Research On Forward-looking Interpolation Of Five Axis NURBS Curves Based On Adams Bashforth Moulton Method

As the supporting force of high-end equipment manufacturing industry,five axis CNC machine tools reflect the development level of a country’s industrial modernization.Its high-speed and high-precision machining ability is the focus of the current scientific researchers in various countries,and the interpolation algorithm of CNC system will directly affect the interpolation speed and machining accuracy.NURBS interpolation technology has become the key to improve the performance and market competitiveness of five axis NC machine tools because of its powerful shape control ability and excellent properties.Therefore,it is of great significance to study NURBS curve interpolation algorithm for highspeed and high-precision machining of five axis NC machine tools.In view of the problems of high machining error and low machining efficiency caused by the low calculation speed and accuracy of interpolation algorithm,the uneven speed transition at the inflection point of complex curve,and the traditional speed planning method does not fully consider the speed and acceleration control of each axis of the machine tool,in this paper,the NURBS curve interpolation algorithm and acceleration /deceleration control algorithm in the tool tip path planning of five axis NC machine tools are taken as the starting point,and the five axis NURBS curve forward-looking interpolation technology based on ADAMS bashforth Moulton method is studied.The main research work and results are as follows:(1)Aiming at the problems of low accuracy and complex operation in parameter densification of existing NURBS curve interpolation algorithms,after studying the existing fourth-order Runge Kutta method,explicit four step fourth-order Adams bashforth method and implicit three-step fourthorder Adams Moulton method,an improved NURBS curve prediction and correction algorithm based on ADAMS bashforth Moulton method is proposed according to their truncation error and the difference in calculation process.The algorithm first replaces the complex derivative relation in the fourth-order Runge Kutta method with approximate calculation to simplify the operation process of solving the initial parameter value,and then uses the explicit four step fourth-order Adams bashworth method to calculate the parameter estimate.In this process,the complex differential is replaced with backward difference to speed up the calculation,and then the estimate is corrected by the implicit three-step fourth-order Adams Moulton method,In this process,the differential is replaced by the derivative definition to improve the correction accuracy and reduce the number of iterations.Finally,the local truncation error is used to correct the estimated value and the corrected value to reduce the error caused by the parameter value in the prediction and correction process.The MATLAB software is used to simulate and compare it with the existingNewton iteration method,improved Euler method and Adams predictor corrector method.The results show that the velocity volatility of the improved Adams bashforth Moulton predictor corrector algorithm is reduced by 34.12%,26.53% and 10.37% respectively,and the average value of correction times is reduced from 0.624,0.473 and 0.039 to 0.021respectively;In addition,it is compared with the improved Euler method and Adams predictor corrector method in feed speed,acceleration and acceleration respectively.The simulation results further verify that the algorithm has better machining stability.(2)In order to solve the problem that the existing acceleration and deceleration algorithms can not deal with the speed transition at the corner of the curve,a five axis forward-looking acceleration and deceleration control algorithm based on S-type and cubic polynomial is proposed on the basis of the adaptive speed control algorithm.The algorithm first uses adaptive speed control to constrain the composite speed of the tool tip,then controls the speed and acceleration of each axis under the servo constraint of the five axis NC machine tool,and then segments the curve according to the speed sensitive points,and performs forward-looking acceleration and deceleration control for each segment,that is,the S-type acceleration and deceleration algorithm is used to plan the speed in the non frequent acceleration and deceleration segments,and the cubic polynomial acceleration and deceleration algorithm is used to deal with the frequent acceleration and deceleration segments,Finally,the ideal interpolation step length obtained from velocity planning is transferred to NURBS curve interpolation module for interpolation calculation.The adaptive speed control algorithm,S-type acceleration and deceleration algorithm,polynomial five segment acceleration and deceleration algorithm and the five axis forward-looking algorithm are simulated and compared by MATLAB software.The results show that the maximum pantograph height error is 1.178 μm、0.571 μm、0.447 μm reduced to 0.395 μm;In addition,the comparison results of the total interpolation time,feed speed,acceleration and other data verify that the algorithm can improve the machining efficiency,machining accuracy and stability.(3)Firstly,on the embedded CNC hardware system with S3C2410 as the core,the embedded CNC platform based on Linux is built: the photoelectric isolation module and motor control module are designed,the bootloader and Linux kernel are transplanted and optimized,and the human-computer interaction qt/e graphical interface is developed.Then,the tool path planning strategy of five axis NC machine tool is given.Finally,the correctness and effectiveness of the interpolation algorithm are verified by the complete and correct operation of the interpolation algorithm in the embedded CNC system and the comparison of the actual machining effect.