中文摘要：

基于非球面最接近球面的计算方法分析,构建成型设备与工件间坐标变换矩阵,借鉴并优化材料去除量最小原则,计算最接近球面与理论非球面间的偏离量,建立数学模型.针对典型的圆形口径和矩形口径同轴、离轴非球面元件的比较球面求解进行仿真.结果表明,所建立的数值求解模型可有效计算同轴、离轴非球面元件的比较球面使材料去除量最小,对加工实践起到指导作用.

英文摘要：

Beginning with the principium of aspheric fabrication,the transformation matrix between equipment coordinate and work-piece coordinate is set up.Based on the principle of the least material removal,the material removal from the sphere to the aspheric shape is calculated and the mathematical model is established.The circular and rectangular aperture,the on-axis and off-axis aspheric components are simulated and compared,the results showed that the numerical solution model is effective for off-axis（on-axis） aspheric component,the material removal is minimum,and is thus capable to play a guiding role in processing.