Geometric Modeling and Fatigue Strength Simulation of Bevel Gears with Variable Radius Tooth Root

Aiming at the problem that most of the teeth root of straight bevel gears adopt fixed radius fillet transition with 0.3 times of modulus， which tends to to cause large bending stress on the tooth root and reduce the service life of bevel gears， a design method of variable radius tooth root fillet bevel gears is proposed. The general equation of the variable radius tooth root fillet under the standard tooth root bevel is established. Based on the fixed-radius non-standard planetary gear of an electric vehicle differential， the general equation of tooth root variable-radius fillet under different tooth root cones is derived， and the variable-radius non-standard planetary gear is optimally designed. Through finite element dynamics and fatigue life simulation analysis， it is concluded that the average tooth root bending stress of the bevel gear is reduced by 10.8% and the fatigue damage is reduced by 6.6% for the variable radius tooth root fillet compared with the fixed radius fillet with the largest radius. Therefore， the proposed design method improves the mechanical performance and fatigue life of the bevel gear.