, which depends on the density of the dislocations occurring after treatment.

The overlap of the indentations made by individual balls on the specimen surface is defined by the particle mass flow and travel speed. The shot-peening parameters for the 2007 and 6082 alloys are given in Table 3. Individual specimens of both alloys, which were treated under different conditions, are marked with numbers. The same conditions were applied to both alloys and only air pressure, particle mass flow, and nozzle speed values varied. Based on Almen values, it can be concluded that the first two specimens were subjected to very similar conditions, i.e. 10 A and 12 A, while sharper conditions were applied to the remaining two, with a substantial deviation from mild conditions. 21 A and 28 A were selected as sharp shot-peening conditions. The results of the surface treatment can, therefore, be compared with the actual conditions or, alternatively, a comparison based on the Almen intensity test can be applied.

Table 1. Chemical composition of the treated aluminium alloys

DesignationElement [%wt]

Si Fe Cu Mn Mg Cr Ni Zn Ti AlENAW 2007 0.8 0.8 3.3-4.6 0.5-1.0 0.4-1.8 0.1 0.2 0.8 0.2 restENAW 6082 0.7-1.3 0.5 0.1 0.4-1.0 0.6-1.2 0.25 / 0.2 0.1 rest

Table 2. Mechanical properties of the treated aluminium alloys

Designation State Chemical designation

Rm[MPa]

Rp0,2[MPa]

A[%]

Hardness[HV0.2]

ENAW 2007 T351 AlCu4PbMgMn 370 240 9 118ENAW 6082 T651 AlSi1MgMn 310 260 13.5 89

Table 3. Shot peening parameters of the treated aluminium specimens

Alloy Specimen Working pressure p [bar]

Mass flow m [kg/min]

Nozzle speed vN [mm/min]

Arc height h [mmA]

2007

#1 1.6 1.0 1800 0.25#8 1.6 1.5 2400 0.31#9 4 1.6 2600 0.53#13 8 1.5 2800 0.7

6082

#3 1.6 1.0 2800 0.25#7 1.6 1.5 3000 0.31#12 4 1.6 3200 0.53#16 8 1,5 3400 0.7




2.1 Surface Roughness

Surface roughness was determined in all specimens immediately after they were cut and after the surfaces were treated by shot peening. Surface roughness was measured in various directions according to cutting direction. The specimens were also measured for microhardness and residual stresses before and after treatment. In addition, a microstructural analysis of the material before and after shot peening was performed by using optical microscopy.

The arithmetic mean roughness Ra of the surface profile and the mean roughness depth Rz were chosen as the properties used to estimate the roughness of shot-peened specimens. In their studies, authors generally focus only on one of these when describing surface profile. In our research, however, both values were calculated in order to achieve a better view of the surface arch formation. The values (Ra and Rz) were determined based on the captured surface profile utilizing Taylor Hobson’s Surtronic 3+ profile meter and their software, TalyProfile Lite 3.1.4.

The profiles of the shot-peened specimen surfaces were captured at a length of L = 8 mm, with 10 repetitions, and recorded at different reference points, namely, in two directions at the specimen edge and in the specimen centre. The measuring positions and surface profile directions are indicated in Fig. 1. Eight measurements were performed at the edge of the shot-peened specimen, four of them longitudinally and four transversely. The remaining two measurements were obtained in the centre of the shot-peened specimen in both directions. Based on the ten surface profile records of a single specimen, both mean rougness values, Ra and Rz, were calculated. To obtain surface roughness values under different shot-peening conditions, both mean values, Ra and Rz, were calculated for the two aluminium alloys. The data on these two properties help to estimate the differences occuring in the surface layer before and after the shot peening of specimens under different shot-peening conditions. When comparing different measurement directions, deviations in surface roughness can only be found in untreated specimens, which is attributed to

uneven cutting due to the pressure variation of the cutting wheel. The resulting abrasions are proportionally uneven, directed, big, and clearly visible.

Fig. 1. Measuring positions in both treated aluminium alloys

After the surface was treated by shot peening using hard steel balls, its profile varied based on treatment conditions. The calculated values confirm this fact. The column diagrams representing the calculated arithmetic mean of surface roughnesses Ra and the mean values of profile depth Rz are shown in Figs. 2 and 3. The calculated values of both properties, Ra and Rz , differentiate on the multiple level before as well as after specimen treatment.

After the surface treatment by shot peening, surface roughness increases with an increase in the working pressure, with constant mass flow and nozzle speed. The specimens treated at the same working pressure, i.e. 1.6 bar, but with different particle mass flows reveal no significant differences in the calculated surface roughness values. The results show that by increasing the particle mass flow from 1 kg/min to 1.5 kg/min, while air pressure remains constant, surface roughness even slightly decreases, as expected. The lesser degree of roughness with greater mass flow is attributed to increased impact coverage of the treated surface. This means that a greater degree of overlap between individual arch formations and lesser surface roughness is achieved with increased particle mass flow.



The specimens treated with higher working air pressures (4 bar and 8 bar) confirm that the particles’ kinetic energy used for the shot peening treatment of the surface is greater and, with constant mass flow, contributes to increasing surface roughness profile. Surface roughness can be estimated based on the arch height and given in Almen intensity. The results reveal that roughness increased with an increase in Almen intensity. An increase in roughness of the shot-peened surfaces is characteristic of softer materials, including the selected aluminium alloys [16].

2.2 Metallography of Treated Specimens

Overlapping of individual arch formations generated by the particles impacting the specimen surface can be revealed through microanalysis. The depth of the formation in the surface layer of the treated specimens can be estimated from specimen cross-section. For this purpose, one

fourth of the specimen was cut off and measured under the microscope. Macro images of specimen cross-sections, magnified 200 times, were recorded and a 500x microscopic analysis was performed.

Fig. 4. Microstructure of the treated sample

Fig. 4 depicts the specimen microstructure before shot peening, consisting of a soft matrix and precipitates. The frame in Fig. 4 indicates an area of increased precipitate concentration and the

a) b)Fig. 2. Surface roughness before treatment for both aluminium alloys;

a) alloy 2007-T351, b) alloy 6082-T651

a) b)Fig. 3. Surface roughness after treatment for both aluminium alloys;

a) alloy 2007-T351, b) alloy 6082-T651



encircled area is the area with a smaller precipitate concentration. The increased concentration of more solid precipitation influences the level of plastic deformation of the surface resulting in less surface roughness.

The surface after shot peening is represented by the macro images given in Figs. 5 and 6, with clearly visible indentations made by individual particles. Specimen microstructures examined under magnitudes of 200x and 1000x after the shot peening of the ENAW 2007 and ENAW 6082 aluminium alloys are shown in Figs. 5 and 6, respectively. The microstructure is visible due to extrusion, along with the fine distribution of the crystallized phases. The cross-section of the thin surface layers shown in Figs. 5c, 5d, 6c and 6d, which represent specimen microstructure after the specimens were treated by sharp shot peening conditions, p = 4 bar, m = 1.6 kg/min and p = 8 bar, m = 1.5 kg/min. Various defects, such as

surface damage, can be detected. They indicate that the selected shot peening conditions were inadequate.

The specimens subjected to lower working air pressure, i.e. 1.6 bar, reveal no noticeable surface or under surface defects that might reduce material longevity. Additional microhardness and residual stress measurements of the thin surface layer confirmed the treatment results related to dislocation density.

The extreme shot peening conditions also yielded fractures occurring because the critical level of the specimen’s local cold deformation after the impact was exceeded. Surface defects and fractures in the shot-peened surface layer reduce material quality in terms of longevity and stability in dynamic loading of mechanical parts through local stress concentrations. As a result, the existing fractures may be enhanced during operation by the

M 200:1 M 200:1 M 200:1 M 200:1

M 1000:1 M 1000:1 M 1000:1 M 1000:1

M 40:1 M 40:1 M 40:1 M 40:1a) p1 = 1.6 bar, m =1.0 kg/min, Rz = 29.97 μm, Ra = 6.03 μm

b) p2 = 1.6 bar, m =1.6 kg/min, Rz = 25.91 μm, Ra = 5.19 μm

c) p3 = 4 bar, m =1.5 kg/min, Rz = 39.81 μm, Ra = 8.31 μm

d) p4 = 8 bar, m =1.6 kg/min, Rz = 55.89 μm, Ra = 12.13 μm

Fig. 5. Microstructure of aluminium alloy after shot peening treatment; a) 2007/1, b) 2007/8, c) 2007/9, d) 2007/13



stress-concentration factor causing a collapse of the mechanical part.

2.3 Microhardness

Microhardness measurement was performed in the adequately prepared specimen cross-sections. The specimens were cut in fourths, inserted into bakelite, ground, polished and etched to ensure a smooth surface and a clearly visible microstructure and to separate the indentations in order to determine microhardness profiles. The primary aim of the research was to establish a correlation between the microstructure and indentation size or the microhardnesses of individual specimens subjected to different shot peening conditions.

After the specimens were thus prepared, a reliable microhardness profile of the thin surface

layer was determined based on the selected microhardness measurement method given in Fig. 7. The microhardness of the specimens was measured only by examining the treated layer where the material hardness is greater than the hardness of the alloy in its primary phase. As reference, a distance of 25 μm between individual indentations was selected following a line 18° to the surface. In this way, a sufficient number of measurements were performed to allow for an accurate presentation of microhardness profile. In measuring microhardness perpendicular to the line of the treated surface, the measurements were performed horizontally with 25 μm gaps while the specimen was moved vertically in three diagonal lines 75 μm apart. This procedure prevents the results of the microhardness measurements to be influenced by material hardening due to previous measurements. The selected microhardness

M 200:1 M 200:1 M 200:1 M 200:1

M 1000:1 M 1000:1 M 1000:1 M 1000:1

M 40:1 M 40:1 M 40:1 M 40:1a) p1 = 1.6 bar, m =1.0 kg/min, Rz = 33.41 μm, Ra = 6.82 μm

b) p2 = 1.6 bar, m =1.6 kg/min, Rz = 31.75 μm, Ra = 6.38 μm

c) p3 = 4 bar, m =1.5 kg/min, Rz = 47.98 μm, Ra = 10.33 μm

d) p4 = 8 bar, m =1.6 kg/min, Rz = 65.73 μm, Ra = 13.93 μm

Fig. 6. Microstructure of aluminium alloy after shot peening treatment; a) 6082/1, b) 6082/8, c) 6082/9, d) 6082/13



measurement method was then repeated at three measuring positions indicated in Fig. 7 as I, II, and III. The measurements were performed in both cross-sections, 1 and 2. This makes up six microhardness measuring sets performed at different measuring points in each specimen.

Fig. 7. Sample preparation for microhardness measuring

100

110

120

130

140

150

160

0 50 100 150 200 250 300 350 400

Depth z [µm]

Mic

roha

rdne

ss H

V0.

2

2007 as recived

2007/1 p=1.6 bar

2007/8 p=1.6 bar

2007/9 p=4 bar

2007/13 p=8 bar

Fig. 8. Microhardness profiles for aluminium alloy ENAW 2007

Figs. 8 and 9 represent microhardness profiles in the surface layer for different parameters applied to the treated specimens of the ENAW 2007 and ENAW 6082 alloys respectively. The microhardness profile is a good indicator of the hardened surface layer which significantly influences the operation of mechanical parts in dynamic loading. A higher degree of cold plastic deformation in the surface layer of the material indicates an increased density of dislocations, influencing, together with the density and size of the precipitates, the properties of the surface layer.

Fig. 8 shows the microhardness profiles of the ENAW 2007 alloy, measured in the specimens treated with the working air pressure of 1.6, 4, and 8 bar. The microhardness profiles predictably

mildly descent in all cases. In the specimens treated with 1.6 bar, the surface microhardness values and microhardness in-depth profile are lower than those in the specimens treated with a higher air pressure. There is a substantial difference in the hardness achieved, amounting up to 20 HV0.2, i.e. 20% of the hardness of the material in its primary phase. Based on the microhardness profiles, hardness depth can be estimated for individual surface treatment parameters. Hardness depth in the specimens treated with the working air pressure of 1.6 bar was 260 μm, while in the specimens treated with a higher air pressure its values were cosiderably higher, even up to 390 μm. The following can be concluded from the measurement of the microhardness profiles:• The profiles of the measured microhardnesses

are very similar and differ only in hardness depth and absolute values.

• Important differences are found in microhardness values for specimens treated with air pressure lower than 1.6 bar and those treated with higher air pressures, 4 or 8 bar.

• The depth of the hardness achieved also depends on treatment parameters, amounting to about 260 μm for lower and to about 390 μm for higher air pressure values.

80

90

100

110

120

0 50 100 150 200 250 300 350 400

Depth z [µm]

Mic

roha

rdne

ss H

V0.

2

6082 as recived

6082/3 p=1.6 bar

6082/7 p=1.6 bar

6082/12 p=4 bar

6082/16 p=8 bar

Fig. 9. Microhardness profiles for aluminium alloy ENAW 6082

Fig. 9 shows the microhardness profiles in individual ENAW 6082 specimens treated with the same parameters as the ENAW 2007 specimens. Based on individual microhardness measurements in the specimens treated with the intensities of I = 0.53 mmA and I = 0.7 mmA, a 30% increase in microhardness is found after shot peening compared to the average hardness values of non-hardened specimens. An important factor is a falling trend of microhardness values in



the thin surface layer. In addition to air pressure, nozzle speed and particle mass flow also show a significant influence on microhardness profiles or microhardness profile in-depth gradient.

The microhardness profile of the treated surface layer is indicative of the degree and depth of material hardening that influence residual stress size and profile. The achieved residual stresses improve the fatigue strength of the material in dynamic loading of mechanical parts, which prolongs its life cycle. The soft-state hardness of the ENAW 6082 alloy is 89 HV0.2 but is increased to 111 HV0.2, i.e. by 25%, when subjected to shot peening with the working air pressure 4 bar and a mass flow of 1.6 kg/min. Based on the microhardness profiles, the depth of the hardened layer was determined in relation to the hardening conditions. The results reveal a hardening depth of 240 μm in shot peening with a pressure of 1.6 bar and a depth of 390 μm for higher pressure values.

2.4 Residual Stresses

The residual stresses were measured by applying the ASTM standard-based hole-drilling method of stress relaxation [17] and [18]. The measurements were performed by using the Vishay RS 200 device with a pneumatic turbine for high-speed drilling. Due to the increased roughness of the specimen surface, the preparation of the specimens and the setting of the resistance-measuring rosette needed to be carried out very carefully for each residual stress measurement. The CEA-06-062-UM resistance-measuring rosette manufactured by Measurements Group Inc. was used to measure the deformations. The enhanced measuring signal was recorded by using the AT-MIO-16XE-50 data acquisition card and the National Instruments Lab VIEW 4.0 program. The results were processed with the H-DRILL program and the residual stress values were calculated using the integral method, which delivers a separate residual stress estimation for each step of the in-depth drilling process. The graphical representation of the results was given in Microsoft Excel.

Fig. 10 shows the profiles of the minimal values of the main residual stresses in the specimen surfaces of the ENAW 2007 alloy treated with hard steel particles with different air

pressure values. By measuring the deformations in each step of the resistance measuring, the necessary data was obtained to calculate the size of the main deformations and the main residual stresses.

-400

-300

-200

-100

0

100

200

300

400

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Depth z [mm]

Res

idua

l stre

sses

σm

in [M

Pa]

2007 as recived2007/1 p=1.6 bar2007/8 p=1.6 bar2007/9 p=4 bar2007/13 p=8 bar

Fig. 10. Residual stress profiles for aluminium alloy ENAW 2007

The values of the residual stresses in the starting state of the ENAW 2007 specimen, which occur in the mechanical specimen preparation (i.e. cutting of specimens), are minimal. The minimal residual stresses in the specimen surface even amount to about -50 MPa. In the 2007/1 and 2007/8 specimens, treated with lower Almen values, 10 and 12 A, a very similar residual stress profile can be found. The residual stresses achieved in these specimens are approximately -295 MPa, reaching a depth of about 250 μm. Likewise, the specimen marked 2007/9, which was treated with a working air pressure of 4 bar and a mass flow of 1.6 kg/min, a residual stress of -340 MPa was calculated for the depth of 270 μm. The 2007/13 specimen, which was subjected to the most severe conditions of working air pressure of 8 bar, only a minor increase in compressive stress value was determined, i.e. -362 MPa, at the depth of about 290 μm.

