NURBS curve interpolation algorithm for simplified calculation of  S shaped acceleration and deceleration

QIN Zhenying, ZHAO Dongbiao, ZHOU Diqi

(College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China)

Abstract: Aiming at the deficiency of acceleration and deceleration control method in NURBS curve interpolation, and to realize the smooth transition of feedrate during the manufacturing process, a new method of NURBS interpolation was proposed, including feedrate planning and real time interpolation. In feedrate planning, a new simplified calculation method of sshaped acceleration and deceleration based on curvature adaptive algorithm was adopted, and to prevent excessive chord error, the idea of bidirectional interpolation to predict the deceleration point in real time was also used. In real time interpolation, Muller interpolation method and Newton iterative method were utilized to calculate the interpolation parameter of the next period, and the space coordinates of the next period was given as well. Finally, the algorithm was compared with the existing interpolation methods for simulation analysis. The results indicate that this method can guarantee the continuity of acceleration and the boundedness of jerk, effectively reduce the chord error and feedrate fluctuation, and improve the stability of machine tool operation.

Key words: NURBS; feedrate planning; realtime interpolation; Newton iterative method