Differential hypoid gears: the necessity for a multi-physics approach

A multi-physics approach to investigate the dynamics and tribology of differential hypoid gears is presented in this work. A multi-body dynamics model of hypoid gears has been developed using ADAMS commercial software. The stiffness and damping of the lubricant film are key parameters for the system dynamics. They establish the coupling between dynamics and tribology of the hypoid gears. The stiffness of the lubricant film depends on its rheological state under the prevailing dynamic conditions. At low loads, a hydrodynamic regime of lubrication is prevalent and the lubricant film exhibits compressible behaviour. Therefore, the lubricant film stiffness can be the determining factor in the overall contact stiffness and it may well contribute to the system damping. At high loads, an Elasto-hydrodynamic regime of lubrication is prevalent (EHL), where the lubricant film behaves as incompressible body. EHL conditions present insignificant damping and relatively high stiffness in a way that if the only aim is to obtain the system dynamics, then the assumption of dry elastostatic Hertzian contact may be sufficient. Therefore, an iterative solution between tribology and the dynamics is required. Time restrictions are forcing the use of extrapolated equations for the tribological calculations coupled with the dynamic model. In parallel, a fully numerical model of EHL elliptical point contact has been developed, taking into account non-Newtonian and thermal effects. In the case of highly loaded teeth contacts, a mixed regime of lubrication is encountered due to thin films. The EHL model predicts the film thickness and power loss in a quasi-static manner (by following some snapshots during a typical meshing cycle). These calculations give detailed distributions of pressure, temperature and film thickness between the contacting teeth. Therefore, the numerical model is suitably developed to produce information about the energy consumed by the hypoid gears. To conclude, on one hand tribological predictions are essential for studying the system’s parasitic losses (efficiency). On the other hand, dynamic modelling returns the transient behaviour of the gear pair (dynamic transmission error) which is a predictive tool for Noise, Vibration and Harshness behaviour.