含滚阻摩擦平面多体系统的建模和数值方法

摘要

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.%针对含滚阻和摩擦的平面多体系统,给出了通用的力学模型,利用第一类Lagrange方程建立了系统的动力学方程,为便于约束力的计算,利用局部方法列写约束方程,并以矩阵形式给出了该系统滚阻力偶和摩擦力的广义力.该系统动力学方程是非光滑的,通过建立滚阻定律的互补条件以及光滑铰链约束力的互补条件,给出了具有约束稳定化的基于事件驱动法的数值算法,将非光滑约束力、铰链约束力的求解以及滚轮滑动与粘滞的判断问题统一转化为一个线性互补问题进行求解.对两个算例进行了数值仿真,算例数值结果表明了该方法的可行性和有效性.