Proceedings of IMECE 2004 2004 ASME International Mechanical Engineering Congress and RD&D Expo

November 13-19, 2004, Anaheim, California USA

IMECE2004-59806

A MODULAR MODELING APPROACH FOR THE DESIGN OF RECONFIGURABLE MACHINE TOOLS

Tulga Ersal Graduate Student Research Assistant

Department of Mechanical Engineering University of Michigan, Ann Arbor

tersal@umich.edu

Jeffrey L. Stein Professor

Department of Mechanical Engineering University of Michigan, Ann Arbor

stein@umich.edu

Loucas S. Louca Lecturer

Department of Mechanical and Manufacturing EngineeringUniversity of Cyprus lslouca@ucy.ac.cy

ABSTRACT A new generation of machine tools called Reconfigurable

Machine Tools (RMTs) is emerging as a means for industry to be more competitive in a market that experiences frequent changes in demand. New methodologies and tools are necessary for the efficient design of these machine tools. It is the purpose of this paper to present a modular approach for RMT servo axis modeling, which is part of a larger effort to develop an integrated RMT design and control environment. The components of the machine tool are modeled in a modular way, such that the model of any given configuration can be obtained by assembling the corresponding component models together based on the topology of the machine. The component models are built using the bond graph language that enables the straightforward development of the required modular library. These machine tool models can be used for the evaluation, design and control of the RMT servo axes. The approach is demonstrated through examples, and the benefits and drawbacks of this approach are discussed. The results show that the proposed approach is a promising step towards an automated and integrated RMT design environment, and the challenges in order to complete this goal are discussed.

INTRODUCTION

The ever-growing competition forces manufacturers to respond more quickly to changes in demand. As a result, manufacturers have to deal with short product life cycles, short ramp-up times and frequent changes in product mix and volumes, without compromising product quality and cost.

Being the heart of a manufacturing system, improved machine tools hold the key in meeting the above mentioned requirements. The shortcomings of conventional machine tools, which can be classified as dedicated and flexible, are being felt more today than in the past: With their design focus being a single part, dedicated machines lack the flexibility and scalability that the flexible machines offer. On the other hand, flexible machines cannot achieve the robustness, the cost-effectiveness and the throughput levels of dedicated machines [1].

A new generation of machine tools is being developed in the Engineering Research Center for Reconfigurable Manufacturing Systems at the University of Michigan, Ann Arbor, as part of an effort to overcome the insufficiencies of current manufacturing systems. These machine tools are called ‘Reconfigurable Machine Tools (RMTs)’ [2], and they combine the advantages of their dedicated and flexible counterparts. They are designed around a part family and their structure, in terms of both hardware and software, can be changed quickly and cost-effectively to achieve the exact functionality and capacity desired [3].

Containing several configurations to provide the needed flexibility and scalability, RMTs intrinsically lead to more complex machine tool design problems. Methodologies and tools that would help facilitate the design of RMTs could highly benefit and encourage the employment of reconfigurable manufacturing systems [4-6].

One important aspect of the RMT design problem is developing dynamic models for the design, evaluation and control of servo axes. What makes the problem of modeling

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RMTs unique is that even though there is a single machine tool, there exist several configurations, which separate models have to be developed for. Developing dynamic models for all possible configurations could be a cumbersome and time-consuming task if ad hoc methods are utilized. Moreover, without a systematic methodology modeling would require a lot of expertise and would be prone to errors, which would degrade the efficiency of using models in the design.

In this paper we present a methodology that could help make the RMT modeling task less time demanding, less error-prone and less challenging. The key idea of this methodology is to take advantage of the modular structure of the RMTs and adopt modular modeling concepts into the RMT modeling methodology. First, the physical components of an RMT are modeled in a modular way using the bond graph modeling tool [7]. The bond graph model is encapsulated in a schematic representation with defined connection ports. Then, the schematic component models are assembled by following the topology of a given configuration to obtain the model of the configuration. The configuration model can be easily integrated with the modules of non-energetic components such as interpolators and controllers, which can be conveniently represented with block diagrams; however this is beyond the scope of this paper.

