Nonlinear Dynamics

, Volume 45, Issue 3–4, pp 353–365 | Cite as

Simulating Multibody Dynamics With Rough Contact Surfaces and Run-in Wear

  • Janko SlavičEmail author
  • Miha Boltežar


The overall dynamics of a multibody system is actually a multi-scale problem because it depends a great deal on the local contact properties (coefficient of restitution, friction, roughness, etc). In this paper we found that the briefly presented force-based theory of plane dynamics for a multibody system with unilateral contacts was appropriate for simulating detailed multi-contact situations of rough contacting surfaces.

The focus of the paper is on a geometrically detailed description of rough surfaces. To achieve the run-in effect of the contacting surfaces under dynamical loads the contacting surfaces need to be re-shaped. For the re-shaping a wear model based on the local loss of mechanical energy under dynamical loads is presented.

The new ideas are presented for a numerical analysis of measuring the coefficient of friction at the rim of a wheel (rotating body). With the help of the analysis the experimentally observed change in the measured coefficient of friction of up to 30% for only slightly altered experimental conditions is explained.


brake dynamics loss of mechanical energy at contacts multibody dynamics re-shaping rough unilateral contacts wear model 


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  1. 1.
    Anitescu, M. and Potra, F., ‘Formulating dynamic multi-rigidbody contact problems with friction as solvable linear complementarity problems’, Nonlinear Dynamics 14, 1997, 231–247.zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Armstrong, W. and Green, M., ‘The dynamics of articulated rigid bodies for purposes of animation’, The Visual Computer 1, 1985, 231–240.CrossRefGoogle Scholar
  3. 3.
    Featherstone, R., Robot Dynamics Algorithms, Kluwer, 1987.Google Scholar
  4. 4.
    Glocker, C., ‘Dynamik von Starrkörpersystemen mit Reibung und Stöss en’, Ph.D. thesis, Technische Universitüt Mänchen, 1995.Google Scholar
  5. 5.
    Glocker, C., ‘Formulation of spatial contact situations in rigid multibody systems’, Comput. Methods Appl. Mech. Engrg. 177, 1999, 199–214.zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Glocker, C., Set-Valued Force Laws: Dynamics of Non-Smooth Systems, Lecture Notes in Applied Mechanics 1, Springer Verlag, Berlin, 2001.Google Scholar
  7. 7.
    Glocker, C. and Studer, C., ‘Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics’, Multibody System Dynamics 13, 2005, 447–463.zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Harsha, S. P., Sandeep, K., and Prakash, R. ‘Nonlinear Dynamic Response of a Rotor Bearing System Due to Surface Waviness’, Nonlinear Dynamics 37(2), 2004, 91–114.zbMATHCrossRefGoogle Scholar
  9. 9.
    Heilig, J. and Wauer, J., ‘Stability of a Nonlinear Brake System at High Operating Speeds’, Nonlinear Dynamics 34(3–4), 2003, 235–247.zbMATHCrossRefGoogle Scholar
  10. 10.
    Le Saux, C., Leine, R. I., and Glocker, C., ‘Dynamics of a Rolling Disk in the Presence of Dry Friction’, Journal of nonlinear science 15(1), 2005, 27–61.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Leine, R. I., Brogliato, B., and Nijmeijer, H., ‘Periodic motion and bifurcations induced by the Painlevé paradox’, European Journal of Mechanics A/Solids 21, 2002, 869–896.zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Leine, R. I. and Glocker, C., ‘A set-valued force law for spatial Coulomb-Contensou friction’, European Journal of Mechanics A/Solids 22, 2003, 193–216.zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Leine, R. I., Glocker, C., and Van Campen, D., ‘Nonlinear Dynamics and Modelling of Some Wooden Toys with Impact and Friction’, Nonlinear Dynamics 9, 2003, 25–78.zbMATHMathSciNetGoogle Scholar
