一种复杂二次曲面轮廓度评定方法

A Method for Evaluating Complicated Conicoid Profile Error

为了建立复杂二次曲面轮廓度评定中计算机数据处理的理论模型和实现方法,提出了一种不要求满足小误差假设、不使用微分线形化评定二次曲面轮廓度的方法。该方法首先通过最小二乘法得到一个初始二次曲面,然后用模式搜索对初始二次曲面系数进行调整,直到找到满足最小区域原则的理想二次曲面,其目标函数值作为被测曲面的轮廓度。在计算过程中使用坐标变换将一般型的二次曲面化为标准型,既简化了轮廓度的计算,而且被测曲面可以在测量范围内任意放置。对抛物面轮廓度评定表明目标函数随着模式搜索的进行逐渐减小,模式搜索得到的抛物面轮廓度值比用最小二乘法得到的轮廓度值小得多,因此该方法更好地反映了被测二次曲面表面形状误差。

In order to establish the theoretical model of data processing in profile error evaluation of sophisticated conicoid, an profile error evaluation method, which does not need to meet the small error hypothesis and does not use differential linearization, is presented. Firstly an initial conicoid is acquired through least squares method. Then pattern search is used to adjust the parameters of initial conicoid to find out the ideal conicoid conforming to the minimum zone principle. The profile error of the ideal conicoid is regarded as the final profile error of measured surface. In the calculation process, coordinate transform is used to convert the conicoid function from the general form to the standard form, which not only simplify the profile error calculation, but also allow the measured surface to be placed at any position and angle in the measurement space. The profile error evaluation of paraboloid indicates that the objective function becomes smaller in pattern search, and the value of paraboloid profile error is much smaller than that acquired through least squares method. Compared with the least squares method, this method better reflects the conicoid surface profile error.