三维受限刚体的摩擦接触分析

Frictional contacts analysis of 3-D constrained rigid-body

首先建立了摩擦接触约束条件下三维刚体的动力学模型,利用线性互补问题(LCP)理论对其进行了降阶处理,讨论了其解的存在性和唯一性问题,然后利用Kelvin接触模型和奇异摄动理论揭示了受限刚体降阶模型接触力稳定性的附加条件,最后以单接触细长杆为例,分别从滑动接触和滚动接触两种情况讨论了运动的稳定性,验证了理论分析的正确性。

A dynamic model of 3-D constrained rigid-body with frictional contact was established first. Then the reduced-order rigid-body model was obtained with the linear complementarity problem （LCP） theory. Then existence and uniqueness of the solutions to the model were discussed. And the contact force was modeled according to the Kelvin＇ s Model. A singular perturbation was used to reveal the additional necessary conditions to ensure the contact force stability in the reduced rigid-body model. At last the stability of a slender rod with one frictional contact was discussed for the cases of sliding contact and rolling contact, respectively, which proved the correctness of the theoretical analysis.