Toolpath generation for ultraprecision machining: Freeform surface generation and extrapolation

The rise in complexity of freeform optics drives the development of equally complex manufacturing processes needed to produce them. Complex optical designs, however, require equally complex machining toolpaths and techniques that can generate them. This paper and subsequent research develops and investigates toolpath generation techniques for explicitly defined surfaces of the form Z(X,Y). A generalized approach is developed for the toolpath generation of optical surfaces themselves as well as techniques for transitioning between surfaces in an array. All surfaces herein are continuous, well-behaved, and differentiable - constraints satisfied by most optical prescriptions today. The current paper describes the toolpath generation and extrapolation process for a tilted freeform surface defined inside a non-circular boundary. Boundaries are defined so that some nonconvexity is acceptable, and it is simple to determine whether a toolpath coordinate lies inside or outside them. Using the proposed coordinate frame transformation and boundary definition, it is shown that by tilting a surface and boundary together, the tilted surface retains its original form and boundary in a rotated coordinate frame. With the proposed extrapolating surface, it is possible to modify a freeform surface outside its defined boundary so it is smooth and well-behaved inside its overall region of interest - an important consideration for both toolpath generation and opto-mechanical design. By combining freeform and extrapolating surfaces together, a smooth piecewise surface is generated whose overall continuity increases as the order of the extrapolating surface increases. As a result, it is possible to increase the overall continuity of a toolpath along its cutting direction. To verify the utility of the proposed extrapolating surface, experimental data are presented for several spiral toolpaths generated for a 6th order polynomial surface prescription defined inside a rectangular boundary. Subsequent research, using the techniques herein as a starting point, develop and investigate blending multiple freeform surfaces together.

Automated summary

The complexity of freeform optics drives the complexity of manufacturing processes. This paper develops toolpath generation techniques for specified surfaces and explores the transition between surfaces. The proposed extrapolating surface can modify a freeform surface outside its defined boundary to increase overall continuity of the toolpath.