A cutter contacting point trajectory prediction method combining harmonic functions and dimensionality reduction for improving machining precision in flat-end milling

In five-axis machining, deviations between actual and theoretical cutter contacting (CC) point trajectories lead to nonlinear errors, adversely affecting machining precision. This paper presents a novel method aimed at reducing nonlinear errors at CC points, enhancing overall accuracy in machining processes. We establish that interpolated CC points within a machining segment lie on the same plane, which provides a foundational insight into the geometric behavior of the machining system. To simplify the calculation process, we apply a geometric method to reduce the dimensionality of CC points, making the subsequent analysis more efficient. A harmonic function is then utilized to predict CC point trajectories, enabling effective compensation for identified errors. Our approach is integrated into five-axis linear trajectory interpolation, where it quantitatively addresses nonlinear errors that exceed tolerance limits. Comprehensive simulation and experimental validation demonstrate that this method not only maintains CC point errors within allowable limits but also significantly reduces tool center point errors. The results confirm the effectiveness of our method in enhancing machining precision, paving the way for improved performance in five-axis machining applications.