Mesh stiffness of an internal spur gear pair with ring gear rim deformation

• A model indicating the effect of gear ring flexibility on mesh stiffness is proposed.
• Effect of support type and number of supports are investigated.
• Influence of the amplitudes of the applied forces is studied.
• Ring thickness effect on the mesh stiffness of internal gear pair is explored.

Planetary gear has a broad application in industry due to its advantages. However, most of the mesh stiffness calculation for the planetary gears is based on the assumption that the effect of the ring flexibility is ignored. In this paper, the ring deformation based on the uniformly distributed Timoshenko beam theory is coupled into the gear mesh stiffness model of the internal gear pair. Based on this model, the effect of the ring deformation on the internal gear mesh stiffness can be carried on. In this paper, the effect of the support type (fixed support and pin support), ring thickness and number of supports on the mesh stiffness are investigated. It is demonstrated that the ring thickness and the number of supports have a great impact on the mesh stiffness of the internal gear pair while the influence of the support type is little. In addition, the mesh stiffness appears to be periodic with the number of the periodicities exactly equal to the number of the supports.