星载大型可展开索网天线结构设计与型面调整
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摘要
星载大型环形桁架索网天线是近年来备受各国宇航界学者关注的一种空间可展开天线结构形式。三向网格索网天线是该类天线中的一种重要形式。以工程项目为背景,本文对环形桁架索网天线结构的型面几何设计、索网预拉力设计以及型面精度调整方法进行了比较详细而深入的研究。主要内容如下：
首先,以索网型面的原理误差最小为设计目标,提出了三向网格索网天线型面几何设计的新方法。方法中,索网型面在天线光学口径面上的投影取为正三角形网格,索网型面结点均取在与理想抛物面同轴且等焦距的某一抛物面上,正三角形网格的边长由天线型面的设计精度要求来确定。以轴向均方根误差为天线型面精度的衡量标准,从理论上证明了本文方法所设计的索网型面为最佳索网型面。设计算例结果表明,该方法优于已有文献中所给出的型面设计方法。
其次,为优化设计带预应力的环形桁架索网天线结构,将天线结构的整体设计分为两步：第一步,不考虑环形桁架结构变形,提出了索网结构预拉力优化设计的两种新方法；第二步,以索网结构预拉力的设计结果为基础,考虑环形桁架结构在索网预拉力作用下的变形,提出了基于环形桁架结构变形补偿的天线索网结构整体设计方法。
索网结构预拉力优化设计中,所提第一种方法专门用于三向网格旋转抛物面索网结构的预拉力优化设计。以索网面中的索段拉力尽可能均匀为设计目标,并基于该类索网结构的力平衡特性,构建了该类索网结构预拉力优化设计的思路与方法。该方法简便易行,且效果较好。第二种方法以矩阵论中线性方程组的极小范数解理论为依据,从索网结构的结点力平衡方程组出发,并结合索网结构预拉力优化设计问题的特点,将以所有索段预拉力为设计变量的非线性数学规划问题转化为仅以前、后索网面中的索段拉力均值为设计变量的数学规划问题。与第一种方法相比,该方法的优化效果略差,但其具有较好的通用型,能够对偏置抛物面索网结构、准测地线索网结构等多种复杂索网结构的预拉力进行设计。结合旋转抛物面、偏置抛物面等多个索网结构的预拉力设计算例,说明了以上两种方法的正确性和有效性。
以索网结构预拉力的优化设计结果为基础,构建了天线整体结构的有限元模型,模型中加入了天线环形桁架结构,并进行了天线整体结构的找形分析,天线整体结构的找形分析结果表明,网面索段的拉力均匀性发生了较大的恶化。为有效设计索网天线整体结构的预拉力,给出了带桁架索网天线结构的预拉力设计方法。方法以反复迭代的办法对天线索网结构进行预拉力设计,迭代过程中的每一次索网预拉力设计,都是以天线整体结构的找形分析结果中索网结构的位形作为预拉力重设计时索网结构的基础模型,且该索网模型中边界节点固支,其索段预拉力优化设计采用极小范数方法求解。在每一次索网预拉力重设计之后,将索网结构重新与桁架结构组合并进行整体结构的找形分析,直到天线整体结构中网面索段最大拉力比趋于稳定为止。算例结果说明了天线整体结构的预拉力优化设计方法的有效性。
最后,为尽可能减少索网型面调整的工作量,并保证计算机辅助索网型面优化调整的实时性,以工程实际中逐根索段进行调整的事实为依据,提出了一种新的索网型面优化调整方法,即以每根索段的调整都能够使索网型面精度具有最大的提升量为目标,在每次的优化过程中,仅选取单根索段作为最佳待调整索段,并以最佳待调整索段的调节量为设计变量,以所有索段的应力均小于许用应力且大于零为约束条件,构建当前索网型面优化调整所需的数学模型。以天线结构基频和索网预拉力大小的预期值为依据,方法中详细给出了最佳待调节索段的选择方法。算例结果说明了方法的正确性和有效性,同时也表明,将所有纵向拉索的调节量同时作为设计变量进行优化是不必要的。
Large deployable Astromesh antenna, which is attracting more and more attention of space navigation scholars all over the world, is an important type for deployable mesh antenna for satellites. Triangular cable-net structure is a main form of the cablenet structure of this type antenna. Based on some engineering projects, the methods of geometrical design, pretension design and profile adjustment of structure of Astromesh antenna are mainly discussed in this paper. The main research works are as follows:
Firstly, aimed at minimizing the principle error of the large reflector, a geometric design method for Astromesh 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 regular 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. Certain formulas are established 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, the validity of the proposed method has been proved theoretically. Furthermore, illustration is provided to compare the results designed with the method proposed and with other methods.
