An Analytical Solution for the Maximum Tensile Stress and Stress Concentration Factor Investigations for Standard, Asymmetric fillets, Asymmetric Pressure Angle and Profile Shifted Helical and Spur Gears

Abstract

This research introduces a developed analytical method to determine the nominal and maximum tensile stress and investigate the stress concentration factor. The required tooth fillets parametric equations and gears dimensions have been reformulated to take into account the asymmetric fillets radiuses, asymmetric pressure angle, and profile shifting non-standard modifications. An analytical technique has been developed for the determination of tooth weakest section location for standard, asymmetric fillet radiuses, asymmetric pressure angle and profile shifted involute helical and spur gears. Moreover, an analytical equation to evaluate gear tooth-loading angle at any radial distance on the involute profile of spur and helical gears, (taking into account the effect of profile shift factor) has been derived. In addition, numerical solution for the evaluation of the maximum fillet tensile stress and the combined tensile stress concentration factor for the verification of the analytical method using computer-aided engineering software (ANSYS Version 18.1). The analytical and FE result have been compared and found to be very close. The most effective method for reducing the stress concentration factor have been found by applying negative profile shifting on asymmetric tooth with lower unloaded pressure angle and high loaded pressure angle and fillet radius, which can lead to an enhancement percentage of (20%) when using a (35^o/20^o) asymmetric spur gear of a (24) teeth number with a shift factor of (-0.3m_o) compared with standard (20^o) one.