评定二次曲面轮廓度误差的角度分割逼近法

提出一种基于角度分割逼近算法和粒子群算法计算二次曲面轮廓度误差的最小区域评定方法来准确评定任意位姿的二次曲面轮廓度误差。首先，给出了能够实现角度分割逼近算法的两条前提假设；基于假设，给出了更合理的算法网格布局递推公式。根据曲面轮廓度误差的定义建立了误差评定的精确模型。然后，采用角度分割逼近法求取测点到拟合二次曲面轮廓的距离；通过粒子群算法，以所有的点与二次曲面距离中的最大值为适应度值拟合出二次曲面一般方程，并实现被测轮廓与理论轮廓位置的匹配。最后，采用上述方法对某抛物面天线进行了评定，并与参数分割法、SMX-Insight和最小二乘法进行比较。实验结果显示：该方法测得的天线轮廓度误差为0.659 8 mm，比其它方法准确。结论表明：基于角度分割算法能够更有效地评定任意位姿二次曲面轮廓度误差，计算准确、迅速，而且无需确定待分割区域。

Angle subdivision approach algorithm for conicoid profile error evaluation

A method based on angle subdivision approach algorithm and Particle Swarm Optimization (PSO) was proposed to evaluate concicoid profile error accurately in any position and orientation with the requirement of the minimal zone。 Two hypotheses were proposed to realize the angle subdivision approach algorithm. According to the hypotheses, a recursion formula for more reasonable girdding was given. Then, an accurate evaluating model was established according to the definition of conicoid profile error. The angle subdivision approach algorithm was adopted to calculate the distance between measurement points and fitting quadric surface. The position between measured profile and theoretical profile was matched through fitting the general quadric surface equation. A paraboloid antenna was evaluated by the above method in an experiment, and the results were compared with those of parameter subdivision approach algorithm, SMX-Insight and Least Square Method (LSM). Experimental results indicate that the profile error is 0.659 8 mm more accurate than that of other methods. The results show that angle subdivision approach algorithm is more efficient in concicoid profile error evaluation and its calculation is accurate, rapid, and no need to find the division area.