Comparison of Maximum Gear-Tooth Operating Bending Stresses Derived from Niemann's Analytical Procedure and the Finite Element Method

Abstract

Problem statement: Main purpose of this study was to investigation toothed gear loading problems using the Finite Element Method. Approach: We used Niemann’s equations to compare maximum bending stress which was developed at critical gear-tooth flank point during gear meshing, applied for three distinct spur-gear sizes, each having different teeth number, module and power rating. Results: The results emerging after the application of Niemann’s equations were compared to the results derived by application of the Finite Element Method (FEM) for the same gear-loading input data. Results were quite satisfactory, since von Mises’ equivalent stresses calculated with FEM were of the same order with the results of classical analytical method. Conclusion: Judging from the emerging results, deviation of the two methods, analytical (Niemann’s equations) and computational (FEM), referring to maximum bending stress is fairly slight, independently of the applied geometrical and loading data of each gear.