Research On Efficient NURBS Curve Interpolation Algorithms For Cutting & Polishing

As a powerful shape-controlled parameter curve or surface, NURBS (Non Uniform RationalB-Spline) has been determined to be the only geometric form to describe complex free-formcurves and surfaces parts by ISO. So, NURBS curve interpolation has become an importantfunction parameter to measure a high-grade CNC system. How to make the processing quality andprocessing efficiency coordinated control is the eternal goal of modern efficient NURBS curveinterpolation algorithms. By now, the shortcomings of the previous NURBS curve interpolationalgorithms are mainly as follows: Firstly, the chord error, feed rate, and machine toolsacceleration/deceleration performance have been taken into account by the past NURBS curveinterpolators for cutting, but there is the lack of the multi-objective coordination control forchord error redundancy. And the real time, reliability, and processing parameters matching are notconsidered adequately. Secondly, there is no available NURBS curve interpolation algorithms toconsider the dwell time of polishing machining process. Therefore, it is very necessary to optimizeprevious NURBS interpolation algorithms and expand the application of the methods to polishing.And there is great theoretical and engineering significance for improving the performances ofcutting and polishing CNC control systems. For this reason, the differential geometry theory, openexperimental platform, VC + + ,etc. are applied in this thesis. And a multi-objective coordinationcontrol efficient NURBS curve interpolation algorithm for cutting is explored to include the chorderror redundancy, and a dwell time considered NURBS curve interpolation algorithm is alsostudied for flexible polishing. The main works are as follows:1) An efficient NURBS curve interpolation algorithm for multi-objective coordinated controlis proposed and defined the format of the G code . The algorithm can also satisfy the maximumchord error, the chord error redundancy, the machine tools acceleration/deceleration performances,and real time. In particular, the relationship and matching method between the chord error and thenormal acceleration are identified in this thesis. So, it can enhance the coordination ability tocontrol the processing quality and processing efficiency.2) A efficient NURBS curve interpolation algorithm is proposed to consider dwell time forflexible polishing based on machining error model. And defined the format of the G code. Themachining errors can be eliminated by using of the developed algorithm in the NURBSinterpolation process. So, the algorithm provides a reference for improving machining quality offlexible polishing and other machining methods which need to control the dwell time.3) Based on the above researches, the NURBS curve interpolation simulation software is developed by means of VC++ and Matlab. And an open CNC system hardware platform isconstructed in the form of 'PC+ motion controller'. the digital simulation and physical machiningexperiment results demonstrate the effectiveness of the proposed algorithm and there G code iseffective.In conclusion, the research works in this thesis make the NURBS curve interpolationmachining process for cutting more efficient and expand it's application to polishing.