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

a b s t r a c t
Article history:
Received 8 August 2011
Received in revised form 2 January 2012
Accepted 7 May 2012
Available online 18 June 2012
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 fourparameter
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.