However, regardless of any shot peening parameters, the compressive residual stresses in the specimens are directed towards the tensile area with a gradient similar to the one in the surface, i.e. 1.05 MPa/μm. The transition from the compressive to the tensile area occurs between 650 and 700 μm almost independently of the treatment conditions, except in the 2007/1 specimen, treated with the least severe conditions, where the residual stresses, having reached the tensile area, remain almost constant at 20 MPa all the way through to the measuring depth of 1000 μm.



-400

-300

-200

-100

0

100

200

300

400

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Depth z [mm]

Res

idua

l stre

sses

σm

in[M

Pa]

6082 as recived6082/3 p=1.6 bar6082/7 p=1.6 bar6082/12 p=4 bar6082/16 p=8 bar

Fig. 11. Residual stress profiles for aluminium alloy ENAW 6082

Fig. 11 shows the profiles of the minimal values of the main residual stresses in the EN AW 6082 aluminium alloy. The compressive residual stresses in the specimen’s starting state after the cutting were very low, i.e. -15 MPa, reaching to a depth of 150 μm, and achieving the value of 10 MPa at 950 μm. The lowest residual stress value is found in the 6082/7 specimen, treated with a mass flow of 1.5 kg/min and a working air pressure of 1.6 bar. The main residual stress which was calculated is of a compressive nature with the highest value of -115 MPa at 450 μm that remains practically constant all through to 550 μm. At greater depths, the residual stress profiles gradually turn towards the tensile area, except in the 6082/7 specimen, where it remains within the compressive area all through to the measuring limit of 1000 μm.

The 6082/3 specimen, treated with the lowest Almen intensity of 10 A, shows a greater residual stress value compared to the former, which amounts to -167 MPa at a depth of 250 μm. After having reached the highest value, the residual stress profiles in the surface layer of this specimen are always directed towards the tensile area which they reach at a depth of 500 μm. The achieved residual stresses in the specimens treated with the highest working air pressures are obtained with similar residual stress profiles, amounting to -203 MPa in the 6082/12 specimen and to about -180 MPa in the 6082/16 specimen. In shot peening of the specimen surface with the highest air pressure, the maximum residual stress value is obtained immediately below the surface where the first measurement was performed at a depth of 33 μm. In both specimens subjected to the most severe conditions the tensile area is reached at about 550 μm.

3 CONCLUSIONS

To ensure the optimal properties of the surface layer hardened by cold deformation, the relevant parameters need to be reconciled, including the working air pressure that provides the necessary kinetic energy of the particle’s impact with the specimen surface. By applying the shot peening technique, a very uniform hardening of the entire specimen surface is guaranteed with the aim of improving the fatigue strength of the material required for the operation of mechanical parts in dynamic loading. Shot peening parameters optimization allows to control the size and the profiles of residual stresses, i.e. microhardness. Therein lies the importance of research on the influence of the surface shot peening parameters in different materials [19].

Based on the performed microhardness and residual stress measurements, the following can be confirmed:• The maximum values of the minimal

compressive residual stresses in the ENAW 2007 alloy are -362 MPa at a depth of 290 μm and -167 MPa at a depth of 250 μm in the ENAW 6082 alloy;

• In the treatment of both alloys, the values of the compressive residual stresses obtained in the surface layer were lower than the maximum values and amount to about 100 MPa. A very small residual stress gradient confirms an immensely favourable effect of the surface treatment process. In relation to the yield stress of both alloys, which is about 250 MPa, the obtained compressive residual stress value means a substantially increased fatigue strength of the material;

• The macro- and microscopic surface examination revealed that lower air pressure values should be selected with the same particle mass flow. The results of the research confirmed that by applying the particles’ kinetic energy obtained with lower air pressure values, a defect-free surface is guaranteed along with a substantial fatigue strength of the material. On the other hand, the treatment of the surface with higher air pressure values results in surface defects which influence the occurrence or growth of



surface cracks and may lead to a collapse of the material.

4 REFERENCES

[1] Rodopoulos, C.A., Curtis, S.A., de los Rios, E.R., SolisRomero, J. (2004). Optimisation of the fatigue resistance of 2024-T351 aluminium alloys by controlled shot peening-methodology, results and analysis. International Journal of Fatigue, vol. 26, no. 8, p. 849-856.

[2] Sharp, P.K., Clark, G. (2003). The effect of peening on the fatigue life of 7050 aluminium alloy. TSP, vol. 16, no. 4.

[3] Shot Peening Applications, 9th Ed., Metal Improvement Company, 2005.

[4] George, P.M., Pillai, N., Shah, N. (2004). Optimization of shot peening parameters using Taguchi technique. Journal of Material Processing Technology, vol. 153-154, p. 925-930.

[5] Benedetti, M., Bortolamedi, T., Fontanari, V., Frendo, F. (2004). Bending fatigue behaviour of differently shot peened Al 6082 T5 alloy. International Journal of Fatigue, vol. 26, no. 8, p. 889-897.

[6] Sidhom, N., Laamouri, A., Fathallah, R., Braham, C., Lieurade, H.P. (2005). Fatigue strength improvement of 5083 H11 Al-alloy T-welded joints by shot peening: experimental characterization and predictive approach. International Journal of Fatigue, vol. 27, p. 729-745.

[7] Sahaya Grinspan, A., Gnanamoorthy, R. (2006). Surface modification by oil jet peening in Al alloys AA6063-T6 and AA6061-T4: Residual stress and hardnes. Applied Surface Science, vol. 253. p. 989-996.

[8] Wagner, L. (1999). Mechanical surface treatments on titanium, aluminum and magnesium alloys. Materials Science and Engineering, vol. A263, p. 210-216.

[9] Jaensson, B., Magnusson, L. (1987). An investigation into the influence on the fatigue strength of aluminium alloy parts of load spectrum base level and residual stresses induced by shot peening or straightening.

Proceedings of the 3rd International Conference on Shot Peening, p. 423-430.

[10] Herzog, R., Zinn, W., Scholtes, B., Wohlfahrt, H. (1996). The Significance of almen intensity for the generation of shot peening residual stresses. Proceedings of the 6th International Conference on Shot Peening, San Francisco.

[11] Guagliano, M. (2001). Relating Almen intensity to residual stresses induced by shot peening: a numerical approach. Journal of Material Processing Technology, vol. 110, no. 3, p. 277-286.

[12] Hong, T., Ooi, J.Y., Shaw, B. (2008). A numerical simulation to relate the shot peening parameters to the induced residual stresses. Engineering Failure Analysis, vol. 15, no. 8, p. 1097-1110.

[13] Kek, T., Grum, J. (2010). Influence of the graphite absorber during laser surface hardening. Strojniški vestnik – Journal of Mechanical Engineering, vol. 56, no. 2, p. 150-157.

[14] Trdan, U., Ocaña, J.L., Grum, J. (in press). Surface modification of aluminium alloys with laser shock processing. Strojniški vestnik – Journal of Mechanical Engineering, DOI:10.5545/sv-jme.2010.119.

[15] Zupanc, U., Grum, J. (in press). Surface integrity of shot peened of 7075-T651 aluminium alloy. Strojniški vestnik – Journal of Mechanical Engineering, DOI:10.5545/sv-jme.2010.124.

[16] Grum, J. (2008). Surface integrity after shot peening applied to a precipitation hardened aluminium alloy. Metal Finishing News, vol. 9, no. 9, p. 54-56.

[17] Standard Test Method for Determining Residual Stresses by the Hole Drilling Strain Gage Method (1995). ASTM E 837-01, p. 694-703.

[18] Tech note TN 503-5 (1993). Measurement of Residual Stresses by the Hole-Drilling Strain Gage Method, Vishay Measurements Group.

[19] Schulze, V. (2005). Modern Mechanical Surface Treatment: States, Stability, Effects, WILEY-VCH Verlag Gmbh & Co. KGaA, Weinheim.

http://www.sv-jme.eu/scripts/download.php?file=/data/upload/2010/Clanki_za_web/Nov_10/2010_119_Trdan_06.pdf

http://www.sv-jme.eu/scripts/download.php?file=/data/upload/2010/Clanki_za_web/16_12_10/2010_124_Zupanc_04.pdf

http://www.sv-jme.eu/scripts/download.php?file=/data/upload/2010/Clanki_za_web/16_12_10/2010_124_Zupanc_04.pdf


*Corr. Author’s Address: Department of Applied Sciences, University of Quebec at Chicoutimi, Saguenay, (Qc), Canada, G7H 2B1. [email protected] 345

Fatigue Failure Study of the Lower Suspension Vehicle Arm Using a Multiaxial Criterion of the Strain Energy Density

Saoudi, A. ‒ Bouazara, M. ‒ Marceau, D.Abdelhamid Saoudi ‒ Mohamed Bouazara* ‒ Daniel Marceau

Department of Applied Sciences, University of Quebec at Chicoutimi, Canada

The objective of this study is to evaluate the potential of light alloy mechanical part use in automobile industry by studying their fatigue life using various parameters such as effect of suspension dynamic, excitation type, geometry and mechanical part weight. The studied part is the lower suspension arm made from 7075-T6 aluminium alloy. The strain density energy approach enables us to compare two same order tensor: the multiaxial and uniaxial cases. The random displacement excitation is obtained analytically from the power spectral density PSD. The force excitation is obtained by a simple normalisation of spectrum displacement. To avoid the use of Newton-Raphson method during the partial fatigue life calculation step in all mesh elements, a Matlab interface to identify the critical elements is developed. The strain energy density (SENER) signal of the critical element is corrected to remove anomalies by WAFO Matlab interface algorithm. Rainflow cycles are extracted using Markov formulation in order to calculate the number of signal repetitions to failure, which is calculated from Miner law.©2011 Journal of Mechanical Engineering. All rights reserved.Keywords: fatigue failure, vehicle, dynamic, suspension, aluminium

0 INTRODUCTION

Weight reduction not only improves the slip angle between tires and the road, reaction to turns and the stability of the vehicle, but it also makes driving more effective and safe over long distances and yields lower gasoline consumption [1] to [3]. In this framework, the research goals are to study the dynamic and vibratory effects on certain aluminium alloy parts, in particular fatigue life of the lower suspension arm. Fatigue causes cracking, which develops gradually under the action of random loading repetition. These random loadings can lead to rupture by fatigue during the application of stress levels. Failure occurs when a crack reaches a critical length lc and the stress intensity factor K [4] reaches a critical value Kc. The complexity of the fatigue problem led many researchers to approach the subject using several methods. Bazergui et al. [5] based their work on the curves of fatigue SN (stress S depending on the number of cycles to failure N) and two empirical models of fatigue to prevent rupture. They report rotational bending as a cheaper standardized test. To improve the ability of predicting fatigue life of a part, they practised on standard test-tubes before installing the operational part on apparatus. In practice, stress variation is often periodic, but it

is not always sinusoidal. The average value of the stress is not null because of the static contribution from the weight of the part and premature tightening. Cervello [6] analyzed and studied the design of railway wheels with weak noise. A numerical procedure was used for calculation of the loss factor. This procedure was checked on plates by means of experimental modal analyses. It allowed better treatment of smoothness and the choice of a commercially available arrangement with feasible technology. Elmarakbi et al. [7] studied the validity of multiaxial criterion of fatigue failure based on strain energy density equivalent to uniaxial case. They performed three-dimensional finite element analysis on SAE notch axis, which is used as a test component to evaluate the criterion of multiaxial damage caused by fatigue. They also equalized energy density of multiaxial case obtained from finite element commercial software. The analytical equivalent strain density energy in uniaxial cases is calculated and compared to numerical multiaxial one, since both of them have the same tensor order (order zero). March [8] based his study on the same criterion as Elmarakbi et al., density of the energy of cracking. March performed tension-torsion fatigue tests and compared the results with the energy density criterion. The model aimed to


346 Saoudi, A. ‒ Bouazara, M. ‒ Marceau, D.

predict fatigue life of rubber particles using two approaches. One focused on crack initiation, giving the history of some parameters such as stress state and deformations. Other approaches were based on ideas of the breaking process and dealt with predicting the propagation of particular cracks, giving the history of released energy rate. Crack propagation approach was developed by Rivlin and Thomas using reference [8] who applied Griffith’s criterion to rubber. The difficulty in applying the crack propagation approach to rubber is that it requires advance knowledge of the initial specimen and crack state which causes the final failure. Instead of part endurance prediction models that were based on Paris law, De-Andrés et al. [9] used element cohesive law. In this approach, the creation of new surfaces is the final result of a process of gradual loss of elasticity as separation increases.

In the present paper, prediction of an automotive part’s fatigue life is suggested by developing a multiaxial elasto-plastic numerical model. Knowing mechanical properties of aluminium alloy 7075-T6, fatigue failure prediction will be simulated with commercial

finite element software Abaqus and a Matlab interface. The lower vehicle suspension arm of a quarter vehicle suspension system is studied in a critical case, where the part is embedded at suspension joint. The stress state gives values of shorter and safer fatigue life by underestimating their true value. Treatment and analysis of the numerical results include: • development of a dynamic vehicle suspension

system model,• development of a road irregularity model,• development of a numerical model using

commercial finite element software,• analysis of results of strain density energy

time evolution of the multiaxial case in all mesh elements,

• filtering of the results to extract the critical elements in the elasto-plastic case,

• correction of critical element signal from anomaly of strain density energy,

• extraction of rainflow cycles by Markov algorithm,

• calculation of partial and total fatigue life of the part from the uniaxial criterion equivalent to the multiaxial case.

Fig. 1. Vehicle suspension control and the lower suspension arm


347Fatigue Failure Study of the Lower Suspension Vehicle Arm Using a Multiaxial Criterion of the Strain Energy Density

1 VEHICLE SUSPENSION MODEL

The vehicle part studied is the lower suspension arm of vehicle suspension system. It is necessary to evaluate the dynamic behaviour of suspension system and roadway profile model. Rahnejat [10] studied the dynamics of Macpherson suspension system in a quarter vehicle. He represented spring and shock absorber as a single element with stiffness constant. In the present study a simple model is developed as illustrated in Fig. 1.

In this model, partial stability of a vehicle is ensured by control suspension system. For an action chain this system has a tire of stiffness constant Kt and for a return chain in negative feedback a spring of stiffness Ks assembled with a shock absorber Cs. The excitation force F2 of road irregularity, is balanced through the tire by the F1 negative feedback. F1 negative feedback brings back the suspension arm to its place of equilibrium linearly. For cases of small disturbances and domination of elastic behaviour of material, it produces a state of low stress. Then, the following relation is deduced:

22

11

2

2

1

1 xLL

xLx

Lx

=⇒= . (1)

Eq. (1) gives the deflexion x2, compared to equilibrium position and caused by road profile, allowing us to deduce displacement x1. Unsprung mass, such as mass of spring, tire and shock absorber is negligible compared to the dynamic stress brought into play. However, the suspension parameters such as: the spring stiffness constant Ks =16000 N/m; Shock absorber Cs = 1000 Ns/m and tire stiffness constant Kt =160 000 N/m [11].

The forces applied to the lower suspension arm by a quarter vehicle are: F2 = Kt x2 exerted on the tire by x2 and 111 xCxKF ss += negative feedback force exerted by spring and shock absorber.

