Analytical solution to bending and contact strength of spiral bevel gears in consideration of friction

Abstract

Friction is not considered in the calculation of load capacity for spiral bevel gears according to either ISO or AGMA gear standard, and friction effects on the bending, contact and shear of the gears have rarely been discussed. In this regard, the present work establishes analytical solutions to calculate bending and contact strength for spiral bevel gears incorporating friction on the tooth surface, which are verified by ISO gear standard and finite element method (FEM). The bending strength is calculated based on Lewis cantilever beam approximation, utilizing the modified normal force and the friction component. The modified normal force is derived at the highest point of single tooth contact (HPSTC) in the normal equivalent gear. Follow Hertz contact theory, the contact strength is calculated when the modified normal force and the friction component are exerted at the lowest point of single tooth contact (LPSTC) in the normal equivalent gear. The calculated bending and contact stresses agree well with those obtained from the FEM analysis while considering the influence of friction. Both theoretical predictions and FEM analysis have shown that friction has a crucial effect on load capacity of a spiral bevel gear drive, and that it exerts stronger influence on the bending strength (compared with the contact strength). When friction coefficients become larger (with the same input torque), the bending stress considering only the modified normal force decreases at HPSTC, whereas it increases if both the modified normal force and the friction component are included. In comparison, the contact stress will increase at LPSTC under both scenarios. Furthermore, it is illustrated that shear strength check of the tooth is necessary as large friction occurs in the contact zone. This developed analytical solution can be well applied to the determination of load capacity of spiral bevel gears, especially under harsh working conditions or in the demand for higher performance.