Study on the Evaluation Methods of Circularity Errors in Three-dimensional Space
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摘要: 为解决三维空间中圆度误差的精确评定问题,针对三坐标测量机检测圆度误差时因存在测量误差而使各实际测点不是精确地位于同一理想截平面上的特点,根据计算几何学和误差理论,提出了基于空间测点集算术平均中心点的最小二乘平面拟合方法,推导了其数学模型;并对国家标准中圆度误差评定的最小外接圆法、最大内接圆法和最小区域圆法进行了三维扩展;还对前两种方法作了改进,建立了此3种方法的数学模型和算法流程。最后的数字实验表明:以上3种算法是有效的。Abstract: Aiming at the characteristic that actual measured points obtained from coordinate measuring machine(CMM) were not located on the same ideal plane precisely due to the existence of measurement errors,in order to improve the evaluation accuracy of circularity errors in three-dimensional space,the least squares plane based on the center point of arithmetic average of the measured points set(LSPBC) was proposed and the mathematical model was derived,according to computational geometry and errors theory.Then three circularity error evaluation methods with minimum circumscribed circle,maximum inscribed circle and minimum zone circle in the national standard were extended into the three-dimensional space.On the basis of them,the first two kinds of methods were improved; the mathematical models and evaluation steps of the three kinds of methods were built.Finally,the validity of proposed methods was verified through numerical experiments.
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Key words:
- computational geometry /
- estimation /
- feature extraction /
- mathematical models
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