Analysis of Displacement-Controlled Fretting Between Crossed Parabolic Cylinders in Elasto-Plastic Contacts

In practice, it is difficult to avoid the axis angle deviation when some regular surfaces are in micro-sliding, such as gears and machined surfaces. In order to better investigate the micro-motion contact characteristics, a crossed paraboloidal contact model under frictional condition is proposed to simulate both tangential displacement-controlled fretting and the evolution of the energy dissipation in a load cycle. By deriving the theoretical of the normal and tangential contact course of the model, the load–displacement curves during initial loading, unloading, and reloading stage are presented. On this basis, the hysteresis curve is then obtained by integrating the closed area surrounded by load–displacement during unloading and reloading, which also means that the empirical formulation for microslip in a load cycle is constructed. This study also reveals the plastic yield phenomenon under pure normal loading and plastic shakedown behavior caused by cyclic reciprocating displacement loads. In addition, the research on the junction growth, the evolution of tangential load, and hysteresis curve with different COFs under multiple-cycle load is also carried out. The implications of involved parameters, such as friction coefficient, axis intersection angle, normal load, and so on, are discussed with respect to hysteresis curve shape and energy dissipation. The difference in hysteresis and energy dissipation curves between the paraboloidal contact model and other classic contact models is then presented. It is discovered by comparison with other models that the paraboloidal contact model presents a relatively high energy dissipation in a load cycle.