基于五轴运动优化的数控成形磨齿精密齿向修形

Accurate lead modification of CNC gear profile grinding based on five-axis motions optimization

为解决数控成形磨齿过程中齿向修形存在的双齿面磨削精度差和单齿面磨削效率低的问题,通过优化机床的五轴运动多项式系数,实现双齿面磨削的精密齿向修形。依据空间曲面包络原理建立实际齿面的数学模型,并计算实际齿面相对于标准齿面的拓扑偏差。以机床的五轴运动多项式系数为优化参数、以齿面实际拓扑偏差与目标拓扑偏差差值最小为优化目标,建立了优化模型并对其进行求解,得到机床的五轴运动。通过数值分析和磨削试验验证了该方法可以有效地减小传统方法中加工齿向鼓形修形产生的齿面扭曲。

Aiming at the problem of low accuracy of double flank grinding and inefficiency of single flank grinding,the precision of tooth surface modification was realized in double flank grinding by optimizing the five-axis motions ofComputer Numerical Control （CNC） gear profile grinding machines. The mathematical model for actual tooth sur-face was built according to the spatial surface enveloping theory, and the topographical deviations of actual toothsurface relative to standard tooth surface were calculated. An optimization model was established by using the five-axis motion polynomial coefficients as the optimization parameters and the minimum difference between actual andtarget tooth deviations as the optimization objective. The five-axis motions were solved using the optimization model. Through the numerical analysis and experiment, the proposed method was proved to reduce the tooth twist effectively resulted from crowning the tooth lead with conventional method.