基于Moore-Penrose逆的索网天线预拉力设计方法  

Least-norm Method for Pretension Optimization of Mesh Reflector

作　　者：杨东武[1] 仇原鹰[1] 保宏[1] 

机构地区：[1]西安电子科技大学机电工程学院,西安710071

出　　处：《机械工程学报》2012年第21期22-27,共6页Journal of Mechanical Engineering

基　　金：国家自然科学基金资助项目(50775170;51175397)

摘　　要：为保证星载索网天线反射型面具有一定的刚度和热稳定性,展开态的索网结构须具有一定的预应力。结合天线索网结构的组成特点,将索网结构的预拉力设计过程分为三个阶段:优化设计前索网面索段的预拉力;计算纵向拉索的索段预拉力;优化设计后索网面的索段预拉力。在前、后两次网面索段预拉力的优化设计中,网面索段预拉力的均匀化程度以网面中各索段拉力与网面索段的拉力均值之间的差值平方和大小来衡量;认为差值平方和越小,网面索段拉力越均匀。以索网结点在理想位置力平衡所需满足的方程为主要约束条件,建立索网预拉力优化设计的数学模型。结合线性相容方程组极小范数解的概念,通过模型等效转换讨论其有效求解方法。算例结果表明,以网面索段拉力与其均值的差方和最小为目标来优化设计索网预拉力的方法简便、有效。To ensure space-borne mesh antenna reflector on state has a stable surface shape under vibration and thermal environments,the mesh structure shall be pre-stressed.Based on the component characteristics of mesh antenna structure,the cable pretension design process is divided into three stages,i.e.,the tension optimum design of cables in the front net,the calculation of tensions in the tension ties,and the tension optimum design of cables in the rear net.While optimization design on tensions is done for the cables in the front net or in the rear net,the squared deviation of each tension from the mean is used to measure the uniformity of the tensions,and the smaller is the squared deviation,the more evenly the net cable tensions are thought to be.With the force balance equations of the net structure as the main constraints,tension optimum design models are established.Based on the concept of the least-norm solution of consistent linear equation system,method for solving the optimization models is developed.Simulation results show the effectiveness of the measure criterion on the uniformity of the cable tensions,and the effectiveness of the resolution method on solving the optimization models.

关 键 词：反射面天线 索网反射面 预拉力 极小范数 

分 类 号：V443[航空宇航科学与技术—飞行器设计]