Study On NURBS Fitting And Interpolation Technology Of Five-Axis Tool Path

With the increasing application of free-form surface in the industrial field,five-axis machining of free-form surface has received more and more attention.Because of its prominent ability in shape controlling,NURBS has been identified by ISO as the only mathematical method of describing the geometry of the industrial products.Comparing with the wide application of NURBS in Computer Aided Design,it is relatively lagging behind in Computer Aided Manufacturing.The application of NURBS in NC machining accords with the development trend of five-axis machining technology of high speed and high precision,and it can help to improve the overall level of CNC machining technology.Five-axis CNC technology of our country still lags behind that of developed countries,five axis NURBS interpolation function has already been integrated with foreign high-grade CNC systems,but there still exist export restrictions and technology embargo on China.Therefore,continuous research should be carried out to key technologies of the numerical control including NURBS technology,and it has important strategic significance to the transformation and upgrading of Chinese equipment manufacturing industry.Because of above-mentioned background,aiming at discrete tool path of the free-form surface in five-axis machining,research on NURBS fitting and interpolation technologies for tool path was carried out in this article.The main contents are as following:Firstly,the methods of NURBS curve and surface fitting were studied.For orderly dense data points,in order to compress data effectively on the premise of the fitting precision,a NURBS curve fitting method based on curvature advantage points was put forward.Calculating the curvature of the discrete points first,and then select the points of dominant curvature as date points and gain initial curve and calculate the fitting deviation,after that new data points were added to where the deviation exceeds allowable value and update the fitted curve,until the NURBS curve satisfy the precision requirement.On this basis,adopt the minimum public node vector method to solve the compatibility problem between the curve clusters,and the surface control network and the two-dimensional node vector parameters were obtained,and finally the NURBS surface reconstruction and solid modeling were achieved.Secondly,the dissertation has studied the NURBS curve direct interpolation technology.To avoid complicated derivation arithmetic,a kind of NURBS curvereal-time interpolation algorithm based on the recursive nature was put forward.Using Simpson numerical method to calculate the length of the curve first,and then find out minimum speed point as node to divide the original curve into several sub-curves,acceleration and deceleration planning,respectively.In the speed planning stage,a kind of interpolation method was explored that interpolate from both ends to the deceleration point simultaneously,and each step-length constrained by accuracy is calculated combined with interpolation cycle and the feed-rate.To obtain expected interpolation step-length,according to the approximate linear relationship deduced by the author between the chord length and the parameter increment,and after necessary iterative calculation,the parameters of interpolation points were gained at last.Thirdly,dual NURBS smoothing technique was studied for linear tool-path in five-axis machining,and it can be divided into smoothing fitting and interpolation.First using the aforementioned curve fitting method,for discrete cutter location data of five-axis machining,NURBS curve for tool-tip and tool-axis points were fitted respectively,and linear tool-path was smoothing description by dual NURBS.On this basis,for the effective control of the tool-axis deviation in the process of interpolation,this paper proposes an algorithm of double NURBS curve interpolation base on parameter synchronization between partitions.In order to ensure the span of the two interpolation points remain the same,make the interpolation progress of two curve keep the linear synchronous in the corresponding intervals,and then implement smoothing interpolation of tool motion.In addition,referring to the method of spatial helical motion expression of the rigid body,dual quaternion method was studied to describe the position and posture of cutting tool,a combination of translational motion and rotation motion in the process of five-axis machining,isometric double NURBS tool paths are obtained.Fourthly,the key problems of post processing in five-axis machining were studied.At first the implementation of rotational axis of five-axis machine tool was summarized,and a machine of A-C dual rotary tables was taken for example for the kinematics modeling and solution.As to multiple solutions selection for rotary axes,according to the relation between the maximum angle of cutter-axis and the stroke limit of rotary axis,determine the corresponding solution interval of the first cutter location,the selected solution can balance the axis limit stroke and the continuity of the movement.For nonlinear error caused by the axis of rotation,the error calculation model was established,and the non-linear error was effectively controlled by inserting the middlecutter location point.As for instructional feed-rate planning,based on the velocity and acceleration constraints and mapping relation between workpiece coordinate and machine tool coordinate system,calculate the programmed feed-rate inversely,the smooth feed-rate was achieved eventually.Finally,a post processing program was developed,and NC code has been generated subjected to the above constraints,and the simulation machining verification was implemented in VERICUT.Fifthly,the experimental study of the proposed approach was performed on the basis of theoretical analysis.On an open NC experimental platform,the interpolation method base on recursive nature and the Taylor series expansion method of NURBS curve interpolation experiments were conducted,through analyzing the experimental data,computational efficiency and precision of interpolation of the algorithm were verified.Furthermore,on five-axis machine platform of artificial tooth,the interpolation algorithm experiment of dual NURBS curve was carried out,and surface finish of the part machined by the algorithm proposed.