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超精密磨削是加工复杂光学大镜的重要手段.复杂光学镜面的超精密磨削传统上采用五轴磨床,难以保证磨床很高的刚度和精度要求.少轴磨削方法减少了磨床轴数,提高了磨削系统的刚性,可以最大程度地减小机床磨削硬脆材料时的变形.但是少轴磨削时砂轮表面的磨削作用点不确定、且随工件表面曲率变化的特点增加了其几何学上的复杂性,并且对砂轮工作表面形状几何精度提出了更高的要求.本文针对少轴磨削时砂轮磨削点不确定的特点,对砂轮几何形状进行了参数化表征,从几何学的角度揭示了少轴磨削与五轴磨削之间的关联关系,建立了少轴磨削虚拟轴等效原理模型;提出了基于光学镜面几何性质、磨床特性、工艺要求的弧面砂轮几何参数与轴倾角的定量确定方法;基于曲面一点处Gauss曲率的性质,获得了三移动轴磨削方式下弧面砂轮磨损规律以及因磨损导致的镜面面形误差分布.最后通过仿真验证了以上原理与方法的正确性.
Ultra-precision grinding is an important tool for processing complex optical large mirror.Extra-precision grinding of complex optical mirror has traditionally used five-axis grinding machine, it is difficult to guarantee the high rigidity and precision of the grinding machine.Low-axis grinding method reduces the number of grinding machine axis , Which improves the rigidity of the grinding system and minimizes the deformation of the machine when grinding hard and brittle materials.But the grinding point of the grinding wheel surface is indefinite when the shaft grinding is small and increases with the curvature of the workpiece surface The geometrical complexity of the grinding wheel and the geometric precision of the working surface shape of the grinding wheel are put forward higher requirements.In this paper, the geometry of the grinding wheel is parameterized and characterized according to the indeterminate characteristics of the grinding wheel grinding point in the case of less shaft grinding, From the perspective of geometry, the correlation between the low-axis grinding and the five-axis grinding is revealed, and the equivalent principle model of the low-axis grinding virtual axis is established. The arc based on the geometry of the optical mirror, the characteristics of the grinding machine, Based on the properties of Gauss curvature at a point on the surface, the wear law of the surface grinding wheel under three moving axis grinding methods and the wear law of the surface grinding wheel due to the wear guide Induced mirror surface error distribution.At last, the correctness of the above principles and methods is verified by simulation.