Multi-body contact in non-linear dynamics of real mechanical systems

Abstract

The considerable number of real mechanical systems operates in conditions of multi-body contact. Very often, elastic properties in contact areas couldn't be neglected, so the elastic deformations exist in contact area of each two deformable bodies in contact. When there are two or more contacts at the same time and rotations and/or translations of contact bodies, these conditions cause the continuous changes of contact areas' geometry, friction, load distribution and other parameters. Therefore, the problem of non-linear dynamics of mechanical system becomes very complex. In this paper, the new approach for analyzing the non-linear dynamics of mechanical systems with multi-body contacts will be presented. In this approach, the contact bodies in mechanical systems are simulated with basic geometric deformable bodies coupled with elements with time-varying stiffness and damping. The main principles of mathematical phenomenological mapping are used for multi-body contact reduction to simple single-degree of few-degrees of freedom systems with total stiffness as main characteristic. The cases of two and three basic geometric bodies in contact are modeled to enable the investigation of influence of main parameters (stiffness, damping, external load, friction coefficient) in non-linear dynamics of multi-body contacts. The Finite Element Analysis is used to calculate the time-varying contact deformations, total stiffness and external load distribution. A particular attention is paid to the presentation of new approach application on real mechanical systems with multi-body contacts, such as gears and ball bearings. The analyses of non-linear dynamics of a particular gear pair and a particular ball bearing will illustrate the capabilities and advantages of presented new approach for comfortable and qualitative analysis of nonlinear dynamic behavior of real complex mechanical systems.