Knowing the power spectral density (PSD) experimental values, x2 is deduced and consequently, F2, enabling x1 spectrum. Once x1 is known, complete determination of F1 values is done. The road profile spectrum is a function of the vehicle speed, which is obtained from PSD. Normalisation of the road profile spectrum is necessary to keep the same frequency band and to be able to transform it into a force excitation. The

factor, which must be multiplied by PSD values, depends on numerical values of suspended mass, tire stiffness constant and shock absorber coefficient, and the damping ratio of both the shock absorber and the unsprung mass. In this study, numerical value of this factor is estimated at 0.025. 1x is numerically given by:

ttxttxx

∆−∆+

=)()( 11

1

The excitation caused by the road profile has a random nature estimated from power spectral density PSD. The road profile is defined by function X(t) and by assuming the road surface is a random, stationary, Gaussian and centered process: all its statistical properties are invariable with any change in argument t, that distribution law of variable X(t) is a Gaussian law, and that the average of X(t) for any t pertaining to [0, T], is null. The stationary random process and the Gaussian law X(t) can be regarded as a periodic function in time t, of amplitude α, circular frequency ω and phase ϕ [11]. Thus, the random process X(t) can be written according to the following equation:

)cos()( φωα −= ttX . (2)

X(t) can be expressed by the sum of a series of harmonic functions called Fourier series where i = 1 to N:

∑ −=N

iiii ttX )cos()( φωα . (3)

The phase ϕi is random and distributed in the interval [0, 2π]. So the average of Eq. (3) is given by:

[ ] 0])[cos()( =−= ∑N

iiii tEtXE φωα , (4)

thus:

0)21)(cos()][cos(

2

0== ∫

πφ

πφφ iii dE , (5)

Consider the mean square of X(t):

[ ] ∑∑ ∑ =−−==

N

ii

N

i

M

jjjjiii ttEtXE 2

1

2

21])cos()cos([)( αφωαφωα . (6)

Eqs. (5) and (6) show that the process is stationary. In the case of a random process, stationary, Gaussian, the following equation must be satisfied by using the mean m and standard deviation δ:



δ ω ω2 2= −−∞

+∞

∫ S d mXX ( ) , (7)

as m = 0, Eq. (7) become:

2 2 212 ( ) ( )2

N N

XX i ii i

S E x tδ ω ω α = ∆ = = ∑ ∑ , (8)

Eq. (9) is deduced:

α ω ωi XX iS= 4 ( ) ( )∆ . (9)

Finally, the process X(t) according to power spectral density is given by:

X t S tXX ii

N

i i( ) ( ) cos( )= −∑ 4 ω ω ω∆ Φ . (10)

For spatial frequency range spanning from 0.01 to 10 cycles/m, power spectral density SXX(γ) from experience can be represented by an exponential function [11] given by:

SS

S

q

q( )

( ) if

( ) if

γ

γγγ

γ γ

γγγ

γ γ

=

≤

>

−

−

00

1

0

00

2

0

, (11)

with π

γ21

0 = (cycles/m), q1 = 3.14 ± 0.76 and q2

= 2.11 ± 0.38. γ is the spatial frequency linked to circular frequency w and the vehicle speed V by:

ω = 2πVγ. (12)

From Eqs. (10) and (11), power spectral density and time history displacement can be plotted as shown in Figs. 2 and 3 [11]. The road spectrum thus obtained corresponds to a vertical random displacement. However, the present study takes into account direct excitation by a random dynamic force. Thus, it is necessary to transform the random displacement into a random force while keeping the same pulsation. Therefore, the minor road spectrum is normalised. The spectrum values are multiplied by a common factor estimated from the statistical data. For a minor road, the speed of the vehicle is lower than 75 km/h (21 m/s). For 75 km/h, a 960 kg vehicle has a momentum equal to 20160 kg·m/s. Thus in 0.5 second, the maximum force excitation is estimated to be 40320 N. This force is distributed equally on

four quarters of the vehicle’s suspension system. In the undamped cases, the vehicle weight opposes about 3750 N in the return chain to the maximum 4000 N random excitation value. The maximum value of the force of excitation through a tire of stiffness 160000 N/m is about 4000 N. Figs. 4 and 5 depict a comparison between damped and undamped spectrums. It also illustrates opposition phases between excitation F2 and force F1 of the return chain in vehicle control suspension system.

2 ELASTO-PLASTIC NUMERICAL MODEL

Aluminium alloys have an elasto-plastic behaviour with a plastic contribution of about 36% in certain cases (Table 1). Gbadebo [12] and [13] proposed an analytical solution for elasto-plastic case, where the matrix of total tensor deflection increments is the sum of elastic and plastic contributions. They extrapolated the nonlinear uniaxial behaviour of the material in multiaxial case to calculate strain energy density. In the plastic behaviour Gbadebo et al. [12] and [13] have developed the endochronic theory of plasticity. This approach is the same as the one used in the commercial finite element software Abaqus.

Table 1. Elasto-plastic behaviour of some aluminium alloys

Allo

y

Code

Ultimate limit

σu[MPa]

Yield stress

σe[MPa]

Ratio [%]:

σ σσ

u e

u

−

Alu

min

ium

al

loy 2024-T351

2024-T4 Al7075-T6 Al

455476578

379303469

16.7036.3418.85

This model takes into account two cases of nonlinearity: non-geometric linearity (variation of the geometrical configuration of the system in time) and material nonlinearity expressed by elasto-plastic coupling. The numerical diagram of integration depends on its stability, computing time and accuracy of the method. In this study implicit integration scheme is used [14] and [15]. The loading and boundary conditions specify the



places of excitation and the degrees of freedom imposed on the system. The mesh takes into account the stress state and critical points: load location, and boundary conditions area. The analytical equivalent strain density energy in uniaxial cases is calculated, and compared to the numerical multiaxial one, since both of them have the same tensor order (order zero). The critical element is filtered through all the elements of the mesh, giving the maximum sum of positive variations. The critical element loading signal is corrected from anomaly in order to apply the Markov algorithm conditions. The rainflow cycles are extracted using Markov method. Due to the

non linearity of the Mansson-Coffin equation, partial fatigue life is calculated by the Newton method. The number of random cycle repetitions leading to part failure is determining at final stage using Miner law. To determine local stress state and fatigue criterion, Lachowicz [16] used multiaxial strain energy density criterion without specifying the calculation of density of plastic deformation energy. Pan et al. [17], Lee et al. [18] and Li et al. [19] compared experimental results of multiaxial fatigue with models of multiaxial criterion of strain energy density already existing as the criterion of critical plan which generalizes the Smith Watson Topper SWT uniaxial model.

Fig. 2. Power spectral density PSD as a function of frequency

Fig. 3. Displacement as a function of time



The local stress plane state, characterized by: σ1, σ2, φp, and λ = σ2 / σ1, that represents the two principal stresses, phase angle between σ1 and local axis OX and the ratio of biaxiality [20], respectively. The stress state in a material can take the following aspects:• uniaxial case: λ = σ2 / σ1 = 0 and φp are

constant in time. In this case an uniaxial model is used such as the SWT criterion;

-1,5E+04

-1,0E+04

-5,0E+03

0,0E+00

5,0E+03

1,0E+04

1,5E+04

0 1 2 3 4 5 6Time (s)Forc

e (N

)

-5,0E+03

-4,0E+03

-3,0E+03

-2,0E+03

-1,0E+03

0,0E+00

1,0E+03

2,0E+03

3,0E+03

4,0E+03

5,0E+03

0 1 2 3 4 5 6Time (s)Forc

e (N

)

Fig. 4. Road excitation F2 in undamped (- - -) and damped modes (‒‒)

Fig. 5. Damped mode: road excitation F2 (‒‒) and feedback chain F1 (- - -)

• proportional multiaxial case: varies in time and φp is constant. In this case the effective strain criterion is used;

• nonproportional multiaxial case: both λ = σ2 / σ1 and φp vary in time. In this case the critical plane is used.

In all three cases the uniaxial criterion equivalent to the multiaxial case as suggested by Elmarakbi et al. [7] can be used. Indeed the uniaxial



criterion of strain density energy equivalent to the multiaxial one, is used in all cases of λ and φp, because it is a complete integral calculation in case of uniaxial analytical integration and all components of shear and distortion in multiaxial numerical case are calculated.

Since aluminium alloys present more significant plastic than elastic behaviour, the nonlinear profile is given by cyclic Ramberg-Osgood behaviour law as:

'1

)'

( naaa KE

σσε += , (13)

where '

'

'' n

f

fKεσ

= is coefficient of endurance limit, n′ = b/c cyclic hardness exponent, σ′f coefficient of fatigue strength, c exponent of fatigue ductility, b fatigue strength exponent and ε′f coefficient of fatigue ductility. The strain energy density, relative to multiaxial case, can be expressed as:

Us = Uσ or S de dij ij

e

ij ijij ij

=∫ ∫0 0σ ε

ε. (14)

In the present study, the model of three-dimensional elastic finite element (FEM) analysis is used. The value of strain energy density obtained from the analysis in three-dimensional FEM, is equalized to the strain density energy of uniaxial case. The mathematical formulation of total uniaxial deformation energy per unit of volume, obtained by an exact integration is represented as [7]:

U U U da ae ap a aa

= + = ∫ σ εε

0. (15)

We know that:

'1

)'

( naaa KE

σσε += , (16)

thus:

'

1

)''1(

''

1

n

nn

a

a

a

knEd

d−

+=σ

σε

, (17)

Eq. (15) becomes:

a

n

nn

aaa d

KnE

U σσ

σ

+=

−

∫'

1

)''1(

''

1 , (18)

and finally, the following relation is obtained:

'

12

'1'2naaa

a KnEU

+

+=σσσ . (19)

A resolution of Eq. (19) gives necessary constraint to produce same energy density as in the uniaxial case. If replacing the stress value in Eq. (16), gives the corresponding deformation, then fatigue life can be predicted by using the following Manson-Coffin equation:

( ) ( )cf

bf NNE

22'

2'ε

σε+=

∆, (20)

where Δε = εmax ‒ εmin is strain interval, σ′f coefficient of fatigue strength, N number of cycles to failure, E Young modulus, C exponent of fatigue ductility, b exponent of fatigue strength and ε′f coefficient of fatigue ductility.

3 ELASTO-PLASTIC NUMERICAL MODEL UNDAMPED RIGID CASE

According to Rahnejat [10] the suspension arm cannot support a negative feedback force of a quarter vehicle, which is superior to 3750 N, corresponding to the rigid case. This part is subjected to random excitation of the road described by PSD and to quarter weight of vehicle which opposes it. The right end of the part is linked to a suspension joint in order to allow a rotation around y-axis as illustrated by Fig. 6. The suspension arm is 2.5 cm thick, 50 cm long and 30 cm wide. As shown in Fig. 6, the concentrated forces are replaced by uniform surface pressures following:

SF

SfP =∂∂

= (21)

Fig. 6. Loading and boundary conditions in a portion of the Al 7075-T6 alloy part

Abaqus-6.4 offers us tetrahedral elements. A controlled mesh is necessary to refine the



number of elements close to critical zones as illustrated in Fig. 7. Moreover, due to bending in a stress plane state, the mesh must be refined in thickness to represent state of stress plane better. Vertical partitions are created in the thickness. The linear elements of reduced integration tolerate distortion, therefore, a refined mesh of these elements is used in any simulation where the distortion levels can be very high. Thus, linear tetrahedral elements are chosen in an implicit integration stable scheme.

Fig. 7. Mesh of the lower suspension arm

The need for determining the critical element and its coordinates led to choose a strategy which allows isolation of the element having maximum positive variation. Contrary to the static case, the rough maximum value of strain energy density does not necessarily correspond to the critical element. This allows an application of the Newton-Raphson algorithm to only one element instead of applying it to all the mesh elements in the structure. In order to extract the number of cycles to failure, the nonlinear Mansson-Coffin equation is used. This filter generalizes the case where excitation is multipoint and shifted in time, giving a tangle of mesh material element signals. This filter is based on the following algorithm:

xc and zc are the critical element coordinates having:

M i j M Max U m nc c ncm

tf

( , ) ( ( ( , )))==∑∆

0

,

where:m = time parameter, k = simulation duration,

tf kkk=⊂ =−

2

2 2!

!( )!

n = spatial parameter to make ic and jc in the same column ncΔU(m,n) = U(l,n) ‒ U(p,n), when U(l,n) > U(p,n).

Indeed, it is a variation of strain energy density which is involved in failure by fatigue in case of the dynamic stress and not absolute value of strain energy density as in the static case. Fig. 8, illustrates strain energy density profile (SENER) within the part. The SENER is critical in neighbourhoods of boundary conditions. Fig. 9, shows time evolution of strain energy density in centroid element 169. The critical element is located in the area where the part is embedded.

Fig. 8. Instantaneous strain energy density in the 25 mm specimen

Fig. 9. Strain energy density time evolution of critical element no. 169

The critical element strain energy density time evolution signal has a random profile. To apply Miner law, rainflow cycle must be extracted.



Each rainflow cycle is described by direct passage of power spectral density PSD at each mesh element and was then solved by a rigorous theory based, on one hand, on the definition of a rainflow cycle suggested in 1987 by Rychlik [21] and on the other hand, on the theory of Markov chains. Indeed, a rainflow cycle, as illustrated in Fig. 10, can be mathematically characterized in the following way:

Let us consider σ(t) where [ ]Tt ,0∈ and the stress maximum Mi of level K occur at time ti. The extents ( )ii Mm ,− and ( )+ii mM , are defined, where : • −

im is the minimum of σ(t) and Mi is between last passage to negative slope of σ(t) and the maximum Mi. This minimum is on the left of Mi and occurs at time −

it ,• +

im is the minimum σ(t) which is between Mi and the first passage to positive slope of σ(t) by the level K. This minimum is on the right of Mi and occurs at time +

it .

Fig. 10. Mathematical characterization of rainflow cycle

If there is no passage of s(t) by the level K before or after time ti, then 0=−

it and Tti =+ . The rainflow extracted at time ti is then defined either as the extent ( i

rfci Mm , ), or ( rfc

ii mM , ). This minimum rfc

im is given by applying the condition:

⟩

=+

−+−

else

0 if ),max(

i

iiirfci m

tmmm . (22)

Fig. 11 shows the critical element SENER signal and rainflow cycles counting. When loadings are composed of various cycles of various amplitudes and various average values, it is necessary to measure total damage produced by these cycles by using the laws of damage calculation, which were developed from linear damage rule suggested by Palmgren in 1924 [18]. The mathematical formulation under which it is currently known was proposed by Miner in 1945 and it is expressed as Eq. (23).

∑=

=n

i i

i

Nn

D1

. (23)

Random stress history is described as a sequence of blocks of constant amplitude. Each block i is composed of Ni cycles of amplitudes. Partial fatigue life Ni corresponding to this stress amplitude is determined from the strain energy density approach. Failure is predicted when damage D is equal to 1. It is thus necessary to find the number of times that random loading is repeated, so that D is equal to unit. It is necessary to find the Bf number which one must multiply by D to reach rupture. Bf is calculated using Eq. (24).

Fig. 11. Counting rainflow cycles



BnN

fi

ii

=

∑1 ,

since, B D B

nNf f

i

ii

= =∑( ) .1 (24)

Table 2 shows the metallurgical fatigue parameters of aluminium 7075-T6 alloy used in lower suspension arm.

Table 2. Metallurgical parameters of aluminium 7075-T6 alloy

Young modulus E [MPa]

n' σ'f[MPa] ε’f b c

71000 0.106 1466 0.262 -0.143 -0.619

The relative cycle fatigue life part’s is estimated as 8.86×1011. Indeed critical element maximum Von Mises stress is about 31 MPa and corresponding maximum deformation is 4×10-4.

These slightly low values can be further attenuated to make part safer by reinforcing it at critical points. Optimization of the part shape will make it possible to increase the number of repetitions needed to failure, make vehicle safer and further decrease vehicle weight in non critical places.

4 ELASTO-PLASTIC NUMERICAL MODEL, DAMPED AND RIGID CASES

Damping suspension largely decreases the applied force in the feedback chain middle part section. Vehicle weight is considered at 3750 N, not exceeding absolute value of F1max = 1200 N in the case of damping by a spring and shock absorber. This force is opposed in feedback chain by road random excitation deadened by tire stiffness Kt = 160000 N/m, and maximum value F2max = 4000 N. Feedback chain F2 is useful to stabilize the vehicle, but will not compensate F1 in terms of stress since difference between F1 and F2 is higher in case of damping than in rigid case. This is confirmed by a strain energy density (SENER) packing illustrated in Fig.12. The critical element filtered in both cases is element 169 located at the level of embedding as illustrated in Fig. 8. The model part and mesh are the same in both cases. Consequently, the fatigue life part in the damping case will be lower than in the rigid case. This shows that despite the comfort gain when using damper and spring, the fatigue life value of certain automotive parts such as a lower suspension arm of a vehicle decreases due to load order.

Fig. 12. Critical element strain energy density time evolution; a) 25 mm rigid case, b) 25 mm damping case



5 CONCLUSION

The principal objective of this research was to develop a hybrid model in order to study the potential of an aluminium alloy as the new material for a lower suspension arm of a vehicle. Analytical and numerical model were developed to simulate dynamic behaviour of a suspension system as well as the state of stress and strain energy density in the lower arm of vehicle suspension. The spectral aspects of fatigue and dynamic behaviour of a vehicle suspension system were studied. The multiaxial criterion of the uniaxial case strain energy density equivalent to the multiaxial one represents a rational approach. Moreover, strain energy density criterion, independent of average value of loading, is more practical than the Morrow model, which requires corrections due to effect of the average value of loading. The Morrow model needs some correction due to mean value, because it is a tensor of order 1, which depends on orientation.

In this study, the maximum value of force transmitted by tire and the feedback chain of the force were evaluated. Then a model of negative feedback and forward path of the vehicle’s lower suspension arm, which is subjected to very important dynamic stresses, was established using the road irregularity model power spectral density.