Secondly, the pretension design of the structure of large mesh antenna is discussed, which falls into two steps. In the first step, based on the assumption that the ring truss is rigid enough or the cablenet structure has an ideal boundary condition, pretension optimization for the pure cablenet structure of mesh antenna is done. Then, with the designed pretension cable-net structure as input, and taking the truss's elasticity into account, the ring truss of the mesh antenna is redesigned.
When we discuss the pretension design of the pure cable-net structure of mesh antenna, two approaches are developed. The first optimum design method is especially for the cable-net structures of axi-symmetric parabolic antenna with a triangular net form, based on the characteristic of such structures. The second, otherwise, is a method for the pretension design of most general cable-net structures of mesh antenna, the optimization model of which is deduced from the static force balance equations of the structure by the concept of minimum norm solution of linear equations. By a comparison of the design results in some illustrations with the two approaches, it is showed that the first method takes less computation and gives a little better results, but the second method is always more applicable when the application scope is taken into account.
Then, with the pretension cable-net structure designed under an ideal boundary condition as input, the elasticity of the ring truss is fully taken into account. Based on the feature of the deformation of the truss structure induced by the cable-net structure's pretension, a reiteration method to redesign the pretensions of cable-net structure of the mesh antenna is proposed. In each iteration step, the tension of the cable net structure is firstly redesigned using the minimum norm method with the position of the deformed structure as initial conditions, and then with the redesigned cable net structure as a part of the whole antenna structure, form-finding analysis of the whole structure is done. The iteration procedure is repeatedly done until the maximum tension ratio of the cables on the mesh surface is stabled. An illustrative example is given to clarify the effectiveness of the reiteration method proposed.
Finally, with the goal to improve the reflector's precision in its assembling and setting procedure, the problem of optimal adjustment of the profile of mesh antenna is discussed. Aimed at minimizing the total adjustment workload and improving the calculative efficiency while we decide which cables are to be adjusted and how much the according adjustment are to be made, a new method for the profile adjustment of mesh antenna is proposed. Base on the fact that the cable adjustment is always done one by one in the factory, the method chooses only one cable as the adjusting cable and designates its adjustment quantity as the design variable at each optimization process. In order to gain maximum efficiency while only one cable is to be adjusted every time, certain criterion is established for selecting the suitable cable among all the adjustable cables. Simulation results show that the method has a certain validity and feasibility.
首先,以索网型面的原理误差最小为设计目标,提出了三向网格索网天线型面几何设计的新方法。方法中,索网型面在天线光学口径面上的投影取为正三角形网格,索网型面结点均取在与理想抛物面同轴且等焦距的某一抛物面上,正三角形网格的边长由天线型面的设计精度要求来确定。以轴向均方根误差为天线型面精度的衡量标准,从理论上证明了本文方法所设计的索网型面为最佳索网型面。设计算例结果表明,该方法优于已有文献中所给出的型面设计方法。
其次,为优化设计带预应力的环形桁架索网天线结构,将天线结构的整体设计分为两步：第一步,不考虑环形桁架结构变形,提出了索网结构预拉力优化设计的两种新方法；第二步,以索网结构预拉力的设计结果为基础,考虑环形桁架结构在索网预拉力作用下的变形,提出了基于环形桁架结构变形补偿的天线索网结构整体设计方法。
索网结构预拉力优化设计中,所提第一种方法专门用于三向网格旋转抛物面索网结构的预拉力优化设计。以索网面中的索段拉力尽可能均匀为设计目标,并基于该类索网结构的力平衡特性,构建了该类索网结构预拉力优化设计的思路与方法。该方法简便易行,且效果较好。第二种方法以矩阵论中线性方程组的极小范数解理论为依据,从索网结构的结点力平衡方程组出发,并结合索网结构预拉力优化设计问题的特点,将以所有索段预拉力为设计变量的非线性数学规划问题转化为仅以前、后索网面中的索段拉力均值为设计变量的数学规划问题。与第一种方法相比,该方法的优化效果略差,但其具有较好的通用型,能够对偏置抛物面索网结构、准测地线索网结构等多种复杂索网结构的预拉力进行设计。结合旋转抛物面、偏置抛物面等多个索网结构的预拉力设计算例,说明了以上两种方法的正确性和有效性。
以索网结构预拉力的优化设计结果为基础,构建了天线整体结构的有限元模型,模型中加入了天线环形桁架结构,并进行了天线整体结构的找形分析,天线整体结构的找形分析结果表明,网面索段的拉力均匀性发生了较大的恶化。为有效设计索网天线整体结构的预拉力,给出了带桁架索网天线结构的预拉力设计方法。方法以反复迭代的办法对天线索网结构进行预拉力设计,迭代过程中的每一次索网预拉力设计,都是以天线整体结构的找形分析结果中索网结构的位形作为预拉力重设计时索网结构的基础模型,且该索网模型中边界节点固支,其索段预拉力优化设计采用极小范数方法求解。在每一次索网预拉力重设计之后,将索网结构重新与桁架结构组合并进行整体结构的找形分析,直到天线整体结构中网面索段最大拉力比趋于稳定为止。算例结果说明了天线整体结构的预拉力优化设计方法的有效性。
最后,为尽可能减少索网型面调整的工作量,并保证计算机辅助索网型面优化调整的实时性,以工程实际中逐根索段进行调整的事实为依据,提出了一种新的索网型面优化调整方法,即以每根索段的调整都能够使索网型面精度具有最大的提升量为目标,在每次的优化过程中,仅选取单根索段作为最佳待调整索段,并以最佳待调整索段的调节量为设计变量,以所有索段的应力均小于许用应力且大于零为约束条件,构建当前索网型面优化调整所需的数学模型。以天线结构基频和索网预拉力大小的预期值为依据,方法中详细给出了最佳待调节索段的选择方法。算例结果说明了方法的正确性和有效性,同时也表明,将所有纵向拉索的调节量同时作为设计变量进行优化是不必要的。
