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Geometric Approximation Technique for Minimum Zone Sphericity Error

机译：最小区域球形度误差的几何近似技术

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摘要

The mathematical modeling for evaluation of the sphericity error is proposed with minimum radial separation center. To obtain the minimum sphericity error from the form data, a geometric approximation technique was devised. The technique regarded the least square sphere center as the initial center of the concentric spheres containing all measurement points,and then the center was moved gradually to reduce the radial separation till the minimum radial separation center was got where the constructed concentric spheres conformed to the minimum zone condition. The method was modeled firstly then the geometric approximation process was analyzed and finally the software for data processing was programmed. As evaluation example five steel balls were measured and the measurement data were processed with the developed program. The average iteration times of the approximation technique is 4. 2, and on average the obtained sphericity error is 0. 529 mm smaller than the least square solution, with accuracy increased by 7.696 percent.
机译：提出了具有最小径向分离中心的球形度误差评估数学模型。为了从形状数据中获得最小的球形误差，设计了一种几何近似技术。该技术将最小的正方形球心作为包含所有测量点的同心球的初始中心，然后逐渐移动中心以减小径向间距，直到达到最小径向间距中心为止，其中所构造的同心球符合最小值区域条件。首先对该方法进行建模，然后对几何近似过程进行分析，最后对数据处理软件进行编程。作为评估例，测量了五个钢球，并使用开发的程序处理了测量数据。近似技术的平均迭代时间为4、2。平均获得的球度误差比最小二乘解小0. 529 mm，精度提高了7.696％。

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