To filter the critical element and to extract the fatigue life, Matlab interface was generated to locate automatically the critical elements without applying Newton-Raphson algorithm in every mesh element. This filter produces the case where excitation is multipoint and shifted in time giving a tangle of signal mesh elements.

The elastoplastic nonlinear case was described using the Ramberg-Osgood uniaxial relation binding stress to deformation. The commercial finite element software Abaqus version 6.4 extrapolates this relationship in the multiaxial case. The sensitivity of certain types of mesh elements makes the execution of the stable implicit integration scheme difficult. Ramberg-Osgood and Mansson-Coffin relation allow us to describe two areas: high-cycle fatigue area and low cycle fatigue area. In the case of damping then in the rigid case even despite the comfort gain when using a damper and a spring, the fatigue life value of certain automotive parts such as a lower

suspension arm of a vehicle decrease due to load order.

In the future, a complete model should be developed to study the various cases, most importantly the effect of the “Jounce bumper” rubber support of suspension.

6 REFERENCES

[1] Bignonnet, A., (2001). A Global Approach for Vehicle Weight Reduction. Mechanics & Industries. 2, p. 173-180. (In French).

[2] Miller, W.S., Zhuang, L., Bottema, J., Wittebrood, A.J., De Smet, P., Haszler, A., Vieregge, A. (2000). Recent development in aluminium alloys for the automotive industry. Materials Science and Engineering, A280 p. 37-49.

[3] Saito, M., Iwatsuki, S., Yasunaga, K., Andoh, K. (2000). Development of aluminium body for the most fuel efficient vehicle. JSAE Review, vol. 21, p. 511-516.

[4] Wilfred, K., Jean, P.M., Gérald, Z. (1991). Introduction of Material Sciences, 2nd edition Presse Polytechniques et Universitaires Romandes (EPFL Press). (In French)

[5] Bazergui, A., Bui-Quo, T., Biron, A., McIntyre, G., Laberge, C. (1993). Résistance des matériaux. École Polytechnique de Montréal, 2nd ed., Montreal.

[6] Cervello, S., Donzella, G., Pola, A. (2001). Analysis and design of a low-noise railway wheel. Proceedings of the Institution of mechanical Engineers. Part F, Journal of Rail, vol. 215, p. 79-92.

[7] Elmarakbi, A., El-Hage, H., Bhattacharjee, S. (2002). Multiaxial fatigue crack initiation by strain energy density using finite element method. CSME Forum 2002, Kingston.

[8] Mars, W.V. (2002). Cracking energy density as a predictor of fatigue life under multiaxial conditions. Rubber Chemistry and Technology, p. 1-17.

[9] De-Andrés, A., J., Pérez, L., Ortiz, M. (1999). Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminium shafts subjected to axial loading. International Journal of Solids and Structures, vol. 36, p. 2231-2258.



[10] Rahnejat, H. (1998). Multi-Body Dynamics: vehicles, machines and mechanisms. Society of Automotive Engineers, Warrendale.

[11] Bouazara, M. (1997). Étude et analyse de la suspension active et semi-active des véhicules routiers Ph.D. thesis, Laval University, Laval.

[12] Gbadebo, M., Meera, O., Sing, N.K. (2006). A comparison between analytical models that approximate notch-root elastic-plastic strain-stress components in two-phase, particule-reinforced, metal matrix composites under multiaxial cyclic loading: Theory. International Journal of Fatigue, vol. 28, p. 910-917.

[13] Gbadebo, M., Meera, O., Sing, N.K. (2006). A comparison between analytical models that approximate notch-root elastic-plastic strain-stress components in two-phase, particule-reinforced, metal matrix composites under multiaxial cyclic loading: Experiments. International Journal of Fatigue, vol. 28, p. 918-925.

[14] Sun, J.S., Lee, K.H., Lee, H.P. (2000). Comparison of implicit and explicit finite element methods for dynamic problems. Journal of Materials Processing Technology, vol. 105, p. 110-118.

[15] Rebelo, N., Nagategaal, J.C., Taylor, L.M. (1992). Comparison of implicit and explicit finite element methods in the simulation

forming processes. Numerical methods in industrial forming processes: Proceedings 4th international conference , p. 99-108.

[16] Lachowicz, C.T. (2001). Calculation of the elastic-plastic strain energy density under cyclic and random loading. International Journal of Fatigue, vol. 23, p. 643-652.

[17] Pan, W.F., Hung, C.Y., Chen, L.L. (1999). Fatigue life estimation under multiaxial loadings. International Journal of Fatigue, vol. 21, p. 3-10.

[18] Lee, B.L., Kim, K.S., Nam, K.M. (2003). Fatigue analysis under variable amplitude loading using an energy parameter. International Journal of Fatigue, vol. 25, p. 621-631.

[19] Li, B., Reis, L., De Freitas, M., (2006). Simulation of cyclic stress/strain evolutions for multiaxial fatigue life prediction. International Journal of Fatigue, vol. 28, p. 451-458.

[20] Haiba, M., Barton, D.C., Levesley, P.C. (2003). The development of an optimization algorithm based on fatigue life. International Journal of Fatigue, vol. 25, p. 299-310.

[21] Pitoiset, X. (2001). Spectral Methods for Fatigue Analysis of Metallic Structures under Multiaxial Random Loading. Ph.D. thesis, Universite libre de Bruxelles, Brussels. (in French)


*Corr. Author’s Address: University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11000 Belgrade, Serbia, [email protected] 357

Taguchi-Based and Intelligent Optimisation of a Multi-Response Process Using Historical Data

Šibalija, T. ‒ Majstorović, V. ‒ Soković, M.Tatjana Šibalija1,* ‒ Vidosav Majstorović1 ‒ Mirko Soković2

1 University of Belgrade, Faculty of Mechanical Engineering, Serbia 2 University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Optimisation of manufacturing processes is typically performed by utilising mathematical process models or designed experiments. However, such approaches could not be used in the case when explicit quality function is unknown and when actual experimentation would be expensive and time-consuming.

The paper presents an approach to optimisation of manufacturing processes with multiple potentially correlated responses, using historical process data. The integrated approach is consisted from two methods: the first relays on Taguchi’s quality loss function and multivariate statistical methods, the second method is based on the first one and employs artificial neural networks and a genetic algorithm to ensure global optimal settings of a critical parameters found in a continual space of solutions.

The case study of a multi-response process with correlated responses was used to illustrate the effective application of the proposed approach, where historical data collected during normal production and stored in a control charts were used for process optimisation. © 2011 Journal of Mechanical Engineering. All rights reserved. Keywords: optimisation, historical data, Taguchi method, neural networks, genetic algorithm

0 INTRODUCTION

Process optimisation is typically performed by analysing the process responses obtained from designed experiments, carried out on the actual manufacturing process. However, conducting experiments on the actual process tends to cause distruption in the plant and may be uneconomic. The possibility to use process historical data (i.e. from the control charts) has not been explored videly in the literature. There are few studies that used historical data for optimisation, but they discuss only single-response problems [1] and [2].

A customer usually considers several characteristics of product quality. In such cases, a single optimum setting of process parameters needs to be identified so that the specifications of all quality characteristics (responses) are met. Complexity of the problem increases when the responses are correlated.

Response surface methodology (RSM) is the most commonly used method for process optimisation by experimentation, proven to be effective in many applications. However, there are certain concerns regarding RSM application for multi-response optimisation: the RSM does not enable simultaneous optimisation of both

mean and variance of the responses; a RSM model may not find the overall (global) best solution and might be trapped easily in a local minimum when a process is influenced by a large number of variables and is highly non-linear with multiple outputs. Taguchi’s experimental robust design has been proven effective in solving many optimisations for single-response processes. However, it has not proved functional for optimising the multi-response problem; the sole path was relying on engineers’ judgement.

There are various methods for multi-response optimisation for correlated responses based on the transformation of Taguchi’s quality loss function [3] or SN ratio [4] that employ principal component analysis (PCA) to uncorrelate responses. However, the mentioned approaches in PCA considers only components whose variance (eigenvalue) is greater than or equal to one, enclosing a larger portion of variance but not the total variance of responses. Wang and Tong [5] used PCA and grey relational analysis (GRA) to transform quality losses into a single measure, and Wu [6] proposed an approach based on the proportion of quality losses with respect to the known starting conditions. The soft-computing methods for multi-response process optimisation


358 Šibalija, T. ‒ Majstorović, V. ‒ Soković, M.

are based on the application of artificial neural networks (ANNs) (i.e. [7]). Hsu [8] combined ANNs and PCA to uncorrelate the process model, but only components with eigenvalue greater or equal to one were considered. The above approaches consider only discrete parameter values used in the experiment. In addition, they could not solve multi-response problems where optimisation requires the implementation of expert knowledge into the formulae. A detailed discussion regarding the above and other related approaches for multi-response optimisation could be found in [9].

The GA-based approaches to multi-response problems found in literature are designed to solve one particular problem, and they could not be applied to some other problem. Roy and Mehnen [10] used Pareto front genetic optimisation assuming that the analytical model of the process is known, which is not always the case in the practice. Drain [11] proposed methods that combine RSM and GA. Lau [12] used GA for the optimisation of moulding operations. Jeong [13] employed GA for shadow mask manufacturing. Hou’s method [14] based on RSM, ANN and GA presents an integrated system for wire bonding optimisation. Tong’s approach [15] is based on case-based reasoning, ANN and GA, designed to optimise transfer moulding in microelectronics.

The paper presents two methods for optimisation of a process with multiple correlated responses using historical process data. The first method, based on Taguchi’s quality loss function and multivariate statistical methods, considers only discrete parameter values recorded in a control charts. Based on this statistical method, the second intelligent method was developed that uses ANN and GA to find optimal parameters solution in a continual multi-dimensional space, using historical data from a control charts.

1 THE PROPOSED APPROACH

The proposed integrated approach to multi-response process optimisation for correlated responses is based on Taguchi quality loss function, multivariate statistical methods and artificial intelligence techniques, as follows [16].

1.1 The Factor Effects Method

1.1.1 Taguchi’s Quality Loss Function

Quality loss function directly represents a financial measure of the customer dissatisfaction with a product’s performance as it deviates from a target value. Unlike the conventional weighting methods, the quality loss function adequately presents relative financial significance of responses, thus providing the right metric for multi-criteria decision making. In the proposed approach, Taguchi’s robust design was not applied directly, as not every response may have the same measurement unit and may not be of the same type in the SN ratio analysis.

The average quality loss is QL = K·MSD, where QL is the existing average loss per unit, K is the coefficient, and MSD is the sample mean square deviation for n units (measurements) [17]:

MSD

nyi

i

n

=

=∑1 2

1

............................................ ffor STB

ny m n

ns y m for NTB

n y

ii

n

i

.

( ) ( ) ... .

......

1 1

1 11

2 2 2

2

=∑ − =

−+ −

...................................... .for LTBi

n

=∑

1

(1)

where y is the measurable response; STB, NTB, LTB is smaller-the-better, nominal-the-best, larger-the-better type of response, respectively; y is the sample mean and s2 is the sample variance. The quality loss of the ith quality characteristic in the kth point QLik could be transformed into normalised value NQLi(k) (NQLi(k) [0;1] ∈ ):

NQL kQL QL

QL QLi

iki

ik

iik

iik

( )min

max min=

−

−

, (2)

where i = 1, …, p is the number of quality characteristic, and k = 1, …, m is the number of control point in a historical data set.

1.1.2 Principal Component Analysis (PCA)

PCA is considered as an effective means of transforming correlated responses into uncorrelated linear combinations (principal components). The sum of variances of the principal components (eigenvalues) is equal to the sum of variances of the original responses.


359Taguchi-Based and Intelligent Optimisation of a Multi-Response Process Using Historical Data

In the presented approach, PCA is performed on NQL data resulting in a set of uncorrelated components. In contrast to the usual practice [3] and [4] where only components with eigenvalue greater than or equal to one are considered, here principal component scores include all components, thus including the total variance of the original data. If the component of eigenvector of the first principal component PC1 is denoted as I1i, (i = 1, …, p), the multi-response performance statistics corresponding to PC1 for NQL can be expressed as:

Y k I NQL ki ii

p

1 1( ( ) )= ⋅=∑

1. (3)

The larger the Yi(k) value, the better is the performance of the product/process.

1.1.3 Grey Relational Analysis (GRA)

GRA provides an effective means of dealing with one event that involves multiple decisions and deals with poor, incomplete and uncertain data.

In the presented approach, GRA is performed on the absolute value of principal component scores Yi(k). Linear preprocessing method is employed to transform the principal component scores |Yi(k)| into a set of standardised multi-response performance statistics Zi(k):

Z kY k Y k

Y k Y kii

i i

ii

ii

( )max ( ) ( )

max ( ) min ( )=

−

−

. (4)

The grey relational coefficient ξi(k) is:

ξς

ii k

ii k

i

i

kZ k Z i Z k Z i

Z k Z( )

min min ( ) ( ) max max ( ) ( )

( )=

− + −

−

0 0

0 (( ) max max ( ) ( )i Z k Z ii k

i+ −ς 0

, (5)

where Z0(i) are ideal sequences with value of 1, and ς is the distinguishing coefficient. The Grey Relational Grade γk is calculated by a weighted mean, where the weights are the percentage of variance of the NQLs in PCA:

γ ω ξk i ii

p

k==∑ ( )

1

, (6)

where ωi is the percentage of variance of the ith component in the PCA.

In the proposed approach, the Grey Relational Grade γk is adopted as the synthetic performance measure for multi-response process. The application of GRA resulted in a single multi-response performance measure that takes into account all, possibly correlated, responses. The weights used for determining synthetic performance measure are based on the total variance of the original responses, which results in improved objectivity of the analysis.

Knowing the γk values and factor (parameter) values for all control points in a historical data set (k = 1, …, m), it is possible to calculate the effects of factors on the synthetic performance measure for all parameter values used in the data set. The optimal factor conditions can be obtained by selecting the maximum of factor effects on multi-response performance measure γk. Hereafter, the above procedure is referred to as the factor effects approach [9] and [16]. The shortcoming of the factor effects approach is that it considers only discrete values of factors recorded in a historical data set.

1.2 The ANN&GA-Based Method

1.2.1 Artificial Neural Networks (ANNs)

ANN is a powerful technique of generating complex multi-response and linear and non-linear process models without referring to a particular mathematical model, proven as effective in various applications [1], [7] and [8].

In the proposed approach, multilayer feed forward ANNs were developed to model the relationship between critical parameters and the synthetic performance measure (γk). For the training of ANNs, the input set contains values of parameters from a historical data set; output set accommodates synthetic performance measure γk. The error back-propagation (BP) learning method, improved by Levenberg-Marquardt algorithm, was adopted. In order to reduce likelihood that the network would find weights that are a local but not global minimum, the adopted values for training parameters are: learning rate = 0.01 and momentum factor = 0.9. Transfer functions for hidden neurones are tangent sigmoid, while for the output neurones they are linear functions. It was proven that such a choice of transfer functions makes ANN capable of performing successful



approximation of various complex functions. BP learning employs a gradient descent algorithm to minimise the mean square error (MSE) between the original data and the actual output of ANN. Since process modelling is the most sensitive part of the proposed method, various ANNs with different topology (number of hidden neurons) were developed in Matlab, until MSE of 10-3 is achieved. The best ANN was chosen according to the minimum MSE criterion. In addition, the coefficient of the correlation (R) between original data and the actual network output (R) was considered [16].

1.2.2 Genetic Algorithm

In the presented approach for multi-response problems, GA was chosen for optimisation because it has been proven to be a potent multiple-directional heuristic search method for optimising highly nonlinear, nonconvex and complex functions and it is less likely to get trapped at a local optimum than traditional gradient-based search methods [10] to 15] and [18].

The selected neural model presents an objective (fitness) function for GA, which, by maximising the objective function finds the optimal parameters setting among all possible solutions in continual multi-dimensional space. In order to obtain optimal performance of GA, a large number of GA’s parameters must be tuned. According to the results of previous analysis [18], the choice of the basic GA’s operations (selection and crossover functions) depends on the application. In order to accept the specifics of each particular problem, nine GAs are developed in Matlab combining the most commonly used types of selection and crossover function. The rest of GA’s parameters are: natural presentation of chromosomes, population size equals five times dimensionality (the number of critical parameters), scaling function ‘rank’, crossover fraction = 0.9, mutation ‘adaptive feasible’. Since the parameters setting obtained by the factor effects method presents a potentially good solution, it serves as a basis of forming initial population in GAs. This feature of the suggested model is of essential importance, because it allows GAs to converge to the global optimum faster and enhance its capability to find the actual global solution in the

given number of generations. Nine GAs were run for 2000 repetitions (generations). The best GA is chosen according to the best fitness value (on-line performance criteria), presented by the synthetic performance measure (γ). The most desirable solution with the highest fitness function value (γ) presents the final solution. An additional criterion is the best off-line performance criteria (the mean of the best fitness values through the whole run). The solution of the best GA is adopted as the final solution of the multi-response problem [16].

