Research On Modeling And Interpolating Of The Tool-path Based On Cylindrical Helix Splines

To realize the high accuracy and high speed NC machining of surface, the tool-path interpolating algorithm should be simple and stable. When the tool-path of surface is represented with NURBS curves, the important interpolating data, such as the position of interpolating point, the interpolating error, the feed speed etc. have not direct and apparent relationship with the arc length of curves. In this case, the amount of calculation is too large to meet the real time interpolating computation. While the tool-path for surface machining are approximated by small straight line segments, the number of segments is large, the length of segments are short, and it is inevitable to transfer cross segments frequently in the continuous interpolation. So, it is difficult to control the feedrate waving and interpolating error. Circular arcs, cylindrical helixes and conic helixes splines etc. are not only real and accurate arc-length parameter curves but also tool-path can be approximated by their less segment number. Based on this kind of characteristics, a new tool trajectory expressed by cylindrical helix splines has been presented in NC surface machining, the methods of fitting and interpolating on cylindrical helix have also discussed in this dissertation.The interpolation method of spatial double cylindrical helix, single cylindrical helix and the blending interpolation between single cylindrical helix and arc have been studied, and the efficiencies of three methods have been tested by simulation. In order to construct the cylindrical helix splines, a new algorithm'Try-Approximation-Interpolation'which assembles the strong points of interpolation and approximation has been presented. Approximated the cubic B splines with the little straight line segments and cylindrical helix segments by this method, the cylindrical helix splines have less segments and more smoothness.The method of real-time trajectory generation in NC machining and feed rate control in the continuous interpolation of cylindrical helix splines have been researched, and the recursive de-coupling interpolation formula has been deduced, the method is simple and efficient, and the chord error of real-time interpolation segment has also been studied theoretically and calculated numerically, we acquired an effective approximate formula. The formulae and profiles of acceleration/deceleration, velocity and displacement in one segment can be gained. A new control algorithm of corner speed within the given error and the computation of transfer point in the across segment interpolation has been presented. Because the interpolating points have close relationship with arc length, the algorithm is simple and stable. The methods of modeling and interpolating of helix splines have been researched and experimented by the large-scale marine propeller. Given the error of 0.001mm, we can get the helix splines of 2234 segments and the linear splines of 6010 segments on the ten sections of every piece blade. By contrast the interpolating calculation of two kinds of tool-path, we can find that every one interpolating point need 6.1μs for helix splines, and 4.2μs for linear segments, but helix splines consumes less time wholely. The contour errors made by two interpolations are equivalent, and less than one pulse equivalent. We can also find that the oscillation of feed rate of helix splines is smaller than linear segments from the maximum deviation and standard deviation. To interpolate this B-splines segment directly, every one interpolation point costs 42.6μs, it consumes much more.An experiment platform for validating the algorithm of space cylindrical helix splines interpolation has been designed. The efficiency of the interpolation algorithm for cylindrical helix splines has been testified. Comparation with the existed little straight lines segments continuous interpolation of Huazhong Century Star CNC from the consuming of interpolation time and velocity oscillation, the experiment results show the cylindrical helix splines is better. The practical applications of arc splines and cylindrical helix splines have been discussed, three practical examples, i.e. machining of non-circular gear sector, grinding of the blade curve of short track skates, the grinding of cylindrical and taper milling cutter show that cylindrical helix splines has a good application foreground.