Optimized design of straight bevel gear tooth root transition surface

At present, most straight bevel gears use a root fillet transition surface with a radius of 0.3 modulus. This tends to cause excessive root bending stress and reduces the service life of bevel gears. In order to solve this problem, a root fillet transition surface controlled by a set of third-order Bezier curves is designed based on spherical involute tooth surface. In the common cone apex coordinate system of the bevel gear, the spherical involute tooth surface equations and the third-order Bezier curve equations controlling the root transition surface are established. The feasibility of gear manufacturing is verified by precision forging simulation. A Box–Behnken experiment was designed, and the response surface model was developed from the experimental results. The response surface model reflects the mathematical relationship between the four variables controlling the third-order Bezier curve and the maximum tooth root bending stress. Then, the nonlinear programming was used to optimize the four variables, and the optimal root transition surface was obtained.