Real-time arc length parameter-based integrated control strategy of contour error compensation for free-form curve CNC machining

The contour following task of a multi-axis servo system is one of the most important applications of modern computer numerical control (CNC) machining. Reducing the contour error is an important content in the multi-axis contour following task. A common method to solve this problem is the cross-coupling control (CCC). Since the traditional CCC method cannot meet the requirements of tracking accuracy and contour control accuracy at large curvature positions in free-form curve machining, the main contribution of this paper is to propose a novel integrated control strategy based on arc length parameters for contour error compensation, which consists of a double-circle weighted approximation contour error estimation model based on arc length parameters module, an improved cross-coupling position command shaping controller (CPCSC) module, and an improved position error compensator (PEC) module. To improve the accuracy of contour error estimation for large free-form curvature trajectories, a double-circle weighted approximation contour error estimation model based on arc length parameters is proposed. The method first finds the nearest interpolation point by backtracking method and calculates the backward reference points by using the method based on arc length parameters. Then, the obtained backward reference points are used as the expected instruction points by the double-circle weighted approximation method, and the estimated value of contour error is calculated. Moreover, an improved structure of CPCSC is proposed. Compared with the traditional biaxial CCC structure, the advantage of this new structure is that the compensator design and stability analysis in its CCC are relatively simple, and it can be easily implemented on most current systems by reprogramming the reference position command subroutine. In addition, an improved PEC method is further proposed to reduce contour error. The main advantage of this module is that it can simultaneously improve tracking and contouring performances by compensating position errors in advance. The feasibility of the proposed integrated control strategy is verified by serval non-uniform rational B-spline (NURBS) parametric curve contour following experiments. Moreover, the results of comparative experiments indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy of biaxial contour following tasks compared with none-CCC method and CCC method, and has better contour control performance in large curvature positions.