An innovative tooth root profile for spur gears and its effect on service life

An innovative approach to the design of the gear-tooth root-profile, and its effects on the service life is reported in this paper. In comparison with the widely used trochoidal and the recently proposed circular-filleted root profiles, the optimum profile proposed here is a (G^2)-continuous curve that blends smoothly with both the involute of the tooth profile and the dedendum circle. Following the AGMA and ISO standards for fatigue loading, the von Mises stress at the critical section and stress distribution along the gear tooth root are studied. The process leading to gear-tooth failure is composed of the crack initiation phase, in number of cycles (N_i), and the crack propagation phase, in (N_p) cycles. The strain-life ((epsilon)-N) method is employed to determine (N_i), where the crack is assumed to initiate at the critical section. Based on the ANSYS crack-analysis module, the effects of (G^2)-continuous blending on the stress intensity factor (SIF) are investigated for different crack sizes. Paris’ law, within the framework of Linear Elastic Fracture Mechanics, is used to correlate the SIF with crack size and, further, to determine (N_p). The optimum profile provides a significant reduction in SIF and improvement in both (N_i) and (N_p). Spur gears are made of high-strength steel alloy 42CrMo4, the effects of its properties and surface treatment on service life improvement not being included in this study.