In this work, a numerical model simulating friction hysteresis for lubricated rough and textured surfaces in contact is presented. Friction hysteresis occurs in sliding contacts that are subjected to a non-constant (e.g., sinusoidal) motion. It refers to the phenomenon where the observed friction force during acceleration differs from that during deceleration. Besides the dynamics of the sliding system, a classic mixed friction model is adopted, in which the transient Reynolds equation for the description of the thin lubricant film is combined with a statistical Greenwood–Williamson model for the description of rough surface asperity contacts. The model enables the prediction of the friction hysteresis for predefined contact descriptions (i.e., surface profile and roughness, lubricant, etc.) and allows the study of the physics and parametric influences of dynamically sliding contacts. In this paper, it is shown that (i) friction hysteresis is captured by classic transient models for mixed lubrication; (ii) system parameters, such as roughness, applied load, viscosity and velocity, including the offset, amplitude and motion reversal, influence the shape and area of friction hysteresis; and (iii) the selection of the aforementioned parameters may minimize friction hysteresis.

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.