The paper is organized as follows: The next section introduces the nomenclature used in the models. The section after that briefly reviews the background work. Then, the proposed RMT modeling methodology is presented. Examples of the modeling methodology are given, followed by a discussion of the approach. The paper concludes with summary and conclusions.

NOMENCLATURE C

Pr : position vector of point P with respect to the inertial frame I expressed in frame C

CPr : time derivative of C

Pr with respect to the inertial frame I

CBω : angular velocity vector of frame B with

respect to the inertial frame I expressed in frame C

2 1,B BA : coordinate transformation matrix from frame to frame 1B 2B

BACKGROUND The RMT concept was introduced by Koren and Kota [2],

and since their introduction, the design of RMTs has been an active research area. Methodologies and tools for designing RMTs [4] as well as evaluating structural stiffnesses [5] and tool tip errors [6] of design alternatives have been developed. However, the problem of developing a system level modeling methodology for RTMs has not been addressed yet.

Traditionally, machine tool models depict the machine tool as a group of servomotor and feed drive assemblies that are modeled as first or second order systems [8,9]. Chen and

Tlusty, however, showed that the structural dynamics of the feed drive could affect the system performance once high-speed machine tools are considered [10]. Many researchers identified the necessity to use higher order models for high-speed machine tools to cope with structural dynamics in order to be able to design the control system successfully [11-13]. These publications clearly indicate that modeling a machine tool is not a trivial task and care must be taken when deciding on the complexity of the model, but they do not provide a systematic way of modeling and, therefore, remain application specific approaches.

There have been research efforts to help the design and control of machine tool feed drives by automatically providing simulation models. Wilson and Stein developed a software program called Model-Building Assistant to automatically synthesize a minimum order model of the machine tool drive system for a given frequency range of interest (FROI) [14]. The complexity of the model, which includes a flywheel, a torsional shaft, a ballscrew, a ballnut, a DC motor, a torsional coupling, a belt-drive and a gear-pair as components, is automatically increased until the eigenvalues of the system fall beyond the specified FROI. This work was a proof of concept for a model deduction algorithm and can not be applied to any real machine tool system. However, such algorithm can be used to determine the appropriate model complexity after the development of the system model.

Gautier et al. have developed a software package called SICOMAT (SImulation and COntrol analysis of MAchine Tools) which helps with the modeling, simulation, modal analysis and controller tuning of one or two decoupled or two coupled machine tool axes [15]. Their models describe the dynamics of the mechanical system by a number of masses and springs. This work makes the modeling of a machine tool process more systematic, and is therefore a valuable tool to the modeling engineer; however, it lacks the generality, modularity and flexibility that the RMT design methodology demands.

THE RMT MODELING METHODOLOGY Figure 1 shows the envisioned RMT modeling

environment. It is desired to automate the task of RMT modeling, where the model of a given RMT configuration is automatically assembled from a library of modular component models. This way, all the candidate designs, which are generated either manually or automatically [4], can be modeled quickly and the models can be used to evaluate the candidates in terms of their servo axis dynamic performance and help with their design.

As Figure 1 also implies, the modular component model library is a key part for the automated RMT modeling environment. Therefore, the first step of the proposed methodology is to develop modular models for the components that are used to generate the RMT configurations. This paper puts the emphasis on mechanical parts and discusses their modeling in a modular way, because the energy interaction between the mechanical components makes their modular

2 Copyright © 2004 by ASME

modeling more intriguing. Modular modeling of components that only exchange signals, e.g. interpolators and controllers, presents a relatively simpler problem and are not discussed here.

To promote modularity and to be able to deal with the energy interactions between the components and their environment rather easily, bond graphs are utilized as the modeling language. Bond graphs provide a power-based graphical representation of a physical system. Moreover, bond graphs describe different energy domains in a unified way, which is a relevant advantage for RMT modeling, since their servo axes may include components from different energy domains, such as mechanical, electrical or hydraulic.

