Geometry-feedrate dual-scale planning for CNC machine tools

In CNC machining, the limitations of geometric smoothing and feedrate smoothing methods often result in non-smooth tool motion, leading to workpiece vibrations and deteriorating machining quality. To address the above problem, this article proposes a geometric-feedrate dual-scale planning method that enhances both machining path and feedrate smoothness. At the geometric level, an energy-based approach smooths the machining path while ensuring bounded path errors. By constructing a stiffness matrix, the method formulates path smoothing as an energy minimization problem. A modified Particle Swarm Optimization (MPSO) algorithm effectively solves this problem, significantly improving path smoothness. At the feedrate level, a gradient-based strategy initially updates the feedrate to minimize fluctuations. Traditional S-curve-based feedrate planning methods require recalculations, increasing computational burdens. To overcome this, a four-time hybrid filtering structure (a first-order morphological filter followed by a three-time FIR filter) is introduced. The morphological filter employs an erosion-dilation strategy with a predefined filtering radius to preserve local feedrate minima. The three-time FIR filter smooths the feedrate by applying a predefined time parameter T , ensuring compliance with kinematic constraints. Meanwhile, a bidirectional interpolation method is proposed to reduce feedrate fluctuations caused by interpolation, in which the step size is determined by considering both previous and next interpolation cycles. Finally, Simulations and experiments confirm the effectiveness of the proposed method.