High-fidelity modelling of lubricated transmissions using a coupled finite element approach

Abstract

This work presents a high-fidelity lubricated transmission model, coupling Flexible MultiBody (FMB) dynamics with ElastoHydrodynamic Lubrication (EHL). The EHL model is discretised with a coupled finite element approach, in contrast with the more iteration-intensive finite difference approach using relaxation schemes. The finite element method yields nonlinear system matrices, requiring matrix reevaluation in each iteration. To mitigate computational overhead, tensorisation replaces integrals to compute the system matrices with tensor-vector multiplications. Furthermore, this work optimises the use of the discretised EHL model by scaling and reusing it across different contact conditions. Coupling of the contact force resulting from the EHL model with the rigid body displacement resulting from the FMB model enables the computation of steady-state equilibrium for a given torque applied to the gear pair. However, local deformations should be excluded from the FMB model to ensure proper coupling with the EHL model, which exclusively computes local deformation within the contact zone. Newly developed global line contact attachment modes allow the FMB model to exclusively calculate global tooth bending in response to a given contact force.