GA considers all continual parameter values between corresponding bounds, in contrast to traditional experimentation methods that consider only discrete values which were used in the experiment. Relaying on this and setting GA’s parameters as described above, the proposed approach ensures optimal performance of GA to converge to the global rather than local optimum.

2 THE CASE STUDY

The goal of the presented study was to select the optimal settings of critical-to-quality (CTQ) parameters of automatic enamelling process in a cookware production. Conducting designed experiments in current circumstances was found inappropriate, since it would cause disruption in the production process. Hence, it was decided to optimise the process using the historical data from the process control charts.

2.1 Quality Characteristics (Responses) and Control Parameters (Factors)

The quality of the considered automatic enamelling process is characterised by the base enamel thickness and the cover enamel thickness.

The first quality characteristic considered a response in the study is base enamel thickness. The X R− control chart for base enamel thickness has been formed within statistical process control (SPC), containing base enamel thickness mean (t1) [μm] and standard deviation and the values of the following CTQ parameters for base enamelling:• base enamel parameters: deposit weight

(DW1) [gram/cm3] and specific weight (SW1) [gram/cm3]; and



• base enamelling process parameter: automat speed (AS1) [parts/min].

Since it is not possible to measure cover enamelling thickness directly, it is presented over the total enamel thickness. Hence, the second quality characteristic considered a response is the total enamel thickness. The corresponding X R− control chart for cover enamel thickness has been set up that comprehends cover enamel thickness mean (t2) [μm] and standard deviation and the values of the following parameters found as CTQ for the cover enamelling:• cover enamel parameters: deposit weight

(DW2) [gram/cm3] and specific weight (SW2) [gram/cm3]; and

• cover enamelling process parameter: automat speed (AS2) [parts/min].

The part of a two-week sample data from both control charts (historical data set) is presented in Table 1. The two responses are in direct correlation since the total enamel thickness presents a sum of base and cover enamel thickness. Both characteristics are of a continual numerical type. According to SN ratio they belong to NTB type because the goal of the study is to achieve the nominal value specified by customer for both characteristics. Specification limits, defined by the customer, for the base enamel thickness are 80 to 120 μm and nominal value is 100 μm. For the total enamel thickness, specification limits are 180 to 300 μm and nominal required value is 240

μm. The parameters DW1, SW1, DW2 and SW2 are continual numerical type of variables, and parameters AS1 and AS2 are discrete numerical.

2.2 Implementation of the Factor Effects Method

MSD values were computed according to Eq. (1). Normalisation of QL values was performed by using Eq. (2), with respect to the maximal QL value in k points of a data set and the ideal case where QL = 0. PCA was performed on NQL values. The QLs and principal component scores Yi(k) are listed in Table 1. Tables 2 list the eigenvalues and proportions of NQL of each response for the principal components. Both principal components were considered in this method in contrast to the common approach where only PC1 would be taken into account (eigenvalue greater than one), enclosing only 51.6% of the total variance of responses. According to the eigenvectors from Table 2, the principal component scores were computed as follows [16]:

Y k NQL NQLY k NQL

t t

t

1

2

( - 0.707 ,( 0.707

) .) .= ⋅ ⋅

= ⋅ +

0 7070 707

1 2

1 ⋅⋅NQLt 2 . (7)

The principal component scores Yi(k) were transformed into a set of comparable sequences Zi(k) by using (4). Next, the Grey Relational

Table 1. A part of critical parameters and response values from a historical data, corresponding quality losses, principal component scores and data of grey relational analysis

Con-trol

point no.

Critical parameters Response values Quality losses

Yi(k) i = 1, 2;

k = 1, ..., 55

ξi(k) i = 1, 2;

k = 1, ..., 55γk

k = 1, ..., 55DW1 SW1 AS1 DW2 SW2 AS2 t1 t2 QLt1 QLt2 Y1(k) Y2(k) ξ 1 ξ 2

1 1.69 10 8 1.72 11 7 103.5 232.0 33.36 77.17 0.3438 0.5677 0.4618 0.5213 0.49062 1.69 10 8 1.73 12 7 104.7 232.2 42.94 76.19 0.4762 0.6972 0.3826 0.4700 0.42493 1.69 10 8 1.71 11 7.5 103.1 230.1 26.48 110.52 0.2016 0.5222 0.5941 0.5421 0.56894 1.68 10 8 1.71 11 7.5 103.2 231.5 26.44 86.20 0.2362 0.4863 0.5553 0.5597 0.55755 1.69 10 6 1.72 11 7 102.9 231.8 25.17 82.47 0.2243 0.4636 0.5681 0.5715 0.56976 1.70 10 6 1.71 11 8 102.3 228.4 17.19 148.03 0.0202 0.4496 0.9359 0.5789 0.76317 1.70 10 7 1.72 11 7 103.3 231.9 29.61 74.97 0.2958 0.5132 0.4994 0.5464 0.5221… … … … … … … … … … … … … … … …53 1.68 9 8 1.73 13 7 105.2 231.6 51.74 80.60 0.5901 0.8239 0.3333 0.4287 0.379554 1.70 10 6 1.71 11 8 101.9 228.3 17.23 153.29 0.0130 0.4577 0.9577 0.5746 0.772355 1.68 9 8 1.73 12 7 105.0 230.2 47.29 112.65 0.4828 0.8096 0.3793 0.4330 0.4053



Coefficient ξi(k) was calculated by (5) and the Grey Relational Grade γk by using (6), where the weights (proportions) ωi are listed in Table 2. The results of GRA are listed in Table 1.

Table 2. Results of PCA

Principal components PC1 PC2Eigenvalues 1.0319 0.9681Proportions 0.516 0.484

Eigenvectors NQL t1 0.707 0.707NQL t2 -0.707 0.707

From γk and the factor values in Table 1, the factor effects can be tabulated. The optimal setting of each factor is the one that yields the highest multi-response performance measure, hence the optimal conditions obtained from the factor effects method was: DW1 = 1.70; SW1 = 11; AS1 = 6; DW2 = 1.71; SW2 = 11; AS2 = 8 [16].

Since the factor effects method discusses only discrete parameter values used in a historical data set, the above parameters setting was adopted as a basis to form the initial population in GA, to find the optimal solution in continual multi-dimensional space.

2.3 Implementation of the ANN&GA-Based Method

The set of BP ANNs were trained to model the relationship between synthetic performance measure γ and critical parameters. Each of the developed networks has six neurons in the input layer corresponding to six parameters, and one neuron in the output layer corresponding to a single synthetic multi-response performance measure. The number of neurons in the hidden layer varies from 1 to 9. The results of training of ANNs are presented in Table 3. The network with topology 6-5-1 showed the least error (MSE = 0.000588) and therefore it was selected to present the process model (Fig. 1) [16].

Fig.1. Topology of the selected ANN model

The selected network present an objective functions for GA. Nine GAs were developed; the initial population was seeded close to the set suggested by the factor effects method; population size was 30. The results of a tested GAs are given in Table 4. All the tested GAs showed the same result in terms of the best fitness value (γ = 0.88120) and the optimal parameters setting: DW1 = 1.70; SW1 = 11; AS1 = 5; DW2 = 1.71; SW2 = 11; AS2 = 9. This set is adopted as a final solution of the observed problem [16].

The results of different GAs show robustness with respect to GA’s own settings. Regarding the additional criteria, it could be seen that algorithms GA3, GA6 and GA9 that use ‘tournament‘ selection showed the lowest off-line performance. Since it was proven in previous studies that the loss of diversity increases with the increase of tournament size, and, from the other side, favourable selection intensity also increases with the increase of tournament size, in the observed study, it was decided to use the tournament size of 4. Almost identical results were obtained with the tournament size 2; however, tournament size 8 showed significantly lower off-line performance. One of the characteristics of a ‘tournament‘ selection is high variance in the distribution; ‘stochastic uniform‘ and ‘roulette‘ selection minimises this mean variance. These observations might be related to low off-line performance of GAs that use ‘tournament‘ selection in this study. However, interpretation of these results may be difficult as it depends on the optimisation problem.

Initial population in GA was formed in the proximity of the set suggested by the factor effects method. All GAs converged to the optimal solution in the first generation, which is a consequence of a good-seeded initial population. If the initial population was not set properly, the GA would need more generations to find the actual optimal solution.

2.4 Discussion

The analysis of the implementation of the intelligent method was performed by a comparison to the factor effects application. Since the actual experiment was not conducted in the study, it was not possible to compare the results



to some experimentation analysis method, such as RSM. Table 5 provides a comparison of the synthetic multi-response performance measure γ and optimal parameters setting obtained from two methods of the analysis.

It could be seen that regarding the synthetic performance measure the intelligent method resulted in a better solution than the factor effects due to search over continual space within the specified bounds for parameters. The synthetic performance measure achieved by using optimal parameters setting obtained by the presented intelligent integrated approach (γ = 0.8211) is satisfactory, considering the fact that the maximum theoretical γ value is 1 ( γ k ∈ [ ; ]0 1 ) [16].

3 CONCLUSION

The paper presented two methods of the multi-response process optimisation for correlated responses, which employ historical data. Since the factor effects method could consider only

factor values used in a historical set, based on it the intelligent approach was developed to perform search in continual space of parameter solutions.

The major advantages of the presented factor effects method are [9], [16] and [19]:• By using Taguchi’s SN ratio [20] and quality

loss, relative significances of responses are adequately represented and the response mean and variation are assessed simultaneously.

• Multivariate statistical methods PCA and GRA are employed to uncorrelate and synthesise responses, ensuring that the weights of responses in synthetic performance measure are based on the total variance of the original data, which results in improved objectivity of the analysis.

In addition, the advantages of the ANN&GA-based method are [16] and [19]:• The GA’s capacity of performing global

search among all solutions in continual multi-dimensional space ensures convergence to the global optimal parameter settings.

Table 3. Results of training of ANNs (MSE and R values for ANNs with different topology)

Topology of ANN 6-2-1 6-3-1 6-4-1 6-5-1 6-6-1 6-7-1 6-8-1 6-9-1

MSE 0.000882 0.0007232 0.000693 0.000588 0.000641 0.000715 0.000722 0.000732R 0.9004 0.91028 0.93602 0.90797 0.91372 0.89458 0.91889 0.9104

Table 4. GAs settings and results GA GA 1 GA 2 GA 3 GA 4 GA 5 GA 6 GA 7 GA 8 GA 9

Selection function Stochastic uniform

Roulette wheel

Tourna-ment

Stochastic uniform

Roulette wheel

Tourna-ment

Stochastic uniform

Roulette wheel

Tourna-ment

Crossover function Single point Two point ArithmeticFitness function γ 0.82114 0.82114 0.82114 0.82114 0.82114 0.82114 0.82114 0.82114 0.82114

Off-line performance 0.82114 0.82114 0.55 0.82114 0.82114 0.56 0.82114 0.82114 0.59

Optimal param-

eters setting

DW1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7SW1 11 11 11 11 11 11 11 11 11AS1 5 5 5 5 5 5 5 5 5

DW2 1.71 1.71 1.71 1.71 1.71 1.71 1.71 1.71 1.71SW2 11 11 11 11 11 11 11 11 11AS2 9 9 9 9 9 9 9 9 9

Table 5. Comparative analysis of optimal parameter settings obtained by using two different methods

Method The factor effects method The ANN&GA-based methodOptimal parameters setting [1.70; 11; 6; 1.71; 11; 8 ] [1.70; 11; 5; 1.71; 11; 9 ]

Synthetic multi-response performance measure γ 0.7647 0.8211



• The initial population in GA is formed in the proximity of the potentially good solution (the parameter settings obtained by the factor effects method), which advances the convergence to the global solution, meaning that the probability of finding the actual global parameters solution in the given number of generation is significantly improved. If the initial population was not defined at such way (e.g. if the initial population was randomly generated), in general, GA might not be able to find the actual global solution in a limited number of iterations.

• The proposed method does not depend on the type of the relations between responses and critical parameters, type and number of process parameters and responses, existence of correlations between responses or process parameters, or their interrelations.

The case study illustrated that the suggested approach can be effectively used to identify the optimal settings of critical parameters based on historical data, without any disruption caused by experimentation. The potential utility of the proposed integrated approach for process optimisation using historical data has increased because many companies today collect and store large quantities of a process data. On the other hand, the most significant limitation of the proposed approach is related to process data availability. In order to use this approach as an alterative to actual experimentation, it is necessary to monitor all parameters that are potentially critical for the observed responses and involve these data into corresponding control charts, prior to implementation of the proposed integrated approach.

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Strojniški vestnik - Journal of Mechanical Engineering 57(2011)4Vsebina

Vsebina

Strojniški vestnik - Journal of Mechanical Engineeringletnik 57, (2011), številka 4

Ljubljana, april 2011ISSN 0039-2480

Izhaja mesečno

Povzetki člankovCengiz Erdönmez, Cevat Erdem İmrak: Tehnike modeliranja geometrij na osnovi pletenih

vijačnih struktur za numerično analizo SI 57Jinpeng Chen, Marko Hočevar, Brane Širok: Merjenje volumskega pretoka taline v proizvodnji

kamene volne SI 58Milomir M. Gašić, Mile M. Savković, Radovan R. Bulatović: Optimizacija trapeznega prereza

roke avtodvigala z Lagrangeevimi multiplikatorji in diferencialnim evolucijskim algoritmom (DE) SI 59

Gregor Škorc, Jure Čas, Simon Brezovnik, Riko Šafarič: Adaptivno položajno vodenje nanorobotske celice SI 60

Jacek Mucha: Študija parametrov kakovosti in vedenja aluminijaste pločevine, kovičene z zabijalnimi kovicami, za različne pogoje spajanja SI 61

Sebastjan Žagar, Janez Grum: Integriteta površine po mehanskem utrjevanju različnih aluminijevih zlitin SI 62

Abdelhamid Saoudi, Mohamed Bouazara, Daniel Marceau: Študija utrujenostnega zloma spodnje ročice obese z večosnim kriterijem gostote deformacijske energije SI 63

Tatjana Šibalija, Vidosav Majstorović, Mirko Soković: Inteligentna optimizacija procesa z več odgovori na osnovi Taguchi pristopa in predhodnih podatkov SI 64

Navodila avtorjem SI 65

Osebne vestiDoktorati, magisteriji, specializacije in diplome SI 67

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)4, SI 57 Prejeto: 09.01.2009 Sprejeto: 12.01.2011

*Naslov avtorja za dopisovanje: Tehnična univerza v Istanbulu, Institut za informatiko, Maslak, Istanbul, Turčija, [email protected] SI 57

Tehnike modeliranja geometrij na osnovi pletenih vijačnih struktur za numerično analizo

Erdönmez, C. - İmrak, C.E.Cengiz Erdönmez1,* - Cevat Erdem İmrak2

1 Tehnična univerza v Istanbulu, Institut za informatiko, Turčija 2 Tehnična univerza v Istanbulu, Fakulteta za strojništvo, Turčija

V članku je predstavljena nova metodologija za opredeljevanje in modeliranje posameznih in pletenih vijačnih struktur (NHS) žičnih vrvi v treh dimenzijah, ki so uporabne za analizo po metodi končnih elementov. Glavni razlog za obravnavo tega problema pri modeliranju so težave z mreženjem, ki nastopijo pri analizi po metodi končnih elementov. Pri mreženju pride do degeneracije nekaterih delov modela, zato takšen model v fazi analize z metodo končnih elementov ni uporaben. Prav tako trenutno še ni možno neposredno ustvarjanje pletenih vijačnih struktur s CAD-orodji.

Pri 3D-modeliranju teles se uporabljajo parametrične matematične enačbe za posamezne in pletene vijačne žice. Matematične definicije srednjic posameznih in pletenih vijačnih žic se najprej izračunajo s programsko kodo, izračunana vozlišča pa se nato uvozijo v HyperMesh za ustvarjanje mrežene 3D-geometrije. V članku je podan algoritem, ki podaja postopek za 3D-modeliranje žice kot telesa.

