Dynamic analysis of spur gear teeth

Abstract

This paper presents a new approach to the stress analysis of spur gear teeth using finite element method and cyclic symmetry. The boundary conditions imposed between the two adjacent teeth in the conventional F.E.M. are avoided in this approach. Each tooth is considered as an identical substructure of the gear wheel. The contact line load at one such substructure leads to an asymmetric loading of the wheel as a whole. This force system is resolved into a finite Fourier series to calculate the static stresses. Frequency analysis is carried out using a simultaneous iteration scheme to solve the eigenvalue problem. Out of core techniques such as submatrices elimination methods are adopted. These values are compared with the ones obtained by considering the tooth as a cantilever beam using Rayleigh's method. Transient response is obtained by using the modal superposition technique.