Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints

作     者：Fang-Fang Zhuang Qi Wang 

作者机构：Beihang University 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2014年第30卷第3期

页      面：437-446页

核心收录：

学科分类：08[工学] 0802[工学-机械工程] 0701[理学-数学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundation of China(11372018 and 11172019) 

主　　题：Multibody systems Lagrange multipliers Driving constraints Coulomb's friction Horizontal linearcomplementarity problem (HLCP) 

摘      要：An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces （or moments） and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb＇s dry friction. Combined with the theory of the horizontal linear complementarity problem （HLCP）, an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.