含摩擦滑移铰及驱动约束多刚体系统数值算法

THE NUMERICAL METHOD FOR MULTIBODY SYSTEM WITH FRICTIONAL TRANSLATIONAL JOINTS AND DRIVING CONSTRAINTS

研究了具有驱动约束及非光滑滑移铰多体系统动力学方程的建模与数值计算方法.将驱动约束视为非定常约束,非光滑滑移铰视为双边定常约束,滑移铰的摩擦模型采用库仑摩擦模型;应用第一类Lagrange方程建立系统的动力学方程,应用距离函数建立滑移铰的约束方程;将线性互补方法和Baumgarte约束稳定化方法引入,以解决滑移铰法向约束力的计算以及约束方程违约问题.最后应用曲柄摇杆机构作为算例,说明该方法的有效性.

This paper presented a modeling and simulation method for the rigid multibody system with frictional translational joints and driving constraints. The geometric constraints of the translational joints were treated as bilateral scleronomic constraints and the driving constraints were rheonomic constraints. The frictional model of translational joint was characterized by the type of Coulomb＇s law. The dynamic equations were obtained by the Lagrange equation of the first type and the constraint equations of translational joints were given by distance function. The problem about the translations of the normal constraint forces acting on the sliders of translational joints was formulated and solved as a horizontal linear complementarity problem. The Baumgarte＇s stabilization method was used to decrease the constraint drift. Finally, a crank-rocker mechanism was considered as a demonstrative application examples. The numerical results of this example show some dynamical behaviors of the system with frictional translational joints and constraint stabilization effect .