Static and Dynamic Analysis of High Contact Ratio Spur Gear Drive

Abstract

In this work, an analytical method has been presented for calculating the load sharing among the meshing teeth in high contact ratio spur gearing. Assumption for this procedure is that the tooth deflection at each of two or three pairs of contact is equal in all cases and the sum of normal loads contributed by each of two or three pairs of contact is equal to maximum normal load. Dynamic loads on high contact ratio spur gears are calculated by using an analytical model based on torsional vibration of gears. Dynamic load variations during a mesh cycle of a tooth are determined. Variable stiffnesses of gear teeth which are required for dynamic load calculations are found by using analytical expressions. Bending, shear, axial compression and Hertzian contact deflections are considered for tooth stiffness calculation. Viscous damping and friction among the mating teeth are also included in this analysis. Contact stresses are calculated by using analytical expressions developed for two elastic bodies held in contact by forces normal to the area of contact and accompanied by tangential frictional force. Contact stress variations during a mesh cycle of a tooth are determined. It is found that the operating speed has a significant influence on the dynamic load acting on the gear tooth. The magnitude and location of maximum dynamic load changes with operating speed.