Asymmetrical transition-based corner rounding method driven by overlap elimination for CNC machining of short-segmented tool path

Abstract

For realizing the continuous and stable motions of computer numerical control (CNC) machine tools, the linear motion commands (G01) have to be smoothed at the corners. Most of methods, which employ the symmetrical spline curves to round the corners, avoid the potential overlaps between the adjacent spline transition curves by imposing excessive constraints on the transition lengths or by reducing proportionally their approximation error to the corners. However, these methods will force the transition curves to over-approach the corners, thus failing to increase fully the feedrate at the corners. For solving this problem, an asymmetrical transition-based corner rounding method driven by overlap elimination is proposed to achieve the smoothness of short-segmented tool path. In this method, the effect of geometry of tool path on transition overlaps is first analyzed by means of an unconstrained pre-cornering transition model. Then, the overlaps are identified and classified according to the transition lengths and their positions on the linear segment, and the eliminating strategy for each type of overlap, which adjusts independently the transition lengths on both sides of the corner, is discussed in detail. On the basis of this, an asymmetrical spline transition curve is constructed, which can round the corners with curvature as small as possible within the specified approximation error, thereby increasing fully the feedrate at the corners. Finally, the computer simulations and machining experiment are both conducted to validate the proposed method in increasing the feedrate at the corners and shortening the machining time.