Abstract

Co-simulation techniques enable the coupling of physically diverse subsystems in an efficient and modular way. Communication between subsystems takes place at discrete-time instants and is limited to a given set of coupling variables, while the internals of each subsystem remain undisclosed and are generally not accessible to the rest of the simulation environment. In noniterative co-simulation schemes, commonly used in real-time applications, this may lead to the instability of the numerical integration. The stability of the integration in these cases can be enhanced using interface models, i.e., reduced representations of one or more subsystems that provide physically meaningful input values to the other subsystems between communication points. This work describes such an interface model that can be used to represent nonsmooth mechanical systems subjected to unilateral contact and friction. The dynamics of the system is initially formulated as a mixed linear complementarity problem (MLCP), from which the effective mass and force terms of the interface model are derived. These terms account for contact detachment and stick–slip transitions, and can also include constraint regularization in case of redundancy in the system. The performance of the proposed model is shown in several challenging examples of noniterative multirate co-simulation schemes of a mechanical system with hydraulic components, which feature faster dynamics than the multibody subsystem. Using an interface model improves simulation stability and allows for larger integration step-sizes, thus resulting in a more efficient simulation.

References

References
1.
O. A.
Bauchau
,
2011
,
Flexible Multibody Dynamics
,
Springer
,
Dordrecht, The Netherlands
.
2.
Dopico
,
D.
,
Luaces
,
A.
,
González
,
M.
, and
Cuadrado
,
J.
,
2011
, “
Dealing With Multiple Contacts in a Human-in-the-Loop Application
,”
Multibody Syst. Dyn.
,
25
(
2
), pp.
167
183
.10.1007/s11044-010-9230-y
3.
Samin
,
J. C.
,
Brüls
,
O.
,
Collard
,
J. F.
,
Sass
,
L.
, and
Fisette
,
P.
,
2007
, “
Multiphysics Modeling and Optimization of Mechatronic Multibody Systems
,”
Multibody Syst. Dyn.
,
18
(
3
), pp.
345
373
.10.1007/s11044-007-9076-0
4.
Rahikainen
,
J.
,
Kiani
,
M.
,
Sopanen
,
J.
,
Jalali
,
P.
, and
Mikkola
,
A.
,
2018
, “
Computationally Efficient Approach for Simulation of Multibody and Hydraulic Dynamics
,”
Mech. Mach. Theory
,
130
, pp.
435
446
.10.1016/j.mechmachtheory.2018.08.023
5.
Naya
,
M.
,
Cuadrado
,
J.
,
Dopico
,
D.
, and
Lugris
,
U.
,
2011
, “
An Efficient Unified Method for the Combined Simulation of Multibody and Hydraulic Dynamics: Comparison With Simplified and Co-Integration Approaches
,”
Arch. Mech. Eng.
,
58
(
2
), pp.
223
243
.
6.
Gomes
,
C.
,
Thule
,
C.
,
Broman
,
D.
,
Larsen
,
P. G.
, and
Vangheluwe
,
H.
,
2018
, “
Co-Simulation: A Survey
,”
ACM Comput. Surv.
,
51
(
3
), pp.
1
33
.10.1145/3179993
7.
Benedikt
,
M.
, and
Holzinger
,
F.
,
2016
, “
Automated Configuration for Non-Iterative Co-Simulation
,”
Proceedings of the 17th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems
(
EuroSimE
),
Montpellier, France
, Apr. 18–20, pp. 1–7.10.1109/EuroSimE.2016.7463355
8.
Kübler
,
R.
, and
Schiehlen
,
W.
,
2000
, “
Modular Simulation in Multibody System Dynamics
,”
Multibody Syst. Dyn.
,
4
(
2/3
), pp.
107
127
.10.1023/A:1009810318420
9.
Schweizer
,
B.
,
Li
,
P.
, and
Lu
,
D.
,
2015
, “
Explicit and Implicit Co-Simulation Methods: Stability and Convergence Analysis for Different Solver Coupling Approaches
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
5
), p.
051007
.10.1115/1.4028503
10.
Meyer
,
T.
,
Li
,
P.
,
Lu
,
D.
, and
Schweizer
,
B.
,
2018
, “
Implicit Co-Simulation Method for Constraint Coupling With Improved Stability Behavior
,”
Multibody Syst. Dyn.
,
44
(
2
), pp.
135
161
.10.1007/s11044-018-9632-9
11.
