Research On NURBS Curve Direct Interpolation Based On Dynamical Characteristic Of Machine Tools

NURBS curve interpolation is one of the most important functions of CNC system, and is also a necessary method to realize high-speed and high-precision machining. Based on the analysis of local and global constraint of NURBS curve and dynamical characteristic of machine tools, a self-adaptive interpolation algorithm is developed. This algorithm considers all the parameters related to machining. The detailed realization of the algorithm is developed as follows:Based on Kaien equation, the dynamical equation of the CNC machine's drive system is researched. At the same time, based on the current research, the relationship between cut force, friction force, drive moment of servo-motor and machine's motion state is obtained. Finally the constraint equation of the machine's motion state is obtained. On the basis of analyzing the local constraint of the NURBS curve, combined with the dynamical constraint equation and the interpolation precision, the following important information is obtained:⑴ the maximum feed-rate at the interpolation point; ⑵ the maximum acceleration and deceleration at the interpolation point under a certain velocity; ⑶ the checkout content of the next interpolation segment. Based on two-step GA, the global constraint of NURBS curve is analyzed. Therefore the global control information that can guide the whole interpolation process is obtained. Under the united control of the local and global constraint of NURBS curve and the dynamical constraint equation of CNC machine tools, the high-speed and high-precision self-adaptive NURBS curve interpolator is realized, which satisfies the demand of the interpolation precise and the dynamical characteristic of CNC machine tools.On the basis of the research above, the self-adaptive interpolation algorithm of NURBS curve is realized in C language. A specific example is given, with related parameters of the machine's dynamical characteristic, the result of interpolation is inputted to a simulation system, and the simulation result and its analysis verifies the correctness of the algorithm.