Offline Prediction Method of Contour Errors for Five-Axis Machine Tools Based on Processing Instructions

针对数控机床五轴联动轨迹误差影响加工精度的问题，文章提出了一种基于数控加工指令(G代码)计算轨迹误差的离线预测方法。首先分析了五轴联动线性插补的RTCP算法和数控系统的插补过程，基于G代码中所包含的数据得到程序段之间的位移当量、加工时间和实际速度等关键信息，结合RTCP算法与机床运动学正逆变换获得了任意插补周期的插补数据；然后，分别对平动轴与旋转轴建立包含三环控制环节、永磁同步电机、机械传动机构的伺服进给系统Simulink仿真模型，从而实现各轴实际位置的预测；之后采用三次样条插值法计算轮廓误差，通过构建连续轨迹模型提升误差估算精度。实际加工验证在五轴数控机床上完成，最终实验结果表明：该方法无需依赖机床硬件即可实现误差精准预测，各轴动态误差预测精度控制在±3 μm以内，复杂加工轨迹轮廓误差预测精度达±2 μm，验证了该方法的有效性。To address the issue of trajectory errors affecting machining accuracy in five-axis CNC linkage systems, this paper proposes an offline prediction method for trajectory errors based on CNC machining instructions (G-code). The approach first analyzes the RTCP algorithm for five-axis linear interpolation and the interpolation process of CNC systems. By extracting key information such as displacement equivalents, machining times, and actual speeds from G-code data, combined with RTCP algorithms and forward/inverse kinematic transformations of machine tools, interpolation data for arbitrary interpolation cycles are obtained. Subsequently, three-loop control structure models incorporating permanent magnet synchronous motors and mechanical transmission mechanisms are established for both translational and rotational axes using Simulink, enabling the prediction of actual axis positions. Cubic spline interpolation is then applied to calculate contour errors, constructing a continuous trajectory model to enhance estimation accuracy. Experimental validation was conducted on a five-axis CNC machine tool. Results demonstrate that the proposed method achieves precise error prediction without relying on machine tool hardware, with dynamic error prediction accuracy controlled within ±3 μm for individual axes and ±2 μm for complex trajectories, thereby validating its effectiveness.