Bond graphs are only one level in the hierarchy of model representations used in this work. Underneath the bond graph level the mathematical equations represent the physical phenomena captured by the bond graph and this mathematical representation is the lowest level in the hierarchy. In the highest level bond graphs are encapsulated in a schematic representation, which not only allows for a compact representation, but also shows the connection ports where the model can interact with its environment. Figure 2 illustrates this hierarchy of model representations.

In this paper all the models are shown in the schematic level, because the goal of this paper is not to discuss their

derivation, but rather to show what can be done once those models are obtained. A detailed description of the models used in this paper can be found in [16].

Figure 1: The envisioned RMT modeling environment

In order to be able to cope with any spatial motion that the mechanical components may go through in different configurations, models that capture the three-dimensional dynamics are used. Moreover, the initial assumption is made that in the mechanical domain all components can be adequately represented as rigid bodies.

Figure 3 shows the schematic representation of a generic rigid body with N connection ports, which is one of the main model modules in the library. The ports correspond to points of interest on the rigid body, , 1iP i = …N , where the physical interactions with the environment occur. Bonds (lines with half arrows) are used to indicate that a port is a power port, i.e. the body can exchange energy with its environment through those ports, whereas active bonds (lines with full arrows) indicate signal ports, i.e. only information is transferred through these ports.

The model library also contains three-dimensional joint models that can be used to describe the relative motions between the component models. These joint models are also developed in a modular way with ports, where they can be connected to other model modules. The library offers two ways to express the constraints: (1) stiff springs and dampers can be used to implement more realistic constraints or to approximate ideal constraints, or (2) Lagrange multipliers can be introduced to express the constraints ideally. For a discussion of joint models the reader is also referred to [16].

Once the model library is populated with some basic modular rigid body and joint models, the modeling procedure can be carried out as follows: The RMT components are broken down into subcomponents and each subcomponent is associated with a model in the library. If none of the model modules in the library can describe the subcomponent adequately, a new model has to be developed for that subcomponent and added to the library. Then, the models are assembled by following the topology of the components and using the necessary joint models. Once a component model is obtained, it can be stored in the library for reuse. Finally, the component models are assembled by following the topology of a given configuration to obtain the model of that configuration. The process is illustrated in Figure 4 as a flowchart and demonstrated in the following section through examples.

1Sf

C k

1

R b

01

Im

Schematic

representation

Bond graph

representation

Mathematical

representation

Figure 2: The hierarchy of model representations

RigidBody-N

A I B,rPB1

rPB2

ωBB

rBB

rPBN

Figure 3: The schematic representation of a rigid body with N connection points

3 Copyright © 2004 by ASME

Figure 5: A fictitious slide

Provide RMT

configuration

Break the

components down

into subcomponents

Associate

subcomponents with

model modules

Assemble the

component models and

add to the database

Component

models exist in the

library?

Assemble the

configuration

model

No

Yes

Subcomponent

models exist in the

library?

Develop subcomponent

models and add to the

database

Yes

No

Figure 4: The RMT modeling procedure

Motor

rPBB2

2

A I B, 2

ωBB

2

2

A I B,

V

ωBB

rBB

rPB1

Figure 6: The schematic motor model

EXAMPLES The following two examples give an overview of the

proposed modeling methodology. The first example shows the modeling of a slide and the second example employs that slide model to develop a model for a RMT.

The purpose of these examples is to give a general idea about how the modularity of the components can be exploited in the modeling procedure, rather than to explain the details of how each (sub)component can be identified and modeled. Therefore, the details of the model modules, such as their level of complexity, are not discussed.

Modeling a Slide A slide is a basic component of most machine tools,

including RMTs. Different RMT configurations can be obtained by adding/removing slides to/from the configuration or by rearranging the existing slides in the configuration. Therefore, it is useful to demonstrate the modeling procedure of a slide.

