华中科技大学 博士学位论文 自生长造型、自基准测量与自引导加工方法的研究 姓名：黄东兆 申请学位级别：博士 专业：机械制造及其自动化 指导教师：师汉民 20090906 华 中 科 技 大 学 博 士 学 位 论 文 I 摘 要 本文以自组织为出发点，对曲线的造型、测量与加工进行了研究，提出了自生 长造型、自基准测量与自引导加工三个概念，研究了相关的技术。对自基准测量与 自引导加工进行了仿真实验与实际实验。 本文分析了几种主要的曲线曲面造型方法，参照生物细胞的分裂与个体发育过 程，以含弧长、曲率、挠率等信息的数据单元构造曲线、曲面的基本元胞，通过设 计元胞的生长规则实现自由曲线的造型。提取了抛物线、Corun- Euler 曲线、阿基米 德螺线、分形曲线、螺旋线等曲线的元胞及其生长规则，对它们的自生长造型进行 了仿真实验，并通过设计元胞的生长规则生成了一些具有特色的平面曲线与空间曲 线。 如何从已知曲线/曲面中提取元胞及其生长规则，这是自生长造型的正问题；如 何设计与控制元胞的生长规则来生成曲线/曲面，这是自生长造型的逆问题。研究正 问题是为了加工的需要，这在自引导加工中有所体现；研究逆问题是为了造型的需 要，这在自基准测量中有所应用。 分析了现阶段几何测量的方法，首次提出了一种自基准的测量方法，以被测对 象已经测出的部分作为继续测量的基准，从而可以用小尺寸的量仪测量大尺寸的工 件。设计了 3 种自基准测量的实现方案：叠加式自基准测量、滚轮前置式自基准测 量与测头前置式自基准测量。针对叠加式测量进行了多次仿真实验，肯定了方法的 可行性。研制了滚轮前置式自基准测量的装置，利用该装置对圆、椭圆、凸轮与冰 刀弧进行了测量，并重构出形状，实现了自基准测量的构想。 目前数控系统的轨迹控制方法都是基于坐标，而不是基于几何形状，在它们的 控制回路中没有零件的几何形状模型。因此本文提出了自引导加工的概念，它将工 件的实际轮廓与指令轮廓相匹配，用已加工出的部分引导下一步的加工，它是基于 几何形状的直接反馈。本文就连续小直线段与圆弧的自引导加工分别给出了相应的 算法，研究了自引导加工中的轮廓匹配与误差预估，并进行了相应的仿真实验。 本文将自引导加工方法初步应用于实际加工。对于波浪曲面形状试件与山丘形 华 中 科 技 大 学 博 士 学 位 论 文 II 状试件的加工轨迹，用连续小直线段来表达时，分别需 128212 段与 184954 段，是 G0连续；而用圆弧元胞来表达时，分别需 15838 段与 21669 段，是 G1连续，更重要 的是圆弧元胞含有加减速控制所需要的曲率与弧长信息。在实际加工中，用连续小 直线段方式加工时，两试件的平均加工速度分别为 10.83mm/s与 11.35mm/s，表面粗 糙度 Ra 值分别为 1.93um 与 1.86um；而用圆弧元胞来表达加工轨迹时，两试件的平 均加工速度分别为 39.01mm/s 与 40.12mm/s，表面粗糙度 Ra 值分别为 1.38um 与 1.34um。故用圆弧元胞来表达试件的加工轨迹时，加工速度与表面质量均有较大的 改善。 关键词：自组织 自生长造型 自基准测量 自引导加工 华 中 科 技 大 学 博 士 学 位 论 文 III Abstract Based on the thought of self- organization, modeling, measuring and machining of curves are studied, three concepts (including self- growing modeling, self- reference measuring and self- guided machining) are presented in this thesis, relative techniques are also studied. Simulation and actual experiments are made for self- reference measuring and self- guided machining. Several major curve and surface modeling methods are analyzed in this thesis, the process of biological cell division and individual growth is used for reference, data unit that includes arc- length, curvature, torsion and etc is used as basic cell of curve and surface. And modeling of free- form curve is achieved by designing growth- rules of cell. The cells and grow rules of some curves including parabola, Corun- Euler curve, Archimedes curve, fractal curve and spiral line are extracted, some simulation experiment are made for self- growing modeling of the above curves. By designing the grow rules, some characteristic planar curves and space curves are created. How to extract cells and grow- rules from a known curve and surface, which is positive issue of self- growing modeling. And how to generate the curve and surface by designing and controlling the grow rules, which is inverse issue of self- growing modeling. Studying the positive issue is for machining, it is applied in self- guided machining. Studying the inverse issue is for modeling, it is applied in self- reference measuring. The methods of geometric measurement are analyzed at present, a method of self- reference measurement is first presented. It uses known part of measured object as the reference for continuing to measure, so the large- size workpiece can be measured by use of small- size measuring instrument. Three implementation projects for self- reference measuring are designed, which are superposition- type self- reference measurement, roller- preposed self- reference measurement and prope- preposed self- reference measurement. The feasibility of superposition- type measurement method is checked through many simulation experiment. The device for roller- preposed self- reference measurement is developed. The shape of circle, ellipse, cam and skate- arc are measured by using the device, and the shapes are reconstructed. The idea of self- reference measurement 华 中 科 技 大 学 博 士 学 位 论 文 IV is achieved through these above experiment. The trajectory controlling methods in current NC systems are all based on coordinates, not baseded on geometrical shape. There are not geometrical shape models of parts in control loops of NC systems. The concept of self- guided machining is presented in this thesis. It make the machining profile matching instruction profile, use the part processed to guide the next process. It is direct feedback for geometrical shape. The corresponding effective algorithm is presented for the self- guided machining of the consecutive small blocks and arc, respectively. The profile matching and error prediction of self- guided machining are studied, and relevant simulation experiments are made. Self- guided machining is preliminary applied to actual machining. For specimens of wave surface shape and massif shape, when their machining paths are described by use of consecutive linear blocks, they need 128212 and 184954 linear blocks, respectively. When their machining paths are described by use of arc- cells, they need 15838 and 21669 arc- cells, respectively. It s more important that these arc- cells have information of curvatures and arc- lengths to control acceleration and deceleration. When the above two specimens ar