基于磨削工艺参数的大口径非球面轮廓测量及误差映射关系研究

Aspheric profile with a aperture of larger than 600mm could not be measured using optical method during grinding stage, and the CMM measurement and profile measurement is not applicable due to the measuring accuracy and aperture restriction. In order to solve the profile error compensation problem during grinding stage, error analysis, optimization method and simulation analysis were adopted, and the large aperture three-dimension (3D) profile measurement and error mapping relationship will be studied based on the grinding parameters. According to the grinding parameters, self-adaptive sampling method will be proposed to obtain the optimal sampling numbers and distribution based on the established error distribution and sampling functions. Combing with the in-situation position and gesture correction, mathematical model of 3D profile error evaluation will be established, as well as the optimization algorithms. To improve the aspheric grinding compensation accuracy, according to the path planning during the grinding stage, the profile error will be averaged and dispersed, and the off-line measurement error and compensation path mapping relationship will be proposed. The study will provide the theoretical foundation for the large aspheric profile error measurement during the grinding stage, and it would be quite meaningful to the connection of the off-line measurement and grinding error compensation.

口径大于600mm非球面轮廓无法在铣磨阶段采用光学方式测量，而三坐标测量和轮廓测量方法由于受测量精度和口径问题的制约已不能满足需求。本项目针对铣磨阶段的轮廓误差补偿问题，采用误差分析、优化算法和仿真分析的方法，研究基于磨削工艺参数的大口径非球面三维轮廓测量及误差映射关系。基于磨削工艺参数，根据构建的误差分布和采样函数，提出以最佳采样点数分布规律为目标的自适应采样方法；在位姿误差校正基础上，建立三维轮廓误差评定的数学模型并进行优化算法研究；以提高非球面磨削补偿精度为导向，针对磨削过程中的路径规划方案，对轮廓误差进行均化和离散处理，研究离线测量误差与补偿路径的映射关系。项目研究成果将为大口径非球面铣磨阶段的轮廓误差测量提供理论基础，同时实现了离线测量与磨削误差补偿的关联，具有较重要的科学研究意义和实用价值。

大口径非球面光学元件具有优越的光学特性，在激光聚变、天文对地观测和光刻机系统中扮演了极其重要的角色，其制造精度要求越来越高，需求越来越大。由于大口径非球面制造工艺流程复杂，特别是磨削阶段的加工精度和效率尤为关键。根据磨削阶段大口径非球面加工的工艺参数，针对离线大口径非球面测量和路径规划进行了理论和实验研究。首先对磨削阶段的非球面测量方案进行了总结，针对非球面镜进行了磨削和离线测量实验，通过位姿误差校正，建立了三维轮廓误差评定的数学模型，对非球面磨削轮廓的三维轮廓误差进行了计算和测量比较。其次，根据测量数据采样方案和评定方法，对离线大口径非球面轮廓测量技术进行了深入研究，根据现有测量路径规划方案，包括子午线扫描、光栅式扫描、圆周等角度扫描方案进行分析，并建立三维轮廓误差评定的数学模型，根据位姿误差校正后的数据进行三维轮廓误差的评定，采用非线性最小二乘算法对未知参量计算，评定结果表明所建立的模型可靠。最后根据NURBS插补方案，对离轴非球面的路径规划和测量理论进行了研究，并进行了理论分析和仿真。通过非线性最小二乘法对偏心和倾斜误差进行计算，对测量数据进行误差校正后明显提高了测量的精度。对三维误差评定和映射关系的磨削工艺进行研究，大大提升了大口径非球面镜的磨削阶段的加工效率和精度，为高精度、高效率和大批量非球面镜的制造提供了理论和实验参考，具有较重要的科学研究意义和实用价值。