反射式衛星天線之展開機構設計與折疊幾何研究

Abstract

運送配置反射式天線衛星的太空載具其內部空間通常為圓筒狀，且橫切面的面積遠小於展開後的反射式衛星天線。因此，如何讓折疊後的反射式天線其橫切面的截面積變小，使其折疊後尺寸能順利裝入太空載具內部為一個重要的議題。 本研究針對用於衛星天線的展開機構提出一個系統化的設計方法，此方法是以圖論與流值法為基礎，設計的展開機構由數根連桿所組成，桿件之間的連結，可藉由圖論來描述之間的關係。依據需求而定的設計準則，搭配以負載的傳遞路徑及損失所建構出的流值法，在所有被列舉出的運動鏈裡，選擇出適合的機構。依此，本研究提出一個能最有效率傳遞負載的展開機構。 太空中使用的薄膜反射式天線，是一種輕量化的結構且可以被緊密的折疊。為了設計可以在衛星上展開的薄膜反射式天線，本研究從仿生學在工程上的應用尋求解決的方法，反射式天線在展開後的幾何輪廓相似於完全綻放後的旋花類植物。既然，這二者展開後的幾何輪廓相似，則可以將展開後的反射式天線，折疊成像旋花類植物的花苞一樣的外型。本研究將薄膜反射式天線，經由來自仿生學的靈感，折疊而成旋花類植物的花苞，並將其幾何輪廓用方程式表示，調整方程式裡的參數，得到較高的折疊前與後反射式天線面積的比值，表示經由設計後的天線反射面可折疊的更小。 本研究也製作了兩個展開機構，分別具有5與10支拋物狀的骨架。這兩個機構可以將薄膜反射面分別折疊成像是5或10瓣旋花類植物的花苞。接著，使用影像處理的方法比較理論值與模型在折疊狀態時二者間幾何特徵的差異性。比較的結果呈現出，經由影像處理所量測到的反射面折疊後直徑與理論值所計算的結果非常接近。本研究中所提出的幾何輪廓設計，適合用於被置入太空載具內的折疊反射面。

The space available inside rockets for transporting satellites with reflector antennas is typically cylindrical in shape, and its cross-sectional area is considerably smaller than the reflector antenna after deployment. Therefore, the cross-sectional area of the folded reflector must be smaller than the available interior rocket space. This thesis presents a systematic method for designing a deployable mechanism of reflector antennas. The procedure is based on the graph theory and a flow value method. The mechanism is composed of several links. Connections between these links are represented by using the graph theory. Rules representing design criteria and the flow value method based on load flow are taken into account to evaluate and select mechanisms among those that are enumerated in the database. Accordingly, this study presents a deployable mechanism that transmits load the most efficiently. Membrane reflectors in aerospace are a type of lightweight structure that can be packaged compactly. To design membrane reflectors from the perspective of deployment processes, bionic applications on morphological changes of plants are investigated. Creating biologically inspired reflectors, this thesis deals with fold geometry of reflectors, which refer to flower buds. This study uses mathematical formulation to describe geometric profiles of flower buds. Based on the formulation, new designs for deployable membrane reflectors derived from bionics are proposed. Adjusting parameters in the formulation of these designs leads to reflector area decrease before deployment. This study has also manufactured two test deployable mechanisms with five and ten parabolic ribs, respectively. Both mechanisms can fold the membrane similar to the morning glory buds of five and ten petals. Image processing is carried out to compare geometric characteristics between the formulation and test models in the fold state. Comparison results show that fold diameters obtained from measurement and formulation are very close. The proposed designs are suitable for the use of folded reflectors to be put inside a rocket.