Study On The Algorithms Of The Tool Radius Compensation And Read-time B-spline Curves Interpolation Based On The NC System

With the rapid development of modern manufacturing, NC (Numerical Control) technology is widely used in modern manufacturing industry, and the open NC system is the mainstream of NC technology. Interpolation algorithm, as the core of the open NC system, has become an important research direction.This dissertation focuses on the algorithm of the real-time B-spline curves interpolation based on the open NC system, which has been studied deeply and systematically in this dissertation, as well as on the technology of the tool radius compensation of the open NC system. The main contents of the dissertation are as follows:Firstly, through the study of the theories about the C (Complete) tool radius compensation, the dissertation put forward a new algorithm of C tool radius compensation for the effective reduction of overcut while NC-machining. C++ programming language is adopted to realize the algorithm, and examples of simulation are given to demonstrate the achievements of the algorithm.Secondly, an adaptive real-time interpolation algorithm for B-spline curves is proposed combined with the chord error control and the largest centripetal acceleration control based on the differential geometry and the properties of B-spline curves. At the same time in accordance with the characteristics of NC system, a method of B-spline curves matching is proposed.Thirdly, the model of the discrete S-shape acceleration and deceleration (ACC/DEC) feedrate control algorithm is established in this dissertation. And based on the principles of B-spline curves, the requirements of B-spline curves construction conditions are used in the real-time interpolation of B-spline curves. And a method of the rapid determine of the deceleration point is given based on the theories of the approximate of arc length parameterize and the symmetry of the S-shape ACC/DEC feedrate profile. At the same time the solution of the problem that the length of interpolation path is shorter than the one of S-shape ACC/DEC path is proposed. At last, the S-shape ACC/DEC feederate control is realization in the real-time B-spline curves interpolation, and some examples are given to prove its validity.Finally, a new interpolator based on the algorithms of real-time B-spline curves and the S-shape ACC/DEC feedrate control is studied by this dissertation, which is able to automatically determine a straight line or a B-spline interpolation, is implemented by C++ langue. And after the depth analysis of the function of the interpolator according to the simulation results, the validity and feasibility of the relative algorithms in the interpolator is proved.