Prediction of transmission error in spur gears as a consequence of wear

The aim of this article is to investigate how the so-called transmission error in a gear develops in a wear process. A finite-element procedure for calculating wear between two elastic bodies in contact is developed that includes constitutive laws, representing the behavior of the interacting surfaces. When treating a gear problem, large rotations must be included. This is done by analyzing a sequence of finite-element models along with an interpolation procedure. The constitutive laws of interacting surfaces are Signorini's contact law, Coulomb's law of friction, and Archard's law of wear. By formulating both Signorini's contact law and Coulomb's law of friction by means of projection equations, the complete formulation of a time increment of a quasistatic wear-friction evolution problem becomes a system of nonsmooth equations. Then, a modified Newton method is applied to solve this system. The transmission error can be found from the infinitesimal displacement field superposed on the rigid body configuration. Results from the simulations show that wear will increase the peak-to-peak value of the transmission error. This is most significant in a gear when some kind of modification of the gear flank is applied to minimize the transmission error in an initial state.