Analytical Solution of Bending Stress Equation for Symmetric and Asymmetric Involute Gear Teeth Shapes with and without Profile Correction

Abstract

In this work, a developed analytical method based on a previous trial graphical method has been introduced to find the solution of bending stress equation for symmetric and asymmetric involute gear teeth shapes with and without profile correction and for different gear design parameters. In order to achieve this analytical solution, certain geometrical properties for gear tooth shape of tooth loading angle,  tooth critical section thickness, the load height from this section and Lewis form factor which are imperative to formulate the final form of the tooth bending stress equation must be determined analytically step-by-step. As a result of this work, the trial graphical method has been avoided by establishing a simple analytical expression which can be easily solved and it gives a higher accuracy and requires a shorter time.

Keywords: Gear, Involute Teeth, Symmetric, Asymmetric, Profile Correction, Critical Section Thickness, Lewis Form Factor, Bending Stress Equation, Analytical Solution.