| With the rapid development of modern manufacturing, Non-Uniform Rational B-Spline(NURBS) is determined as the only mathematical method to describe the geometry of industrial products defined by the International Organization for Standardization(ISO). Due to the superiority of NURBS method in complex geometric modeling, NURBS method has more and more widely been used in the fields of CAD/CAM and Computer Graphics, etc. The NURBS interpolation function has become an important indicator to define advanced CNC system. In order to meet the requirements of high speed and high accuracy in modern manufacturing, NURBS curve interpolation algorithm has become one of the core content s of numerical control system to be researched and developed. Nowadays, how to realize the coordination and optimization control between machining precision and efficiency is the trend of research on NURBS interpolation algorithm. The quality of the interpolation algorithm mainly depends on the reasonable adjustment between the accuracy and feed speed. In order to satisfy the requirement of curve interpolation under curvature changing, an adaptive feed rate interpolation is adopted. Meanwhile, the feed rate is constantly changed in the process, which inevitably leads to the motion with acceleration and deceleration. Without effective control of feed rate, it will lead to higher acceleration and jerk, affect the stability of interpolation, and even cause the shock and vibration of machine tool. In addition, CAD/CAM has supported output curve form of NURBS format, but cutter compensation of CNC system considering the NURBS curve interpolation is still in the stage of research and development.Therefore, the differential geometry theory, open experimental platform, S-shape control for acceleration and deceleration, VC++, MATLAB, etc. are applied in this thesis. An optimal NURBS curve interpolation algorithm and its cutter radius compensation are explored in this paper. The main works are as follows:(1)A multi-constraints integrated control NURBS curve interpolation algorithm is proposed in this paper. The algorithm takes consideration of analysis and summary the existing NURBS curve interpolation algorithms, and the influences of the multi-constrained conditions, such as the geometrical property of NURBS curve, and kinematics and dynamic of machine tools. And the adjustment method between multi-constrained conditions and the feed rate is identified in this thesis.(2) A motion model is built based on S-shape control for acceleration and deceleration in this paper. And, the back-trace backward interpolation theory is applied also which will improve the accuracy of interpolation and stability of machining processes.(3) A two-dimensional cutter radius compensation of the NURBS curve interpolation is studied. According to the mathematical characteristic of NURBS curve and the mechanism of cutter radius compensation, the simulation software is developed to achieve the function of cutter radius compensation to further improve the programming flexibility and practicability of NURBS curve trajectory.(4) The experimental analysis and verification. The ‘PC+ motion control card’model experimental system is built based on the Gugao opening electro-mechanical experimental platform. The NURBS curve interpolator is programmed in language of VC++ 6.0 to carry out interpolation simulation and experiments, MATLAB is also used to verify the accuracy and efficiency of the algorithm by comparing and analyzing the experiment results.In conclusion, this study provides an efficient & high-precision interpolation optimization algorithm for the NURBS curves and realization of its two-dimensional cutter radius compensation function, which has engineering and theoretical reference value to enhance the quality of CNC system. |
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