A linear formulation for misaligned helical gear contact analysis using analytical contact stiffnesses

Abstract

A comparative assessment of analytical gear mesh stiffness modelling techniques is presented in this study, culminating into an optimized method for spur and helical gear stiffness modelling. First, by selectively combining different analytical methods presented in literature, the total stiffness of a spur gear pair is obtained as a series and parallel connection of springs. In doing so, an overall compliance matrix is obtained that relates the linear transmission error of the gear pair to the gear contact force distribution. Starting from the spur gear stiffness model, the model is extended to a novel method for analytically computing the contact stiffness of helical gears, with particular attention devoted to axial stiffness and slice coupling effects. The couplings between slices, which relate forces and deflections of different slices, are included in the compliance matrix analytically using a combination of exponential decay functions and the moment image method. The performance of the novel method is numerically validated by comparing the model predictions for spur and helical gears under both perfectly aligned and misaligned conditions, including microgeometry modifications, with finite element simulations.