Simulating Multibody Dynamics With Rough Contact Surfaces and Run-in Wear
Tóm tắt
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.
Tài liệu tham khảo
Anitescu, M. and Potra, F., ‘Formulating dynamic multi-rigidbody contact problems with friction as solvable linear complementarity problems’, Nonlinear Dynamics 14, 1997, 231–247.
Armstrong, W. and Green, M., ‘The dynamics of articulated rigid bodies for purposes of animation’, The Visual Computer 1, 1985, 231–240.
Featherstone, R., Robot Dynamics Algorithms, Kluwer, 1987.
Glocker, C., ‘Dynamik von Starrkörpersystemen mit Reibung und Stöss en’, Ph.D. thesis, Technische Universitüt Mänchen, 1995.
Glocker, C., ‘Formulation of spatial contact situations in rigid multibody systems’, Comput. Methods Appl. Mech. Engrg. 177, 1999, 199–214.
Glocker, C., Set-Valued Force Laws: Dynamics of Non-Smooth Systems, Lecture Notes in Applied Mechanics 1, Springer Verlag, Berlin, 2001.
Glocker, C. and Studer, C., ‘Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics’, Multibody System Dynamics 13, 2005, 447–463.
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.
Heilig, J. and Wauer, J., ‘Stability of a Nonlinear Brake System at High Operating Speeds’, Nonlinear Dynamics 34(3–4), 2003, 235–247.
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.
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.
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.
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.
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.
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.
Lötstedt, P., ‘Coulomb friction in two-dimensional rigid body systems’, Z. Angewandte Math. Mech. 61, 1981, 605–615.
Lötstedt, P., ‘Mechanical systems of rigid bodies subject to unilateral constraints’, SIAM J. Appl. Math. 42(2), 1982, 281–296.
Monteiro-Marques, M., Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction, Vol. 9. Birkhäuser Verlag, Basel, Boston, Berlin, 1993.
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.
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.
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.
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.
Pfeiffer, F. and Glocker, C., Multibody Dynamics with Unilateral Contacts, John Wiley & Sons, Inc, New York, 1996.
Rossmann, T. and Glocker, C., ‘Efficient Algorithms for Non-Smooth Dynamics’, In: ASME International Mechanical Engineering Congress and Exposition, Dallas, Texas, 1997.
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.
Stewart, D., ‘Rigid-body dynamics with friction and impact’, SIAM Review 42(1), 2000, 3–39.
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.
Tabor, D., ‘Friction-The present state of our understanding’, J. Lubr. Technol. (183), 1981, 169–179.
Vereshchagin, A., ‘Computer simulation of the dynamics of complicated mechanisms of robot manipulations’, Engineering Cybernetics 6, 1974, 65–70.
Wósle, M. and Pfeiffer, F., ‘Dynamics of spatial structure-varying rigid multibody systems’, Archive of Applied Mechanics 69(4), 1991, 265–285.
Zhao, X., Reddy, C., and Nayfeh, A., ‘Nonlinear Dynamics of an Electrically Driven Impact Microactuator’, Nonlinear Dynamics 40(3), 2005, 227–239.