| The development of modern industrial technology leads to higher requirements in CNC machining accuracy and speed, while the demand for free-form surface machining is also increasing. As a commonly used mathematical model in computer graphics for generating and representing curves and surfaces, NURBS (Non-uniform rational basis spline) offers great flexibility and precision for handling both analytic and modeled shapes. NURBS are also commonly used in computer-aided design (CAD), manufacturing (CAM), and engineering (CAE). NURBS curve interpolation technique for CNC system can improve processing efficiency, accuracy and the surface of parts. Now it is a key technology in the development of CNC system In this paper, on the basis of studying relevant theories in NURBS interpolation technology, I conduct research on precise control of speed, estimate-iterative calculation of curve parameter, adaptive interpolation algorithm and S-curve acceleration and deceleration algorithm of NURBS curve interpolation. The main research contents and achievements of this paper are as follows:To ensure precision and compliance with the machine dynamics, I applied mathematical methods to achieve fast and accurate calculating of contour error, curve curvature, normal acceleration and other key factors affecting the NURBS curve interpolation;I elaborated and compared different methods in evaluation of NURBS curve point and its derivative. I also applied the iterative search method to fast yet accurate calculation of NURBS curve length and its curvature;I proposed a fast way to calculate the displacement given a curve parameter and the reverse with application of different numerical methods meeting the accuracy requirements.I researched and analyzed the control of machining speed in NURBS curve interpolation. I combined it with controllable chord error interpolation theory and proposed the segmented adaptive NURBS curve interpolation method based on S-curve acceleration and deceleration algorithm. |
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