Fractal Prediction of Surface Morphology Evolution During the Running-In Process Using Monte Carlo Simulation

A Monte Carlo based fractal prediction model is proposed to describe the evolution of surface morphology during the running-in process. The model accounts for the random and fractal characteristics of worn surfaces. The Weierstrass–Mandelbrot function is employed to simulate rough surfaces and establish the correlation between fractal dimension and surface roughness. By integrating traditional sliding wear models with surface effect functions, a unified prediction framework is developed. Experiments are conducted to obtain worn surface parameters and calculate fractal dimensions at different running-in stages. Model parameters are optimized by minimizing the variance between experimental and predicted results. Monte Carlo simulations are then introduced to represent the stochastic nature of the friction system, thereby improving prediction accuracy and objectivity. The proposed model reveals locally random yet globally convergent patterns, which are consistent with experimental observations. It effectively captures the stochastic evolution of surface morphology and provides a reliable approach for predicting worn surface behavior during running-in.