Abstract
This article presents an online three-axis non-uniform rational B-splines preprocessing and feedrate scheduling method with chord error, axial velocity, acceleration, and jerk limitations. A preprocessing method is proposed to accurately locate the critical points by reducing pre-interpolation feedrate in feedrate limit violation regions. In the preprocessing stage, the non-uniform rational B-splines curve is subdivided into segments by the critical points and the corresponding feedrate constraints are obtained. A sliding look-ahead window-based feedrate scheduling method is proposed to generate smooth feedrate profile for the buffered non-uniform rational B-splines segments. The feedrate profile corresponding to each non-uniform rational B-splines block is constructed according to the block length and the given limits of acceleration and jerk. The feedrate modification method for non-schedulable short blocks is also described which aimed at avoiding feedrate discontinuity at the junction of two non-uniform rational B-splines blocks. With the proposed method, a successful feedrate profile could be generated with sufficient look-ahead trajectory length in the buffer, which enables that the preprocessing and feedrate planning to be performed progressively online. Simulation and experimental tests with different non-uniform rational B-splines curves are carried out to validate the feasibility and advantages of the proposed method. The results show that the proposed method is capable of making a balance between the machining efficiency, machining precision, and computational complexity.
Highlights
Conventional computer aided design (CAD)/computer aided manufacturing (CAM) systems usually fit a curved cutter paths proximately with a set of small linear/circular (G01, G02) blocks
The results show that the presented local fine preprocessing method can significantly improve the curvature estimation accuracy without a large increasing the computation burden
The proposed non-uniform rational B-splines (NURBS) preprocessing method and windowing look-ahead feedrate scheduling method are developed as a real-time component of LinuxCNC and run cyclically in the kernel space
Summary
Conventional computer aided design (CAD)/computer aided manufacturing (CAM) systems usually fit a curved cutter paths proximately with a set of small linear/circular (G01, G02) blocks. The geometry model and control polygon of the trident shape are shown, and its NURBS parameters are as follows: Order p: 2; Knot vector fUig: {0,0,0,0.2,0.4,0.6,0.8,1,1,1}; accuracy as the local fine preprocessing method, the pre-interpolation feedrate of constant feedrate method should be reduced to 5 mm=s; the preprocessing stage becomes very time-consuming. The chord error–limited feedrate limitation is supposed to be equal at sharp corners A and E; VA is much higher than VE due to the curvature estimation error A WM-shape NURBS curve with both high and low curvature zones is employed to validate the proposed look-ahead feedrate scheduling algorithm. All the actual values in terms of axial feedrate, axial acceleration, and tangential jerk are constrained within the set limitations
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