On the Non-Dimensional Modelling of Friction Hysteresis of Conformal Rough Contacts

Friction hysteresis, ingaphenomenon observed when a sliding contact is subjected to an oscillatory motion has significant implications in fields such as tribology and robotics. Understanding and quantifying friction hysteresis is essential for improving the performance and efficiency of many sliding contacts. In this paper, we introduce six non-dimensional groups to characterize and study friction hysteresis behaviour for rough conformal sliding contacts. The proposed non-dimensional groups are specifically designed to capture the essential features of friction hysteresis loops encountered based upon previous work of present authors. The non-dimensional groups are derived from a mixed friction model composed of the transient Reynolds equation, a statistical mixed friction contact model, and the load balance. The non-dimensional groups capture physical parameters that influence friction behaviour, including normal load, sliding speed, viscosity, density, and surface roughness. By expressing these parameters in non-dimensional form, the proposed groups provide a concise and generalizable framework for analysing friction hysteresis across different systems and scales. To demonstrate the effectiveness of the non-dimensional groups, we establish a comprehensive relationship between the proposed groups and typical friction hysteresis loops encountered. Through numerical simulations, we find relationships that govern the transition between different hysteresis loop shapes and sizes. This knowledge can inform the design and optimization of systems where friction hysteresis plays a crucial role.