An investigation of tooth mesh nonlinearity and partial contact loss in gear pairs using a lumped-parameter model

A three-dimensional lumped-parameter model for a pair of helical gears is developed and shown to be equivalent to an arbitrary tooth contact force distribution. The nonlinearity of the gear mesh is due to portions of gear teeth contact lines losing contact (partial contact loss). The lumped-parameter model accounts for the net force and moment arising from an arbitrary load distribution including partial contact loss. This model is shown to be equivalent to a four-parameter model defined by a translational stiffness acting at the center of stiffness and a twist stiffness. The twist stiffness generates a moment, which is solely due to the spread of contact across the tooth face. The movement of the translational stiffness across the tooth face generates an additional moment. The four parameters in the model are useful post-processing output quantities to track and interpret the gear mechanics and the mesh forces and moments that develop under static or dynamic conditions. The translational and twist stiffnesses and the center of stiffness depend strongly on the relative translation and twist at the gear mesh, introducing nonlinearity. Tooth surface modifications smoothen the translational stiffness profile and decrease the twist stiffness. The twist stiffness fluctuates periodically with gear rotation generating fluctuating moments (shuttling) that can potentially excite vibrations.