Positioning method of a cylindrical cutter for ruled surface machining based on minimizing one-sided Hausdorff distance

Motivated by the definition of the machining errors induced by tool path planning methods, a mapping curve of the tool axis of a cylindrical cutter is constructed on the tool surface. The mapping curve is a typical one that can be used to express the closeness between the tool surface and the surface to be machined. A novel tool path planning method is proposed for flank or plunge milling ruled surfaces based on the minimization of the one-sided Hausdorff distance (HD) from the mapping curve to the surface to be machined. It is a nonlinear optimization problem in best uniform approximation (BUA) or Chebyshev sense. A mathematical programming model for computing the minimum one-sided HD is proposed. The linearization method of the programming model is provided and the final optimal solutions are obtained by simplex method. The effectiveness of the proposed BUA method is verified by two numerical examples and compared with the least squares (LS) and double point offset (DPO) methods. The variation in tool orientation induced by the optimization of the tool positions is also evaluated.