Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach

Multibody System Dynamics

Volumn 23, Issue 2, 2010, Pages 165-190

  Flores, Paulo ^a   Leine, Remco ^b   Glocker, Christoph ^b  

^a UNIVERSITY OF MINHO   (Portugal)

^b Institute of Mechanical Systems (IMES)   (Switzerland)

Author keywords

Clearance joints; Contact impact mechanics; Linear complementarity problem; Moreau time stepping method; Non smooth dynamics; Rigid multibody systems

Indexed keywords

LINEAR COMPLEMENTARITY PROBLEMS; MOREAU TIME-STEPPING METHOD; MULTI BODY SYSTEMS; NON-SMOOTH; RIGID MULTIBODY SYSTEMS; TIME STEPPING METHOD;

FRICTION; MECHANICS; NUMERICAL ANALYSIS;

EQUATIONS OF MOTION;

EID: 75149147999     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11044-009-9178-y     Document Type: Article

References (44)

1. P. Flores J. Ambrósio 2004 Revolute joints with clearance in multibody systems Comput. Struct. 82 1359 1369 10.1016/j.compstruc.2004.03.031
2. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies. Lecture Notes in Applied and Computational Mechanics, Vol. 34. Springer, Berlin (2008)
3. T. Qiang Y. Zhang L. Chen P. Flores 2009 Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints Comput. Struct. 87 913 929 10.1016/j.compstruc.2009.03.006
4. C.-S. Liu K. Zhang R. Yang 2007 The FEM analysis and approximate model for cylindrical joints with clearances Mech. Mach. Theory 42 183 197 05128383 10.1016/j.mechmachtheory.2006.02.006 (Pubitemid 44880415)
5. A.R. Crowthera R. Singha N. Zhangb C. Chapman 2007 Impulsive response of an automatic transmission system with multiple clearances: Formulation, simulation and experiment J. Sound Vib. 306 444 466 10.1016/j.jsv.2007.05.053 (Pubitemid 47259107)
6. P. Flores J. Ambrósio J.P. Claro 2004 Dynamic analysis for planar multibody mechanical systems with lubricated joints Multibody Syst. Dyn. 12 47 74 1174.70307 10.1023/B:MUBO.0000042901.74498.3a
7. S. Erkaya I. Uzmay 2008 A neural-genetic (NN-GA) approach for optimising mechanisms having joints with clearance Multibody Syst. Dyn. 20 1 69 83 05319051 10.1007/s11044-008-9106-6 2415005
8. P. Flores 2009 Modeling and simulation of wear in revolute clearance joints in multibody systems Mech. Mach. Theory 44 6 1211 1222 05620389 10.1016/j.mechmachtheory.2008.08.003 1130093
9. P. Flores J. Ambrósio J.C.P. Claro H.M. Lankarani 2008 Translational joints with clearance in rigid multibody systems J. Comput. Nonlinear Dyn. 3 1 0110071 10
10. J. Awrejcewicz G. Kudra C.-H. Lamarque 2003 Dynamics investigation of three coupled rods with horizontal barrier Meccanica 38 687 698 1062.70593 10.1023/A:1025881409419 2028268
11. E.D. Stoenescu D.B. Marghitu 2003 Dynamic analysis of a planar rigid-link mechanism with rotating slider joint and clearance J. Sound Vib. 266 394 404 10.1016/S0022-460X(03)00053-1
12. F. Farahanchi S.W. Shaw 1994 Chaotic and periodic dynamics of a slider crank mechanism with slider clearance J. Sound Vib. 177 3 307 324 0945.70539 10.1006/jsvi.1994.1436
13. Thümmel, T., Funk, K.: Multibody modelling of linkage mechanisms including friction, clearance and impact. In: Proceedings of Tenth World Congress on the Theory of Machine and Mechanisms, Oulu University, Finland, vol. 4, pp. 1375-1386 (1999)
14. R. Wilson J.N. Fawcett 1994 Dynamics of slider-crank mechanism with clearance in the sliding bearing Mech. Mach. Theory 9 61 80 10.1016/0094- 114X(74)90008-1
15. R.W. Cottle G.B. Dantzig 1968 Complementary pivot theory of mathematical programming Linear Algebra Appl. 1 103 125 0155.28403 10.1016/0024-3795(68) 90052-9 226929
16. Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problem. Academic Press, London (1992)
17. J. Rohn 1993 A note on solvability of a class of linear complementarity problems Math. Program. 60 13 229 231 10.1007/BF01580611 1239599
18. R.I. Leine B. Brogliato H. Nijmeijer 2002 Periodic motion and bifurcations induced by the Painlevé paradox Eur. J. Mech. A, Solids 21 5 869 896 1023.70009 10.1016/S0997-7538(02)01231-7 1936904
19. J. Pang J.C. Trinkle 1996 Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with Coulomb friction Math. Program. 73 2 199 226 10.1007/BF02592103 1392162