Consider the slide shown in Figure 5. It is assumed that the components are identified as shown in the figure. For the purposes of this example, all the subcomponents except the motor can be modeled as rigid bodies with various number of connection points. The motor dynamics can be broken down into two domains: the three-dimensional rigid body dynamics of the housing and the electromechanical dynamics that drive the relative rotational motion between the rotor and the stator. A model has been developed for the motor that captures the dynamics in both domains and its schematic representation is given in Figure 6.

Now that all the subcomponent models are included in the library, the slide model can be assembled as shown in Figure 7. Note that some model modules are reused, e.g. both the Ballscrew and the Adapter are represented by Rigid Body-2. Since the slide model will typically be used in a complete machine tool model, its model as shown in Figure 7 can be encapsulated in an even higher level representation and included in the library. Figure 8 shows the schematic representation of the slide model, which encapsulates the model in Figure 7.

For validation purposes, this slide model was compared with a hand driven simple model of the same slide. A simulation was run, where a step voltage input was applied to the motor and the resulting saddle speed was recorded. Figure 9 compares the results of both simple and modular models. Practically, the modular model gives the same response as the simple model. Figure 10 shows the time history of the difference between the two models. This difference occurs because in the modular model the constraints are satisfied only within a numerical tolerance, whereas in the simple model the ideal constraints are eliminated from the equations of motion.

Modeling the Arch-type RMT The Arch-type RMT, which was developed by the NSF

Engineering Research Center for Reconfigurable Manufacturing Systems at the University of Michigan, is the world’s first full scale RMT. It is a three-axis machine tool that is designed around a part family with five different surface inclinations ranging from -15° to 45° at 15° increments and has the flexibility of doing machining operations such as milling

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and drilling at any of those angles. The reconfigurability of the Arch-type RMT comes from the spindle unit, which can be configured at the five angles mentioned above by moving it along the curved guideway of the arch module and fixing it at

any of the five locations on the arch module that are defined by mechanical stops. Figure 11 shows a CAD model of the Arch-type RMT along with its main components.

Rig

idB

ody-3

AI

B,r PB 1 r PB 2 r PB 3

ωBB r BB

Rig

idB

ody-2

AI

B,

r PB 1 r PB 2

ωBB r BB

Moto

r

r PB B 2

2

AI

B,2

ωBB 22

AI

B,

V

ωBB r BBr PB 1

Fix

edJo

int

AI

B,1

r PB B 11r PB B 2

2

AI

B,2

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Scr

ewJo

int

AI

B,1

r PB B 2

2

AI

B,2

ωBB 11

ωBB 22

r BB 11

Fix

edJo

int

AI

B,1

r PB B 11r PB B 2

2

AI

B,2

ωBB 11

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ody-3

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ota

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B,2

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r PB 1 r PB 2

ωBB r BB

1

Ba

llsc

rew

Ad

ap

ter

Ra

ilS

ad

dle

Figure 7: The assembled slide model

Slide

A I B,

rPB1

rPB2

ωBB

V

Figure 8: The schematic slide model

0 1 2 3 4 5time �s�

0

0.005

0.01

0.015

0.02

0.025

sadd

lesp

eed�m�s�

modularsimple

Figure 9: Comparison of saddle speeds to a step

input

0 1 2 3 4 5time �s�

0

1�10�6

2�10�6

3�10�6

4�10�6

5�10�6

sadd

lesp

eed

diff

eren

ce�m�s�

Figure 10: The difference in saddle speeds of the

two models

For the purposes of this example the base module is assumed to be identical to the ground and it has no effect on the dynamics of the machine tool. The worktable, the column and the spindle are essentially slides and their models are based on the slide model given above. The arch is modeled as a rigid-body with a connection port for each mechanical stop. Finally, the model of the Arch-type RMT is assembled by following the topology of the actual machine as shown in Figure 12. Note that the figure shows the model for one of the configurations only. The models for the other configurations can be obtained by changing the connection port of the arch model.

