Calculation of the kinematics of hypoid gears towards developing a method for an equivalent crossed helical gear pair selection for use in tribological experimental evaluations

Abstract

To experimentally verify power loss and friction for hypoid gears, measurements in a closed power-loop test rig are necessary. However, these are costly and mechanically complex, since they require additional spur gear reducers in the loop. ISO directives document the use of crossed helical gear pairs as virtual gears for hypoids to calculate the sliding velocity, since the flank geometry at the mean point can be precisely represented. The use of such pairs can be a cost effective and simpler alternative for testing purposes. However, the validity of this analogy regarding contact mechanics and tribology for the full mesh cycle has not been investigated hitherto. In the current study, a new method for calculating the sliding and rolling speed along the full path of contact of a hypoid gear pair is presented. Cutter kinematics are considered, for the accurate definition of the contact bodies. Using tooth contact analysis, the load distribution on the tooth under quasi-static conditions and the sliding velocity are calculated for comparison purposes. By applying a selection algorithm, a single experimental crossed helical gear pair is chosen aiming to simulate the contact conditions of hypoid gears. Two test scenarios are studied using elastohydrodynamic film thickness equations and friction models for evaluating the power loss. The contact is an elongated ellipse with varying directions of the sliding and sum velocities, which are considered in the model. The kinematic equivalence shows good agreement, while the tribological equivalence is achievable using a reduced input torque.