A novel convex hull method for optimum multi-point 5-axis tool positioning for machining of complex sculptured surfaces

The Point-In-Convex-Hull-Control (PICHC) method is presented for the calculation of the optimum tool orientation during the 5-axis simultaneous CNC machining of sculptured surfaces. More specifically, this novel exact multi-point algorithm minimizes the clearance and/or overclosure of the contact surface between the tool and the workpiece and maximizes the material removal rate. It can be used in sculptured surfaces, where conventional algorithms allow up to two points of tool-workpiece contact, leading to suboptimal material removal rate. The proposed method allows a third contact point which makes an ideal matching of the tool-workpiece surface and its application is validated both numerically and experimentally in two case studies that are published in the literature. In the first case study, the PICHC method is compared with an exact algorithm, whereas in the second case study, it is compared with an evolutionary optimization algorithm coupled with a commercial software. The numerical and experimental results, apart from being more accurate and less computationally demanding than other commercial software algorithms, prove the suitability, versatility, and robustness of the developed methodology, which can be extended to describe and control more advanced machining problems, either stand-alone or within an API.