Abstract:Abstract: Considering of mesh deformation of gears, bending deformation of shafts and stiffness of beatings, the dynamic model of hypoid gear transmission was established with contact finite element method, and the support reaction of bearings was computed with LS-DYNA. Using the support reaction as input excitation, the dynamic model of hypoid gearbox was built and solved with ANSYS. Then compare the result of transient response analysis and that of experiment. At last taking the mean square root of vibration acceleration as the objective function, structure parameters of gearbox as design variables, the static stress, displacement and volume of housing as constraint condition, and sub-problem approximation method as solving method, the optimum design sets of housing can be obtained.