A novel curvature circle iterative algorithm for contour error control of multi-axis CNC machine tools

High-precision real-time estimation of contouring errors is a prerequisite for contouring errors control of multi-axis CNC machine tools. This paper focuses on developing a nearest point projection curvature circle iterative (NPP–CCI) algorithm to achieve real-time estimation of multi-axis contouring errors. It is found that the traditional curvature circle iterative (CCI) method has two major shortcomings. The first is that the iterative process may terminate incorrectly at the local contour position, and the other is that the actual tool position and local curvature circle are not necessarily coplanar in three-dimensional space, which would lead to inaccurate calculation of the delay time parameter and eventually affect the estimation accuracy. In order to address the problem of false termination, an index method is used to find the closest reference position with respect to the actual position. At the same time, the projection technology is proposed to overcome the problem met in extending the planar curvature circle iterative method to the spatial applications. The proposed NPP-CCI algorithm is more suitable for spatial contouring errors estimation in tracking complex trajectories and has higher estimation accuracy than the traditional CCI algorithm. Various experiments with different tool paths are conducted on an in-house developed multi-axis experimental platform to verify the effectiveness of the proposed algorithm. The experimental results show that the NPP-CCI algorithm can estimate the contouring errors with higher accuracy than the traditional CCI algorithm, and with the help of real-time computation and compensation, the contouring errors are reduced by more than 44% in terms of the MAX and RMS values.