To study the planar multi-body systems with rolling resistance and Coulomb friction, the generalized mechanics model with a number of rigid bodies and disks was established and the dynamical equations of the system were derived from Lagrange-s equations of the first kind in Cartesian coordinate. In order to compute constraint forces, constraint equations of the system were expressed by local approach and the generalized forces of rolling resistance couples and Coulomb friction forces were given in the matrix notation. The complementarity conditions of the rolling resistance law and the reaction forces of the hinge were formed to solve the non-smooth differential equations. A constraint-stabilized event-driven method for the system was given. So the problems of the computation for non-smooth forces and the reaction forces of the hinge and the judgment for the stick-slip were transformed into a linear complementarity problem. The disk and the planar rigid multi-body system with rolling resistance and Coulomb friction were respectively considered as demonstrative application examples and numerical results were presented.
Pfeiffer F,Foerg M,Ubrlch H.Numerical aspects of non-smooth multibody dynamics [J].Computer Methods in Applied Mechanics and Enginneering.2006,195(50/51):6891-6908
Cepon G,Boltezar M.Dynamics of a belt-drive system using a linear complementarity problem for the belt-pulley contact description [J].Journal of Sound and Vibration.2009,319(3/4/5):1019-1035
Le Saux C,Leine R I,Glocker C.Dynamics of a rolling disk in the presence of dry friction [J].Nonlinear Science.2005,15(1):27-61
Leine R I,Glocker Ch.A set-valued force law for spatial Coulomb-Contensou friction [J].European Journal of Mechanics A:Solids.2003,22(2):193-216
�����.�������ϵͳ����ѧ[M].����:�ߵȽ���������,1999:202-206 Hong Jiazhen.Computational dynamics of multi-body systems [M].Beijing:Higher Education Press,1999:202-206(in Chinese)
�����,����Բ,����.�õ�һ��Lagrange�������ƽ�����ϵͳԼ�����ķ���[J].������ѧ,2008,25(12):65-71 Peng Huilian,Guo Yiyuan,Wang Qi.A method for solving constrained force of planar multi-body system via the first kind of Lagrange-s equations[J].Engineering Mechanics,2008,25(12):65-71(in Chinese)