Interpolators play a core and important role in CNC systems, and the scheduling of feedrate is a main task of CNC interpolators. It is routine to schedule the feedrate of linear/circular toolpaths because of their regular geometry; however, the feedrate scheduling of spline toolpaths remains challenging due to the freely and unpredictable geometric shape. Most of the existing methods require looking ahead or pre-processing to acquire sufficient toolpath information for generating drive-bounded smooth feedrate profile, which limits the integral machining efficiency. This paper presents a FIR (finite impulse response) filtering-based interpolation algorithm for spline toolpath, thus realizing the fully real-time capability without using time-consuming optimization such as looking ahead or pre-processing. The presented method merely utilizes the curvature radius information of the current interpolation point on the spline toolpath, and the scheduled feedrate can be generated within one step. Furthermore, the global tangential smoothness of the feedrate profile is guaranteed by directly applying convolution with a chain of two cascaded FIR filters. However, the FIR filtering induces interpolation error which plays as a negative cost during the one-step feedrate scheduling. To solve this issue, the principle of the filtering induced error is analyzed, so that it is computed by feed parameters and curvature radius, and the maximum error is added as an extra constraint beyond the commonly considered axial kinematic constraints. Effectiveness of the presented approach is demonstrated by both numerical illustration and experimental tests.

插补器在CNC系统中起着核心和重要的作用，进给率的调度是CNC插补器的主要任务。由于线性/圆形刀具路径的规则几何形状，通常要安排进给率。然而，由于自由且不可预测的几何形状，样条刀具路径的进给率调度仍然具有挑战性。现有的大多数方法都要求进行前瞻性或预处理，以获取足够的刀具路径信息，以生成与驱动有关的平滑进给率曲线，从而限制了整体加工效率。本文提出了一种基于FIR（有限脉冲响应）滤波的样条刀路插补算法，从而实现了完全实时的功能，而无需使用诸如前瞻性或预处理等耗时的优化。提出的方法仅利用样条刀具路径上当前插补点的曲率半径信息，并且可以在一个步骤内生成计划的进给率。此外，通过直接使用两个级联FIR滤波器的链进行卷积，可以保证进给率曲线的整体切向平滑度。但是，FIR滤波会引起内插误差，该误差在单步进给率调度中起到负成本的作用。为了解决这个问题，分析了滤波引起的误差的原理，以便通过进给参数和曲率半径计算出误差，并且将最大误差作为附加约束添加到了通常认为的轴向运动学约束之外。数值说明和实验测试都证明了该方法的有效性。