20. D.E. Stewart J.C. Trinkle 1996 An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and Coulomb friction Int. J. Numer. Methods Eng. 39 15 2673 2691 0882.70003 10.1002/(SICI)1097-0207(19960815)39: 15<2673::AID-NME972>3.0.CO;2-I 1403689
21. Leine, R.I., Nijmeijer, H.: Dynamics and Bifurcations of Non-Smooth Mechanical Systems. Lecture Notes in Applied and Computational Mechanics, vol. 18. Springer, Berlin (2004)
22. Glocker, C.: Set-Valued Force Laws: Dynamics of Non-Smooth System. Lecture Notes in Applied Mechanics, vol. 1. Springer, Berlin (2001)
23. Leine, R.I., van de Wouw, N.: Stability and Convergence of Mechanical Systems with Unilateral Constraints. Lecture Notes in Applied and Computational Mechanics, vol. 36. Springer, Berlin (2008)
24. C. Glocker C. Studer 2005 Formulation and preparation for numerical evaluation of linear complementarity systems in dynamics Multibody Syst. Dyn. 13 4 447 463 1114.70008 10.1007/s11044-005-2519-6 2149449 (Pubitemid 40859671)
25. Signorini, A.: Sopra alcune questioni di elastostatica. Atti della Societa Italian per il Progresso della Scienza (1933)
26. R.I. Leine N. van de Wouw 2008 Stability properties of equilibrium sets of non-linear mechanical systems with dry friction and impact Nonlinear Dyn. 51 4 551 583 1170.70340 10.1007/s11071-007-9244-z
27. S. Djerassi 2009 Collision with friction; Part A: Newton's hypothesis Multibody Syst. Dyn. 21 37 54 1163.70007 10.1007/s11044-008-9126-2 2483298
28. S. Djerassi 2009 Collision with friction; Part B: Poisson's and Stornge's hypotheses Multibody Syst. Dyn. 21 55 70 1163.70008 10.1007/s11044-008-9127-1 2483299
29. A. Bowling D.M. Flickinger S. Harmeyer 2009 Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction Multibody Syst. Dyn. 22 27 45 05593810 10.1007/s11044-009-9147-5 2519830
30. R.I. Leine C. Glocker 2003 A set-valued force law for spatial Coulomb-Contensou friction Eur. J. Mech. A, Solids 22 2 193 216 1038.74513 10.1016/S0997-7538(03)00025-1 1980806
31. M. Jean 1999 The non-smooth contact dynamics method Comput. Methods Appl. Mech. Eng. 177 3-4 235 257 0959.74046 10.1016/S0045-7825(98)00383-1 1710453 (Pubitemid 30510498)
32. F. Pfeiffer M. Foerg H. Ulbrich 2006 Numerical aspects of non-smooth multibody dynamics Comput. Methods Appl. Mech. Eng. 195 50-51 6891 6908 1120.70305 10.1016/j.cma.2005.08.012 2258321 (Pubitemid 44296365)
33. Haug, E.J.: Computer-Aided Kinematics and Dynamics of Mechanical Systems. Volume I: Basic Methods. Allyn and Bacon, Boston (1989)
34. Nikravesh, P.: Computer-Aided Analysis of Mechanical Systems. Englewood Cliffs, Prentice-Hall (1988)
35. Moreau, J.J.: Unilateral contact and dry friction in finite freedom dynamics. In: Moreau, J.J., Panagiotopoulos, P.D. (eds.) Non-Smooth Mechanics and Applications. CISM Courses and Lectures, vol. 302, pp. 1-82. Springer, Wien (1988)
36. P.D. Panagiotopoulos C. Glocker 2000 Inequality constraints with elastic impacts in deformable bodies. The convex case Arch. Appl. Mech. 70 5 349 365 0958.74044 10.1007/s004199900067
37. M. Förg F. Pfeiffer H. Ulbrich 2005 Simulation of unilateral constrained systems with many bodies Multibody Syst. Dyn. 14 2 137 154 1146.70317 10.1007/s11044-005-0725-x 2192343
38. Moreau, J.J.: Bounded Variation in Time. In: Moreau, J.J., Panagiotopoulos, P.D., Strang, G. (eds.) Topics in Non-smooth Mechanics, pp. 1-74. Birkhäuser, Basel (1988)
39. Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Contacts. Wiley, New York (1996)
40. C. Glocker 2001 On frictionless impact models in rigid-body systems Philosophical Transactions: Math. Phys. Eng. Sci. 359 1789 2385 2404 1005.70012 10.1098/rsta.2001.0857 1884306
41. M. Anitescu F.A. Potra D.E. Stewart 1999 Time-stepping for three-dimensional rigid body dynamics Comput. Methods Appl. Mech. Eng. 177 3 183 197 0967.70003 10.1016/S0045-7825(98)00380-6 1710450 (Pubitemid 30510495)
42. C. Studer R.I. Leine C. Glocker 2008 Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics Int. J. Numer. Methods Eng. 76 11 1747 1781 10.1002/nme.2383 2468394
43. Greenwood, D.T.: Principles of Dynamics. Englewood Cliffs, Prentice-Hall (1965)
44. Flores, P.: Contact-impact analysis in multibody systems based on the non-smooth dynamics approach. Post Doctoral Report. ETH-Zurich, Switzerland (2009)