Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Single and Double Helical Planetary Gears With Flexible Ring Gears

Abstract

This paper is mostly aimed at analyzing optimum profile modifications (PMs) in planetary gears (PGTs) with regard to dynamic mesh forces. To this end, a dynamic model is presented based on 3D twonode gear elements connected to deformable ringgears discretized into beam elements. Doublehelical gears are simulated as two gear elements of opposite hands which are linked by shaft elements. Symmetric tip relief on external and internal gear meshes are introduced as timevarying normal deviations along the lines of contact and timevarying mesh stiffness functions are deduced from Wrinckler foundation models. The equations of motion are solved by coupling a Newmark timestep integration scheme and a contact algorithm to account for possible partial or total contact losses. Symmetric linear PMs for helical and doublehelical PGTs are optimized by using a genetic algorithm with the objective of minimizing dynamic tooth loads over a speed range. Finally, the sensitivity of these optimum PMs to speed and load is analyzed.