By introducing the concept of ideal transmission

the expressing way of meshing force and meshing damping is given

which is a foundation to establish complex dynamic equations of spiral bevel gears and hypoid gear drives.Meanwhile

the torque produced by meshing force and meshing damping is given

which is various in different meshing regions under multiple-teeth meshing.The non-linear dynamic equations of spiral bevel gears and hypoid gear drives are established

which include the input and output rotating inertia

transmission error and time-varying mesh stiffness as well as backlash.The frequency response curves

phase portraits

time histories and dynamic load factor can be obtained by calculating the dynamic equations.