Multiscale Fractal Analysis of Thermo-Mechanical Coupling in Textured Tribological Interfaces

The line contact behavior of multiscale meshing interfaces necessitates synergistic investigation spanning nano- to centimeter-scale ranges. When nominally smooth gear teeth surfaces come into contact, the mechanical-thermal coupling effect at the meshing interface actually occurs over a collection of microscale asperities (roughness peaks) exhibiting hierarchical distribution characteristics. The emergent deformation phenomena across multiple asperity scales govern the self-organized evolution of interface conformity, thereby regulating both the load transfer efficiency and thermal transport properties within the contact zone. The fractal nature of the roughness topography on actual meshing interfaces calls for the development of a cross-scale theoretical framework that inte-grates micro-texture optimization with multi-physics coupling contact behavior. Conventional roughness characterization methods based on statistical parameters suffer from inherent limitations: their parameter values are highly dependent on measurement scale, lacking uniqueness under varying sampling intervals and instrument resolutions, and failing to capture the scale-invariant nature of meshing interface topography. In contrast, a scale-independent parameter system grounded in fractal geometry theory enables essential feature extraction and quantitative characterization of three-dimensional interface morphology. This study establishes a progressive deformation theory for gear line contact interfaces with fractal geometric characteristics, encompassing elastic, elasto-plastic transition, and fully plastic stages. By systematically investigating the force-thermal coupling mechanisms in textured meshing interfaces under multiscale conditions, the research provides a theoretical foundation and numerical implementation pathways for high-precision multiscale thermomechanical analysis of meshing interfaces.