导　　师： 唐伟

学科专业： H0202

授予学位： 硕士

作　　者： ;

机构地区： 山东大学

摘　　要： 现代制造业对曲面加工的需求和质量要求不断提高，而传统的以直线、圆弧逼近样条曲线的插补方法，已经远远不能满足这一要求；nurbs曲线直接插补技术虽然可以完成自由型曲线曲面的直接插补，但其复杂的计算方法和庞大的计算量导致插补过程的实时性很难实现，而采用一些简化算法在保证实时性的前提下却不可避免地要付出降低加工精度的代价，在一些精度要求较高的场合的应用受到很大的限制。 本课题研究的pythagorean hodograph（ph）曲线插补技术，充分利用ph曲线适合于数控加工的优点，实现对自由型曲线曲面的直接插补，从而改善零件的加工效率和加工质量，以适应现代数控技术的发展要求。 本文首先给出了ph曲线的定义，分析了ph曲线的弧长计算的表达式和偏置曲线的表示形式。随后研究了两类常用ph曲线的构造方法，研究了bézier曲线成为ph曲线的条件，给出了相应的控制顶点计算公式。在初始数据不满足直接插值的条件下，通过插入满足条件的中间数据来构造段数最少的ph样条曲线的方法完成对三次ph曲线的c1插值。对五次ph曲线，用bézier曲线形式给出其hermite插值并给出了最佳解的选取方法。对这两类ph曲线的构造方法分别通过数值实验进行了验证。 然后给出了ph曲线的插补方案，在进给速度为常数、时间的函数、弧长的函数和曲率变量的函数的情况下分别推导了ph曲线数控插补的插补算法，采用前加减速控制方法解决了数控插补过程中的速度控制问题，提出了实现ph曲线插补器的流程图，并提出了ph曲线插补技术的计算机数控编程方法。接下来对基于ph曲线的曲面插补技术进行了初步探讨，讨论了其实现过程并给出了刀具中心轨迹的确定方法。 最后给出了ph曲线插补技术的应用实例，通过仿真实验证明ph曲线插补技术的应用可以改善磨料射流加工的加工质量。 While modern manufacturing's needs and quality requirements for curved surface machining keep increasing, the traditional manner based on interpolation of beeline and circle arc approaching spline is far from sufficient to satisfy the needs; although NURBS interpolation can accomplish the direct interpolating of freeform curves and curved surfaces, its complicated calculating way and enormous amount of calculation makes it hard to realize the real-timing of interpolation process. Some simplified calculating manners can make sure its real-timing at the cost of reduction of machining precision and thus was restricted greatly in some occasions which have high requirements for precision. The Pythagorean Hodograph/(PH/) curve interpolation of this research which makes full use of the advantages that PH curve is fit for CNC machining, realizes direct interpolation to freeform curves and curved surfaces, thus improving the parts' machining efficiency and quality in order to adapt to the development requirements of modern CNC techniques. At the beginning of this thesis, the definition of PH curve is provided, and the expression of PH curve's arc calculation and the form of its offset is analyzed. Then the constructing methods of two common PH curves are studied which give the conditions of Bezier curve being PH curve and the computing formula of controlling points. Under the condition that the initial data can't meet direct interpolating, C~1 interpolating of PH cubic curve is accomplished by interpolating appropriate midterm data to construct PH curve of least segments. PH quintic curve's interpolating is accomplished by Bezier curve' form and the method to find its best answer is also provided. The data experiments about the constructing methods of PH cubic and quintic curves are presented then. After that, it gives the plan to realize PH curve interpolation and analyses the computing manner of PH curve according to the different feedrate forms of constant, function of time, arc and curvature, solves the problem of speed control in the process of interpolation by adopting preceding acceleration//deceleration control. Then, the actualizing flow of PH curve interpolator is provided, and the way of PH curve interpolation's CNC programming is put forward. It then probes into curved surfaces interpolation based on PH curve tentatively, discusses the process of PH curve interpolation for curved surfaces and provides the method to find tool's center locus. Finally, the application of PH curve interpolation is provided, and it's proved that the application can improve the machining quality of Abrasive Water Jet System.

关 键 词： 曲线 直接插补技术 数控编程 磨料水射流加工 速度控制

分 类 号： [TG664]

领　　域： [金属学及工艺]