A real-time high-precision interpolation algorithm for general-typed parametric curves in CNC machine tools

Abstract

The machining accuracy of computer numerical control (CNC) machine tools largely depends on the interpolation algorithms implemented. In this paper, a real-time high-precision interpolation algorithm for a general-typed parametric curve is proposed. As with other time-partition interpolation algorithms, the linear motion trajectory (employed to approximate the real trajectory) in a sampling cycle is determined from the current position of the tool to another point (target point) on the target trajectory. To determine the target point in a sampling cycle, a neighbourhood interval containing the point is first determined, the target point is then iteratively approached by means of the bi-section or secant method for equation resolutions. Simulation results show that the order of magnitude of the maximum feedrate relative errors (the relative deviation of the computed feedrate from the desired one) is −8 or less, while the order of magnitude of the maximum chord errors in the unit of meter is −6 or less. The performance indices can be further improved with more computation iteration in each sampling cycle. The algorithm is general, and applicable to any smooth curve that can be formulated in parametric equations.

Keywords:

• interpolation algorithm
• motion trajectory
• numerical control
• real-time

Acknowledgement

The author would like to express their appreciation for the financial support from National Natural Science Foundation of China under grant No. 50675166, 50905133 and No. 50620130441.