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Now that the model is assembled, the equations of motion can be derived from the graphical model automatically, and simulations can be performed. Although the mathematical model is ready, we cannot provide any simulation results in this paper due to the current lack of good estimates of system parameters. Simulations can be carried out easily once the parameter values are available.

DISCUSSION In this paper, modular and hierarchical modeling concepts

are identified as the key characteristics of the RMT modeling methodology. The modular structure of RMTs makes this

modeling approach beneficial, because the models contain all the key characteristics of reconfigurability [17]:

Figure 11: The Arch-type RMT

1. Modularity: The (sub)components are modeled in a modular way

2. Integrability: The models can be integrated with other modules through their connection ports

3. Customization: The level of detail included in the model modules can be customized for individual components

4. Convertibility: Models can be easily converted from one configuration to another

5. Diagnosability: Model verification can be carried out easily on model modules

The approach presented in this paper allows for the separation of the modeling task into two steps: (1) Developing component models, and (2) assembling the configuration model. While the first step still requires a significant modeling expertise, the second step is much more systematic, and can even be automated, which is left as a future work. Also, the two steps have different focuses: The first step focuses on the dynamics within a component, whereas the second step focuses on the dynamics between the components.

Slide

A I B,

rPB1

rPB2

ωBB

V

RigidBody-6

A I B,rPB1

rPB2

rPB3

ωBB

rBBrP

B4

rPB5

rPB6

FixedJoint

A I B, 1

rPBB1

1 rPBB2

2

A I B, 2

ωBB

1

1 ωBB

2

2

FixedJoint

A I B, 1

rPBB1

1 rPBB2

2

A I B, 2

ωBB

1

1 ωBB

2

2

Slide

A I B,

rPB1

rPB2

ωBB

V

Slide

A I B,

rPB1

rPB2

ωBB

V

1

1

Worktable

Spindle

Column

Arch

Sf0 :

1

Sf0 :

1

Figure 12: The assembled model of the Arch-type RMT

Compared to the existing approaches of servo axis modeling, where every different RMT configuration would potentially be a new modeling problem, the approach presented in this paper allows for a faster development of configuration models. Configurations can be assembled quickly using the model modules in the library, provided that all the components utilized in a given configuration have a corresponding model module in the library. Therefore, having a comprehensive model library is essential for this methodology to be efficient.

A three-dimensional multibody approach to modeling the mechanical components of the machine tool promotes modularity in the mechanical domain. Thus, for example, the model of the machine tool slide can be used in any configuration without having a special slide model for circumstances where the base of the slide is constrained to move in more restricted ways. With a multibody approach, generic component models can be created without a-priori knowledge of the connectivity of the components.

A drawback of the three-dimensional multibody approach is, however, that the generic models might be more complex than a certain configuration actually demands. For example, in a given configuration a component can be limited to a planar motion only, in which case a three-dimensional model would be overcomplex. The model should be simplified; otherwise unnecessary complexity is retained in the model and reduces the computational efficiency of the model. The proposed modular modeling methodology would benefit from the integration with a model order reduction algorithm. This will be the focus of future work.

Currently the bodies are considered rigid, which is not always an adequate approximation. In order to be able to study the effects of the structural dynamics, flexible body models should also be developed and included in the library.

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Finally, it is worthwhile to note that commercially available software packages, such as ADAMS, DADS, EASY5, Dymola etc, could also be used for the purposes of RMT modeling. However, to take advantage of the unified power based approach that the bond graphs provide and to make a future model reduction easier to implement, bond graphs are chosen as the modeling language.

SUMMARY AND CONCLUSIONS A modular modeling approach is proposed as a RMT

modeling methodology. The components are modeled in a modular way, so that the modeling task of a given RMT configuration merely involves assembling the corresponding model modules together. Two examples are given to illustrate the methodology, and advantages and disadvantages of this approach are discussed.

