Analysis and synthesis of multi-axis sculptured surface machining

New 5-axis tool positioning and orientation algorithms are presented that apply differential geometry techniques to match curvatures between the cutting tool and local machined surface regions. Both the instantaneous and swept silhouette contact between standard end milling cutters and parametric and implicit surfaces are studied. These algorithms eliminate local gouging errors and improve the efficiency of the finish surface machining process. Methods for computing adjacent tool passes that reduce or eliminate the subsequent grinding of sculptured surfaces are also discussed. Gouging, the most difficult machining problem to correct once it has physically occurred, has traditionally been examined after the entire tool path has been programmed. Polynomial resultants, the determinants of the coefficients of systems of n equations in n variables, are used to resolve the intersection conditions between a positioned and oriented cutting tool and the lower offset tolerance bound of the design surface. With both the current tool position and the next tool position determined so that positional gouging is avoided, this work then discusses methods for checking the gouge conditions of the swept tool between these positions. Traditional methods for machining surfaces are reviewed and analyzed as a basis for comparison. Examples demonstrate the significance of applying this work to concave geometries. These methods are not restricted to 4- and 5-axis machining but can also be applied to the programming of robotic grinders