The Principle Of The Ball-end Milling Cutter Radius Compensation Of NURBS Curve And Surface

With the development of the manufacturing industry,the free curve and surface modeling technology with NURBS(Non-Uniform Rational B-Spline)as core has been further developed,which has promoted the progress in the field of NC machining.At present,the numerical control system manufactures represented by FANUC have developed the numerical control system which supports NURBS curve interpolation function.But this technology in china is disabled.Therefor this feature is missing in imported machine.China is a manufacturing country.We have a lot of NC machine tools.However,traditional CNC system only supports linear,circular and parabolic interpolation.The processing capacity for complex curves and surfaces is insufficient.So it has realistic significance how to realize the NURBS curve interpolation in traditional CNC machine tools,and overcoming the problem of CAM software to generate program,including the vast cutter location files and the problem of surface quality caused by the machine tools vibration.In this paper,the over cutting phenomenon in NURBS curve and surface machining is analyzed.Through the cutter radius compensation of the interpolation point of NURBS curve and surface,the machining ability of NURBS curve and surface without overcut interpolation is realized based on XK715 D CNC vertical milling machine with FANUC 0i-MB system.Firstly,according to the over cutting phenomenon existed in the process of the NURBS curve interpolation,the algorithm of the ball-end tool radius compensation is studied.The results of the algorithm of non-the ball-end cutter radius compensation and the algorithm of the ball-end tool radius compensation are calculated and compared,and the results of the NURBS curve interpolation are verified by VERICUT software and actual machining.In this study,regardless of the influence of the relations between the curvature radius of the NURBS curve and tool radius.It is proved that the algorithm of the ball-end tool radius compensation for NURBS curves can avoid overcutting by making the tangency of the point of interpolation and the cutting edge.Secondly,the situation when the curvature radius of the NURBS curve is smaller than the tool radius is considered.And the algorithm of over cutting pre judgement is studied,namely,the interpolation process is determined through comparing the radius of curvature of NURBS curve and the radius of the tool radius,early to judge whether exist overcutting.It is found that we can not only judge whether exist overcutting and plan the process of interpolation,but also get the maximum allowable cutter diameter.Finally,it is verified by VERICUT software.Finally,the algorithm of the ball-end tool radius compensation for the NURBS surfaces is studied in this paper.It is similar to that for NURBS curves.The points of interpolation are calculated by the equal arc length interpolation algorithm,and then the the ball-end cutter radius compensation is performed on the interpolation point.The cutting tool path is controlled by making the tangency of the point of interpolation and the cutting edge to realize the cutting for NURBS surface.The removal volume between without the ball-end tool radius compensation algorithm and the ball-end tool radius compensation algorithm is compared through simulation.It is proved that this algorithm of the ball-end tool radius compensation for NURBS surface is feasible.Finally,it is verified by the actual processing.