Analysis of Spur and Straight Bevel Gear Teeth Deflection by the Finite Strip Method

Abstract

A linear Finite Strip element for the analysis of rectangular and annular sector thick plates is presented to permit the deflection analysis of spur and straight bevel gear teeth, which are respectively modeled as rectangular and annular sector cantilever plates. Plate deflections are obtained by a hybrid procedure based on the minimum total potential energy theorem, which retains advantages of both the orthotropic-plate method and the Finite Element concept and is called the Finite Strip Method. The formulation accounting for transverse shear deformation is based on Mindlin’s plate theory. Since the presented Finite Strip element supports any combination of continuous thickness variations, the true shape of the tooth is used in the solution. The formulation can be easily applied to any boundary conditions and supports any type and combination of transverse loads and moments. Application of the Finite Strip Method to predict the deflection of spur and straight bevel gear teeth is demonstrated and results are compared to those obtained by the Finite Element Method.