A nonlinear dynamic model of a helical gear pair with backlash and time-varying gear meshing stiffness

as excited by the static transmission error under a mean torque load

is established in this paper. The meshing stiffness is calculated by employing 3-dimensional FEM and its function is formed by cubic spline interpolation and approximation of the discrete mesh points in a mesh period. Further more

a numerical integration algorithm with adaptive step size control has been applied to solve the governed equation aiming to obtain the steady state forced response for the internal sinusoidal excitations. By using a dynamics test rig of the helical gear pair

the vibration acceleration of gear teeth is measured and spectral characteristics of dynamic response are obtained. A good agreement between the numerical and experimental results indicates that the presented method is practical and efficient.