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能否在元件铣磨成形阶段制造出与要求非球面元件最为接近的球面是确保实现对大口径离轴非球面元件快速制造的关键一步。该文研究在同轴圆形非球面元件最接近球面半径确定方法的基础上,建立了离轴非球面元件坐标系与机床加工坐标系之间的变换矩阵,并以非球面与比较球面之间残余矢高作为评判参量,分别构建了材料去除量为正准则和材料去除余量最小准则的判断方法。最后以一块770mm×220mm的矩形离轴非球面反射镜为实例进行了模拟分析,确定了其最接近球面半径,通过实验发现加工去除余量大大减少,提高了制造效率,缩短了周期。
The ability to create the closest spherical surface to an aspherical element during component milling is a crucial step in ensuring fast fabrication of large diameter off-axis aspheric elements. In this paper, based on the method of determining the closest spherical radius of a coaxial circular aspheric element, a transformation matrix between the coordinate system of the off-axis aspheric element and the coordinate system of machining is established, and the relationship between the aspheric surface and the spherical surface Residual height as a judge parameter, respectively, to build a material removal of positive criteria and material removal margin of the minimum criteria for judging. Finally, a 770mm × 220mm rectangular off-axis aspherical mirror was taken as an example to simulate and analyze, the closest spherical radius was determined, and the machining removal margin was greatly reduced by experiment, which improved the manufacturing efficiency and shortened the cycle.