基于傅里叶变换与统计检验的圆度误差分离技术研究

Research on Roundness Error Separation Technology Based on Fourier Transform and Statistical Testing

采用傅里叶变换及数理统计假设检验的方法对圆度误差进行分离。针对圆轮廓的高精度测量数据,通过最小区域法拟合圆心。应用傅里叶变换将圆轮廓信号转换成谐波信号,从理想圆轮廓模型出发,逐步添加傅里叶分量,迭代过程中通过偏F检验构造包含未知系统形状误差的主导性模型。通过自相关法检验、卡方检验及J-B检验获取残余的显著性傅里叶分量,进一步构建显著性模型,实现圆度误差中系统误差的分离。通过数控加工16个圆孔的实验数据分析,证明了该方法可以对圆度误差进行有效分离。

The roundness error is separated by Fourier transform and hypothesis test of mathematical statistics.For high-precision measurement point data of circular contours,the minimum area method is used to fit the center of the circle.Fourier transform is applied to transform the circular contour signal into harmonic signal.Starting from the ideal circular contour model,Fourier components are gradually added.In the iterative process,the dominant model containing the unknown systematic form error is constructed through partial F-test.Residual significance Fourier components are obtained through autocorrelation test,chi square test,and J-B test,in order to further construct a significant model and achieve the goal of separating systematic errors from roundness errors.Through the analysis of experimental data on 16 circular holes processed by CNC,it has been proven that this method can effectively separate roundness errors.