Spiral Tool Path Generation Method on Mesh Surfaces Guided by Radial Curves

This paper presents a new spiral smoothing method to generate smooth curved tool paths directly on mesh surfaces. Spiral tool paths are preferable for computer numerical control (CNC) milling, especially for high-speed machining. At present, most spiral tool path generation methods aim mainly for pocketing, and a few methods for machining complex surface also suffer from some inherent problems, such as selection of projecting direction, preprocessing of complex offset contours, easily affected by the mesh or mesh deformation. To address the limitations, a new spiral tool path method is proposed, in which the radial curves play a key role as the guiding curves for spiral tool path generation. The radial curve is defined as one on the mesh surface that connects smoothly one point on the mesh surface and its boundary. To reduce the complexity of constructing the radial curves directly on the mesh surface, the mesh surface is first mapped onto a circular region. In this region, the radial lines, starting from the center, are planned and then mapped inversely onto the mesh surface, thereby forming the desired radial curves. By traversing these radial curves using the proposed linear interpolation method, a polyline spiral is generated, and then, the unfavorable overcuts and undercuts are identified and eliminated by supplementing additional spiral points. Spline-based technique of rounding the corners is also discussed to smooth the polyline spiral, thereby obtaining a smooth continuous spiral tool path. This method is able to not only greatly simplify the construction of radial curves and spiral tool path but also to have the ability of processing and smoothing complex surfaces. Experimental results are presented to validate the proposed method.