Film thickness investigation in heavily loaded hypoid gear pair elastohydrodynamic conjunctions

Introduction: Hypoid gear pairs are some of the most highly loaded components of the differential unit in modern automobiles. Prediction of wear rate and generated friction require determination of lubricant film thickness. However, only very few investigations have addressed the issue of thin elastohydrodynamic films in hypoid gear pairs. The main reason for dearth of analysis in this regard has been the need for accurate determination of transient contact geometry and kinematics of interacting surfaces throughout a typical meshing cycle. Furthermore, combined gear dynamics and lubrication analysis of any pairs of simultaneous meshing teeth pairs is required. Simon [1] was among the first to deal with these issues. He used Tooth Contact Analysis (TCA) in order to calculate the instantaneous contact geometry and load for any teeth pair during their meshing cycle. However, in his study, the load carried by the hypoid pair was quite low, making the application of the results limited and not entirely suitable for real life operating conditions of typical hypoid gear pairs of vehicular differentials, which is of interest in the current paper. Xu and Kahraman [2] performed numerical prediction of power losses and consequently the film thickness for highly loaded hypoid gear pairs. However, in their study only the one-dimensional Reynolds equation was employed. Consequently, the effect of lubricant side leakage in the passage through the contact was ignored. A more recent study by Mohammadpour et al. [3] employed realistic gear geometry data (through the use of TCA) for calculation of film thickness time history through mesh. The two-dimensional Reynolds equation, accounting for the side leakage of the lubricant, was solved numerically. It was shown that the side leakage component of the entraining velocity can significantly influence the film thickness. With regard to hypoid gear dynamics, several studies should be mentioned. Wang and Lim [4] studied the dynamic response of hypoid gear pairs under the influence of time varying meshing stiffness. Yang and Lim [5] created a model able to predict the dynamic response of a hypoid gear pair by taking into account the lateral translations of their shafts due to the compliance of the supporting bearings. Karagiannis et al. [6-7] studied the dynamics of automotive differential hypoid gear pairs by taking into account the velocity dependent resistive torque at the gear caused by aerodynamic drag and tyre-road rolling resistance. The study integrated the gear dynamics with the generated viscous and boundary conjunctional friction.