ZC1蜗杆轴截面齿廓测量误差数值补偿方法

Numerical Compensation Method for Measuring Error of Tooth Profile of ZC1 Worm on Shaft Section

依据ZC1蜗杆轴截面齿廓数学模型,可得到蜗杆轴截面齿廓理论离散点,而在ZC1蜗杆轴截面齿廓坐标测量中,由于x轴对不准引入了原理误差。为此,用细分法、牛顿插值法和三次样条插值法求解出与实际接触点较为接近的齿廓理论接触点,可得到补偿后的齿廓偏差数值。以模数为4 mm的ZC1蜗杆为例,与未作补偿的齿廓总偏差评定结果相比,分别用细分法、3阶牛顿插值法、三次样条法得到补偿后的齿廓总偏差结果,与同一试件在德国克林贝格P26齿轮测量中心得到的法向齿廓总偏差较为接近。给出的补偿方法效果明显,在接触式精密测量中具有一定的通用性。

According to the mathematical model of ZC1 worm shaft section tooth profile,the theoretical discrete points of worm shaft section tooth profile can be obtained.In the coordinate measurement of ZC1 worm shaft section tooth profile,the principle error is introduced due to the misalignment of x axis.Therefore,the tooth profile theoretical contact points close to the actual contact points are solved by subdivision method,Newton interpolation method and cubic spline interpolation method,and the compensated tooth profile deviation can be obtained.Taking the ZC1 worm with modulus of 4 mm as an example,compared with the evaluation results of the total deviation of the tooth profile without compensation,the total deviation results of the compensated tooth profile obtained by subdivision method,third-order Newton interpolation method and cubic spline method are close to the total deviation of the normal tooth profile obtained from the same specimen at the P26 gear measuring center in Klingelnberg,Germany.The compensation method has obvious effect and presents certain universality in contact precision measurement.