论文部分内容阅读
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 equations of the four-point-three-point plane error separation are listed. The general formula of the transfer function G (k, l) of the system corresponding to this kind of method is derived. It is pointed out that G (0,0) = 0 is the planar shape The preconditions for error to be separated first. G (k, l) is related to the placement of multiple displacement sensors in space, while the existing linear three-point method and rectangular four-point method all cause harmonic loss due to improper placement. Accordingly, a new “asymmetric four-point method” is proposed: the workpiece under test is placed on a worktable, four displacement sensors are combined on a measuring rack to scan the workpiece surface and collect data. As long as the four sensors are arranged at the respective end points of the asymmetric quadrilateral and the coordinate distances of the points on the xOy plane (represented by the discretized collection points) are each coprime and are respectively equal to the total on the x or y axis Sampling points N or M can be used to ensure that any harmonic in G (k, l) except G (0,0) = 0 is not suppressed, so that flatness can be measured and separated without distortion.