Research Papers

Substructure Coupling of a Machine Tool in Arbitrary Axis Positions Considering Local Linear Damping Models

[+] Author and Article Information
Thomas Semm

Institute for Machine Tools and Industrial Management,
Department of Mechanical Engineering,
Technical University of Munich (TUM),
Boltzmannstr. 15,
85748 Garching, Germany
e-mail: Thomas.Semm@iwb.mw.tum.de

Michael B. Nierlich

Institute for Machine Tools and Industrial Management,
Department of Mechanical Engineering,
Technical University of Munich (TUM),
Boltzmannstr. 15,
85748 Garching, Germany
e-mail: m.nierlich@gmx.net

Michael F. Zaeh

Institute for Machine Tools and Industrial Management,
Department of Mechanical Engineering,
Technical University of Munich (TUM),
Boltzmannstr. 15,
85748 Garching, Germany
e-mail: Michael.Zaeh@iwb.mw.tum.de

1Corresponding author.

Manuscript received February 3, 2019; final manuscript received May 9, 2019; published online May 30, 2019. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 141(7), 071014 (May 30, 2019) (8 pages) Paper No: MANU-19-1075; doi: 10.1115/1.4043767 History: Received February 03, 2019; Accepted May 10, 2019

Virtual prototypes, e.g., finite element models, are commonly used to reduce the development times of a new machine tool generation. However, the accuracy of these models is often limited by their representation of damping effects and the possibility to efficiently simulate the dynamic behavior in different axis positions. This paper shows the changing local damping distribution within a single-axis machine tool configuration for different axis positions. Based on this investigation, an approach to accurately model the position-dependent dynamics, while keeping the calculation times small, is presented. The virtual model of the machine is divided in several substructures, which consider the local damping behavior of each dissipation source. The reduced mass, stiffness, and damping matrices are coupled in the desired machine position by using multipoint constraints, which are generated at the desired machine position after the reduction of the substructures. Four different approaches to apply multipoint constraints on reduced substructures are compared, followed by an investigation of their influencing parameters. The most promising approach is compared with a model without local damping representation as well as a model without substructuring. By considering the local damping effects within the finite element model and coupling the reduced models of each component in arbitrary axis positions, an efficient analysis and optimization of the dynamic behavior of a machine tool over the whole workspace can be conducted.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Altintas, Y., Brecher, C., Weck, M., and Witt, S., 2005, “Virtual Machine Tool,” CIRP Ann. Manuf. Technol., 54(2), pp. 115–138. [CrossRef]
Rebelein, C., Vlacil, J., and Zaeh, M. F., 2016, “Modeling of the Dynamic Behavior of Machine Tools,” Prod. Eng. Res. Dev., 11(2), pp. 61–74.
Semm, T., Spannagl, M. F., and Zaeh, M. F., 2018, “Dynamic Substructuring of Machine Tools Considering Local Damping Models,” Procedia CIRP, 77, pp. 670–674. [CrossRef]
Brecher, C., Fey, M., and Bäumler, S., 2013, “Damping Models for Machine Tool Components of Linear Axes,” CIRP Ann. Manuf. Technol., 62(1), pp. 399–402. [CrossRef]
Zaeh, M. F., Rebelein, C., and Semm, T., 2019, “Predictive Simulation of Damping Effects in Machine Tools,” CIRP Ann. Manuf. Technol., 68(1).
Klerk, D. D., Rixen, D. J., and Voormeeren, S. N., 2008, “General Framework for Dynamic Substructuring,” AIAA J., 46(5), pp. 1169–1181. [CrossRef]
van Brussel, H., Sas, P., Nemeth, I., de Fonseca, P., and den Braembussche, P., 2001, “Towards a Mechatronic Compiler,” IEEE-ASME Trans. Mech., 6(1), pp. 90–105. [CrossRef]
Garitaonandia, I., Fernandes, M. H., Hernandez-Vazquez, J. M., and Ealo, J. A., 2016, “Prediction of Dynamic Behavior for Different Configurations in a Drilling–Milling Machine Based on Substructuring Analysis,” J. Sound Vib., 365, pp. 70–88. [CrossRef]
Lanz, N., Spescha, D., Weikert, S., and Wegener, K., 2018, “Efficient Static and Dynamic Modelling of Machine Structures With Large Linear Motions,” Int. J. Autom. Technol., 12(5), pp. 622–630. [CrossRef]
Tuysuz, O., and Altintas, Y., 2017, “Time-Domain Modeling of Varying Dynamic Characteristics in Thin-wall Machining Using Perturbation and Reduced-order Substructuring Methods,” ASME J. Manuf. Sci. Eng., 140(1), p. 011015. [CrossRef]
Zaeh, M., 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. Manuf. Technol., 56(1), pp. 383–386. [CrossRef]
Hoffmann, F., and Brecher, C., 2005, “Simulation of Motion Profiles – Moveable Flexible Multi-body Models of Machine Tools,” wt Werkstattstechnik online, 95(7/8), pp. 506–512.
Law, M., Phani, A. S., and Altintas, Y., 2013, “Position-Dependent Multibody Dynamic Modeling of Machine Tools Based on Improved Reduced Order Models,” ASME J. Manuf. Sci. Eng., 135(2), p. 021008. [CrossRef]
Brecher, C., Altstädter, H., and Daniels, M., 2015, “Axis Position Dependent Dynamics of Multi-axis Milling Machines,” Procedia CIRP, 31, pp. 508–514. [CrossRef]
Niehues, K., Schwarz, S., and Zaeh, M. F., 2012, “Reliable Material Damping Ratio Determination in Machine Tool Structures,” Prod. Eng. Res. Dev., 6(4-5), pp. 475–484. [CrossRef]
Rebelein, C., and Zaeh, M. F., 2016, “Friction in Feed Drives of Machine Tools Investigation, Modeling and Validation,” Prod. Eng. Res. Dev., 10(4), pp. 497–507. [CrossRef]
Maia, N. M. M., and Silva, J. M. M., 1997, Theoretical and Experimental Modal Analysis, Vol. 9 of Mechanical Engineering Research Studies Engineering Dynamics Series, Research Studies Press, Taunton, Somerset, England.
MSC Software Corporation, 2012, MSC Nastran 2012 Linear Static Analysis User’s Guide, MSC Software Corporation, Santa Ana.
Heirman, G. H., and Desmet, W., 2010, “Interface Reduction of Flexible Bodies for Efficient Modeling of Body Flex in Multibody Dynamics,” Multibody Syst. Dyn., 24(2), pp. 219–234. [CrossRef]
Craig, R. R., and Bampton, M. C. C., 1968, “Coupling of Substructures for Dynamic Analyses,” AIAA J., 6(7), pp. 1313–1319. [CrossRef]
MSC Software Corporation, 2012, MSC Nastran 2012 Superelements User’s Guide, MSC Software Corporation, Santa Ana.
Fransen, S. H. J. A., 2012, “Methodologies for Launcher–payload Coupled Dynamic Analysis,” CEAS Space J., 3(1–2), pp. 13–25. [CrossRef]
Araujo, X. V., Fransen, S. H., Germés, S., and Thiry, N., 2013, “Validation of Equivalent Viscous Damping Methodologies,” CEAS Space J., 4(1-4), pp. 31–39. [CrossRef]
Dieker, S., Abdoly, K., and Rittweger, A., 2010, “Flexible Boundary Method in Dynamic Substructure Techniques Including Different Component Damping,” AIAA J., 48(11), pp. 2631–2638. [CrossRef]
Girard, A., and Roy, N., 2010, Structural Dynamics in Industry, 1st ed., ISTE. John Wiley & Sons, New York.
Hasselman, T. K., 1976, “Modal Coupling in Lightly Damped Structures,” AIAA J., 14(11), pp. 1627–1628. [CrossRef]
Brecher, C., Fey, M., Tenbrock, C., and Daniels, M., 2016, “Multipoint Constraints for Modeling of Machine Tool Dynamics,” ASME J. Manuf. Sci. Eng., 138(5), p. 051006. [CrossRef]
Quek, S. S., and Liu, G. R., 2003, Finite Element Method: A Practical Course, 1st ed., Elsevier Science, Jordan Hill.
Gasch, R., Knothe, K., and Liebich, R., 2012, Strukturdynamik: Diskrete Systeme und Kontinua, 2nd ed., Springer, New York.
Simeon, B., 2006, “On Lagrange Multipliers in Flexible Multibody Dynamics,” Comput. Method Appl. Mech. Eng., 195(50-51), pp. 6993–7005. [CrossRef]
Cook, R. D., Malkus, D. S., and Plesha, M. E., 1989, Concepts and Applications of Finite Elemente Analysis, 3rd ed, John Wiley & Sons, New York.
Imamovic, N., 1998, Validation of Large Structural Dynamics Models Using Modal Test Data, Imperial College, University of London, London.
Heylen, W., Lammens, S., and Sas, P., 1997, Modal Analysis Theory and Testing, Katholieke Universiteit Leuven, Leuven.


