Mixed thermal elastohydrodynamic lubrication and contact fatigue life analysis of orthogonal face gear pairs

Surface topography and thermal effects strongly influence the lubrication and fatigue performance of orthogonal face gear pairs. However, the lubrication and contact fatigue characteristics of face gear pairs remain insufficiently characterised when both non-Gaussian rough surfaces and micro-scale thermal deformation induced by local temperature rise are considered. This study develops a mixed thermal elastohydrodynamic lubrication (MTEHL) model for orthogonal face gear pairs that considers the combined effect of non-Gaussian rough tooth surfaces and micro-scale thermal deformation. Geometric and kinematic parameters are obtained through tooth contact analysis (TCA). Three-dimensional non-Gaussian rough surfaces are generated using a two-dimensional digital filtering method, and a rank-compressed half space thermal deformation (RHTD) method is developed to efficiently compute micro-scale thermal deformation of the tooth surfaces. A contact fatigue model is formulated to predict relative fatigue life. Model predictions are validated against benchmark solutions, finite element analyses, and oil film thickness measurements. The results indicate that micro-scale thermal deformation of the tooth surface increases the oil film pressure during meshing of the face gear pair. Along the meshing track of the orthogonal face gear pair, the pitch point region exhibits the minimum film thickness and the highest pressure. Higher surface roughness accelerates lubrication degradation and leads to a more dispersed von Mises stress field. Increasing rotational speed intensifies the temperature rise but also thickens the lubricant film and extends relative fatigue life. The proposed framework provides an effective tool for analysing lubrication characteristics and contact fatigue of orthogonal face gear pairs under multiphysics coupling conditions.