Research Papers

Position-Dependent Multibody Dynamic Modeling of Machine Tools Based on Improved Reduced Order Models

[+] Author and Article Information
Mohit Law

Ph.D. Candidate

A. Srikantha Phani

Assistant Professor

Yusuf Altintas

Fellow ASME
e-mail: altintas@mech.ubc.ca
Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC, V6T 1Z4, Canada

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received January 31, 2012; final manuscript received October 19, 2012; published online March 22, 2013. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 135(2), 021008 (Mar 22, 2013) (11 pages) Paper No: MANU-12-1033; doi: 10.1115/1.4023453 History: Received January 31, 2012; Revised October 19, 2012

Dynamic response of a machine tool structure varies along the tool path depending on the changes in its structural configurations. The productivity of the machine tool varies as a function of its frequency response function (FRF) which determines its chatter stability and productivity. This paper presents a computationally efficient reduced order model to obtain the FRF at the tool center point of a machine tool at any desired position within its work volume. The machine tool is represented by its position invariant substructures. These substructures are assembled at the contacting interfaces by using novel adaptations of constraint formulations. As the tool moves to a new position, these constraint equations are updated to predict the FRFs efficiently without having to use computationally costly full order finite element or modal models. To facilitate dynamic substructuring, an improved variant of standard component mode synthesis method is developed which automates reduced order determination by retaining only the important modes of the subsystems. Position-dependent dynamic behavior and chatter stability charts are successfully simulated for a virtual three axis milling machine, using the substructurally synthesized reduced order model. Stability lobes obtained using the reduced order model agree well with the corresponding full-order system.

