Study of ultra-precision turning path calculation of freeform surface with free contours

Ultra-precision turning technology (UPT) plays a critical role in optical freeform surface manufacturing. There are researches focusing on solving problems of UPT tool path generation of freeform surfaces, but most of them are regardless of surface boundary contours. It is not convenient to generate path to machine complex structural parts with more surfaces simultaneously if boundary contours are ignored. To further improve UPT machining capacity, in our study, how to solve the UPT path generation problem about freeform surface with free boundary contours, which is called double free face (DFF), is focused. The Archimedean spiral is generated and discrete to driving point sequence, which is similar to the previous studies. Innovative contents are described as below. First, data structure of DFF topology is proposed, which contains expressions of the surfaces and boundary contours. And then, the surface projection and boundary wire projection algorithms are designed to calculate the projected tool location point. When the projected point is a tangential contact to the surface, this point is cutting point, and when the tool is projected to the contour wire or not projected to any geometry element, the point is not cutting point. How to judge whether the projected point is inside the face or outside is introduced. Third, the transition path is calculated by interpolating the two adjacent cutting paths using iterative cubic spline interpolation method to ensure enough movement smoothness. Finally, tool paths of case DFFs are generated and machined to verify the effectiveness of this proposed UPT path generation strategy.