A Fractal Modeling Method for Wheel Rough Surface Considering Circumferential Characteristics

在工程表面表征领域，分形理论因其对微观形貌特征的多尺度表征能力，已成为比传统统计参数更精确的表面粗糙度描述方法。针对轮轨接触问题，车轮表面形貌的精确建模直接影响接触应力分布、车辆动力学行为及磨损演化机理的仿真精度。本文提出一种基于分形理论的车轮粗糙表面建模新方法，通过Weierstrass-Mandelbrot函数生成分形表面，系统研究分形维数与特征尺度系数对表面形貌的影响规律；引入三维旋转矩阵实现表面离散点的周向变换，建立满足车轮旋转周向特性的表面模型。与传统随机叠加方法相比，本模型能更准确地反映实际车轮运行过程中的表面微观特征，为轮轨接触状态演化分析提供了一种新的理论建模工具。In the field of engineering surface characterization, fractal theory has emerged as a more precise approach for describing surface roughness than traditional statistical parameters, owing to its multiscale characterization capability of microscopic topographic features. For wheel-rail contact problems, the accurate modeling of wheel surface topography directly influences the simulation accuracy of contact stress distribution, vehicle dynamic behavior, and wear evolution mechanisms. This paper proposes a novel fractal-based method for modeling wheel rough surfaces. The Weierstrass-Mandelbrot function is employed to generate fractal surfaces, with systematic investigation of the influence of fractal dimension D and characteristic scale coefficient G on surface morphology. A 3D rotation matrix is introduced to achieve circumferential transformation of discrete surface points, establishing a surface model that satisfies the rotational circumferential characteristics of wheels. Compared with conventional random superposition methods, the proposed model more accurately reflects the microscopic features of actual wheel surfaces during operation, providing a new theoretical modeling tool for analyzing wheel-rail contact state evolution.