Research Papers

Multipoint Constraints for Modeling of Machine Tool Dynamics

[+] Author and Article Information
Christian Brecher, Marcel Fey, Christian Tenbrock

Laboratory for Machine Tools and
Production Engineering,
RWTH Aachen University,
Aachen 52074, Germany

Matthias Daniels

Laboratory for Machine Tools and
Production Engineering,
RWTH Aachen University,
Aachen 52074, Germany
e-mail: m.daniels@wzl.rwth-aachen.de

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received June 15, 2015; final manuscript received September 23, 2015; published online November 18, 2015. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 138(5), 051006 (Nov 18, 2015) (8 pages) Paper No: MANU-15-1292; doi: 10.1115/1.4031771 History: Received June 15, 2015; Revised September 23, 2015

The dynamic properties of machine tools are frequently calculated by means of finite-element (FE) models. Usually, in a first step, the structural components, such as machine bed, slides, columns, spindle housing, spindle, and work piece, are meshed. In a second step, these components are positioned relatively to each other and are connected by joints. Usually, the joints comprise a three-dimensional spring–damper element (SDE) and constraints that connect the SDE to adjacent structural components. Commercial FE programs do rarely offer insight into the underlying constraint equations. Rather, the constraints are realized by selecting the faces or nodes to connect and the type of constraint over a graphical user interface. Moreover, when insight into the underlying equations is offered, it is normally difficult to implement user-defined constraint equations. So far, literature lacks a coherent and in-depth description of constraints that are used for assembly of machine tool FE components. This drawback is addressed here. Different common constraints are revisited while particular focus is put on simulating moving machine axes. Common multipoint constraints (MPC) are supplemented by a shape function based node weighting. Thus, two new MPC are introduced, which improve model quality for ball screw joints (named node-to-beam (NB)-constraint) and linear guides (named RBE4-constraint). A three-axis milling machine serves as an application example for the different constraints. Simulation results are compared to experimentally derived results. Both, frequency response functions (FRF) and time-domain forced responses are considered. Showing reasonable correlation, the comparison of simulation and experiment indicates the validity of the constraints that have been introduced.

