A model of the dynamic behavior of spur gears with consideration of off-line-of-action contacts

Because of deflections under load, contacts on tooth flanks can occur outside the theoretical plane of action between non-conjugated profiles especially when tooth modifications are not appropriate. The main objective of the present paper is to introduce an original model of the dynamic behavior of spur gears when submitted to these particular meshing conditions. The pinion and the gear of the pair are modeled as two rigid cylinders linked by stiffnesses and dampers whose amplitudes and orientations vary in order to simulate the evolutions of the meshing conditions. For the sake of simplicity, only three torsional degrees-of-freedom on the pinion, the gear and the motor are considered. The results show that the contacts between non-conjugated flanks lead to a particular dynamic behavior characterized by i) an actual contact ratio larger than the theoretical one, ii) the possibility of impacts at engagement whose amplitudes depend on transmitted loads and speeds.