Effect of Tooth Count and Rim Thickness on the Operational Durability of Cylindrical Involute Gears

This paper presents a numerical assessment of bending-fatigue durability in the tooth root region of cylindrical involute gears. Multiple gear pairs were modelled with different numbers of teeth and varying gear rim thicknesses. The generated geometry was implemented in the ANSYS 2025 R2 software suite, where the maximum normal stresses at critical locations in the tooth root region were determined through numerical simulation. A deformation-based method derived from Socie’s models was applied to estimate the duration of the phase leading up to fatigue crack formation in terms of load cycle accumulation. The gear geometry, together with the generated finite element mesh, was transferred to the FRANC2D/L version 4 software suite, where fatigue crack propagation was numerically simulated. Numerical analysis provided effective stress intensity factors, which then enabled an estimation of the number of load cycles required for an initiated crack to grow to the critical length associated with tooth failure. The total fatigue life in the tooth root region was evaluated as the sum of load cycles in the crack initiation phase and the crack propagation phase up to the critical crack length. The results show that all analysed factors exhibit very high resistance to fatigue fractures in the tooth root region. Furthermore, for gears with a rim thickness ratio greater than 0.7, the fatigue crack propagates through the tooth and reaches the fracture toughness limit of the material (KIc), whereas for lower rim thickness ratios, crack propagation occurs through the gear rim itself.