大口径非球面加工中最接近参考球面的精确计算

摆臂轮廓测量技术要求将摆臂精准的装调至待检测非球面的最接近参考球面上，需要精确确定非球面的最接近参考球半径及球心位置，而常规的近似法、精确公式法以及最小二乘法不能满足计算的精度和效率等要求。为了弥补现有算法的不足，文章介绍了一种分阶段逼近最接近参考球半径的计算方法，该算法在最小二乘法的基础上，通过精确线搜索技术以及牛顿迭代法，实现了最接近参考球半径求解的高精度、高效率，并且应用于大口径非球面计算时迭代效率有了较大提高。计算实例结果显示，该算法满足摆臂测量时大口径非球面的最接近参考球半径的求解要求。

Accurate Calculation of the Best-fit Reference Spherical Surface in Large Diameter Aspheric Machining

The swing arm profile measurement technology requires the swing arm to be precisely mounted to the best-fit reference sphere of the aspheric surface to be detected, and the best-fit reference sphere radius and sphere center position of the aspheric surface need to be accurately determined, while the conventional approximation method, the exact formula method and the least squares method cannot satisfy the requirements of calculation accuracy and efficiency. In order to make up for the deficiencies of existing algorithms, the paper introduces a calculation method for approximating the best-fit reference spherical radius in stages. The algorithm achieves high accuracy and efficiency in the solution of the best-fit reference spherical radius based on the least squares method, the exact line search technique and the Newtonian iteration method, and the iteration efficiency is greatly improved when applied to the calculation of large-aperture aspheres. The results of the calculation example show that the algorithm satisfies the requirement of solving for the best-fit reference sphere radius for large-aperture aspheric surfaces during swing-arm measurements.