The improvement of ultra-precision machining technology has significantly boosted the demand for the surface quality and surface accuracy of the workpieces to be machined. However, the geometric shapes of workpiece surfaces cannot be adequately manufactured with simple plane, cylindrical, or spherical surfaces because of their different applications in various fields. In this research, a method was proposed to generate tool paths for the machining of complex spherical surfaces based on an ultra-precise five-axis turning and milling machine with a C-Y-Z-X-B structure. Through the proposed tool path generation method, ultra-precise complex spherical surface machining was achieved. First, the complex spherical surface model was modeled and calculated, and then it was combined with the designed model to generate the tool path. Then the tool paths were generated with a numerically controlled (NC) program. Based on an ultra-precision three-coordinate measuring instrument and a white light interferometer, the machining accuracy of a workpiece surface was characterized, and the effectiveness of the tool path generation method was verified. The surface roughness of the machined workpiece was less than 90 nm. Furthermore, the surface roughness within the spherical region appeared to be less than 30 nm. The presented tool path generation method in this research produced ultra-precision spherical complex surfaces. The method could be applied to complex spherical surfaces with other characteristics.

超精密加工技术的进步显着提高了对被加工工件的表面质量和表面精度的要求。然而，由于它们在各个领域的不同应用，工件表面的几何形状不能用简单的平面、圆柱或球面充分制造。在这项研究中，提出了一种基于CYZXB结构的超精密五轴车铣床加工复杂球面的刀具路径生成方法。通过提出的刀具路径生成方法，实现了超精密复杂球面加工。首先对复杂球面模型进行建模和计算，然后结合设计的模型生成刀具路径。然后使用数控 (NC) 程序生成刀具路径。基于超精密三坐标测量仪和白光干涉仪，表征了工件表面的加工精度，验证了刀具路径生成方法的有效性。加工工件的表面粗糙度小于90nm。此外，球形区域内的表面粗糙度似乎小于 30 nm。本研究中提出的刀具路径生成方法产生了超精密球面复杂表面。该方法可以应用于具有其他特性的复杂球面。表征了工件表面的加工精度，验证了刀具路径生成方法的有效性。加工工件的表面粗糙度小于90nm。此外，球形区域内的表面粗糙度似乎小于 30 nm。本研究中提出的刀具路径生成方法产生了超精密球面复杂表面。该方法可以应用于具有其他特性的复杂球面。表征了工件表面的加工精度，验证了刀具路径生成方法的有效性。加工工件的表面粗糙度小于90nm。此外，球形区域内的表面粗糙度似乎小于 30 nm。本研究中提出的刀具路径生成方法产生了超精密球面复杂表面。该方法可以应用于具有其他特性的复杂球面。本研究中提出的刀具路径生成方法产生了超精密球面复杂表面。该方法可以应用于具有其他特性的复杂球面。本研究中提出的刀具路径生成方法产生了超精密球面复杂表面。该方法可以应用于具有其他特性的复杂球面。