一阶不连续光学元件的磁流变抛光问题是制约我国高精高效光学制造领域发展的难题之一, 其涉及锥形、矩形等几何形貌元件的光学元件加工问题以及常见光学元件的边缘效应控制问题。提出了基于一阶不连续光学元件的磁流变抛光流体动力学方法, 建立了该类元件抛光区域流体动力分析的理论方法和数值手段。首先, 对磁流变抛光工况下的流场进行了合理假设, 其次, 从微元流体动力方程出发, 建立了适用于一阶不连续面形的流场分析方法, 最后, 基于有限差分法和数值迭代方法建立了流场控制方程的数值计算方法。通过对切入距离为1~18 mm的抛光过程进行数值仿真, 发现该方法所获取的一阶不连续面形的压力分布形态是正确的, 产生的不连续压降与实验观测一致。

Magnetorheological finishing of first-order discontinuous optical elements is one of the difficult problems that restrict the development of high-precision and high-efficiency optical manufacturing in China. In this paper, a fluid dynamics analysis method for magnetorheological finishing concerning the first order discontinuous optical elements is presented. Firstly, reasonable assumptions are made for the flow field under the practical condition of magnetorheological finishing. Secondly, based on the micro-element hydrodynamic equation, a flow field analysis method suitable for the first order discontinuous surface shape is established. Finally, a numerical calculation method for the flow field governing equation is established based on the finite difference method and numerical iteration method. Through numerical simulation for cutting distance ranging over 1~18 mm, it is found that the pressure distribution pattern of the first-order discontinuous surface obtained by the proposed method is correct, and the discontinuous pressure drop generated by the proposed method is consistent with that of the experimental observation.