An innovative determination approach to tooth compliance for spiral bevel and hypoid gears by using double-curved shell model and Rayleigh–Ritz approach

•A new finite element model is established by double-curved shell considering the flexural behavior characteristic of tooth flank for spiral bevel and hypoid gears•Geometric expression of the flexural behavior of tooth flank is developed to double-curved shell model.•The higher order shear theory of Bhimaraddi shell is applied to model the shear deformation.•Rayleigh-Ritz method based on the strain energy equation of double-curved shell is used to solve for tooth compliance.