Lubrication analysis and sub-surface stress field of an automotive differential hypoid gear pair under dynamic loading

Film thickness and sub-surface stress distribution in a highly loaded automotive differential hypoid gear pair are examined. A 4-Degree of Freedom torsional gear dynamics model, taking into account the torsional stiffness of the pinion and the gear shafts, is used in order to evaluate the contact load, the surface velocities and the contact radii of curvature of the mating teeth during a full meshing cycle. The torsional gear dynamics model takes into account both the geometric non-linearities of the system (backlash non-linearity) as well as the time varying properties (contact radii, meshing stiffness) and the internal excitations caused by geometrical imperfections of the teeth pair (static transmission error). The input torque used for the study of the film thickness and the sub-surface stress distribution corresponds to the region after the main resonance, where no teeth separation occurs. The contact conditions predicted by the gear dynamics are used as the input for the elastohydrodynamic elliptical point contact analysis. The lubricant film thickness, the corresponding pressure and surface traction distributions are obtained quasi-statically using the output load of the dynamic gear pair model. The variation of the induced sub-surface stress field is determined throughout a meshing cycle. Based on the sub-surface reversing orthogonal shear stresses, marginal differences occur when the viscous shear on the conjunctional surfaces are taken into account, which are mainly influenced by the applied pressure distribution. The numerical prediction of lubricant film thickness agrees reasonably well with that predicted using the well-established extrapolated oil film thickness formulae reported in the literature.