Optimization of the loaded contact pattern of spiral bevel and hypoid gears based on a kriging model

In designing spiral bevel and hypoid gears, engineers typically must use trial and error to obtain a satisfactory design. This paper proposes a methodology for optimizing the loaded contact pattern of spiral bevel and hypoid gears. This methodology is divided into two parts: the establishment of an optimization model and a method for solving that model. The optimization model considers the loaded contact pattern, loaded transmission error, contact strength and bending strength. The model is formulated with the parameters of the ease-off surface as the design variables and the indices of loaded tooth contact analysis as the objective function and constraints. To solve the optimization problem with satisfactory computational efficiency and accuracy, a surrogate kriging-based model is introduced. A numerical example addressed by this methodology shows that the loaded contact pattern coincides well with the ideal zone, the loaded transmission error is reduced by 30.3%, and the maximum contact stress and root bending stress also decrease. This methodology is a useful aid for engineers in obtaining favorable designs systematically without trial and error.