Moving beyond Flow Factors: Modeling Full Film Lubrication with Representative Surface Topography Using Heterogeneous Multiscale Methods

Lubrication modeling has long been dominated by the well-established Patir and Cheng flow factors method. The flow factors approach allows for accurate estimates of macroscale parameters (such as friction) in a reasonable amount of time. These methods are stochastic representations of microscale interactions and are not able to predict local scale (pressure, film thickness) phenomena with a suitable degree of accuracy. This contrasts with a deterministic approach, where a numerical grid must be applied that fully defines the microscale surface topography across the contact. The mesh resolution required leads to prohibitively long execution times and lacks scalability to engineering systems, but provides accurate predictions of local scale phenomena. In this paper, heterogeneous multiscale methods (HMM) are expanded to model varying and are, therefore, more representative of surface topography within lubricated contacts. This representative topography is derived from measured data, thereby allowing the accuracy of deterministic methods to be achieved with the speed of a flow factor method. This framework is then applied to compare key performance characteristics (pressure, film thickness, etc.) when idealized, Gaussian, and measured surface topography are modeled. The variations in microscale geometry are defined by measurements from across two tilted-pad bearings, demonstrating the ability of the expanded HMM framework to model representative surface topography. A comparison with a deterministic method is included as validation, and outputs of the HMM are discussed in the context of the lubrication across multiple length scales.