Research On Look-ahead Interpolation Technology Of Non-Uniform Rational B-Splines

The processing ability of modern numerical control systems has been strengthened with the increase of microprocessor computing speed.High speed,flexibility and intelligentize have become important indexs of measuring the machine performance.A large number of data transmission problems generated by discrete small line segments can be avoided with NURBS curve interpolation,and machine vibration problems caused by frequent acceleration and deceleration can be solved with the look-ahead technology.Therefore,it is necessary to study the NURBS curve interpolation technology and the following aspects are researched in the paper.(1)Some mathematical expressions of NURBS curve were given,and the matrix transformation method was selected to calculate values of point coordinates.One order,two order Taylor and Admas expansion algorithm were given.At the same time,Admas expansion algorithm has been improved by predictor corrector method of inverse quadratic interpolation.Finally,velocity fluctuation rate simulations of improved Admas expansion algorithm compared with the unimproved Admas expansion algorithm were carried out and contrast simulation results show that velocity fluctuation rate of NURBS curve interpolation process by the improved Admas algorithm is lower,that is,interpolation performance of improved Admas expansion algorithm is better than the unimproved Admas expansion algorithm.(2)Trigonometric cosine acceleration and deceleration control method including five stages was presented.The displacement,velocity,acceleration and jerk equations were deduced.At the same time,trigonometric cosine acceleration and deceleration control method including five stages was analyzed and discussed based on different conditions.Finally,motion characteristics contrast simulations between S shape acceleration and deceleration control method and trigonometric cosine acceleration and deceleration control method including five stages were carried out,contrast simulation results show that performance of trigonometric cosine acceleration and deceleration control method including five stages is better than S shape acceleration and deceleration control method.(3)Prediction method of deceleration points was given,judgment of sensitive points was provided,adaptive feed step constraints were analyzed,velocity join processing method was provided and adaptive trigonometric cosine acceleration and deceleration control method including five stages with look-ahead function was presented.Finally,the contrast simulation analysis of no look-ahead and look-ahead NURBS curve interpolation algorithm was carried out.The contrast simulation results show that velocity transition with look-ahead algorithm is smoother than no look-ahead algorithm,the final deceleration can be better judged in advance by look-ahead algorithm,acceleration and jerk values are limited to the limit range and a higher flexibility can be obtained by look-ahead algorithm.(4)The NC interpolation experimental platform of NURBS curve was established.Kinematic characteristics of x and y axes in NURBS curve machining process,effects of machined NURBS curve and surface roughness analysis of machined NURBS curve were carried out.Contrast experimental results show that velocities of x and y axes are smoother,acceleration and deceleration are more continuous,inflection point transition is natural smoother and each roughness index is better with look-ahead algorithm in NURBS curve machining process than no look-ahead algorithm.