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Altintas, Y. , Brecher, C. , Weck, M. , and Witt, S. , 2005, “ Virtual Machine Tool,” CIRP Ann. Manuf. Technol., 54(2), pp. 115–138. [CrossRef]
Koenigsberger, F. , and Tlusty, J. , 1970, Machine Tool Structures, Pergamon Press, Oxford, UK.
Weck, M. , and Brecher, C. , 2006, Werkzeugmaschinen—Konstruktion und Berechnung, Springer, Berlin.
Heylen, W. , Lammens, S. , and Sas, P. , 1998, Modal Analysis Theory and Testing, Katholieke Universiteit Leuven, Leuven, Belgium.
Ewins, D. , 2000, Modal Testing—Theory, Practice, and Application, Research Studies Press, Baldock/Hertfordshire, UK.
Brecher, C. , Bäumler, S. , and Daniels, M. , 2014, “ Prediction of Dynamics of Modified Machine Tool by Experimental Substructuring,” 32nd IMAC Dynamics of Coupled Structures, pp. 297–305.
Kolar, P. , and Holkup, T. , 2010, “ Prediction of Machine Tool Spindle’s Dynamics Based on a Thermo-Mechanical Model,” MM Sci. J., 1, pp. 166–171.
Mi, L. , Yin, G. , Sun, M. , and Wang, X. , 2012, “ Effects of Preloads on Joints on Dynamic Stiffness of a Whole Machine Tool Structure,” J. Mech. Sci. Technol., 26(2), pp. 495–508. [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]
“Siemens NX-Nastran—Element Library Reference 2014,” Siemens NX Nastran 10 Help Library, Accessed Oct. 18, 2015, https://docs.plm.automation.siemens.com/data_services/resources/nxnastran/10/help/en_US/tdocExt/pdf/element.pdf
Geradin, M. , and Rixen, D. , 2015, Mechanical Vibrations—Theory and Applications to Structural Dynamics, Wiley, Chichester/West Sussex, UK.
Liu, G. , and Quek, S. , 2003, The Finite Element Method: A Practical Course, Butterworth Heinemann, Oxford, UK.
de Klerk, D. , Rixen, D. , and Voormeeren, S. , 2008, “ General Framework for Dynamic Substructuring: History, Review and Classification of Techniques,” AIAA J., 46(5), pp. 1169–1181. [CrossRef]
Rixen, D. , 1997, Substructuring and Dual Methods in Structural Analysis, Universite de Liege, Liege, Belgium.
Zienkiewicz, O. , Taylor, R. , and Zhu, J. , 2013, The Finite Element Method: Its Basis and Fundamentals, 7th ed., Butterworth Heinemann, Amsterdam, The Netherlands.
Kattan, P. , 2008, matlab Guide to Finite Elements—An Interactive Approach, Springer, Berlin.
Kuratani, F. , Matsubara, K. , and Yamauchi, T. , 2011, “ Finite Element Model for Spot Welds Using Multi-Point Constraints and Its Dynamic Characteristics,” SAE Int. J. Passeng. Cars Mech. Syst., 4(2), pp. 1311–1319. [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(2), pp. 219–234. [CrossRef]
“User Reference Manual for the MYSTRAN General Purpose Finite Element Structural Analysis Computer Program 2011,” MYSTRAN Software User Manual, Accessed Oct. 18, 2015, http://www.mystran.com/Executable/MYSTRAN-Users-Manual.pdf
Rixen, D. , 2004, “ A Dual Craig–Bampton Method for Dynamic Substructuring,” J. Comput. Appl. Math., 168(1), pp. 383–391. [CrossRef]
Voormeeren, S. , 2012, Dynamic Substructuring Methodologies for Integrated Dynamic Analysis of Wind Turbines, Dissertation TU Delft, Uitgeverij BOXPress, Delft, The Netherlands.
Dhupia, J. , Powalka, B. , Galip Ulsoy, A. , and Katz, R. , 2007, “ Effect of a Nonlinear Joint on the Dynamic Performance of a Machine Tool,” ASME J. Manuf. Sci. Eng., 129(5), pp. 943–950. [CrossRef]
Law, M. , Srikantha Pani, A. , 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]
Law, M. , and Ihlenfeldt, S. , 2014, “ A Frequency-Based Substructuring Approach to Efficiently Model Position-Dependent Dynamics in Machine Tools,” J. Multibody Dyn., 229(3), pp. 304–317.
Brecher, C. , Altstädter, H. , and Daniels, M. , 2015, “ Axis Position Dependent Dynamics of Multi-Axis Milling Machines,” Procedia CIRP, 31(1), pp. 508–514. [CrossRef]
Brecher, C. , Fey, M. , and Daniels, M. , 2014, “ Efficient Time-Domain Simulation of the Forced Response of a Moving Axis,” International Conference on Noise and Vibration Engineering ISMA, pp. 2867–2876.


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Fig. 4

(a) Exemplary condensation node-to-face constraint and (b) nomenclature for deflections at condensation and coupling nodes

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Fig. 6

(a) Linear guide model and (b) picture of linear guide

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Fig. 3

(a) Conforming and nonconforming meshes, (b) exemplary planar element and exemplary shape function, and (c) picture of surface-to-surface contact

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Fig. 2

(a) Picture of a machine tool foundation and (b) model for the machine tool foundation

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Fig. 1

(a) Typical joint elements and (b) the conventional joint model

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Fig. 5

(a) Screw joint model, (b) picture of ball screw joint, and (c) linear shape functions for beam element

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Fig. 7

(a) Test assembly for RBE3/RBE4 comparison and (b) position-dependent eigenfrequencies

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Fig. 8

FE model of three axes milling machine and adopted constraint types

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Fig. 10

Simulated FRF Gxx for many different y-positions

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Fig. 9

Measured (a) and simulated (b) FRF Gxx for seven different y-positions

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Fig. 11

Forced response to harmonic excitation—measurement and simulation




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