The outcomes of this work indicate that a modular approach to the problem of modeling RMTs can make the modeling process systematic and thus potentially more useful to practicing engineers if implemented in an automated modeling and design environment. However, there are still challenges, as highlighted in the discussion, that need to be addressed before an automated modeling environment can be implemented in a practical way.

ACKNOWLEDGMENTS This work was supported by the Engineering Research

Center for Reconfigurable Manufacturing Systems of the National Science Foundation under Award Number EEC 9529125.

REFERENCES [1] Mehrabi, M. G. and Ulsoy, A. G., 1997, State-of-the-Art in Reconfigurable Machining Systems, ERC/RMS Technical Report, University of Michigan, Ann Arbor

[2] Koren, Y. and Kota, S., 1999, Reconfigurable Machine Tool, U.S. Patent 5,943,750

[3] Landers, R. G., Min, B.–K., Koren, Y., 2001, “Reconfigurable Machine Tools”, Annals of the CIRP, Vol. 50/1, pp. 269–274

[4] Moon, Y-M., 2000, Reconfigurable Machine Tool Design: Theory and Application, Ph.D. dissertation, Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI

[5] Yigit, A. S. and Ulsoy, A. G., 2002, “Dynamic Stiffness Evaluation for Reconfigurable Machine Tools Including Weakly Nonlinear Joint Characteristics”, Proc. IME, Part B: Journal of Engineering Manufacture, Vol. 216/B1, pp. 87-101

[6] Moon, S-K., 2002, Error Predication and Compensation of Reconfigurable Machine Tool Using Screw Kinematics, Ph.D. dissertation, Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI

[7] Karnopp, D. and Rosenberg, R. C., 1975, System Dynamics: A Unified Approach, John Wiley & Sons

[8] Koren, Y., 1984, Numerical control of machine tools, Khanna, Nai Sarak, Delhi

[9] Gross, H., 1983, Electrical feed-drives for machine tools, John Wiley & Sons.

[10] Chen, Y. and Tlusty, J., 1995, “Effect of low-friction guideways and lead-screw flexibility on dynamics of high-speed machines”, Annals of the CIRP, Vol. 44/1, pp. 353-356

[11] Pritschow, G., Bretschneider, J., Fahrbach, C., 1996, “Control of High Dynamic Servo Axes for Milling Machines”, Production Engineering, Vol. 3/1, pp. 63-68.

[12] Smith, D. A., 1999, Wide Bandwidth Control of High-Speed Milling Machine Feed Drives, Ph.D. dissertation, Department of Mechanical Engineering, The University of Florida, Gainesville, FL

[13] Poignet, Ph., Gautier, M., Khalil, W., 1999, “Modeling, control and simulation of high speed machine tool axes”, IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 617-622

[14] Wilson, B. H. and Stein, J. L., 1993, "Model Building Assistant: An Automated Modeling Tool for Machine Tool Drive Systems", Proceedings of the 1993 International Conference on Bond Graph Modeling, Vol. 25/2, pp. 169-178

[15] Gautier, M., Pham, M.T., Khalil, W., Lemoine, Ph., Poignet, Ph., 2001, “SICOMAT: A system for simulation and control analysis of machine tools”, IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Vol. 1, pp. 665-670

[16] Ersal, T., Stein, J. L., Louca, L. S., 2004, “A Bond Graph Based Modular Modeling Approach towards an Automated Modeling Environment for Reconfigurable Machine Tools”, Proceedings of the 1st International Conference on Integrated Modeling and Analysis in Applied Control and Automation (Part of the 1st International Mediterranean Modeling Multiconference), Genoa, Italy, October 28-31

[17] Koren, Y., Heisel, U., Jovane, F., Moriwaki, T., Pritschow, G., Ulsoy, A. G., Van Brussel, H., 1999, “Reconfigurable Manufacturing Systems”, Annals of the CIRP, Vol. 48/2, pp. 527-540

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