三维空间圆度误差高精度评定算法与编程

High Precision Evaluation Algorithm and Programming on Roundness Error of Three-dimensional Space

在获得高精度基准平面的前提下,三维空间圆度误差评定的另一个关键问题,是如何利用被测圆在基准上的投影,把三维空间问题转化为二维平面问题,对投影点进行平面圆度误差评定。算法以特殊三角形的外角平分线为研究方向,逐步把同心圆的半径之差降下来,令圆度误差计算收敛于真值,算法具备"最小包容区域法"特征,过程与结果均符合"最小条件"原则。算例验证结果表明,经过高精度的基准平面拟合,与符合"最小条件"原则的平面圆度误差计算,所获得的终值为高精度的三维空间圆度误差值。

After receiving the accurate reference plane, evaluating roundness error of the three-dimensional space is a key issue, which uses the projection in the benchmark of measured circle, and turns it from the three-dimen- sional space to a two-dimensional plane. The algorithm makes a research on the angle bisector direction of special triangle exterior angle, decreases the radius of the concentric circles, and makes its error reach the real value, such algorithm has the minimum zone feature, complies with the minimum conditions principle. The fitting of ref- erence plane and roundness error calculation can both verify the conclusion.