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.

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.
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
.
3.
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
.
4.
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
.
5.
Zaeh
,
M. F.
,
Rebelein
,
C.
, and
Semm
,
T.
,
2019
, “
Predictive Simulation of Damping Effects in Machine Tools
,”
CIRP Ann. Manuf. Technol.
,
68
(
1
).
6.
Klerk
,
D. D.
,
Rixen
,
D. J.
, and
Voormeeren
,
S. N.
,
2008
, “
General Framework for Dynamic Substructuring
,”
AIAA J.
,
46
(
5
), pp.
1169
1181
.
7.
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
.
8.
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
.
9.
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
.
10.
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
.
11.
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
.
12.
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
.
13.
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
.
14.
Brecher
,
C.
,
Altstädter
,
H.
, and
Daniels
,
M.
,
2015
, “
Axis Position Dependent Dynamics of Multi-axis Milling Machines
,”
Procedia CIRP
,
31
, pp.
508
514
.
15.
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
.
16.
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
.
17.
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
.
18.
MSC Software Corporation
,
2012
,
MSC Nastran 2012 Linear Static Analysis User’s Guide
,
MSC Software Corporation
,
Santa Ana
.
19.
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
.
20.
Craig
,
R. R.
, and
Bampton
,
M. C. C.
,
1968
, “
Coupling of Substructures for Dynamic Analyses
,”
AIAA J.
,
6
(
7
), pp.
1313
1319
.
21.
MSC Software Corporation
,
2012
,
MSC Nastran 2012 Superelements User’s Guide
,
MSC Software Corporation
,
Santa Ana
.
22.
Fransen
,
S. H. J. A.
,
2012
, “
Methodologies for Launcher–payload Coupled Dynamic Analysis
,”
CEAS Space J.
,
3
(
1–2
), pp.
13
25
.
23.
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
.
24.
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
.
25.
Girard
,
A.
, and
Roy
,
N.
,
2010
,
Structural Dynamics in Industry
,
1st ed.
,
ISTE. John Wiley & Sons
,
New York
.
26.
Hasselman
,
T. K.
,
1976
, “
Modal Coupling in Lightly Damped Structures
,”
AIAA J.
,
14
(
11
), pp.
1627
1628
.
27.
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
.
28.
Quek
,
S. S.
, and
Liu
,
G. R.
,
2003
,
Finite Element Method: A Practical Course
,
1st ed.
,
Elsevier Science
,
Jordan Hill
.
29.
Gasch
,
R.
,
Knothe
,
K.
, and
Liebich
,
R.
,
2012
,
Strukturdynamik: Diskrete Systeme und Kontinua
,
2nd ed.
,
Springer
,
New York
.
30.
Simeon
,
B.
,
2006
, “
On Lagrange Multipliers in Flexible Multibody Dynamics
,”
Comput. Method Appl. Mech. Eng.
,
195
(
50-51
), pp.
6993
7005
.
31.
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
.
32.
Imamovic
,
N.
,
1998
,
Validation of Large Structural Dynamics Models Using Modal Test Data
,
Imperial College, University of London
,
London
.
33.
Heylen
,
W.
,
Lammens
,
S.
, and
Sas
,
P.
,
1997
,
Modal Analysis Theory and Testing
,
Katholieke Universiteit Leuven
,
Leuven
.
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