Schweizer
,
B.
,
Li
,
P.
, and
Lu
,
D.
,
2016
, “
Co-Simulation Method for Solver Coupling With Algebraic Constraints Incorporating Relaxation Techniques
,”
Multibody Syst. Dyn.
,
36
(
1
), pp.
1
36
.10.1007/s11044-015-9464-9
12.
González
,
F.
,
Naya
,
M. A.
,
Luaces
,
A.
, and
González
,
M.
,
2011
, “
On the Effect of Multi-Rate Co-Simulation Techniques in the Efficiency and Accuracy of Multibody System Dynamics
,”
Multibody Syst. Dyn.
,
25
(
4
), pp.
461
483
.10.1007/s11044-010-9234-7
13.
Oberschelp
,
O.
, and
Vöcking
,
H.
,
2004
, “
Multirate Simulation of Mechatronic Systems
,”
Proceedings of the IEEE International Conference on Mechatronics
,
Istanbul, Turkey,
June 3–5, pp.
404
409
.10.1109/ICMECH.2004.1364473
14.
Arnold
,
M.
,
2009
, “
Numerical Methods for Simulation in Applied Dynamics
,”
Simulation Techniques for Applied Dynamics
,
Springer
,
Vienna, Austria
, pp.
191
246
.
15.
Busch
,
M.
,
2016
, “
Continuous Approximation Techniques for Co-Simulation Methods: Analysis of Numerical Stability and Local Error
,”
ZAMM—J. Appl. Math. Mech.
,
96
(
9
), pp.
1061
1081
.10.1002/zamm.201500196
16.
Ben Khaled-El Feki
,
A.
,
Duval
,
L.
,
Faure
,
C.
,
Simon
,
D.
, and
Gaid
,
M. B.
,
2017
, “
CHOPtrey: Contextual Online Polynomial Extrapolation for Enhanced Multi-Core Co-Simulation of Complex Systems
,”
Simulation
,
93
(
3
), pp.
185
200
.10.1177/0037549716684026
17.
Benedikt
,
M.
,
Watzenig
,
D.
,
Zehetner
,
J.
, and
Hofer
,
A.
,
2013
, “
NEPCE—A Nearly Energy-Preserving Coupling Element for Weak-Coupled Problems and Co-Simulation
,”
International Conference on Computational Methods for Coupled Problems in Science and Engineering
,
Ibiza, Spain
, June 17–19, pp.
1
12
.
18.
Sadjina
,
S.
,
Kyllingstad
,
L. T.
,
Skjong
,
S.
, and
Pedersen
,
E.
,
2017
, “
Energy Conservation and Power Bonds in Co-Simulations: Non-Iterative Adaptive Step Size Control and Error Estimation
,”
Eng. Comput.
,
33
(
3
), pp.
607
620
.10.1007/s00366-016-0492-8
19.
Schweizer
,
B.
, and
Lu
,
D.
,
2014
, “
Semi-Implicit co-Simulation Approach for Solver Coupling
,”
Arch. Appl. Mech.
,
84
(
12
), pp.
1739
1769
.10.1007/s00419-014-0883-5
20.
Haid
,
T.
,
Stettinger
,
G.
,
Watzenig
,
D.
, and
Benedikt
,
M.
,
2018
, “
A Model-Based Corrector Approach for Explicit co-Simulation Using Subspace Identification
,”
Proceedings of the Fifth Joint International Conference on Multibody System Dynamics
,
Lisbon, Portugal
, June 24–28, pp.
1
18
.http://imsd2018.tecnico.ulisboa.pt/Web_Abstracts_IMSD2018/pdf/WEB_PAPERS/IMSD2018_Full_Paper_28.pdf
21.
González
,
F.
,
Arbatani
,
S.
,
Mohtat
,
A.
, and
Kövecses
,
J.
,
2019
, “
Energy-Leak Monitoring and Correction to Enhance Stability in the Co-Simulation of Mechanical Systems
,”
Mech. Mach. Theory
,
131
, pp.
172
188
.10.1016/j.mechmachtheory.2018.09.007
22.
Peiret
,
A.
,
González
,
F.
,
Kövecses
,
J.
, and
Teichmann
,
M.
,
2018
, “
Multibody System Dynamics Interface Modelling for Stable Multirate Co-Simulation of Multiphysics Systems
,”
Mech. Mach. Theory
,
127
, pp.
