基于二维 Fourier 变换的平面形状误差分离新方法

New Method with 2 D Fourier Transform for Flat Form Error Separation

列出了四点法－三点法平面误差分离的测量方程，导出了这类方法所对应系统的传递函数Ｇ（ｋ，ｌ）的通式，指出Ｇ（０，０）＝０是平面形状误差赖以先行分离的先决条件．Ｇ（ｋ，ｌ）与多个位移传感器在空间的布点有关，而现有的直线三点法和矩形四点法都因布点不当而引起谐波损失．据此，提出了一种新的“不对称四点法”：被测工件安放在工作台上，四个位移传感器组合在一个测量架上以扫划工件表面和采集数据．只要这四个传感器布置在不对称四边形的各个端点上，且各点在ｘＯｙ平面上的坐标距离（以离散化了的采集点数表示）间各自互质，并分别与ｘ或ｙ轴上的总采样点数Ｎ或Ｍ互质，就可以确保Ｇ（ｋ，ｌ）中除了Ｇ（０，０）＝０外，任何阶谐波都不被抑制，实现平面度的不失真测量和分离．

The measurement equation of four point method and three point method flat form error separation is given. The unified transform function G(k,l) is deduced, and G(0,0) =0 is a prerequisite to separating flat form error. G(k,l) has a relation to the spatial position of sensors, but the present three point and four point methods cause harmonic losses because of the improper arrangement of sensors. Based on it, the paper proposes a new “asymmetrical four point method”:measured part is fixed on the moving table, four sensors are attached on a measurement frame to scan the surface and acquire error signal. If the four sensors are at each point of the asymmetrical quadrangle, and their coordinate distances at xy plane are prime with themselves and the total sample number N in x axis or M in y axis, it is certain that there will be no harmonic losses except that G (0,0)=0 and the measurement and separation of flat form error without distortion can be carried out.