Stress and Strain Analysis of the Front Planetary Sun Gear of a Helical Differential Using the Finite Element Method with Variations in Initial Crack Conditions

Analisis Tegangan dan Regangan pada Front Planetary Sun Gear Diferensial Roda Gigi Miring Menggunakan Metode Elemen Hingga dengan Variasi Kondisi Retak Awal

Abstract

This study aims to analyze the stress and strain distribution on the front planetary sun gear of a helical differential using the Finite Element Method (FEM). The analysis was carried out under two conditions: without a crack and with an initial crack of 1 mm placed at the tensile side tooth root, in order to evaluate the effect of defect presence on the mechanical behavior of the gear under an operational torque load of 175 Nm. Three-dimensional modeling and meshing were performed using ANSYS software, with SCM420 steel as the material, which has an allowable stress of 1,300 MPa. The simulation results show that the maximum stress in the uncracked model reached 8,859.6 MPa, while in the cracked model it increased to 15,258 MPa. Meanwhile, the maximum equivalent elastic strain increased from 4.437 × 10⁻² mm/mm to 1.154 × 10⁻¹ mm/mm. This significant increase indicates that the presence of an initial crack intensifies stress concentration and amplifies local deformation, potentially accelerating crack initiation and propagation due to the increased strain energy accumulated near the crack tip. Based on these findings, optimization of the fillet radius and the application of surface treatments such as shot peening or advanced carburizing are recommended to reduce peak stresses and extend gear fatigue life. The results of this study demonstrate that the FEM approach is effective in predicting structural behavior and serves as a basis for the development of reliability-based design and condition monitoring systems in modern automotive transmissions.