NURBS interpolation is superior to traditional linear or circular interpolation in terms of code size, surface quality, and machining efficiency. However, with the increasing demands for high-accuracy and efficient machining, NURBS interpolation has faced a growing number of challenges. Many researchers are actively involved in this field with great interest. Due to the special form of NURBS curve, there is a nonlinear relationship between its curve and arc length; feed fluctuations and mechanical shocks which are caused during the interpolation process will seriously affect the surface accuracy and quality of machined parts. To solve these problems, a real-time NURBS interpolation is proposed under multiple constraints (RNIC) in this paper. First, the formulas of the constrained feedrate under geometric errors, kinematic constraints, drive constraints, and contour errors are given. Then, the two stages for the proposed interpolation are established. The former stage is offline preprocessing stage, which aims to quickly find feedrate sensitive areas (FSAs), while the latter online stage is the real-time interpolation, which is responsible for smoothing the velocity. In the preprocessing stage, we utilized FSA scan module and feedrate adjustment module to detect the FSAs and adjust the feedrate at the start/end of each subsegment by a bidirectional scanning algorithm. Each segment contains acceleration and deceleration (some contains uniform speed) stages, which can be well matched with the processing process of acceleration and deceleration. Finally, according to the proposed method and the adaptive speed adjustment method, the simulation of a “butterfly-shaped” NURBS curve using the S-shaped ACC/DEC algorithm is carried out, which verifies the reliability and effectiveness of the proposed algorithm.
Aiming at the problem of large number of points and complex calculation of NURBS pre-interpolation, this paper puts forward a look-ahead interpolation with offline feedrate optimization. The NURBS interpolator is divided into two stages: pre-interpolation and real-time interpolation. The pre-interpolation preprocesses the curve segment by segment according to the curvature characteristics, at the same time the exponential function method is adopted during the pre-interpolation in the look-ahead module. This method makes the step increment of interpolation parameters change exponentially in the area with gentle curvature, and greatly reduces the number of pre-interpolation points, which reduces the amount of calculation and improves the real-time performance. The real-time interpolation stage adopts the bidirectional adaptive acceleration and deceleration control method to realize speed smoothing without needing to calculate the deceleration point. The simulation results show that the real-time performance of the algorithm is greatly improved.
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