Abstract
The curvature of the NURBS curve varies along its trajectory, therefore, the commonly used feedrate-planning method, which based on the acceleration/deceleration (Acc/Dec) model, is difficult to be directly applied in CNC machining of a NURBS curve. To address this problem, a feedrate-planning method based on the critical constraint curve of the feedrate (CCC) is proposed. Firstly, the problems of existing feedrate-planning methods and their causes are analyzed. Secondly, by considering both the curvature constraint and the kinematic constraint during the Acc/Dec process, the concept of CCC which represents the relationship between the critical feedrate-constraint value and the arc length is proposed. Then the CCC of a NURBS curve is constructed, and it has a concise expression conforming to the Acc/Dec model. Finally, a feedrate-planning method of a NURBS curve based on CCC and the Acc/Dec model is established. In the simulation, a comparison between the proposed method and the conventional feedrate-planning method is performed, and the results show that, the proposed method can reduce the Acc/Dec time by over 40%, while little computational burden being added. The machining experimental results validate the real-time performance and stability of the proposed method, and also the machining quality is verified. The proposed method offers an effective feedrate-planning strategy for a NURBS curve in CNC machining.
Highlights
The parametric interpolation based on a non-uniform rational B-splines (NURBS) curve is gradually being applied to CNC machining of complex free-form surfaces [1,2,3], such as molds, turbines, and blades, due to its advantages of a smooth machining process, high machining efficiency, and precision [4,5,6,7]
The segment-by-segment planning method divides a NURBS curve into several sub-curves, which are taken as calculation units, and the Acc/Dec model is used to plan the feedrate in each unit
Jia et al [19] divided the regions of the NURBS curve of which the feedrate-constraint value was less than the command value into independent sub-curves, calculated the feedrate-constraint value of each sub-curve according to its minimum radius of curvature, and planned the feedrate
Summary
The parametric interpolation based on a non-uniform rational B-splines (NURBS) curve is gradually being applied to CNC machining of complex free-form surfaces [1,2,3], such as molds, turbines, and blades, due to its advantages of a smooth machining process, high machining efficiency, and precision [4,5,6,7]. Jia et al [19] divided the regions of the NURBS curve of which the feedrate-constraint value was less than the command value into independent sub-curves, calculated the feedrate-constraint value of each sub-curve according to its minimum radius of curvature (hereinafter referred to as “minimum-constraint principle”), and planned the feedrate This method ensures that the feedrate does not exceed the limit, the minimum-constraint principle reduces machining efficiency due to its conservation. The literature [19] first divided a NURBS curve into sub-curves, and the method shown in Figure 1c was adopted for a single sub-curve, conservatively setting the upper limit of C2(s) to the minimum value of C1(s), which affects the machining efficiency. The composite feedrate-constraint curve, which ensures the real-time performance of the C2(s) constructing process is the CCC proposed in this paper
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