基于等矩策略的自由曲面测量方法误差分析

Analysis of Measurement Method Error in Freeform Surface Based on Equal Moment Strategy

针对数字化测量环境中自由曲面测量点的分布问题,首先提出了2点要求:曲率自适应性和分段点之间保持间距.据此提出一类曲率自适应度可控的布点策略,称之为等矩法布点策略.这种策略是指任意相邻3个分段点组成的曲线段中,其左右两曲线段对中间分段点的质量矩大小相等.等矩法的矩次越高,曲率自适应度越小.最后通过2个算例,分析了等矩法的曲率自适应度与测量方法误差之间的关系.以正弦函数为算例,通过计算得出:当采用等4.5次矩布点时,测量方法误差取到最小;另以样条曲线为算例,计算得出满足最小测量方法误差的布点策略为均布.

In order to distribute measurement points in freeform surface in digital measurement environment,two requirements were put forward：being adaptiveness to curvature and keeping spacing between points.A new class of distribution strategies with controllable curvature adaptability was proposed accordingly,which is called equal mo-ment methods.It means that,in a curve segment composed of any adjacent three points,its left part and its right part have an equal mass moment to the intermediate point.The higher order the equal moment method has,the lower its curvature adaptability is.Finally,through two examples,the relationship between curvature adaptability and meas-urement method error was analyzed.In the case of sine function,it was obtained by numerical calculations that, when 4.5th equal moment method was chosen in this strategy,the error of measurement method reached the mini-mum.Taking a spline curve as an example,the calculation results showed that,the distribution strategy meetingthe minimum measurement method error was uniform distribution.