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.

References

References
1.
Altintas
,
Y.
,
Brecher
,
C.
,
Weck
,
M.
, and
Witt
,
S.
,
2005
, “
Virtual Machine Tool
,”
CIRP Ann. Manuf. Technol.
,
54
(
2
), pp.
115
138
.
2.
Koenigsberger
,
F.
, and
Tlusty
,
J.
,
1970
,
Machine Tool Structures
,
Pergamon Press
,
Oxford, UK
.
3.
Weck
,
M.
, and
Brecher
,
C.
,
2006
,
Werkzeugmaschinen—Konstruktion und Berechnung
,
Springer
,
Berlin
.
4.
Heylen
,
W.
,
Lammens
,
S.
, and
Sas
,
P.
,
1998
,
Modal Analysis Theory and Testing
,
Katholieke Universiteit Leuven
,
Leuven, Belgium
.
5.
Ewins
,
D.
,
2000
,
Modal Testing—Theory, Practice, and Application
,
Research Studies Press
,
Baldock/Hertfordshire, UK
.
6.
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
.
7.
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
.
8.
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
.
9.
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
.
10.
“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
11.
Geradin
,
M.
, and
Rixen
,
D.
,
2015
,
Mechanical Vibrations—Theory and Applications to Structural Dynamics
,
Wiley
,
Chichester/West Sussex, UK
.
12.
Liu
,
G.
, and
Quek
,
S.
,
2003
,
The Finite Element Method: A Practical Course
,
Butterworth Heinemann
,
Oxford, UK
.
13.
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
.
14.
Rixen
,
D.
,
1997
,
Substructuring and Dual Methods in Structural Analysis
,
Universite de Liege
,
Liege, Belgium
.
15.
Zienkiewicz
,
O.
,
Taylor
,
R.
, and
Zhu
,
J.
,
2013
,
The Finite Element Method: Its Basis and Fundamentals
,
7th ed.
,
Butterworth Heinemann
,
Amsterdam, The Netherlands
.
16.
Kattan
,
P.
,
2008
,
matlab Guide to Finite Elements—An Interactive Approach
,
Springer
,
Berlin
.
17.
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
.
18.
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
.
19.
“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
20.
Rixen
,
D.
,
2004
, “
A Dual Craig–Bampton Method for Dynamic Substructuring
,”
J. Comput. Appl. Math.
,
168
(
1
), pp.
383
391
.
21.
Voormeeren
,
S.
,
2012
,
Dynamic Substructuring Methodologies for Integrated Dynamic Analysis of Wind Turbines
,
Dissertation TU Delft, Uitgeverij BOXPress
,
Delft, The Netherlands
.
22.
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
.
23.
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
.
24.
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
.
25.
Brecher
,
C.
,
Altstädter
,
H.
, and
Daniels
,
M.
,
2015
, “
Axis Position Dependent Dynamics of Multi-Axis Milling Machines
,”
Procedia CIRP
,
31
(
1
), pp.
508
514
.
26.
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
.
You do not currently have access to this content.