Abstract: To improve the evaluation accuracy of the complex surface's contour error,a prediction method of milling contour error by kriging interpolation was proposed.By considering the contour error's spatial distribution,the method could accurately predict the unmeasured points'contour error by using known measured point contour error.The variogram in different directions were constructed according to the experimental results of contour error in concave spherical milling,and the anisotropic spatial distribution characteristic of concave spherical contour error was revealed.The kriging interpolation models in different directions were established according to the anisotropy of contour error distribution.The validity of the proposed kriging interpolation method for contour error prediction was verified by experiments on concave spherical milling.The results showed that the contour errors of concave spherical surface had  presented significantly difference along the direction of circumference angle and the inclination angle of surface.The average square error of the kriging interpolation method that interpolates 2° along the inclination direction of the surface was the lowest,and it was 17% lower than the linear interpolation method.The proposed spatial kriging interpolation method proposed   provided technical support for accurately predicting the contour error of machined surfaces.

Key words: milling contour error, distribution characteristic, Kriging interpolation, variogram

摘要： 为了提高复杂曲面轮廓误差的评估精度,提出了一种铣削轮廓误差克里金插值预测方法,该方法通过考虑曲面轮廓误差空间分布特点,可以利用已知测量点轮廓误差准确预测未测点的轮廓误差。首先,根据凹球面铣削轮廓误差实验结果构建了不同方向的变异函数,揭示了凹球面轮廓误差空间分布呈现各向异性的特点;其次,根据轮廓误差分布的各向异性建立了不同方向的克里金插值模型;最后,通过凹球面铣削加工实验,验证了提出的克里金插值法对轮廓误差预测的有效性。研究结果表明,凹球面轮廓误差沿圆周角方向和曲面倾角方向呈现明显的差异性;沿曲面倾角方向上插值范围为2°的普通克里金插值方法对轮廓误差的预测均方误差最低,同时,该方法比线性插值方法预测的均方误差降低了17%。本文提出的空间克里金插值方法为准确预测加工曲面的轮廓误差提供了技术支持。

关键词: 铣削轮廓误差, 分布特性, 克里金插值, 变异函数