Optimising tool positioning for achieving multi-point contact based on symmetrical error distribution curve in sculptured surface machining

The multi-point tool positioning algorithms produce much larger machining strip width than the single-point algorithms and apparently reduce the actual machining time. This paper presents a tool positioning algorithm for multi-point machining of sculptured surface, which is excellent at dealing with both of concave and convex surfaces. The proposed method is based on the middle-point error control (MPEC) method, which means the connection point between cutter and surface corresponds to the middle point of error distribution curve. Usually, only one cut contact (CC) point can be obtained with this method. Thus, the proposed method improved the MPEC method for achieving two CC points. At first, the shape of error distribution curve is investigated, and its asymmetry is evaluated. Secondly, the error distribution curve becomes symmetrical after the cutter is rotated with a roll angle, and the cutter is separated with surface at the same time. Finally, the minimum tilt angle is found, and two CC points are obtained without gouging. Machining experiment is conducted to verify the proposed method, and the result reveals that the machining strip width is increased apparently and the tool position is almost unchanged after the adjustment with proposed method. Simulation, measurement, and analysis are also given in the part of the experiment.