On the Spur-Gear Dynamic Tooth-Load Under Consideration of System Elasticity and Tooth Involute Profile

Abstract

A procedure for the dynamic analysis of gears is presented. The procedure is based on Hertz’s impact formula of two cylinders in contact. The radius of curvature at the contact point is considered as an equivalent cylinder radius. A pair of spur gears is used through the analysis. The instantaneous dynamic tooth load is evaluated taking into account the elasticity of each connecting shaft and elasticity of each tooth in contact. Each tooth is considered as a cantilever beam with actual shape of an involute profile. The rigid inertias of existing masses are also included. The dynamic equations presenting the mathematical model are solved using a harmonic series expansion satisfied at three discrete positions during a very small period of time within the contact period. An example is selected such that the arc of contact during the mesh of one pair of teeth corresponds to the circular pitch.