  14. 14.
    Leine, R. I. and Nijmeijer, H., Dynamics and Bifurcations of Non-Smooth Mechanical Systems, Vol. 18 of Lecture Notes in Applied and Computational Mechanics, Springer, 2004.Google Scholar
  15. 15.
    Leine, R. I., Van Campen, D. H., Kraker, A., and Van den Steen, L., ‘Stick-Slip Vibrations Induced by Alternate Friction Models’, Nonlinear Dynamics 16(1), 1998, 41–54.zbMATHCrossRefGoogle Scholar
  16. 16.
    Lötstedt, P., ‘Coulomb friction in two-dimensional rigid body systems’, Z. Angewandte Math. Mech. 61, 1981, 605–615.zbMATHGoogle Scholar
  17. 17.
    Lötstedt, P., ‘Mechanical systems of rigid bodies subject to unilateral constraints’, SIAM J. Appl. Math. 42(2), 1982, 281–296.zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Monteiro-Marques, M., Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction, Vol. 9. Birkhäuser Verlag, Basel, Boston, Berlin, 1993.Google Scholar
  19. 19.
    Moreau, J.-J., Unilateral Contact and Dry Friction in Finite Freedom Dynamics, Nonsmooth Mechanics and Applications. Springer-Verlag, Vienna, New York. International Centre for Mechanical Sciences, Courses and Lectures 302, 1988, pp. 1–82.Google Scholar
  20. 20.
    Oden, J. and Martins, J., ‘Models And Computational Methods For Dynamic Friction Phenomena’, Computer Methods In Applied Mechanics And Engineering 52(1–3), 1985, 527–634.zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Paoli, L. and Schatzman, M., ‘Mouvement á un nombre fini de degrés de liberté avec contraintes unilatérales: Cas avec perte d'énergie’, Math. Model. Numer. Anal. 27, 1993a, 673–717.MathSciNetGoogle Scholar
  22. 22.
    Paoli, L. and Schatzman, M., ‘Vibrations avec contraintes unilatérales et perte d'énergie aux impacts, en dimension finie', C. R. Acad. Sci. Paris S/’er. I 317, 1993b, 97–101.MathSciNetGoogle Scholar
  23. 23.
    Pfeiffer, F. and Glocker, C., Multibody Dynamics with Unilateral Contacts, John Wiley & Sons, Inc, New York, 1996.Google Scholar
  24. 244.
    Rossmann, T. and Glocker, C., ‘Efficient Algorithms for Non-Smooth Dynamics’, In: ASME International Mechanical Engineering Congress and Exposition, Dallas, Texas, 1997.Google Scholar
  25. 25.
    Slavič, J. and Boltežar, M., ‘Nonlinearity and non-smoothness in multi body dynamics: Application to woodpecker toy’, Journal of Mechanical Engineering Science, in press, 2005.Google Scholar
  26. 26.
    Stewart, D., ‘Rigid-body dynamics with friction and impact’, SIAM Review 42(1), 2000, 3–39.zbMATHMathSciNetCrossRefGoogle Scholar
  27. 27.
    Stewart, D. and Trinkle, J., ‘An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and coulomb friction’, J. Numer. Methods Engineering 39, 1996, 2673–2691.zbMATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    Tabor, D., ‘Friction-The present state of our understanding’, J. Lubr. Technol. (183), 1981, 169–179.Google Scholar
  29. 29.
    Vereshchagin, A., ‘Computer simulation of the dynamics of complicated mechanisms of robot manipulations’, Engineering Cybernetics 6, 1974, 65–70.Google Scholar
  30. 30.
    Wósle, M. and Pfeiffer, F., ‘Dynamics of spatial structure-varying rigid multibody systems’, Archive of Applied Mechanics 69(4), 1991, 265–285.Google Scholar
  31. 31.
    Zhao, X., Reddy, C., and Nayfeh, A., ‘Nonlinear Dynamics of an Electrically Driven Impact Microactuator’, Nonlinear Dynamics 40(3), 2005, 227–239.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering, Laboratory for Dynamics of Machines and StructuresUniversity of LjubljanaLjubljanaSlovenia

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