The Research On Interpolation Algorithms Of PH Spline Curve And Its Implementation On Embedded CNC System

CNC(Computer Numerical Control)technology directly affects the quality of workpiece processing and production efficiency.It is an important guarantee for the development of equipment manufacturing industry.High-performance spline curve interpolation technology is the symbolic function of advanced CNC technology and the key to enhance the market competitiveness of CNC equipment.Compared with NURBS and other spline curves,the hodograph modulus of PH(Pythagorean-Hodograph)curve can be expressed as a rational polynomial,which can be used to calculate arc length with less computation and high accuracy.Cubic PH curve has less practical application,but higher PH curve will increase the amount of calculation.Therefore,this thesis takes the quintic PH curve with moderate amount of calculation as the breakthrough point to study its interpolation algorithm.Firstly,the fitting algorithm of C~2 continuous quintic PH spline curve is studied.The fitting curves are divided into open curves and closed curves.Given the corresponding interpolation conditions,the equation is constructed from the tangent vector characteristics of B spline curve under the interpolation conditions,and the quintic PH spline curve is obtained.The smooth transition of PH curve at the interpolation point is realized.Secondly,an interpolation algorithm based on improved Milne-Hamming prediction-correction method is proposed.Compared with Taylor expansion method,which is commonly used in PH curve interpolation,the algorithm in this thesis has higher accuracy and better real-time performance.The interpolation calculation has been carried out under the condition of constant feed speed or function of time,curve arc length and curvature.The interpolation characteristics of each velocity form are analyzed.On the basis of five-stage S-type acceleration and deceleration model,the look-ahead speed control algorithm is studied.The algorithm includes look-ahead interpolation preprocess and look-ahead control of feed speed.Combining with adaptive speed control method,the feed speed planning is realized,which not only meets the requirements of processing accuracy,but also improves the flexibility of CNC system.Finally,on the platform of self-developed dual-core embedded CNC system,the dual-core communication is realized by using DVSDK,the application programs of CNC system such as decoding,interpolation,graphical interface are compiled,and the interpolation function of PH spline curve is developed.The effectiveness of the interpolation algorithm is validated by the correct operation of the interpolation algorithm on the platform and the processing experiments.