MULTI-SCALE DYNAMICS OF MECHANICAL SYSTEMS WITH FRICTION

Contact between rough surfaces occurs in numerous engineering systems and in many instances influences the macro behavior of the system. In many instances, the interaction between rough surfaces, affect the macro behavior of the system. Effective treatment of systems containing rough surface contact requires multiscale modeling and analysis approach. It is the goal of this research to develop simple methods for treating contact of rough surfaces so as to facilitate multiscale analysis of systems containing rough surface contact and friction. This dissertation considers a multi-scale approach that includes interaction at nano-scale, micron-scale and accounting for their cumulative effect as to what we normally perceive to be the influence of contact surfaces and friction. In linking each scale to a higher scale this study employs statistical means to obtain cumulative effect of smaller-scale features. A mixed interactive/optimization technique is used to derive, in approximate closed form, equations for the contact load and real area of contact dependence on approach and parameters of rough surfaces. The equations so derived relate the normal and tangential components of contact load to displacement and surface parameters for three types of contact. The nature of contact interaction that include elastic, elastic-plastic, visco-elastic, and visco-elasto-adhesive behavior are considered and equations relating the normal and tangential contact load to approach and relative sliding are obtained in approximate closed form. The approximate equations provide a tool for efficient calculation of contact force components, especially in surface optimization efforts where repetitive calculation of contact force components may be needed. The approximate equations also facilitate a multi-scale dynamic analysis wherein the effect of contact interaction can be readily included in a mechanical system model. Several dynamical problems involving mechanical systems with friction contact are presented and nonlinear dynamic analyses are employed to link the micron-scale properties of surface to the macro-scale properties of the mechanical system. These lead to, perhaps, the first derivation of contact frequency and damping in rough surface contact