Najprej so bili uporabljeni vsi razpoložljivi CAD-programski paketi za poskus ustvarjanja modelov posameznih in pletenih vijačnih žic. Ugotovljeno je bilo, da s temi paketi ni možno ustvariti dobrega mrežnega modela. Nato je bil uporabljen nov pristop, ki uporablja parametrične enačbe za posamezne in pletene vijačne žice. Najprej se izračunajo vozlišča, ki ustrezajo srednjicam posameznih in pletenih vijačnih žic, tako pridobljena vozlišča pa se nato uvozijo v HyperMesh za ustvarjanje mrežnega 3D-modela telesa. Ustvarjeni 3D-model telesa je bil končno uporabljen za analizo po metodi končnih elementov.

V članku sta opisana nova metodologija in algoritem za konstruiranje posameznih in pletenih vijačnih geometrij. Opisani so problemi, ki nastopajo v fazah ustvarjanja modela in mreže vijačnih struktur, kakor tudi strategije za njihovo reševanje. Postopek odstrani nepravilnosti s površine, ki se pojavljajo pri kompleksnih vijačnih strukturah, in daje natančne geometrije. Istočasno odpade tudi problem omejene dolžine. Predlagani postopek ustvarja natančne geometrije brez vsakih dolžinskih omejitev. Končno so predstavljeni tudi primeri analize MKE, ki prikazujejo prednosti predstavljene sheme modeliranja. Analizirana je bila žična pletenica pod aksialno obremenitvijo. Rezultati analize MKE kažejo, da se žice v pletenici med seboj stikajo v vijačni liniji. Drugi obravnavani primer je 6x7-žična pletenica RLL IWRC. Prikazan je tudi diagram porazdelitve osne sile v žicah, ki je bil pridobljen na osnovi analize MKE in daje podrobne informacije o obnašanju žic v pletenici. Ti primeri prikazujejo prednosti analize MKE v kombinaciji s predlagano shemo modeliranja.

V članku je predstavljen nov postopek modeliranja 3D-geometrije posameznih in pletenih vijačnih žic. Metoda omogoča ustvarjanje modela 3D-žične pletenice brez omejitev glede dolžine. Modeli, ustvarjeni s to shemo, so uporabni za numerično analizo. Na ta način je možno analizirati posamezne žice v 3D-modelih in enostavno preučevati obnašanje žic v pletenici oz. vrvi. Ugotovljeno je bilo, da pletene vijačne žice ni možno neposredno modelirati v razpoložljivih programskih paketih CAD. V članku je opisan postopek ustvarjanja mrežnega modela pletene vijačne žice. Kdor išče numerično rešitev za žično vrv, lahko uporabi to shemo modeliranja za modeliranje in analizo problema.©2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: pletena vijačna struktura, pletena vijačnica, posamezna vijačnica, dvojna vijačnica, Frenet-Serretov okvir


*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, [email protected] 58

Merjenje volumskega pretoka taline v proizvodnji kamene volne

Chen, J. ‒ Hočevar, M. ‒ Širok, B.Jinpeng Chen1 - Marko Hočevar2,* - Brane Širok2

1 Visoka politehnična šola Lanzhou, Fakulteta za elektrotehniko, Kitajska 2 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

Kakovost kamene volne je močno odvisna od procesa razvlaknjenja taline na centrifugi. Pomembno vlogo pri tem ima zagotavljanje enakomernosti pretoka taline, ki iz kupolne peči teče na centrifugo. Neprekinjeno merjenje pretoka taline omogoča nadzor hitrosti proizvodne linije kamene volne, kar zmanjšuje spremembe v gostoti končnega izdelka. Zaradi visokih temperatur taline se klasične metode merjenja pretoka ne uporabljajo. V prispevku predstavljamo metodo za merjenje volumskega pretoka toka taline, ki temelji na hkratni meritvi debeline curka taline in hitrosti toka z vizualizacijo.

Volumski pretok taline kamene volne izračunamo iz meritve debeline in hitrosti taline z metodo vizualizacije s snemanjem slik in njihovo analizo. Premer curka taline določimo z določanjem roba curka, hitrost pa iz dolžine potovanja motnje med dvema zaporednima posnetima slikama z metodo križne korelacije. Za določitev hitrosti curek taline s strani po potrebi vzbudimo z motnjo, generirano s curkom stisnjenega zraka.

Metoda je bila umerjena, na v ta namen izdelani merilni postaji, z uporabo rumeno obarvane vode. Pretok smo merili hkrati na dva načina, z merilnikom pretoka z zaslonko in s predstavljeno vizualizacijsko metodo. Črpalka je črpala vodo iz rezervoarja skozi cev z nameščeno merilno zaslonko v izstopno cev, iz katere je voda prosto v navpični smeri izstopala v območje meritve pretoka z vizualizacijo. Pnevmatska motnja za določanje hitrosti je bila nameščena tako, da je vzbujala tok vode s strani. Pri tem smo zagotovili, da je bil curek na izstopu iz cevi enakomerno osvetljen in, da kamera ni zaznavala odbojev tudi med delovanjem pnevmatskega sistema za vzbujanje motenj v toku. Volumski pretok smo nastavljali s spreminjanjem vrtilne frekvence črpalke.

Merilno metodo smo testirali tudi na proizvodni liniji kamene volne.Z umerjanjem v laboratoriju smo primerjali dejanski pretok vode in pretok, izmerjen z novo metodo.

Zaporedne izmerjene vrednosti pri izbranem pretoku so imele velik povprečen odklon od povprečne vrednosti, medtem ko so povprečne vrednosti za posamezen pretok dobro ustrezale dejanskim povprečnim vrednostim. Pri tem smo dosegli korelacijski koeficient R2=0.96. Metoda je bila testirana tudi v procesu proizvodnje kamene volne. Izmerjene vrednosti pretokov smo primerjali z maso končnega izdelka. Meritve na proizvodni liniji so pokazale, da je ujemanje med izmerjenimi vrednostmi pretoka in maso končnega izdelka dobro, pri čemer je masa končnega izdelka konstantno manjša, saj se del taline ne razvlakna, temveč v obliki perl pade na tla usedalne komore.

Metoda je odvisna od natančnosti določanja premera in hitrosti curka taline. Ob tem predpostavimo, da je hitrost taline po celotnem curku enaka. V primeru, da v talini ni vključkov neraztopljenih kamnin, motnjo za določanje hitrosti taline generiramo pnevmatsko s pulziranjem v prečni smeri, pri čemer je potrebno določiti jakost pulzirajočega toka zraka tako natančno, da v talino ne uvedemo motenj hitrosti v smeri pretoka. Pri merjenju na proizvodni liniji mora operater redno čistiti kanal, po katerem priteka talina na centrifugo, da na njem ne nastane strjen stržen taline, ki poveča merilno negotovost ali celo onemogoči meritev.

V prispevku je prvič opisano merjenje pretoka taline na izstopu iz peči v proizvodnji kamene volne. Z merilno metodo je možen nadzor delovanja proizvodnega procesa, zmanjšanje presežne gostote v končnem izdelku, zmanjšanje stroškov in rabe energije pri proizvodnji.©2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: kamena volna, talina, volumski pretok, merjenje, strojni vid, križna korelacija


*Naslov avtorja za dopisovanje: Fakulteta za strojništvo, Univerza v Kragujevcu, Dositejeva 19, 36000 Kraljevo, Srbija, [email protected] SI 59

Optimizacija trapeznega prereza roke avtodvigala z Lagrangeevimi multiplikatorji in diferencialnim evolucijskim

algoritmom (DE)Gašić, M.M. ‒ Savković, M.M ‒ Bulatović, R.R.

Milomir M. Gašić ‒ Mile M. Savković* ‒ Radovan R. Bulatović Fakulteta za strojništvo, Univerza v Kragujevcu, Srbija

Vodilni proizvajalci avtodvigal zadnja leta posvečajo veliko pozornosti konstruiranju rok kot najvrednejših delov avtodvigala. Oblika prereza roke je zasnovana tako, da zagotavlja čim večjo upogibno in vzvojno togost pri čim manjši masi. Klasične pravokotne oblike rok zamenjujejo bolj kompleksne mnogokotne oblike, ki zagotavljajo ugodno porazdelitev napetosti po roki.

V članku je predstavljena raziskava optimalnih razmerij pri trapezni geometriji prereza po dveh metodah. Prikazani sta metoda Lagrangeevih multiplikatorjev za ugotavljanje ekstremov in metoda diferencialne evolucije (DE). Optimizacija prereza se v obeh primerih izvaja po kriteriju trdnosti. Metoda Lagrangeevih multiplikatorjev daje optimalne vrednosti parametrov geometrije prereza v eksplicitni obliki ter funkcijske povezave parametrov geometrije prereza. Pri DE metodi ciljna funkcija ni nujno konstantna in je v določenem območju diferencialna. Začetne vrednosti konstrukcijskih parametrov je možno izbirati v širokem območju, zato za določanje približnih začetnih vrednosti niso potrebne prejšnje izkušnje na področju konstruiranja.

Verifikacija rezultatov in primerjalna analiza uporabljenih metod je bila izvedena na numeričnem primeru za eno izpeljano rešitev. Obe metodi optimizacije sta pokazali, da ju je mogoče uspešno uporabiti za določanje razmerij med parametri geometrije prereza nosilne strukture roke avtodvigala. Metoda Lagrangeevih multiplikatorjev ima prednost pri določanju ciljnih funkcij v analitični obliki, kar je zelo prikladno za praktično uporabo, pridobljeni vzorci pa so lahko zelo uporabni za konstruktorje; zlasti v prvi fazi konstruiranja, ko se soočajo s problemom določanja začetne geometrije konstrukcije, ki mora biti blizu optimalni. Metoda DE omogoča uvajanje večjega števila omejitev, večjega števila začetnih vrednosti konstrukcijskih spremenljivk in večjega števila rešitev, ki zadovoljujejo podane omejitve. Na osnovi primerjave rezultatov je bilo ugotovljeno, da se metodi v velikem delu prekrivata. Pri celotni analizi daje boljše rešitve metoda DE. Takšni rezultati so pričakovani, saj je bila pri metodi DE izvedena optimizacija s šestimi parametri, medtem ko so bili pri prvi metodi optimizirani trije parametri.

Na osnovi izvedene raziskave lahko zaključimo, da metodi ne zahtevata uporabe obsežnega matematičnega aparata oz. programske in strojne opreme, kakor tudi, da imata pomembno vlogo pri določanju teoretičnih razmerij med osnovnimi geometrijskimi parametri prerezov nosilnih struktur na splošno. Inovacija glede na prejšnje raziskave, ki so navedene v referencah, je uspešna uporaba metode DE, kakor tudi določitev funkcijskih razmerij med parametri optimizacije v eksplicitni obliki.

Nadaljnje raziskave morajo biti usmerjene v sočasno uporabo obeh metod, saj daje metoda Lagrangeevih multiplikatorjev eksplicitne vrednosti parametrov optimizacije, metoda DE pa lahko zajame znatno večje število parametrov optimizacije. Nobena metoda ni omejena po številu parametrov optimizacije, zato je v nadaljnjih raziskavah treba povečati število parametrov optimizacije in število mejnih funkcij.©2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: trapezni prerez, avtodvigalo, roka, Lagrangeevi multiplikatorji, diferencialni evolucijski algoritem, ciljna funkcija, mejna funkcija


*Naslov avtorja za dopisovanje: Resistec UPR d.o.o.& Co. k.d., Krška cesta 8, SI- 8311 Kostanjevica na Krki, Slovenija, [email protected] SI 60

Adaptivno položajno vodenje nanorobotske celiceŠkorc, G. - Čas, J. - Brezovnik, S. - Šafarič, R.

Gregor Škorc1,* - Jure Čas2 - Simon Brezovnik3 - Riko Šafarič2 1Resistec UPR d.o.o. & Co. k.d., Slovenija

2Univerza v Mariboru, Fakulteta za elektrotehniko, računalništvo in informatiko, Slovenija 3Univerza v Mariboru, Fakulteta za strojništvo, Slovenija

V prispevku je predstavljen razvoj proizvodnega sistema s submikrometrsko ločljivostjo. Tako imenovana nanorobotska celica je zasnovana na X/Y manipulatorju, ki je podprt s tremi podajalnimi mizicami, gibljivimi vzdolž osi Z. Nanorobotska celica je vodena položajno, z dvema različnima histereznima tehnikama. Celotna aplikacija je zasnovana na programskem okolju LabView, krmilniku gibanja NI-PCI7356 in petih gonilnikih koračnih motorjev TMCM-090.

Eksperimentalni del prispevka obravnava dva poglavitna problema, s katerima se soočimo ob gradnji natančne pozicionirne naprave. Prvi so nelinearnosti piezolinearnih motorjev, uporabljenih v nanorobotski celici. Nelinearnosti, ki izvirajo iz histerez piezoelektrikov ter iz trenja med piezoelektriki in motorno osjo, omejujejo izbor klasičnih tehnik vodenja, primernih za vodenje takšnega sistema. Drugi problem nastopi v primeru, da proizvodni sistem zahteva večji delovni prostor in hkrati proizvodni proces takšnega sistema zahteva pogoste gibe preko večjih razdalj. Če želimo ohraniti visoke natančnosti pozicioniranja, morajo motorji obratovati v režimu s čim krajšo stopnico. Kratke motorne stopnice imajo za posledico nižje hitrosti manipulatorja, gibi preko večjih razdalj pa s tem postanejo časovno potratni. Eksperimenti na predstavljeni nanorobotski celici so pokazali, da je možno zgrajeni sistem voditi s submikrometrsko natančnostjo z enostavno histerezno tehniko. Kljub temu, da se je osnovna histerezna metoda izkazala za funkcionalno, je pri vodenju preko večjih razdalj predstavljala omejitev sistema. Gibanje z visoko natančnostjo je pogojeno s prej omenjenimi nizkimi hitrostmi.

V prispevku je predstavljena dopolnitev osnovne histerezne metode, ki omogoči, da osnovna histerezna tehnika postane uporabna tudi za vodenje preko večjih razdalj. Dopolnitev je zasnovana na predpostavki, da lahko robotski manipulator izvede gib preko večje razdalje z daljšo motorno stopnico. S tem dosežemo višjo hitrost izvedbe giba. Da bi hkrati obdržali tudi visoko natančnost, dolžino stopnice krajšamo skladno z oddaljenostjo od ciljne točke. Bližje kot smo ciljni točki, krajša je stopnica (nižja hitrost), ciljno točko pa zadenemo bolj natančno.

Dopolnjeno osnovno histerezno tehniko poimenujemo adaptivna histerezna tehnika vodenja. Predlagane dopolnitve so argumentirane s praktičnimi eksperimenti. Trenutno je v prispevku predstavljeni sistem zgrajen do te mere, da omogoča natančno manipulacijo z objekti mikrometrskih dimenzij. Nanorobotska celica je zgrajena fleksibilno v smislu integracije različnih tehnik vodenja in različnih orodij. V prihodnosti se bomo posvetili raziskavi uporabnosti algoritma adaptacije stopnice na drugih tehnikah vodenja (mehka logika, nevronske mreže, itd.). Vzporedno s tem bo potekal razvoj novih orodij, ki nam bodo omogočila izvedbo operacij na objektih, manjših od mikrometra.

Zahvala: Operacijo delno financira Evropska Unija – Evropski socialni skladi.©2011 Strojniški vestnik. Vse pravice pridržane. Keywords: nanorobotska celica, nanopozicioniranje, histerezni krmilnik, proizvodnja MEMS-ov, realno-časovni LabView


*Naslov avtorja za dopisovanje: Tehnični institut Rzeszów, Fakulteta za strojništvo in letalstvo, W. Pola 2, 35-959 Rzeszów, Poljska, [email protected] SI 61

Študija parametrov kakovosti in vedenja aluminijaste pločevine, kovičene z zabijalnimi kovicami,

za različne pogoje spajanjaMucha, J.

Jacek Mucha*

*Tehnični institut Rzeszów, Fakulteta za strojništvo in letalstvo, Poljska

Vse večja uporaba lahkih materialov v sodobni avtomobilski industriji je prinesla tudi razvoj novih tehnologij spajanja. Enostransko kovičenje z dvokrako zabijalno kovico (SPR) je zaradi svojih prednosti v primerjavi s tradicionalnimi postopki spajanja postopoma postalo ena od najpogosteje uporabljenih rešitev za spajanje aluminijastih delov. Postopek predstavlja konkurenco tradicionalnim tehnikam spajanja, kot sta točkovno in obločno varjenje. Pri SPR gre v bistvu za operacijo hladnega preoblikovanja, pri katerem polcevasto kovico zabijemo v dve pločevini, ki sta podprti z majhno matrico.

