New numerical algorithms to optimize cutting operations of a five-axis milling machine Original Research Article

Optimization of cutting operations is an active area of research in CNC-based manufacturing. The limited capabilities of the CAD/CAM systems require development of a new software and new numerical methods verified by practical machining. We formulate the problem of tool-path optimization in terms of interpolation of the required part surface in the curvilinear coordinate system associated with the cutter location points. Next, we present some introductory examples to demonstrate that the concept of adaptive curvilinear grid contains almost all the basic ingredients of tool-path planning, such as: adaptation to regions of large milling errors, conventional zigzag/spiral patterns and constraints related to the scallop height. Consequently, we propose a new grid based optimization procedure characterized by adaptation to a control function which depends on the rotations required to correctly position the tool. We also consider a particular but important optimization of the rotation angles near the stationary points based on the shortest path scheme. Finally, we present an application of the algorithms to tool-path planning and demonstrate the efficiency of the proposed scheme by methodological examples verified by practical machining.