考虑齿顶修形和时变中心距的渐开线直齿轮振动特性研究

For spur gears, the analytic formulas of dynamic pressure angle and backlash are derived with considering the time-varying center distance. Taking into account the time-varying rotational speed, time-varying center distance and tip relief, we calculated the dynamic mesh stiffness with the analytic method. Thus, the gear mesh dynamic model is established. In consideration of the geometry eccentricity, gyroscopic effect and load distribution factor along the tooth width, a 10-DOF lateral-torsional-rocking coupled nonlinear dynamic model of a spur gear system was established. The nonlinear dynamic model and the gear mesh dynamic model are coupled. Comparison analysis on the vibration characteristic with different speeds and torques are carried out. The results show that when the speed exceeds certain value, the dynamic load for the short tip relief are bigger than the non-modification gear, while the long tip relief do not have critical speed. With the increase of the torque, the variation trend of the dynamic load will increase proportionally for the non-modification gear, while increase at first and then decrease for the long and short tip relief, and so an optimal amount of torque exists to acheive a minimum dynamic load factor. There exist critical torques for both long and short tip relief such that when the torque is smaller than these critical value, the dynamic load of modification gear are bigger than the non-modification gear, and the value for the long tip relief are bigger than the short tip relief.