Nekateri tuji članki predstavljajo rezultate raziskav, vendar samo za že osvojene procesne parametre. Podatki o vplivu materiala kovice na deformacije kovice niso znani. Prav tako ni na voljo literatura, v kateri bi bila predstavljena analiza mehanike nastanka spoja in njene posledice za izbiro materiala kovice in obliko matrice.

V članku je predstavljen napredek raziskav na področju napovedovanja dimenzij po montaži na podlagi rezultatov analize po metodi končnih elementov. Obravnavana je študija primera spajanja dveh pločevin iz aluminijeve zlitine z jekleno zabijalno kovico. Za analizo spoja pločevin je bila uporabljena programska oprema za MKE MSC Marc Mentat. Po validaciji parametrov modela lahko numerična orodja pomagajo pri doseganju pomembnih izboljšav na področju snovanja procesov in zniževanja stroškov.

Predstavljen je nov pristop k modeliranju geometrijskih parametrov izdelanega spoja SPR. Predstavljena je analiza vpliva oblike orodja, spremembe materiala kovice in spremembe tornih pogojev na geometrijske parametre izdelanega spoja.

Izbira materiala kovice je zelo pomembna za rabo energije pri procesu. Z ustrezno toplotno obdelavo kovice je možno doseči želene lastnosti utrjevanja z določeno napetostjo tečenja, kar ima velik vpliv na deformacijo kovice in na silo kovičenja.

Raba energije za deformiranje kovice je med drugim odvisna tudi od krivulje deformacijskega utrjanja. Pri izbiri materiala kovice je zato treba upoštevati parametre izdelanega spoja in energijo, potrebno za deformiranje materiala kovice.

Celotna stopnja razsipanja energije se v tem primeru izračuna s seštevanjem stopenj razsipanja energije zaradi notranjih plastičnih deformacij, striga pri hitrostnih diskontinuitetah in trenja na stiku med orodjem in materialom.

Pomemben dejavnik, ki vpliva na izdelan spoj, je tudi geometrija vdolbine na matrici. Pravilna izbira vdolbine na matrici omogoča zmanjšanje sile pri kovičenju in najmanjši premer obrobka na izdelanem spoju. Z zniževanjem koničnega dela vdolbine v matrici (t.j. s poravnavo s čelno ploskvijo matrice) in z zmanjševanjem globine vdolbine so bile dosežene največje vrednosti pri večini kazalnikov.

To informacijo je možno uporabiti za izboljšanje proizvodnega procesa in konstrukcije orodij. V prihodnje bo možna še natančnejša optimizacija komponent s prenosom podatkov iz prejšnjih faz preoblikovanja in spajanja pločevin v računalniško kodo.©2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: kovičenje z zabijalnimi konicami, nastanek spoja, obremenitve pri kovičenju, mehanske lastnosti, modeliranje z metodo končnih elementov, simulacija procesa


*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo,Aškerčeva 6, 1000 Ljubljana, Slovenija, [email protected] 62

Integriteta površine po mehanskem utrjevanju različnih aluminijevih zlitin

Žagar, S. - Grum, J.Sebastjan Žagar - Janez Grum*

Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

Namen prispevka je predstaviti dve vrsti aluminijevih zlitin AlCu4PbMgMn (2007-T351) in AlSi1MgMn (6082-T651), ki sta bili mikro površinsko utrjeni z različnimi pogoji udarnega utrjevanja s kinetično energijo kroglic. Udarno mikroutrjevanje površine je bilo izvedeno s kaljenimi jeklenimi kroglicami premera 0,5 mm, oznake S170 s trdoto 56 HRC, z različnimi tlaki zraka in z masnimi pretoki, ki zagotavljajo različne Almenove intenzitete. Cilj raziskave je, da z eksperimentalnimi metodami raziščemo zvezo med pogoji udarnega utrjevanja aluminijevih zlitin ter hrapavostjo in topografijo površine z mikroskopskimi preiskavami poškodb na površini, podprto z analizo mikrostrukture, trdote in zaostalih napetosti.

Pogosto pa so na površini prisotne različne napake in poškodbe, za katere ni predpisanih postopkov za ocenjevanje z optičnim ali elektronskim mikroskopom in so omejene s stopnjo zahtevnosti strojnega dela. Izbrani sta bili dve značilnosti za vrednotenje hrapavosti na udarno utrjenih vzorcih, in sicer aritmetična srednja hrapavost Ra in srednja globina hrapavosti Rz. S topografsko analizo pa smo ugotavljali vpliv trkov kroglic na nastanek utrjene površine tudi z mikroskopskega vidika z upoštevanjem mikrostrukturnih sprememb. Na vzorcih smo poleg manj nevarnih poškodb zaznali tudi razpoke, ki so nastale zaradi presežene kritične stopnje lokalne hladne deformacije materiala po trku s kroglicami. Z merjenjem mikrotrdote smo popisali spremembe po globini tankega utrjenega sloja. Na vzorcih, obdelanih z blagimi pogoji utrjevanja, so dosežene manjše vrednosti mikrotrdote na površini (140 HV0,2 pri zlitini 2007 in 110 HV0,2 pri zlitini 6082) in tudi plitvejša širitev mikrotrdote v globino kot pri ostrejših pogojih obdelave. Pri zlitini 2007, obdelani pri nižjem delovnem tlaku zraka, smo izmerili globino utrditve le 260 mm, pri višjem delovnem tlaku zraka pa 390 mm. Na podlagi posameznih meritev mikrotrdote pri vzorcih, obdelanih z Almenovo intenziteto 21A in 28A, opazimo, da se mikrotrdota po obdelavi poveča kar za 30%. Največje dosežene tlačne zaostale napetosti pri zlitini 2007 znašajo -362 MPa v globini 290 mm, pri zlitini 6082 pa -167 MPa v globini 250 mm. Poteki zaostalih napetosti v tankem površinskem sloju zelo pomembno vplivajo na trajno dinamično trdnost materiala, kot tudi na nastanek in širjenje razpok, kar se odraža v obratovalni dobi strojnega dela. Tako lahko napetosti v primeru tlačnih zaostalih napetosti v površinskem sloju z malim gradientom znatno izboljšajo odpornost materiala na utrujanje.

Različne tehnike udarnega mikroutrjevanja tankih površinskih slojev v splošnem zagotavljajo zelo enakomerno utrditev površja na želenem delu obdelovanca, s ciljem izboljšati odpornost materiala na utrujanje med obratovanjem strojnega dela pri dinamičnih obremenitvah. Izvedeno je bilo mikro-mehansko utrjevanje površine s kinetično energijo kroglic pri različnih pogojih. Različni pogoji mikro-utrjevanja površin postanejo med seboj primerljivi, če jih povežemo z Almenovim preizkusom, ki določa ustrezno primerjalno število. Z dodatno mikroskopsko analizo smo ugotovili, da pri nekaterih parametrih utrjevanja prihaja tudi do nezaželenih poškodb površine dinamično obremenjenega strojnega dela, kar lahko vpliva na nastanek razpok in kasneje tudi na rast razpok do porušitve strojnega dela. Rezultati raziskave so potrdili, da je treba pogoje mikroutrjevanja izbrati zelo skrbno, da prevladajo koristni učinki prisotnih zaostalih napetosti na utrjeni površini strojnega dela.

Predstavljeni rezultati v prispevku so zanimivi tako za strokovno javnost, kot tudi za industrijske uporabnike. Cilj zbranih rezultatov o mikroudarnem utrjevanju površine lahko ob ustrezni ekspertni podpori omogoči hitrejše in boljše odločanje o izbiri optimalnih pogojev utrjevanja.©2011 Strojniški vestnik. Vse pravice pridržane. Keywords: aluminijeve zlitine, udarno utrjevanje, hrapavost površine, topografija površine, mikrotrdota, mikrostruktura, zaostale napetosti, dinamične obremenitve


*Naslov avtorja za dopisovanje: Univerza v Quebecu, Oddelek za aplikativne znanosti, Saguenay, (Qc), Canada, G7H 2B1. [email protected] SI 63

Študija utrujenostnega zloma spodnje ročice obese z večosnim kriterijem gostote deformacijske energije

Saoudi, A. ‒ Bouazara, M. ‒ Marceau, D.Abdelhamid Saoudi ‒ Mohamed Bouazara* ‒ Daniel Marceau

Univerza v Quebecu, Oddelek za aplikativne znanosti, Saguenay, Kanada

Zmanjšanje mase ne izboljšuje le kota poševnega teka kolesa po cesti, odzivnosti vozila v ovinkih in stabilnosti, pripomore tudi k večji učinkovitosti in varnosti vožnje na dolge razdalje in zmanjšuje porabo goriva. Raziskovalni cilj v okviru želenega zmaljševanja mase je preučevanje dinamike in vibracijskih lastnosti nekaterih komponent iz aluminijevih zlitin, zlasti utrujenostne trajnostne dobe spodnje ročice obese.

Utrujanje materiala povzroča razpoke, ki nastajajo postopoma zaradi ponavljajočih se naključnih obremenitev. Te naključne obremenitve lahko privedejo do zloma zaradi utrujanja materiala z različnimi ravnmi napetosti. Cilj te študije je ovrednotiti potencial za uporabo mehanskih delov iz lahke kovine v avtomobilski industriji s preučevanjem njihove utrujenostne trajnostne dobe ob upoštevanju različnih parametrov, kot so dinamika obes, vrsta vzbujanja, geometrija in masa mehanskega dela. Preučevani del je spodnja ročica obese, izdelana iz aluminijeve zlitine 7075-T6. Pristop z gostoto deformacijske energije omogoča primerjavo dveh tenzorjev istega reda: za večosni in enoosni primer.

Vzbujanje z naključnimi odmiki se izračuna analitično iz gostote energijskega spektra PSD. Sila vzbujanja se izračuna z enostavno normalizacijo spektralnega odmika. Da bi se izognili uporabi Newton-Raphsonove metode, med računanjem delne utrujenostne trajnostne dobe v vseh elementih mreže, smo razvili vmesnik v Matlabu za identifikacijo kritičnih elementov. Signal gostote deformacijske energije (SENER) kritičnega elementa se korigira z vmesniškim algoritmom WAFO Matlab, ki odstrani anomalije. Z Markovsko formulo se določijo t.i. cikli dežnih kapelj za izračun števila ponovitev signala do zloma z Minerjevim zakonom. V tej raziskavi je bil razvit hibriden model za preučevanje potenciala aluminijeve zlitine, kot novega materiala za spodnjo ročico obese vozila. Razvit je bil analitični in numerični model za simulacijo dinamičnega obnašanja sistema obes ter stanja napetosti in gostote deformacijske energije v spodnji ročici obese vozila.

Preučeni so bili spektralni vidiki utrujanja in dinamičnega vedenja sistema obes vozila. Racionalen pristop je uporaba večosnega kriterija gostote deformacijske energije v enoosnem primeru, ki je ekvivalenten večosnemu. Kriterij gostote deformacijske energije, ki je neodvisen od povprečne vrednosti obremenitev, je bolj praktičen kot model po Morrowu, ki zahteva korekture zaradi vpliva povprečnih vrednosti obremenitev. Model po Morrowu potrebuje nekaj korektur zaradi srednje vrednosti, saj gre za tenzor prvega reda, ki je odvisen od orientacije.

V tej študiji je bila ovrednotena maksimalna vrednost sile, ki jo prenaša pnevmatika, in sila povratne verige. Nato je bil na osnovi spektra energijske gostote modela cestnih neravnin postavljen model negativne povratne zanke in direktne poti spodnje ročice obese vozila, ki je izpostavljen pomembnim dinamičnim obremenitvam.©2011 Strojniški vestnik. Vse pravice pridržane.Ključne besede: utrujenostni zlom, vozilo, dinamika, obese, aluminij


*Naslov avtorja za dopisovanje : Univerza v Beogradu, Fakulteta za strojništvo, Kraljice Marije 16, 11000 Beograd, Srbija, [email protected] 64

Inteligentna optimizacija procesa z več odgovori na osnovi Taguchi pristopa in predhodnih podatkov

Šibalija, T. ‒ Majstorović, V. ‒ Soković, M.Tatjana Šibalija1,* ‒ Vidosav Majstorović1 ‒ Mirko Soković2

1 Univerza v Beogradu, Fakulteta za strojništvo, Srbija 2 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

Članek predstavlja nov, generični pristop k optimiranju parametrov procesa z več odzivi, ki temelji na predhodnih podatkih.

Pristop sestoji iz dveh delov. Prvi del temelji na Taguchi funkciji izgube kakovosti (QL) in multivariantnih statističnih metodah PCA in GRA za nekorelirane in sestavljene odgovore znotraj posameznih meritev zmogljivosti procesa. Na osnovi tega je razvit drugi del z uporabo tehnik umetne inteligence (AI): umetnih nevronskih mrež (ANNs) za izvajanje modeliranja procesa in genetskega algoritma (GA), ki poišče optimalno izbiro parametrov v zveznem prostoru.

Podatki o odgovorih procesa se najprej transformirajo v funkcije izgube kakovosti (QLs), ki ustrezno predstavijo relativne finančne značilnosti odgovorov. Metoda PCA, ki se izvaja na funkcijah QLs, oblikuje set nekoreliranih komponent. Uporaba metode GRA poda vrednosti stopnje povezave (γ), privzete kot meritev sintetične zmogljivosti. Optimalne razmere se dosežejo z izbiro maksimuma parametra, ki vpliva na γ. Zgornji postopek se imenuje metoda učinkov faktorjev, ki jemlje v poštev samo diskretne vrednosti parametrov, zabeleženih v setu predhodnih podatkov.

Razvite so umetne nevronske mreže ANNs za modeliranje povezave med kritičnimi parametri in vrednostjo γ. Izbrane ANNs predstavljajo objektivno funkcijo za genetski algoritem GA. Devet razvitih GAs kombinira tako najbolj običajne vrste funkcij izbire kot tudi križne funkcije. Nastavitev parametrov se doseže z metodo učinkov faktorjev, ki se v nadaljevanju rabi kot osnova za oblikovanje začetne populacije v GAs, ki povečuje sposobnost iskanja aktualne globalne rešitve v danem številu generacij. Najboljši GA se izbere glede na maksimalno vrednost stopnje povezave γ .

Učinkovitost pristopa je ilustrirana s praktičnim primerom. Proces je bil nadziran z RX − kontrolnimi kartami; dva korelirana odgovora in štiri vrednosti kontrolnih parametrov so bili shranjeni v kontrolnih kartah. Rezultati analize kažejo, da predlagani pristop poišče optimalne nastavitve parametrov, kar daje visoke vrednosti γ in potrjuje, da se lahko pristop učinkovito uporablja brez kakršnihkoli prekinitev procesa zaradi eksperimentiranja.

Predlagana metoda je omejena na statične procese z več odgovori. Nadaljnje raziskave se bodo nanašale na dinamične probleme, kjer bodo odgovori ponazorjeni kot funkcija signalnih faktorjev.

