Analysis of Rigid-Body Dynamic Models for Simulation of Systems With Frictional Contacts
Analysis of Rigid-Body Dynamic Models for Simulation of Systems With Frictional Contacts
复制标题
DOI：
10.1115/1.1331060
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Peng Song;P. Kraus;Vijay R. Kumar;Pierre E. Dupont
中科院分区：
文献类型：
--
作者：
Peng Song;P. Kraus;Vijay R. Kumar;Pierre E. Dupont
库仑摩擦定律与经典刚体动力学原理的使用引入了数学上的不一致。具体而言，正向动力学问题可以没有解，也可以有多个解。在这些情况下，柔顺接触模型在增加状态向量的维度的同时，可以解决这些问题。然而，刚体模型的简单性和高效性为在刚体解唯一且稳定的模拟过程中使用刚体模型提供了强大的动力。本文利用奇异摄动分析和线性互补理论，建立了刚体动力学模型预测解稳定的条件。我们使用接触柔度的一般模型来推导平面机械系统的稳定性准则。特别地，我们证明了对于只有一个滑动接触的情况，总是至多有一个稳定解。我们的方法不直接适用于库仑摩擦定律不连续的滚动和滑动之间的过渡。为了克服这一困难，我们引入了一个光滑的非线性摩擦定律，它近似于库仑摩擦。这样的摩擦模型还可以提高刚体和柔性接触模拟的效率。对不同模型进行了数值模拟，并与实验结果进行了比较。
The use of Coulomb's friction law with the principles of classical rigid-body dynamics introduces mathematical inconsistencies. Specifically, the forward dynamics problem can have no solutions or multiple solutions. In these situations, compliant contact models, while increasing the dimensionality of the state vector, can resolve these problems. The simplicity and efficiency of rigid-body models, however, provide strong motivation for their use during those portions of a simulation when the rigid-body solution is unique and stable. In this paper, we use singular perturbation analysis in conjunction with linear complementarity theory to establish conditions under which the solution predicted by the rigid-body dynamic model is stable. We employ a general model of contact compliance to derive stability criteria for planar mechanical systems. In particular, we show that for cases with one sliding contact, there is always at most one stable solution. Our approach is not directly applicable to transitions between rolling and sliding where the Coulomb friction law is discontinuous. To overcome this difficulty, we introduce a smooth nonlinear friction law, which approximates Coulomb friction. Such a friction model can also increase the efficiency of both rigid-body and compliant contact simulation. Numerical simulations for the different models and comparison with experimental results are also presented.