对角修形斜齿轮设计与数控磨齿研究

为了减小齿面振动，降低磨削误差，提出对角修形斜齿轮数控磨齿加工方法：通过设计对角修形曲线，经过3次B样条拟合为对角修形曲面；根据齿条展成渐开线齿面原理，建立平面砂轮磨削斜齿轮6轴联动Free-Form型数控磨齿模型，通过齿条与砂轮位矢等效转换，推导各轴运动关系；建立基于CNC机床各轴运动敏感性分析的齿面修正模型，各轴运动用6阶多项式表示，通过判断砂轮与齿面的接触状态，确定磨削齿面的误差，并分析各系数扰动对齿面误差的影响；以齿面误差平方和最小为目标函数，通过粒子群优化方法，得到机床各轴运动参数，该方法计算结果稳定且精度较高。通过算例表明：沿齿向方向压力角、螺旋角、展成角的微调可分别实现一定的对角修形加工；微调6轴联动机床各轴运动参数，可有效减小对角修形斜齿轮的磨削误差，通过机床运动敏感性分析验证理论和算法的正确性。

Research on Design and CNC Grinding Machine for Diagonal Modified Helical Gear

An approach based on CNC grinding machine for diagonal modified helical gear is proposed to reduce vibration and grinding errors. The deviations curve is designed and deviations surface of diagonal modified helical gear is fitted by 3 B-Spline based on tooth surface grid data established by the deviation curve. A Free-Form flank topographic correction method based on a six-axis CNC gear profile grinding machine with flat wheel is established according to principle of rack-cutter generated involutes gear and the kinematic relationships of the axes are derived based on equivalence of rack and flat wheel. An error correction model based on a sensitivity analysis is determined. Besides, each axis of the grinding machine are formulated as a six-degree polynomial and a disturbed polynomial coefficients on the topographic flank errors is developed by estimating whether the wheel contacts with the pinion. Using minimum squared error as the objective function, the particle swarm optimization algorithm are introduced to solve equations of the corrections , and the polynomial coefficients are ascertained, and this method of calculating results are stable and high precision. The result shows that slight variations in pressure angle, helix angle and generating angle along longitudinal tooth can get some specific diagonal modified tooth respectively, besides, diagonal modified tooth can then be efficiently ground by slightly adjusting six-axis movement according to the solved corrections and the validity of this method is numerically demonstrated using the six-axis CNC gear profile grinding machine, which effectively reduces grinding errors. The correctness of the theory and algorithm are supported by the sensitivity analysis of machine tool motion.