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.

高精度实时估计轮廓误差是控制多轴CNC机床轮廓误差的先决条件。本文着重于开发一种最近点投影曲率圆迭代（NPP–CCI）算法，以实现多轴轮廓误差的实时估计。发现传统的曲率圆迭代法（CCI）有两个主要缺点。第一个是迭代过程可能会在局部轮廓位置错误地终止，另一个是在三维空间中实际刀具位置和局部曲率圆不一定共面，这将导致延迟时间参数的计算不正确并最终影响估计准确性。为了解决错误终止的问题，索引方法用于找到相对于实际位置的最接近参考位置。同时，提出了投影技术以克服将平面曲率圆迭代法扩展到空间应用中遇到的问题。与传统的CCI算法相比，提出的NPP-CCI算法更适合于跟踪复杂轨迹的空间轮廓误差估计。在内部开发的多轴实验平台上进行了具有不同刀具路径的各种实验，以验证所提出算法的有效性。实验结果表明，与传统的CCI算法相比，NPP-CCI算法可以更准确地估计轮廓误差，并且借助实时计算和补偿，