Tooth profile modification based on lateral- torsional-rocking coupled nonlinear dynamic model of gear system

In this paper, the influence of tooth profile modification on the vibration of a single gear is studied. Considering geometric eccentricity, gyroscopic moment, teeth to the partial load torque and backlash, a 10 degree of freedom (DOF) lateral-torsional-rocking coupled nonlinear dynamic model of a single gear system is proposed. Considering actual motion state and tooth profile modification, stiffness of the meshing model was studied using an analytical method. Results show influence of the modification amount with different modification types and different modification length on dynamic load. For the case of different modification lengths and modification types, with increasing modification amount, profile of dynamic load coefficient follows a 'V' type pattern. An optimal modification amount can be determined, where dynamic load of gear can be minimized. At the same time, when modification amount exceeds a certain critical value, dynamic load for modified gear was higher than the dynamic load for gear without modification. The optimum modification can effectively slow mutation of meshing stiffness and reduce the dynamic load of gear; the meshing force amplitude of modification gear is decreased significantly in the high order frequency, while the impact load caused by the alternation of single and double teeth is slowed down, and contact rate is basically unchanged.