Copyright © 2013 by ASME
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Altintas, Y., 2000, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge University Press, New York.
Sadek, M. M., and Tobias, S. A., 1970, “Comparative Dynamic Acceptance Tests for Machine Tools Applied to Horizontal Milling Machines,” Proc. Inst. Mech. Eng., 185, pp. 319–337. [CrossRef]
Bianchi, G., Paolucci, F., Van den Braembussche, P., Van Brussel, H., and Jovane, F., 1996, “Towards Virtual Engineering in Machine Tool Design,” CIRP Ann., 45, pp. 381–384. [CrossRef]
Zaeh, M. F., and Siedl, D., 2007, “A New Method for Simulation of Machining Performance by Integrating Finite Element and Multi-Body Simulation for Machine Tools,” CIRP Ann., 56, pp. 383–386. [CrossRef]
Aurich, J. C., Biermann, D., Blum, H., Brecher, C., Carstensen, C., Denkena, B., Klocke, F., Kroger, M., Steinmann, P., and Weinert, K., 2009, “Modelling and Simulation of Process: Machine Interaction in Grinding,” Prod. Eng. Res. Dev., 3, pp. 111–120. [CrossRef]
Okwudire, C., 2009, “Modeling and Control of High Speed Machine Tool Feed Drives,” Ph.D. thesis, University of British Columbia, Vancouver, BC, Canada.
da Silva, M. M., Bruls, O., Swevers, J., Desmet, W., and Van Brussel, H., 2009, “Computer-Aided Integrated Design for Machines With Varying Dynamics,” Mech. Mach. Theory, 44, pp. 1733–1745. [CrossRef]
Fonseca, P. D., 2000, “Simulation and Optimization of the Dynamic Behavior of Mechatronics Systems,” Ph.D. thesis, Katholieke Universiteit Leuven, Leuven, Belgium
Givoli, D., Barbone, P. E., and Patlashenko, I., 2004, “Which are the Important Modes of a Subsystem?,” Int. J. Numer. Methods Eng., 59, pp. 1657–1678. [CrossRef]
Litz, L., 1981, “Order Reduction of Linear State-Space Models via Optimal Approximation of the Non-Dominant Modes,” Large Scale Syst., 2, pp. 171–184.
Feliachi, A., 1990, “Identification of Critical Modes in Power Systems,” IEEE Trans. Power Syst., 5, pp. 783–787. [CrossRef]
Shabana, A., and Wehage, R. A., 1983, “Variable Degree-of-Freedom Component Mode Analysis of Inertia Flexible Mechanical Systems,” ASME J. Mech. Des., 105(3), pp. 371–378. [CrossRef]
Tayeb, S., and Givoli, D., 2011, “Optimal Modal Reduction of Dynamic Subsystems: Extensions and Improvements,” Int. J. Numer. Methods Eng., 85, pp. 1–30. [CrossRef]
Park, K. C., and Park, Y. H., 2004, “Partitioned Component Mode Synthesis via a Flexibility Approach,” AIAA J., 42, pp. 1236–1245. [CrossRef]
Jakobsson, H., Bengzon, F., and Larson, M., 2011, “Adaptive Component Mode Synthesis in Linear Elasticity,” Int. J. Numer. Methods Eng., 86, pp. 829–844. [CrossRef]
Farhat, C. G., and Geradin, M., 1994, “On a Component Mode Synthesis Method and Its Application to Incompatible Substructures,” Comput. Struct., 51, pp. 459–473. [CrossRef]
Heirman, G., and Desmet, W., 2010, “Interface Reduction of Flexible Bodies for Efficient Modeling of Body Flexibility in Multibody Dynamics,” Multibody Syst. Dyn., 24, pp. 219–234. [CrossRef]
Liu, G. R., and Quek, S. S., 2003, The Finite Element Method: A Practical Course, Butterworth-Heinemann, Burlington, MA.
Craig, R. R., Jr., and Bampton, M. C. C., 1968, “Coupling of Substructures for Dynamics Analyses,” AIAA J., 6, pp. 1313–1319. [CrossRef]
Guyan, R. J., 1965, “Reduction of Stiffness and Mass Matrices,” AIAA J., 3, p. 380. [CrossRef]
O'Callahan, J. C., 1989, “A Procedure for an Improved Reduced System (IRS) Model,” Proceedings of 7th IMAC, pp. 17–21.
Friswell, M. I., Garvey, S. D., and Penny, J. E. T., 1995, “Model Reduction Using Dynamic and Iterated IRS Techniques,” J. Sound Vib., 186, pp. 311–323. [CrossRef]
Koutsovasilis, P., and Beitelschmidt, M., 2010, “Model Order Reduction of Finite Element Models: Improved Component Mode Synthesis,” Math. Comput. Model. Dyn. Syst., 16, pp. 57–73. [CrossRef]
Ewins, D. J., 2000, Modal Testing: Theory, Practice, and Application, Research Studies Press, Baldok, Hertfordshire, UK.
Chen, G., 2001, “FE Model Validation for Structural Dynamics,” Ph.D. thesis, Imperial College of Science, Technology & Medicine, University of London, London.
Cao, Y., and Altintas, Y., 2004, “A General Method for the Modeling of Spindle-Bearing Systems,” ASME J. Mech. Des., 126(6), pp. 1089–1104. [CrossRef]
ANSYS V12, 2009, Documentation for ANSYS.
Altintas, Y., and Budak, E., 1995, “Analytical Prediction of Stability Lobes in Milling,” CIRP Ann., 44, pp. 357–362. [CrossRef]
Zulaika, J. J., Campa, F. J., and Lopez de Lacalle, L. N., 2011, “An Integrated Process–Machine Approach for Designing Productive and Lightweight Milling Machines,” Int. J. Mach. Tools Manuf., 51, pp. 591–604. [CrossRef]


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Fig. 1

Overview of the proposed modeling scheme

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Fig. 2

Substructural assembly by enforcing continuity constraints, (a) compatible substructures, (b) incompatible substructures

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Fig. 3

Flow chart for determining mode cut-off number

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Fig. 4

NRFD and MAC comparison for standard component mode synthesis scheme (left) and iterated improved component mode synthesis scheme (right)

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Fig. 5

Substructural assembly of the spindle-spindle housing substructure with the column substructure through constraint formulations

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Fig. 6

Comparison of TCP FRFs for solution: with different constraint formulations (top), and with different numerical methods (bottom)

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Fig. 7

Comparison of full order model and reduced order model TCP FRFs at three different positions: top position (top), mid position (middle), and bottom position (bottom)

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Fig. 8

Stability boundaries at two distinct positions (left) and the corresponding chatter frequencies (right) for machining AISI 1045 common steel

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Fig. 9

Stability boundaries at two distinct positions (left) and the corresponding chatter frequencies (right) for machining Al 7075-T6




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