The Key Technology Research In The CNC Machining Of Complex Surface With Nurbs Tool Path

The application of Nurbs tool path can dramatically improve the machining precision and efficiency in the CNC machining of complex surface.The implement of Nurbs tool path interpolation has become the primary indicator to evaluate the processing ability of CNC machine tool.At present,the core interpolation technique of Nurbs tool path is mastered by only few of foreign CNC machine tool manufactures and the interpolation algorithm is strictly confidential.Therefore,the in-depth analyses and researches on the key issues of Nurbs interpolation play an important role in reducing the manufacturing level of equipment between our country and developed countries.In this paper,systematic studies are carried out on the problems of discrete tool path fitting,feedrate scheduling,high precision and real-time interpolation algorithm for Nurbs tool path interpolation.The problems that the precision control and the determination of knot vector in the fitting process of Nurbs tool path,the high order constraints restriction in the feedrate scheduling and the limitation of feedrate fluctuation in the interpolation process are resolved.The main research contents and methods are summarized as follows:Based on the optimized distribution of knots,a high precision Nurbs tool path fitting method is proposed.The discrete micro tool path is reconstructed precisely and the number of knot vector is reduced effectively.According to the analysis of the rational fractional representation of Nurbs curve,the fast evaluation and derivation methods of Nurbs curve are given.To achieve the continuous as well as smooth processing,the discrete cutter location points generated by CAM are fitted into Nurbs curve.Considering the influence of knot distribution on the fitting precision of Nurbs curve,the knot vector determination method based on the geometric features of discrete points is constructed.The number of knots can be reduced effectively under the same fitting precision.The fitting precision of Nurbs curve can be controlled precisely by means of knot insertion.Simulations and experiments are conducted to verify the effectiveness of the proposed Nurbs curve fitting method.A heuristic iterative feedrate optimization algorithm based on the B-spline velocity curve is proposed for Nurbs tool path interpolation.The feedrate profile is represented by the B-spline form with the same parameter domain as the Nurbs tool path.The feedrate constraints are expressed as the differential of B-spline velocity curve and Nurbs tool path on the parameter uniformly.The knot vector of the B-spline velocity curve is determined by the feature points of coefficients in the feedrate constraint formulas and the number of knots is fixed after several trails.The initial feedrate is a zero-speed velocity curve and the feedrate profile is adjusted by raising the control points of it in sequence from the initial one using the binary search technique with all the feedrate constraints confined.According to the adjusted control points and the determined knot vector,the near time-optimal feedrate profile can be obtained.The effectiveness of the proposed iterative feedrate scheduling method is verified by the simulations and experiments.In the feedrate scheduling with B-spline velocity curve,some problems,such as the complicated knot vector determination and the low computing efficiency,have been encountered.Therefore,this paper proposed a knot vector determination method based on knot insertion and the computing efficiency can be enhanced by the piecewise optimization in parallel.Based on the properties of knot insertion and segmentation of B-spline curve,a segmentation method without altering the continuity of B-spline curve is presented.The knot vector of the B-spline velocity curve is determined by the knot insertion method.The iterative optimization of the B-spline velocity curve is conducted in parallel with the segmentation method in which the boundary constraints of each piecewise interval is appended.Based on the optimization results with segmentation,the parallel optimization of the B-spline velocity curve as indicated above is repeated in the piecewise connection interval.The knot vector determination method of the B-spline velocity curve and the computing efficiency of the parallel optimization are analyzed in detail through the two application cases.By analyzing the capability of real-time and the feedrate fluctuation in the Nurbs tool path interpolation,a high-precision feedrate generation method is proposed based on the arc length compensation and s-u fitting.A feedrate guide curve based interpolation method is constructed by separating the feedrate scheduling from the real-time interpolation.The two main factors that can result in the feedrate fluctuation are analyzed.In this paper,some parametric interpolation methods are summarized briefly,and the capability of real-time and the feedrate fluctuation are analyzed.In order to keep both the real-time of Nurbs tool path interpolation and reduce the feedrate fluctuation,the function of s-u for the Nurbs tool path is constructed by using the B-spline fitting method and the parameter increment in the current interpolation period is calculated in real-time.When the next parametric interpolation point is acquired,the feedrate fluctuation can be further reduced by the arc length compensation method.In order to avoid the complex calculation process of curvature and arc length of Nurbs curve in real-time interpolation,the u-s and u-k fitting curves of Nurbs tool path are constructed offline.The interpolation parameter is corrected by the Newton iteration method with the initial parameter derived from the arc length compensation,and the feedrate fluctuation is limited.The efficiency of the proposed Nurbs tool path interpolation method is verified by simulations and experiments.