52
72
.10.1016/j.mechmachtheory.2018.04.016
23.
Kövecses
,
J.
,
2008
, “
Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part I: General Formulation
,”
ASME J. Appl. Mech.
,
75
(
6
), pp.
1
12
.10.1115/1.2965372
24.
Stewart
,
D. E.
, and
Trinkle
,
J. C.
,
1996
, “
An Implicit Time-Stepping Scheme for Rigid Body Dynamics With Inelastic Collisions and Coulomb Friction
,”
Int. J. Numer. Methods Eng.
,
39
(
15
), pp.
2673
2691
.10.1002/(SICI)1097-0207(19960815)39:15<2673::AID-NME972>3.0.CO;2-I
25.
Erleben
,
K.
,
2007
, “
Velocity-Based Shock Propagation for Multibody Dynamics Animation
,”
ACM Trans. Graph.
,
26
(
2
), p.
12
.10.1145/1243980.1243986
26.
Glocker
,
C.
,
2001
,
Set-Valued Force Laws
,
Springer
,
Troy, NY
.
27.
Stewart
,
D. E.
,
1998
, “
Convergence of a Time-Stepping Scheme for Rigid-Body Dynamics and Resolution of Painlevé's Problem
,”
Arch. Ration. Mech. Anal.
,
145
(
3
), pp.
215
260
.
28.
Moreau
,
J.
,
1966
, “
Quadratic Programming in Mechanics: Dynamics of One Sided Constraints
,”
SIAM J. Control
,
4
(
1
), pp.
153
158
.10.1137/0304014
29.
Anitescu
,
M.
, and
Tasora
,
A.
,
2010
, “
An Iterative Approach for Cone Complementarity Problems for Nonsmooth Dynamics
,”
Comput. Optim. Appl.
,
47
(
2
), pp.
207
235
.10.1007/s10589-008-9223-4
30.
Anitescu
,
M.
, and
Potra
,
F. A.
,
1997
, “
Formulating Dynamic Multi-Rigid-Body Contact Problems With Friction as Solvable Linear Complementarity Problems
,”
Nonlinear Dyn.
,
14
(
3
), pp.
231
247
.10.1023/A:1008292328909
31.
Júdice
,
J.
, and
Pires
,
F.
,
1992
, “
Basic-Set Algorithm for a Generalized Linear Complementarity Problem
,”
J. Optim. Theory Appl.
,
74
(
3
), pp.
391
411
.10.1007/BF00940317
32.
Júdice
,
J. J.
,
1994
, “
Algorithms for Linear Complementarity Problems
,”
Algorithms Contin. Optim.
,
434
, pp.
435
474
.10.1007/978-94-009-0369-2_15
33.
Lemke
,
C.
,
1968
, “
On Complementary Pivot Theory
,”
Mathematics of the Decision Sciences
(Lectures Applied Mathematics, Vol.
2
), American Mathematical Society, Providence, RI, pp.
95
114
.
34.
Acary
,
V.
,
Cadoux
,
F.
,
Lemaréchal
,
C.
, and
Malick
,
J.
,
2011
, “
A Formulation of the Linear Discrete Coulomb Friction Problem Via Convex Optimization
,”
ZAMM-J. Appl. Math. Mech.
,
91
(
2
), pp.
155
175
.10.1002/zamm.201000073
35.
Acary
,
V.
, and
Brogliato
,
B.
,
2008
,
Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics
,
Springer Science & Business Media
, Springer, Berlin.
36.
Lacoursière
,
C.
,
2006
, “
A Regularized Time Stepper for Multibody Systems
,”
Umeå University, Umeå
,
Sweden
,
Report No. UMINF-04
.
37.
Anitescu
,
M.
, and
Potra
,
F. A.
,
2002
, “
A Time-Stepping Method for Stiff Multibody Dynamics With Contact and Friction
,”
Int. J. Numer. Methods Eng.
,
55
(
7
), pp.
753
784
.10.1002/nme.512
38.
CM Labs Simulations Inc
.,
2020
,
Vortex Studio Documentation
.
Montréal, QC, Canada
.
39.
Cardona
,
A.
, and
Geradin
,
M.
,
1990
, “
Modeling of a Hydraulic Actuator in Flexible Machine Dynamics Simulation
,”
Mech. Mach. Theory
,
25
(
2
), pp.
193
207
.10.1016/0094-114X(90)90121-Y
You do not currently have access to this content.