Dynamic modelling of gear–spline system with nonuniform spline clearance and wear evolution of spline

The gear–spline system consisting of the internal spline of gears and the external spline of shafts is widely used in mechanical transmission systems. However, considering the nonuniform spline clearance caused by the assembly and manufacturing errors, the vibration characteristics of the system and the spline wear mechanism are still unclear. This article proposed a dynamic model of the gear–spline system with nonuniform spline clearance and wear evolution of spline. Compared with the existing models, the new contribution of this article is to reveal the coupling vibration mechanism of the gear–spline system under the condition of nonuniform spline clearance through the dynamic model. On this basis, the support stiffness characteristics and wear evolution law of the spline pair under the dynamic gear meshing force are studied. The results show that under the condition of nonuniform clearance, the displacement response of the system is modulated by the rotation frequency, and the motion trajectory tends to be chaotic. The load distribution of spline teeth and the equivalent stiffness of the spline depends on the number of loaded spline teeth, which in turn depends on the input torque and clearance distribution. In addition, the spline teeth with smaller clearance bear more loads and wear faster, and the wear causes the nonuniform clearance to gradually increase and become uniform. This study can provide theoretical guidance for revealing the vibration mechanism of the gear–spline system and calculating the support stiffness of the spline shaft.