A Mixed Lubrication Model for Line Contacts Considering the Micro-scale Strain Hardening Effect

The mixed lubrication state induced by surface micro-topography significantly influences the contact performance of mechanical components. Existing analytical models are generally based on the ideal elastic-plastic material assumption and fail to account for the strain hardening effect after local asperity yielding, leading to considerable deviations between theoretical predictions and engineering reality. This paper establishes a statistical mixed lubrication model for line contacts that incorporates micro-scale strain hardening effects. By integrating the hardening behavior of local solid contacts with the average flow model for rough surface elastohydrodynamic lubrication, the mixed lubrication contact state considering micro-scale strain hardening is obtained through numerical solution. Based on the proposed model, the influences of load, speed, material hardness, surface roughness, and strain hardening exponent on the minimum film thickness and asperity load ratio are systematically analyzed. The results indicate that: (1) Increasing strain hardening intensity notably raises contact pressure, slightly reduces the minimum film thickness, and systematically alters load distribution. Neglecting this effect may lead to prediction errors exceeding 20% for key lubrication parameters; (2) Empirical formulas for the minimum film thickness and asperity load ratio incorporating the strain hardening exponent are derived, with prediction errors within 7%. This study achieves quantitative prediction from microscopic material hardening behavior to macroscopic lubrication performance, providing a new theoretical tool for high-precision lubrication design and analysis.