The Tool-path Planning For High Speed Machining Of Vector Chinese Character In Planar Domain

In engineering field, the engraving of Chinese characters, letters or other figures on workpiece or mould is often encountered. Regarding vector Chinese characters in planar domain as the research subject, the paper has studied the tool-path planning for high speed machining (HSM). The engraving of vector Chinese characters in planar domain is actually pocket machining but slightly different. Since the contours are generally slender and closed domain, traditional approaches like direction-parallel and contour-parallel can only generate C~0 continuous tool-paths, which do not meet the requirements of HSM.The paper obtains the data points of vector Chinese characters' contours by invoking API functions in Windows, then adds some necessary data points as required, fits the new data points with cubic B-spline so as to uniformise the representation of contour curves, which avoids the difficulty of dealing with curves and straight lines simultaneously. On the basis, the points with locally maximal positive curvature of closed B-spline are found through ergodic algorithm, which solves the initial value problem of tracing algorithm and iteration algorithm in this paper.For the domain with curved boundary, its medial axis (MA) is non-rational and the exact computation for medial axis transform (MAT) is very difficult due to the calculational complexity of bisectors among free curves. The recent algorithms mostly approximate the curved boundary by straight line segments or arcs in a given tolerance, and invoke the mature algorithms of curvilinear polygon. The relations of position mapping between medial axis and boundary curves, and the tracing algorithm for MAT have been studied. On that basis, the paper introduces a new iteration algorithm, of which the core idea is as follows, the iterating procedure originates at a convex vertex, and then locates the next point on one edge by the given step size and finds the corresponding point on another edge by applying relations of position mapping, thereby obtains the medial axis point by computing the intersection of normals to the two edges at the two points and checking against curvature criterion. Both algorithms adopt exact representation of free curve boundary without discretization, avoiding the wrong topological result.According to the characteristics of MA, there is a unique MAT for a boundary curve and the boundary curve can be reconstructed by its MAT uniquely. For a profile in planar domain, a tool-path with C~1 continuity can be generated by connecting successive medial axis transform circles (MATCs) using external common tangents. The tool-path keeps the cutter moves in a circle in milling process, which is favourable to increase the speed. And due to the minima] difference of radius between two successive MATCs, the change of radial accelerations is also minimized. Therefore, the tool-path is specially suitable for the high speed CNC machining.For arbitrary C continuous closed contour of vector Chinese character, this paper computes all the MATCs with the above iteration algorithm under a given step size, and designs an algorithm to compute the external common tangent lines of two successive circles, thereby generates a C~1 continuous tool-path for HSM (leaving out the cutter radius). Finally, model of geometrical residual errors is established, the maximal geometrical residual error under the given step size is analyzed, thereby one can control the step size through permissible error.