累积法圆和球拟合及在形状误差评定中的应用

Fitting Circle and Sphere Based on Cumulative-Sum-Methodand Application in Form Error Assessment

针对圆度和球度误差评定中常用方法不符合国标定义或计算复杂的问题,根据普通累积法的优点,提出了运用普通累积法拟合理想圆和球,进行圆度和球度的评定.根据理想要素拟合过程中待求未知量的个数,运用变量代换,将非线性超定方程组转化为线性超定方程组;对变换后的超定线性方程组施加累积算子,进行未知数求解;最后用仿真实例进行了分析,并与CIRP方法进行比较.结果表明,累积法拟合圆和球具有较高的精度,切实可行,是形位误差评定中求解理想要素值得借鉴的方法.

The commonly methods to adopt in roundness and sphericity assessment always have the property of complicate computation or are out of specification in national standards. Based on the advantages of Cumulative-Sum-Method, the paper proposes to compute the ideal circle and sphere, and assess roundness and sphericity. According to the number of unknown variables in ideal element fitting, variable substitution is adopted to convert the overdetermined nonlinear equations into overdetermined linear equations. Cumulative sum operator is used to solve the overdetermined linear equations. Finally, compared with CIRP method, a simulating example is discussed. The result shows that the method has high computing precision, an excellent means and a bright future in form error assessment.