Real-time exact contour error calculation of NURBS tool path for contour control

The requirement of high-speed and high-precision contouring with NURBS tool path to the CNC machining process is increasing. The calculation of the contouring error (CE) of the NURBS tool path to real time is necessary for the advanced contour control like the cross-coupled controller (CCC). Based on the complexity of the CE calculation of NURBS, most studies use estimating methods to approximate the real CE in the controller. However, when the cutter is at the large curvature zones in the high-speed machining, the difference between the estimated the CE and the real one becomes large. To solve this problem, an algorithm to calculate the exact CE of NURBS tool path to real time is proposed. The calculation model of the CE of NURBS is derived. Also, the numerical calculation algorithm from Brent’s method is given to solve the CE model. Multiple solutions of CE model is discussed and real-time solution tracking method is developed to determine the intervals of the candidate solutions for numerical calculation. Contour error for control (CCE) is proposed for controller design to improve the stability of contour control, which is different from the definition of conventional control error for measurement (MCE). The proposed algorithm is validated for both the simulation and the experiment on the X–Y table. Experimental results show the effectiveness of the proposed algorithm and the actual CE is reduced significantly compared with other methods.