A continuous analytical solution for the load sharing and friction torque of involute spur and helical gears considering a non-uniform line stiffness and line load

Abstract

In this work a continuous analytical model for the estimation of the mesh stiffness, load sharing and friction torque for parallel axis involute spur and helical gears is presented. The model has no limitations in the admissible range for the overlap and contact ratios. The main novelty of the work lies on the mathematical approach that allows the continuous description of the gearing phenomena without using functions by domains. At first, a model for the mesh stiffness and load sharing ratio for spur gears is developed. Then, a more advanced approach is used to tackle the same problem for helical gears. Both models consider a non-uniform contact line stiffness sharing function. Afterwards, assuming a constant friction coefficient, two friction torque models are developed, one for spur and the other for helical gears, while considering a non-uniform contact line load. The influence of the model parameters in the mesh stiffness, load sharing and friction torque is evaluated. Finally three gears of different types are selected and compared with reference results.