A transient multiscale framework for elastohydrodynamic lubrication of rough ball-in-socket bearings

Lubrication in ball-in-socket bearings, such as those in total hip replacements, is inherently transient. The load and motion change dynamically while the lubricant cavitates in regions of diverging geometry and the bearing surfaces deform elastically and plastically. Surface roughness with amplitude comparable to the film thickness further modifies the local flow, but resolving roughness directly within a transient elastohydrodynamic (EHL) simulation is computationally prohibitive, while classical flow-factor models rely on assumptions that do not readily transfer to this regime. We present a fully transient multiscale framework, based on the Heterogeneous Multiscale Methods (HMM) for EHL in conformal bearings. A smooth macroscale Reynolds model captures the bearing geometry, deformation, dynamic loading, and velocity profiles and is coupled to representative transient microscale simulations that resolve idealised roughness and return additive adjustments to macroscale flux ( Δ Q ) and load-bearing capacity ( Δ P ). By construction, the multiscale framework reduces to the underlying smooth EHL model as the roughness amplitude tends to zero. With microscale roughness included, the multiscale model agrees with a high resolution deterministic model to within 3% in minimum thickness and pressure with a significant reduction in computational cost for the cases considered. The framework is demonstrated with ASTM F3143 reciprocating hip test velocity profiles.