第46卷第21期 机械工程学报 Vol.46 No.21 2010年11月 JOURNAL OF MECHANICAL ENGINEERING Nov. 2010 DOI: 10.3901/JME.2010.21.187 抛物面索网天线的最佳型面设计方法 杨东武尤国强保宏 (西安电子科技大学机电工程学院西安710071) 摘要：在太空无重力工作环境下，星载索网天线反射面由张紧的网格平面拼合而成。为尽可能降低天线索网型面的原理误差， 提出一种新的索网型面生成方法。方法要求抛物面索网天线型面在天线光学口径面上的投影为正三角形网格，索网反射面的 型面结点均取在与理想抛物面同轴且等焦距的某映射抛物面上，投影正三角形的边长由天线反射面的焦距及型面设计的原理 误差要求确定，映射抛物面的具体位置由投影正三角的边长及反射面的焦距确定。以空间任意三角形与抛物面之间的轴向方 均根误差计算公式的推导为基础，讨论在天线光学口径面上投影面积为定值的空间三角形与抛物面之间轴向方均根误差取得 极小值的条件，得出抛物面索网天线型面在天线光学口径面上投影为正三角形网格时原理误差最小的结论。索网型面设计的 算例结果表明本文方法有效、实用。 关键词：反射面天线近似误差抛物面 星载天线 中图分类号：V443.4 Best Geometry Design Method for Paraboloid Reflectors of Mesh Antenna YANG Dongwu YOU Guoqiang BAO hong (School of Electromechanical Engineering, Xidian University, Xi'an 710071) Abstract: Space-borne mesh antenna works in space environment without gravity. Under the influence of the internal tension, reflectors of mesh antenna are approximated with flat facets. Aimed at minimizing the systematic approximation error of the reflector, a geometry design method for paraboloid reflectors of mesh antenna is developed. To subdivide a paraboloid surface, the first step of the geometric scheme is to subdivide the inscribed regular hexagon of the optical aperture circle into small equilateral triangles. Then the points of intersection of these triangles are projected or mapped on the paraboloid surface using a suitable origin of coordinates to obtain the final nodal coordinates of the facets. Based on the systematic approximation error requirement in design and the paraboloid focal length of the reflector, certain formulas are given to determine the side length of the triangles and the origin coordinates of the paraboloid when the mapping is done. With axial square mean error as the measure of reflector's precision, a formula is derived for calculating the systematic approximation error when a spatial arbitrary triangle is used to approximate part of a paraboloid reflector. And when the spatial triangle has a certain projected area on the optical aperture circle surface, the conditions for the spatial triangle to get the best approximation to the paraboloid reflector is discussed, which gives the result that when the best approximation is expected, the optical aperture circle surface should be divided into small equilateral triangles as far as possible. A comparison is done among all the design methods available in a geometry design example for a paraboloid reflector and results show the validity and feasibility of the proposed method. Key words: Reflector antennas Approximation error Paraboloid surface Space-borne antenna 质、可展开，为满足电性能要求，还需要有较高的 0前言 型面精度。可展开天线一般分为板式、索网式与 充气式三类2，其中索网式天线由于具有收缩比大， 由于发射装置的限制，大型空间天线要求轻 重量轻等优点而成为各国竞相研究的热点。 Astromesh 结构是索网天线的重要结构形式之 *国家部委预研基金(51321040102)、国家自然科学基金(50775170)和高 校基础科研(72104212)资助项目。20100806收到初稿，20110525收 _13-41。索网天线反射面为金属丝网，附着于前索网 到修改稿 背部完成电波反射任务。索网是天线反射面的主要