Research Of Look-ahead And Interpolation Method For NURBS Curves Withminimal Feed Fluctuation

Improving the accuracy and efficiency of CNC machining of complex surfaces hasbeen a hot field for scholars, engineersand technicians, includingNC trajectoryinterpolation theory and method, CNC path control theory and advanced controlmethod. However, there are many shortcomings in the current feedrate scheduling andinterpolation methods, such as the problem of the continuity of current feedratescheduling, the large speed fluctuation of interpolation and the less developed NCmethod.Because of the above problems, this paper studiesthetheory about CNCmachining based on complex surface geometry.In regard tothe feedrate scheduling andinterpolationfor CNC machine, we analyse the algorithm about concrete realization ofinterpolation proceeding in the process of manufacturing for computer numericalcontrol, learn the sixmodules which is designed by predecessors and corresponding toimplementation process, search for the complex and redundant algorithm in themodules, and optimize these modules in this paper.In the feedrate scheduling module,we compute the velocity constraint in the inflection point and make acceleration anddeceleration feedrate scheduling according to trigonometric function, which makes thechange of velocity in the process of interpolation more smooth; in the process ofcomputing the initial value of interpolation, the design of third-order polynomial fittingmethod removes the truncation error, which is different from Talyor expansionmethod;in the feedback correction, we design secant method to iterate, which makesthe program more concise. The algorithm of speed control with jerk trajectorycontinuousfor numerical machining, feedrate scheduling, and interpolationisgiven,furthermore the algorithm isextendedto apply, and is implemented on aDSPcontrol platform for experimental verification.The researchworkcarried out in thispaperis summarized as follows:1. In regard to the feedrate schedulingmodule andon the basis of analyzing trianglesine function, the jerk of mechanical movementis set with the mode of acceleration/deceleration speed for trigonometric function. Velocity mode settingis obtainedthrough integration in turn, three movement base ways including acceleration (ACC),deceleration (DEC), constant feedrate(CF) are set up, therein seven types of velocitycurve which may occur in sub-segments includes ACC+CF+DEC、ACC+DEC、ACC+CF、 CF+DEC、ACC、DEC and CF. 2. In regard to the curve parameters-arc fitting module andon the basis of research ofLagrangian optimization method and dichotomy, the unique AloZeroArkmis fittingalgorithmis designed, firstly third-order polynomialis made use of fitting in thealgorithm, the continuity of curve C0isensured, the polynomial fitting algorithm hasbetter performance, which is verified through simulation experiment, at the same timeit has better wave characteristic(smaller feedrate fluctuation), which is compared withseven-order polynomial fitting algorithm.3. In regard to the existing interpolation scheme, the scheme of fine interpolationcontour error control isproposed. Firstly complete the coarse interpolation calculationon the computer, and then send the interpolation points to motion controller forcontrolling the motorexecution. Through coarse and fine interpolation, theinterpolation cycle was reduced, the higher precision contour tracking interpolationinstruction is generated which can effectively improve the contour accuracy.4. The given algorithms are verified through X-Y experiment platform, at the sametime the model identification of X-Yplatformis carried out by use of sweep method, thePID and feedforward controller is designed for carrying out the two-axiscontourtracing experiment, and the corresponding control algorithmsareverified.