多体系统中深沟球轴承旋转铰内接触分析

将传统方法用于铰内接触分析时,需要通过物体的相对运动细节判断接触位置. 但实际机械系统中的铰,其内部缝隙非常小以至于几乎与计算误差的数量级相同. 在这种情况下,传统方法中的数值病态非常严重,难以得到合理的结果. 结合深沟球轴承旋转铰的构造细节,分析了钢球与轨道接触时运动学描述参数之间的关系、钢球在有效承载时的受力特征以及铰内接触形式的特点. 在此基础上,提出了一种确定多体系统中深沟球轴承旋转铰内接触力和接触位置的方法. 所提方法不需要解除铰的运动学约束,也不必求解非线性互补方程,因此在数值稳定性和计算效率方面具有优势. 数值算例验证了该方法的可行性.

CONTACT ANALYSIS OF DEEP GROOVE BALL BEARING JOINT IN MULTIBODY SYSTEMS

Detecting locations of contacts is the most important issue for contact analysis of a joint in multibody dynamics, which traditionally requires the details of the relative motion of bodies in the joint as well as the solution of the resulted complementarity problem. However, clearances in a joint may be so tiny that it is hard to distinguish the relative displacements from computational errors. In this case, the contact analysis becomes extremely difficult due to the serious numerical ill-conditioned characteristics of traditional methods. In this paper, with the consideration of the structural details of deep groove ball bearing, we found the kinematic conditions for a ball to be simultaneously in contact with the inner and outer races, as well as the characteristic of contact forces on the ball that is carrying a load. Consequently, we present a methodology, in which the forces and locations of contacts can be obtained by means of joint reaction forces instead of relative motions. By the proposed method, the difficulties arising from microscopic relative motions and nonlinear complementarity problems are avoided, and the numerical efficiency is improved. Numerical examples prove the validity of the method.