Grahic Jump Location
Fig. 1

Test object: basic mechanical structure of a single-axis machine tool configuration

Grahic Jump Location
Fig. 2

Linear damping distribution for two positions of the workpiece table: position z0 (left bar) and position z1 (right bar)

Grahic Jump Location
Fig. 3

Model of a coupling point including the considered DOF (a) with RBE and (b) without RBE to allow a position independent coupling

Grahic Jump Location
Fig. 4

Example of a depended MPC

Grahic Jump Location
Fig. 5

Connection of two components with springs

Grahic Jump Location
Fig. 6

(a) Fine-discretized model (BSD5:PRS0) with 4364 DOF compared with (b) the rough-discretized model (BSD40:PRS2) with 1238 DOF

Grahic Jump Location
Fig. 7

Parameter variation of the penalty parameter α

Grahic Jump Location
Fig. 8

Comparison of the NFD value for the rigid- and parameter-based methods in the rear position z1

Grahic Jump Location
Fig. 9

FRF of the substructured system at the workpiece table DP1 for positions z0 and z5 compared with the reference system

Grahic Jump Location
Fig. 10

FRF of the substructured system at the workpiece table DP1 for position z0 and different damping models: local damping models, constant damping, and modal damping evaluated in position z5

Grahic Jump Location
Fig. 11

FRF of the linear-substructured model at the workpiece table DP1 for positions z0 and z5 compared with the measurements of the real system



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In