大口径射电望远镜反射面支承机构研究

发布时间：2018-03-13 02:18

本文选题：FAST　切入点：悬链线方程　出处：《上海交通大学》2014年博士论文　论文类型：学位论文

【摘要】：大型射电望远镜是人类探测宇宙的主要工具,各种各样大型射电望远镜的设计方案层出不穷,而把索网结构作为大型射电望远镜的主动反射面支承机构是一种新颖的设计方案。本文针对500米口径射电望远镜的反射面支承索网机构进行研究,该机构是一种多输入多输出的柔索并联机构,根据最小势能原理和变分原理得到索网中任意两节点之间的柔索方程是悬链线方程,采用悬链线方程建立了多输入多输出的柔索并联机构的数学模型。本文主要研究内容如下:第一,利用最小势能原理和变分原理推导出柔索的方程是悬链线方程,并利用悬链线方程建立了FAST反射面支承索网机构中索网结构的数学模型。第二,根据索网具有层次性的特点把索网分为若干层。用悬链线方程建立的索网数学模型将引入大量的非线性方程组,本文根据相邻层之间的主索具有相似性特点提出了逐层迭代法。逐层迭代法解决了如何设定索网机构建立的非线性方程组的初始值问题,并求解了索网在自然状态下的形状。第三,利用对称法求解索网机构在张紧状态下的数学模型,根据索网机构具有旋转对称和镜像对称的特点对整个索网进行简化。把整个索网划分为若干个部分,这些局部索网分为原对称索网和对称索网,原对称索网经过坐标变换矩阵可以求解出对称索网。另外还提出了用逆迭代法来处理索网的边界问题。第四,介绍了FAST工作状态下旋转抛物面和球冠面之间的关系,并分类讨论了旋转抛物面在移动的过程中其旋转轴与主坐标系三个轴之间的转角关系。提出了同伦算法和逐步迭代法分别对FAST的缩小模型的工作状态进行了求解。通过对比两种算法的计算效率最终确定了逐步迭代法是更理想的算法。
[Abstract]:Large radio telescopes are the main tools for human exploration of the universe, and various design schemes for large radio telescopes have emerged one after another. It is a novel design scheme to take the cable mesh structure as the active reflector supporting mechanism of the large radio telescope. In this paper, the structure of the reflector supporting cable mesh of the 500m aperture radio telescope is studied. The mechanism is a multi-input multi-output flexible cable parallel mechanism. According to the principle of minimum potential energy and variational principle, the cable equation between any two nodes in the cable network is a catenary equation. The mathematical model of multi-input and multi-output flexible cable parallel mechanism is established by using catenary equation. The main contents of this paper are as follows: first, by using the principle of minimum potential energy and variational principle, the equation of flexible cable is derived as catenary equation. By using catenary equation, the mathematical model of cable net structure in FAST reflector supporting cable mesh mechanism is established. According to the hierarchical characteristics of cable network, the cable network is divided into several layers. The mathematical model of cable network established by catenary equation will introduce a large number of nonlinear equations. In this paper, according to the similarity of the main cables between adjacent layers, a layer by layer iterative method is proposed, which solves the problem of how to set the initial value of the nonlinear equations set up by the cable-net mechanism. The shape of cable net in natural state is solved. Thirdly, the mathematical model of cable mesh mechanism under tension is solved by using symmetry method. According to the characteristics of rotational symmetry and mirror symmetry of cable-net mechanism, the whole cable-net is simplified. The whole cable-net is divided into several parts, and these local cable-nets are divided into the original symmetric cable-net and the symmetrical cable-net. The original symmetric cable net can be solved by coordinate transformation matrix. In addition, the inverse iteration method is proposed to deal with the boundary problem of cable network. 4th, the relationship between the rotating parabola and the spherical crown surface under FAST operation is introduced. The rotation angle relationship between the rotation axis and the three axes of the main coordinate system is discussed in this paper. The homotopy algorithm and the stepwise iteration method are proposed to solve the working state of the reduced model of FAST respectively. By comparing the computational efficiency of the two algorithms, it is determined that the step-by-step iterative method is a better one.
【学位授予单位】：上海交通大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TH751

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