MATHEMATICS AND APPLICATIONS OF THE APPROACH OF THE STEEPEST-ASCENDING TOOL PATH PLANNING

摘要

Due to the complex surface shape of sculptured parts, well-planned tool paths can significantly increase the efficiency in the CNC machining and the surface quality of these parts. The steepest-ascending tool path pattern of a sculptured surface has been proposed for its 3-axis CNC milling, and one tool path of this type has been proved to be more efficient than a single tool path of any other type. However, the mathematics of finding a steepest-ascending tool path was not provided in detail. In this work, the necessary mathematics for calculating a steepest-ascending tool path on NURBS surfaces is introduced. First the generic formula of the steepest tangent direction on a part surface is derived, and Newton's method to calculate the cutter contact point on the steepest-ascending tool path is introduced. Second a new gouging check algorithm is applied on the steepest-ascending tool paths of concave shaped surfaces to prevent over-cutting at the bottom. Then the procedure of planning steepest-ascending tool paths is described. Two example sculptured surfaces are used and the steepest-ascending tool paths are planned to verify the feasibility of the algorithm. Finally CATIA CAD/CAM system is used to plan tool paths for one of the sculptured surface and the surface is machined with the CATIA tool paths and the steepest ascending tool paths, respectively. The results are compared to demonstrate the advantages of the steepest-ascending tool paths.