The Torsional Stiffness of Involute Spur Planetary Gears

This paper presents the results of torsional stiffness analysis of involute spur planetary gears in mesh using finite element methods. A planetary gear model with 3 planet gears and its subsystem models have been developed to study the relationship between the overall torsional stiffness and the subsystem torsional stiffness. The subsystem models include one isolated sun-planet-ring pair, one isolated sun-planet external pair and one isolated planet-ring internal pair. A strategy utilising a small preload step via a weak spring was first applied to eliminate the gap between the teeth and then different torque levels were applied to calculate the transmission error due to the resulting elastic deformations. This calculation was repeated at multiple positions covering two tooth mesh cycles in the overall and subsystem models. The theoretical gear contact position was determined using an ANSYS APDL program and the gear rolling range was digitized into equidistant rolling angles. The sun-planet torsional stiffness variation has been shown to dominate the combined torsional stiffness and, based on the subsystem torsional stiffness, an analytical method for predicting the overall torsional stiffness is presented.