Analysis of the Effect of an Initial Crack on the Von Mises Stress Distribution and Elastic Strain of a Reverse Idler Spur Gear Using Finite Element Analysis

Abstract

The reverse idler spur gear is a key component in a manual transmission system that reverses the output shaft rotation during reverse operation. Due to high stress concentration at the tooth root, this component is susceptible to crack initiation and structural failure. This study investigates the effect of an initial crack on the distribution of Von Mises stress and equivalent elastic strain using the Finite Element Method (FEM). Two three-dimensional models were developed: an uncracked model and a cracked model with a semicircular crack of 0.5 mm depth at the tooth root. SCM415 steel was used as the material, and a torque load of 6226.03 Nm was applied. The simulation results showed that the uncracked model produced a maximum Von Mises stress of 805.92 MPa and a maximum equivalent elastic strain of 4.3922 × 10⁻³. In the presence of the initial crack, the maximum stress increased to 1335 MPa and the maximum strain to 6.5499 × 10⁻³, representing increases of 65.65% and 49.13%, respectively. The highest stress and strain concentrations were observed at the crack tip. These findings indicate that even a small initial crack significantly increases local stress concentration and deformation, thereby accelerating crack propagation and increasing the risk of fatigue failure in reverse idler spur gears.