波动转矩下渐开线直齿轮传动齿廓修形研究

Influences of profile modification on dynamic characteristics of involute spur gears under a fluctuating torque

分析了齿轮转速波动和齿面、齿背啮合相位差对啮合点的影响,结合单、双齿啮合和修形边界条件并采用解析法计算啮合刚度,建立了与齿轮实际运动状态和啮合状态相关的非线性啮合刚度模型,该模型可与齿轮非线性动力学方程实时反馈,更加准确地描述齿轮传动过程中的啮合刚度。建立了考虑间隙、非线性啮合刚度的2自由度单级齿轮传动非线性动力学模型,在波动转矩的作用下,对比研究齿廓修形参数对齿轮动态特性的影响。研究结果表明:修形量对齿轮动态特性影响显著,存在最优修形量使动载系数达到最小;当修形量超过某临界值齿轮产生单边或双边冲击现象,齿轮动载荷明显增加;外载荷一定,增加修形长度可降低动载系数最小值;波动转矩作用下,齿轮的最大修形量为最小转矩作用下单齿啮合最高点的变形量。

The influences of rotating speed fluctuation and the phase shift between forward and backward contact on mesh point position were analyzed.Combining boundary conditions of single-tooth meshing,double-tooth meshing,and profile modification and using the analytical method to calculate mesh stiffness,a nonlinear mesh stiffness model was established to achieve a real-time feedback with the nonlinear dynamic model of spur gears and produce a more precise mathematical model of gear meshing process.A 2-DOF nonlinear dynamic model of a spur gear pair with input torque fluctuation was established by taking backlash and nonlinear mesh stiffness into account.Based on the nonlinear dynamic model,the influence of profile modification on the dynamic behavior of the spur gear pair was studied.The resluts showed that the amount of profile modification significantly affects the dynamic characteristics of the spur gear pair,and an optimal amount of profile modification exists to make the dynamic load factor reach the minimum;when the amount of profile modification exceeds a certain critical value,single-side-impact or double-side-impact occurs and the gear dynamic loads significantly increase;increasing the length of profile modification can reduce the minimum value of the dynamic load factor under a certain input torque;the maximum amount of profile modification should be the combined tooth deformation at the highest point of single tooth contact under the minimum input torque.