Research On Key Technique For Generating The Tool Path Of Akima Spline In NC Machining

In CNC machining,the cutter location(CL)trajectory is usually expressed by the short-line during the real interpolation in which the CL trajectory(i.e.G code)is imported to CNC system simulatedly generated by CAM software.Howerver,the CL trajectory produced by the short-segment just reaches to position(C0)continuity which is not good for the subsequent speed-planning,thus the smooth curve-fitting by the spline curve is necessary.The Akima spline curve is adopted to fit the CL points,not only the curve presents geometry(G1)and more continuity,which has good alignment with the actual machining contour,but the deceleration control of tool motion for the real-time processing plays good efficiency,easy to process smoothly.In the paper,in view of tool path generation in CNC machining and Akima curve on the improvement of the fitting method and its evaluation index are studied,mainly including the following aspects:The distinctly different CL trajectory,for different methods in CNC machining,will be generated in the density degree.The processing method is contrapuntally chosen by the various types of contour of the three-dimensional entity model,and the internal factors such as machining allowance,pace and the external ones such as cutting speed,overcut(undercut)phenomenon are globally considered,generating a relatively good tool-path,which facilitates spline fitting for the subsequent tool-path.In accordance with the theory of the Akima spline fitting algorithm,in terms of parameterizing the CL points,the existing node parameterization is replaced by the arc-length parameterization,and the parameterized arc-length Akima spline algorithm with recursive fitting is proposed in the paper.Its fitting procedure is mainly divided into two parts: firstly,the Akima curve is segmentally contraint,namely the bi-chord error test and the tangent error test is used to set their error threshold,then the chord error with Akima curve segment and its chord is judged to restrict the CL points and segmentize the Akima curve;secondly,the recursive fitting for the constraint CL points,that is to say,when the number of CL points is not less than three,the vector of the sharing CL point constraint during the adjoining curve segment will be kept and extended,and then the arc-length parameterization,between the adjacent CL point restricted,is adopted to curve-fiiting the Akima curve segment with the recursive fitting.Node-parameterization Akima curve being unrestrained and Akima curve with arc-length parameterization under restricting the CL points and their fitting status,at the same time,are analytically compared by the example,verifying the validity of the proposed algorithm in the paper.On the basis of two kinds of Akima parametric curve,different chord-lengths and corner angles from small segments generated by CL points,will be divided into four types.On this basis,in order to attain the endpoint vector information of the curve,the three evaluation index namely the maximum of the string with the curve,the maximum curvature and its changeable rate are determined as a standard for evaluating the shape of the Akima curve.In deal with various types of short-line segments,adding to NURBS curve for fitting CL points,the curve-fitting performance of the three kinds of curves are compared under different circumstances,and the corresponding relation to the two Akima parametric curves and the NURBS curve with the optimal processing small-segment types is established.Through MatLab simulation and analysis,the overall fitting of the entity model contour is conducted to compared the fitting effect of three kinds of the curves,so that the Akima algorithm with arc-length parameterization,preferable fairness of the fitted curve and the value of better evaluation index of the curve are obtained,the the fitting performance of Akima curve with the small-line segments(original tool path)will be improved.