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Optimum Tool Path Generation for CNC Machining of Concave Sculptured Surfaces

To create a N/C program of a sculptured surface by using a commercially available CAD/CAM system, one problem encountered is to select a proper ball nose tool size. A smaller size allows access to any concave regions but requires a larger number of cuts. While a larger size runs the danger of undercutting the regions where the radius of curvature of the cutter path is less than the tool radius. In practice a cutter is often chosen by rule of thumb first and readjusted after production and inspection. This paper describes a new procedure by which a proper size of a ball nose cutter can be chosen for a given surface and allowable scallop height before production. Once a surface patch database which represents the geometry of a sculptured surface is generated, a tool size and allowable scallop height are specified. Based on that, a tool path is automatically generated. The curvatures of the path are calculated and the minimum value of curvatures is found. The tool radius is reselected until it is close enough to the minimum value, such that access to any concave regions can be guaranteed while a higher productivity can be achieved. An example involving the die design of a crane hook by a commercial CAD/CAM package, Graftek{TM}, is presented.