Large deployable Astromesh antenna, which is attracting more and more attention of space navigation scholars all over the world, is an important type for deployable mesh antenna for satellites. Triangular cable-net structure is a main form of the cablenet structure of this type antenna. Based on some engineering projects, the methods of geometrical design, pretension design and profile adjustment of structure of Astromesh antenna are mainly discussed in this paper. The main research works are as follows:
Firstly, aimed at minimizing the principle error of the large reflector, a geometric design method for Astromesh 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 regular 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. Certain formulas are established 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, the validity of the proposed method has been proved theoretically. Furthermore, illustration is provided to compare the results designed with the method proposed and with other methods.
Secondly, the pretension design of the structure of large mesh antenna is discussed, which falls into two steps. In the first step, based on the assumption that the ring truss is rigid enough or the cablenet structure has an ideal boundary condition, pretension optimization for the pure cablenet structure of mesh antenna is done. Then, with the designed pretension cable-net structure as input, and taking the truss's elasticity into account, the ring truss of the mesh antenna is redesigned.
When we discuss the pretension design of the pure cable-net structure of mesh antenna, two approaches are developed. The first optimum design method is especially for the cable-net structures of axi-symmetric parabolic antenna with a triangular net form, based on the characteristic of such structures. The second, otherwise, is a method for the pretension design of most general cable-net structures of mesh antenna, the optimization model of which is deduced from the static force balance equations of the structure by the concept of minimum norm solution of linear equations. By a comparison of the design results in some illustrations with the two approaches, it is showed that the first method takes less computation and gives a little better results, but the second method is always more applicable when the application scope is taken into account.
Then, with the pretension cable-net structure designed under an ideal boundary condition as input, the elasticity of the ring truss is fully taken into account. Based on the feature of the deformation of the truss structure induced by the cable-net structure's pretension, a reiteration method to redesign the pretensions of cable-net structure of the mesh antenna is proposed. In each iteration step, the tension of the cable net structure is firstly redesigned using the minimum norm method with the position of the deformed structure as initial conditions, and then with the redesigned cable net structure as a part of the whole antenna structure, form-finding analysis of the whole structure is done. The iteration procedure is repeatedly done until the maximum tension ratio of the cables on the mesh surface is stabled. An illustrative example is given to clarify the effectiveness of the reiteration method proposed.
Finally, with the goal to improve the reflector's precision in its assembling and setting procedure, the problem of optimal adjustment of the profile of mesh antenna is discussed. Aimed at minimizing the total adjustment workload and improving the calculative efficiency while we decide which cables are to be adjusted and how much the according adjustment are to be made, a new method for the profile adjustment of mesh antenna is proposed. Base on the fact that the cable adjustment is always done one by one in the factory, the method chooses only one cable as the adjusting cable and designates its adjustment quantity as the design variable at each optimization process. In order to gain maximum efficiency while only one cable is to be adjusted every time, certain criterion is established for selecting the suitable cable among all the adjustable cables. Simulation results show that the method has a certain validity and feasibility.
引文
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