V nasprotju z večino metod za optimizacijo procesov z več odgovori, ki temeljijo na eksperimentalnih podatkih in so namenjene reševanju posameznih problemov, je zamisel predlagane metode v zagotavljanju generične rešitve za optimizacijo različnih procesov z več odgovori, ki temelji na predhodnih podatkih procesa. V faktorsko učinkoviti metodi je relativna značilnost vsakega posameznega odgovora ustrezno zastopana, rezultirajoča γ vrednost pa temelji na celotni varianci izvirnih podatkov, ki izboljšajo objektivnost analize. V AI-modulu je začetna populacija v GA formirana v soseščini faktorjev, ki vplivajo na izboljšanje konvergence k aktualnemu globalnemu optimumu. Predlagana metoda, kot končni rezultat, ni odvisna od vrste procesa ali relacij med odgovori in/ali kontrolnimi parametri, zato je uporabna pri širokem spektru statičnih problemov optimizacije.© 2011 Strojniški vestnik. Vse pravice pridržane. Ključne besede: optimizacija, predhodni podatki, Taguchi metoda, nevronske mreže, genetski algoritem

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)4, SI 65-66Navodila avtorjem

SI 65

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. opredelitev, 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)4, SI 65-66

SI 66

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)4, SI 67-70Osebne objave

SI 67

Doktorati, magisteriji, specialistična dela in diplome

DOKTORAT ZNANOSTI

Na Fakulteti za strojništvo Univerze v Ljubljani sta z uspehom obranila svojo doktorsko disertacijo:

dne 11. marca 2011 Jaka KOVAČ z naslovom: »Detekcija in karakterizacija napetostno-korozijskega pokanja z metodama akustične emisije in elektro-kemijskega šuma« (mentor: prof. dr. Edvard Govekar, somentor: Andrej Legat (ZAG));

Interkristalno napetostno-korozijsko pokanje (IKNKP) sodi med najnevarnejše in najmanj poznane oblike korozijskih procesov kovin. Namen doktorskega dela je raziskati možnosti detekcije in karakterizacije IKNKP nerjavnega jekla na osnovi merskih podatkov. Raziskave temeljijo na simultani uporabi štirih različnih merilnih metod: detekcija akustične emisije (AE), detekcija elektrokemijskega šuma (EŠ), meritve raztezka preskušanca ter dodatnega spremljanja stanja procesa s pomočjo digitalnih fotografskih posnetkov. Z naštetimi metodami smo predstavili detekcijo nastanka, rasti razpoke in končne porušitve preskušanca pri IKNKP in ocenili možnosti in omejitve posamezne metode. Pokazali smo, da sočasna uporaba več merilnih metod omogoča celovitejši opis procesov pri NKP. Ugotovljene so bile linearne korelacije med karakteristikami digitalnih posnetkov in signali EŠ ter raztezka preizkušanca. Analiza korelacij je pokazala tudi sočasnost izbruhov AE in tokovnih tranzientov EŠ med IKNKP. Zaznane sočasne izbruhe AE in tranziente EŠ smo na osnovi mikroskopske analize prelomne površine povezali s fizikalnim procesom: duktilnimi prelomi ligamentov v okolici korozijsko bolj odpornih kristalnih mej. Na osnovi rezultatov doktorskega dela lahko zaključimo, da potek rasti interkristalne napetostno-korozijske razpoke temelji na dveh procesih: anodnem odtapljanju konice razpoke po korozijsko občutljivih kristalnih mejah in duktilnih porušitvah ligamentov za napredujočo konico razpoke. Poleg tega smo pokazali tudi možnosti uporabe signalov AE pri avtomatskem sprotnem spremljanju in detekciji pojava IKNPK;

dne 30. marca 2011 Jan ČERNETIČ z naslovom: »Zaznavanje kavitacije v centrifugalnih

črpalkah s pomočjo zvoka in vibracij v slišnem delu spektra« (mentor: prof. dr. Mirko Čudina, somentor: akad. prof. dr. IgorGrabec);

V delu je predstavljena metoda zaznavanja kavitacije v centrifugalnih črpalkah s pomočjo merjenja hrupa in vibracij v slišnem delu spektra, torej od 20 Hz do 20 kHz. Podano je teoretično ozadje kavitacije ter dogajanje v dvofaznem toku pri spreminjajočem tlaku. Opravljene so meritve hrupa pri kavitaciji na primeru dveh centrifugalnih črpalk. Za preverjanje rezultatov je bilo opravljeno več dodatnih meritev, in sicer lastni odziv sistema (odziv sistema na impulzno zunanjo motnjo), prehodnost zvoka skozi stene črpalke, meritev z akustično kamero in druge. S pomočjo določevanja merilne negotovosti za več različnih primerov meritve je bila dokazana zanesljivost izmerjenih rezultatov.

Raziskava je pokazala, da je predstavljena metoda zaznavanja kavitacije zanesljiva in učinkovita. Pojav kavitacije v črpalki povzroči velik porast amplitude hrupa in vibracij v širokem frekvenčnem območju, še bolj pa v določenih ožjih območjih, določenih na podlagi preučevanja mehanskih in akustičnih lastnosti črpalke. Rezultati kažejo na veliko uporabnost metode pri zaznavanju kavitacije v centrifugalnih črpalkah.

*Na Fakulteti za strojništvo Univerze v

Mariboru je z uspehom obranil svojo doktorsko disertacijo:

dne 31. marca 2011 Gregor ŠKORC z naslovom: »Robotska celica s submikrometrsko resolucijo« (mentor: prof. dr. Riko Šafarič);

V okviru doktorske disertacije je predstavljen razvoj eksperimentalne robotske celice, ki je zmožna pozicioniranja s submikrometrsko natančnostjo. Robotska celica temelji na petih PiezoLEGS® motorjih, od katerih dva izmed njih formirata X/Y manipulator, ostali trije pa služijo kot podajalne mizice po Z osi.

Konvencionalne izvedbe krmilnikov za vodenje PiezoLEGS® motorjev ne omogočajo avtomatske adaptacije parametrov gibanja motorja. Gibanje v visoki resoluciji botruje nizkim hitrostim, kar ob gibanju manipulatorja na daljše razdalje privede do velike potratnosti časa.


SI 68

Disertacija obravnavana adaptivno položajno vodenje robotske celice s konvencionalnem krmilnikom Trinamic TMC-090, ki je dodelan tako, da omogoča avtomatsko adaptacijo parametrov vodenja. Tri klasične tehnike položajnega vodenja so nadgrajene z adaptacijskim algoritmom in preizkušene v okviru testa odziva na stopnico in testa sledenja trajektoriji.

Predstavljeni sistem robotske celice je zgrajen fleksibilno in omogoča integracijo različnih orodij. Kot praktični primer uporabe takega sistema je prikazana izvedba manipulacije z vakuumskim in piezoelektričnim prijemalom, ter mikroskopiranje z Akiyama sondo.

MAGISTERIJ ZNANOSTI

Na Fakulteti za strojništvo Univerze v Ljubljani je z uspehom zagovarjal svoje magistrsko delo:

dne 10. marca 2011 Saša MARUŠIČ z naslovom: »Projektno vodenje osvajanja serijskega izdelka« (mentor: prof. dr. Marko Starbek, somentor: izr. prof. dr. Janez Kušar);

*

Na Fakulteti za strojništvo Univerze v Mariboru sta z uspehom zagovarjali svoje magistrsko delo:

dne 15. marca 2011 Majda ŠMIGOC z naslovom: »Obdelava predčiščene izcedne vode s kombinacijo adsorpcija / nanofiltracija / razplinjevanje« (mentorica: izr. prof. dr. Marjana Simonič);

dne 28. marca 2011 Petra KRALJ MARHOLD z naslovom: »Metodologija ravnanja s padavinskimi vodami na avtocestah« (mentorica: prof. dr. Aleksandra Lobnik);

SPECIALISTIČNO DELO

Na Fakulteti za strojništvo Univerze v Ljubljani je z uspehom zagovarjal svoje specialistično delo:

dne 1. marca 2011 Franci LES z naslovom: »Procesna oskrba tabletnega obrata« (mentor: prof. dr. Iztok Golobič).

DIPLOMIRALI SO

Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva:

dne 25. marca 2011:Nejc BOŽIČ z naslovom: »Integriran

sistem za vzdrževanje koles tračnih žag« (mentor: izr. prof. dr. Peter Butala);

Andrej HOMAR z naslovom: »Sledilna nosilna konstrukcija 3D ovojev zgradb« (mentor: doc. dr. Boris Jerman);

Andrej LIČEN z naslovom: »Sledenje materialnih tokov v maloserijski proizvodnji s tehnologijo RFID« (mentor: izr. prof. dr. Peter Butala, somentorica: doc. dr. Mira Trebar)

*

Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva:

dne 24. marca 2011:Janko LESKOVAR z naslovom: »Dizajn

in ergonomija toaletnega sedišča« (mentor: prof. dr. Andrej Polajnar, somentor: izr. prof. Vojmir Pogačar);

dne 31. marca 2011:Miha HRIBERŠEK z naslovom:

»Zadovoljitev kakovosti vrat za končnega kupca po metodi Šest sigma v Gorenju d.d.« (mentor: izr. prof. dr. Miran Ulbin, somentorica: doc. dr. Nataša Vujica Herzog);

Gregor MOGEL z naslovom: »Individualno vozilo za golf igrišča« (mentor: prof. dr. Srečko Glodež).

*

Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva:

dne 9. marca 2011:Andrej BAŠA z naslovom: »Vpliv

zračne reže med rotorjem ter statorjem na hrup alternatorja« (mentor: prof. dr. Miha Boltežar);

Matej IVANČIČ z naslovom: »Konstrukcija in dimenzioniranje grelnika za diesel gorivo za motorje moči do 180 kW« (mentor: prof. dr. Franc Kosel, somentor: doc. dr. Tomaž Videnič);


SI 69

dne 14. marca 2011:Boštjan JANEŽIČ z naslovom: »Ščitenje

sestavnih delov žarometov pri vakuumskem oslojevanju« (mentor: prof. dr. Janez Kopač);

Andrej PIKOVNIK z naslovom: »Biološki vpliv vibracij med letenjem« (mentor: prof. dr. Rastko Golouh, somentor: doc. dr. Tadej Kosel).

*

Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva:

dne 24. marca 2011:Bojan LEŠ z naslovom: »Optimizacija

razvrščanja nalogov v proizvodnji po naročilu« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Iztok Palčič);

dne 31. marca 2011:Rok ANŽELAK z naslovom: »Določevanje

odvisnosti in zakonitosti postopka odrezavanja« (mentor: prof. dr. Franci Čuš);

Tomaž AVGUŠTIN z naslovom: »Dimenzioniranje nosilnih elementov drsnih vrat« (mentor: doc. dr. Janez Kramberger);

Sandi CIMERMAN z naslovom: »Varnost strojev in vzdrževanje glede na nove standarde« (mentor: doc. dr. Darko Lovrec, somentor: doc. dr. Samo Ulaga);

Simon HAUPTMAN z naslovom: »Tehnološka zasnova obdelovalnega CNC stroja za obdelavo gravur v les in plastiko« (mentor: izr. prof. dr. Ivan Pahole, somentor: doc. dr. Mirko Ficko);

Milan KRČMAR z naslovom: »Modifikacija varilne priprave za varjenje avtobusnih ogrodij« (mentor: doc. dr. Janez Kramberger);

Jenisej LAKOTA z naslovom: »Koncipiranje in groba zasnova avtomatskih lisic za roke« (mentor: izr. prof. dr. Stanislav Pehan);

Jaka PARADIŽ z naslovom: »Analiza uspešnosti službe vzdrževanja v podjetju« (mentor: doc. dr. Samo Ulaga, somentor: doc. dr. Darko Lovrec);

Jurij PERŠE z naslovom: »Posodobitev klimatizacijskega sistema v proizvodni hali Grammer automotive Slovenija d.o.o.« (mentor: doc. dr. Matjaž Ramšak);

Ljubo ŠTRAKL z naslovom: »Optimizacija izdelave modularnih bivalnih enot v podjetju Arcont d.d.« (mentor: izr. prof. dr. Miran Brezočnik, Somentor: Simon Brezovnik);

Anton TIRŠEK z naslovom: »Optimizacija aparata za vroče napitke« (mentor: izr. prof. dr. Miran Brezočnik, somentor: izr. prof. dr. Bojan Ačko);


SI 70

V spomin prof. dr. Janezu Deklevi

in pričel z akademsko kariero. Ko je iz IJS odšel akademik Peterlin je prof. Dekleva sprejel ponudbo Fakultete za elektrotehniko, strojništvo in ladjedelništvo v Splitu in od leta 1963 kot profesor in dekan prispeval k razvoju ustanove. Prav zaradi njegove uspešnosti pri organizaciji visokega šolstva je bil povabljen še v Zagreb na Visoko tehniško šolo JLA in bil imenovan tudi za člana Znanstvenega sveta oboroženih sil Jugoslavije. Želja po povratku v Slovenijo je bila vseskozi močna. Zato je leta 1970 sprejel funkcijo direktorja Prometnega inštituta v Ljubljani. Kot odličen matematik, teoretik in raziskovalec je pričel intenzivneje delovati na področju organizacijskih ved, operacijskih raziskav in upravljalskih funkcij v podjetjih. Tako je leta 1972 prav na teh področjih pričel z delom na FS in drugih fakultetah UL kot redni profesor, kot vodja laboratorija in kot predstojnik katedre. FS je pridobila odličnega strokovnjaka za področje, ki je bilo sicer pedagoško in na raziskovalno premalo razvito. Pokojnikovo delo je bil začetek sistematične dograditve programov. Sodelavci smo se večkrat pošalili, da smo strojniki dobili »direktorski modul študija«, za katerega je pokojnik napisal program, zbral pedagoški in raziskovalni tim ter vedno vzbudil zanimanje študentov za to področje. Menim, da lahko v imenu sodelavcev in študentov fakultete tudi danes izrazim našo posebno zahvalo prav za ta pokojnikov prispevek k bogatitvi programa. Štirje doktorji znanosti, devet magistrov znanosti in 140 diplomantov FS UL, katerim je bil mentor od 1973 do upokojitve 1991 leta, bo zagotovo pritrdilo.

Prof. Deklevi v življenju ni bilo »lepo postlano«. Pa vendar je ves čas obdržal napredno držo, in se neprestano zavzemal za boljše, popolnejše. Svoje prepričanje je vneto zagovarjal, a tudi pozorno poslušal sogovornike. Sam zagotovo ne bom pozabil na dolge razprave o aktualnih družbenih vprašanjih. V zadnjem obdobju pa je užival v pogovorih o lepotah, o vsaki sliki prijatelja Miheliča iz pokojnikove čudovite zbirke je lahko govoril še in še. Govoril je o lepotah, ki jih je doživel na potovanjih. Čutili smo njegovo veselje v harmoniji družine. Izgubili smo dobrega in velikega človeka, spomin na profesorja Deklevo pa ostaja, kot tudi ostaja hvaležnost za vse, kar je dobrega storil.

Prof. dr. Matija Fajdiga

Profesorja sem spoznal leta 1972, ko je na Fakulteto za strojništvo prvič prišel predavat Operacijske raziskave. Od takrat dalje, pa vse do upokojitve leta 1991 sva delovno in prijateljsko preživela skupaj marsikatero uro. Zato lahko v imenu

FS, njegovih sodelavcev in prijateljev ter svojem imenu povzamem nekaj misli o pokojnikovi življenjski poti in občutkih, ki nas prevevajo ob izgubi.

Rojen je bil v Ljubljani, materi iz Ribnice in očetu iz Primorske. V rani mladosti se je močno navezal na sorodstvo v Ribnici. V osnovni šoli in realki v Ljubljani je bil odličnjak. Takoj po maturi leta 1943 se je vključil v Tomšičevo brigado in kasneje v Primorskem odredu prevzel organizacijo osvobodilnega gibanja, partizanstva in naše oblasti na osvobojenih ozemljih slovenske Istre. Od 1945 do 1949, ko je z odliko diplomiral na Tehniški fakulteti, oddelku za elektrotehniko v Ljubljani je sodeloval kot asistent s prof. dr. Grudnnom in akad. prof. dr. Peterlinom. V tistem času je oblast centralno razporejala strokovne kadre in pokojnik je moral, kot mlad strokovnjak za telekomunikacije in antene, v Beograd, v centralo vojaške oblasti. In tam ga je doživela zagotovo najtežja življenjska izkušnja. Zaradi zamenjave imena in osebe je nedolžen preživel skoraj dve leti v zaporih. Sodstvo je sicer priznalo napako, vendar tortur Golega otoka pokojnik ni mogel nikoli pozabiti. Pokojnik se navkljub komaj verjetni golgoti v procesu in zaporu, o kateri je spregovoril sicer redko in samo najboljšim prijateljem, ni uklonil, se ni zaprl in umaknil, temveč je v vsem svojem nadaljnjem življenju ostal optimist, aktiven in dosleden svojemu napredenemu prepričanju in najboljši vzornik.

Strokovno pot je nato nadaljeval na IJS, kjer je vodil laboratorij in pomembne projekte na področju spektrometrije. IJS mu je s posebnim priznanjem priznal prvenstvo na tem področju, na katerem je leta 1956 tudi doktoriral. Po petih letih dela v MIT (Massachusetts Institute of Technology) v Ameriki, kjer je tudi predaval, se je vrnil na IJS, vodil oddelek za pospeševalnike

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

President of Publishing CouncilJože DuhovnikUL, Faculty of Mechanical Engineering, Slovenia

PrintTiskarna Present d.o.o., Ižanska cesta 383, Ljubljana, Slovenia

General informationStrojniški vestnik – The 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.

We would like to thank the reviewers who have taken part in the peer-review process.

Cover: An independent wire rope core (IWRC) is composed by a simple straight strand as the core and six outer strands. Outer strands includes both single and nested helical wires. This figure is composed to show a right lang lay IWRC from different aspects. An IWRC is used as a core component to compose more complex wire ropes such as Seale and Warrington type.

Image courtesy: Cengiz Erdönmez

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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