Real-time Bezier interpolation satisfying chord error constraint for CNC tool path

Abstract

G01 code generated by a computer-aided manufacture (CAM) system is the most common form of tool trajectory in computer numerical control (CNC) machining. A tool path composed of short line segments has discontinuous tangency and curvature, generating large fluctuations of feedrate and acceleration, which in turn produces vibration in a machine tool. To obtain a smooth tool path, many methods on tool-path smoothing have been developed. However, the shortcomings in these methods exist when they are employed in a CNC system. It is difficult to simultaneously to guarantee the following requirements of CNC machining: (1) chord error should be rigidly constrained; (2) G01 points should be interpolated; (3) curvature should be continuous (G 2); (4) machining should be applicable to spatial cases; (5) real-time performance of computation is required. Based on these various requirements, this study proposes an interpolation scheme using cubic Bezier curves and includes an adjustment strategy to eliminate deficiencies in the tool path. The tool path generated is G 2, chord-error-constrained, G01-point-interpolated, loop-free, and optimized for both stretch and jerk energy. The method is applicable to 3D cases and involves only simple algebraic computations. Thus, the algorithm can be applied to real-time CNC machining. A simulation is conducted to validate the efficiency of the algorithm. In addition, an experiment reveals its advantage over Hermite interpolation in surface quality and machining efficiency.