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

In high-performance sophisticated flank design for the spiral bevel and hypoid gears, tooth compliance is always an important input for identifying the tooth mechanical properties. Distinguished with the conventional modeling, a new accurate finite element structure model is established to determine tooth compliance by using elasticity-based deformation solution. In full consideration of the flank flexural behavior characteristic, a double-curved shell model with varying thickness is established to get a more accurate representation of geometric shape for face-milling or face-hobbing gear than a beam or plate model. In determination of tooth compliance, the high order shear theory of Bhimaraddi shell is used to set the displacement assumption, and the Rayleigh-Ritz approach having algebraic polynomial trail functions is performed to obtain an expression for the transverse deflection and shear rotation by considering the geometric boundary conditions. A given numerical result for the face-milling spiral bevel and hypoid gear is provided to verify the proposed methodology by comparing with the loaded tooth contact analysis (LTCA) using well-known finite element method (FEM).