天线机电热多场耦合理论与综合分析方法研究
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摘要
在影响军用电子装备性能指标的诸多因素中，机电耦合已成为一个重要的瓶颈问题，其具有典型的多学科交叉的特点。本文利用西电在天线结构研究方面的优势，在已有基础上，对面天线、相控阵天线设计与分析过程中的结构位移场、电磁场、温度场的多物理场耦合问题(CMFP)作深入探讨，就其建模理论与综合分析方法进行了研究。
提出了基于最小二乘原理的拟合抛物面方法，并分别给出了精确计算天线表面轴向、法向和径向误差的方法。基于反映变形天线反射面的形状的目的，提出了一种不同于传统最佳吻合方法的分块拟合变形反射面的方法(DFM)，利用周向函数与径向函数来确定每个块域的边界曲线，同时利用Coons曲面拟合每个块域。这里边界拟合函数包括三角函数、多项式函数以及B样条函数等。同时也给出了变形反射面精度的可靠性模型以及两种探索性的变形反射面拟合方法。
基于天线结构的变形分析，建立了天线的结构位移场模型。利用变形天线口径面的相位分布，根据PO法和傅立叶变换得到天线远区电场分布，建立了面天线机电两场耦合模型。针对天线工程中机电设计分离的现状，利用所建立的面天线机电耦合模型，研制了面天线机电性能综合分析系统，并结合工程案例对平台系统进行了实际测试。同时根据面天线机电耦合理论，直接以天线电性能为优化目标，建立了面天线机电综合优化设计模型。
通过引入天线电磁计算中包含天线焦距和口径的相关因子，提出了一种新的计算天线增益损失的数学公式，并分别给出了利用表面法向误差和径向误差进行计算的具体公式。利用脉动风荷的风压、风速与反射面结构变形之间的关系，建立了瞬态风荷下与平均风荷下的天线增益损失之间的关系式。
结合大型空间桁架天线结构的特点，基于提高空间天线电磁性能以及降低作动器能耗的目的，利用拟合变形反射面，建立了一种以天线轴向增益和作动器能耗为目标函数的空间桁架天线机电耦合优化模型，以用较低的作动器能耗，满足天线结构精度控制与电磁性能要求。耦合模型的约束条件主要包括杆件结构强度(应力)、作动器结构强度(轴力)和作动器的行程(变形)。把热载荷作为外载荷，通过智能桁架天线的结构——电磁耦合优化模型，建立了其机电热耦合优化分析模型，从而实现空间智能桁架天线反射面的准静态与动态形状调整与控制。
分析了矩形阵面APAA辐射单元位置误差对天线电场和方向性的影响，推导出了场强概率公式。针对APAA阵面的两种基本变形，建立了天线阵面热变形误差的数学模型。分析了结构误差对天线副瓣电平和增益的影响，并给出了一个可应用于工程实践的确定公差指标的方法。基于APAA的结构变形分析、热功耗分析，以及相位误差的引入，建立了矩形栅格APAA的机电热三场耦合模型，给出了多场耦合分析的流程，并对阵面弯曲变形和碗状双曲变形下的APAA电性能讲行了仿真分析。
The electromechanical coupling problem has been an important bottleneck of many factors influencing the performances of military electronic fumishments, which have a typical multidisciplinary characteristic. Using the advantage and research achievements of Xidian University in antenna structural design, the dissertation discusses the coupled multifield problems (CMFP) involving the mechanical structural displacement field, electromagnetic (EM) field and temperature field, which mainly take place in design and analysis period of parabolic antenna and phased array antenna. The modeling theory and synthesis analysis method of CMFP are studied in detail.
The least squared criterion based paraboloid fitting method is proposed. And the accurate calculation method for errors in axial, normal and radial direction of reflector surface is submitted. Based on the actual shape of distorted reflector and according to antenna mechanical structural analysis, a new divided-fitting method (DFM) is presented which is quite different from the traditional best-fit paraboloid method. It determines the boundary condition of each zone by first dividing the distorted reflector into many zones, then adopting Coons surface to fit each zone and combining the hoop function and radial function fitting methods. The boundary fitting functions include a trigonometric, polynomial and B spline functions etc. The reliability model of distorted surface precision and other two explored fitting methods are also introduced.
Based on the analysis of distorted antenna structure, an accurate structural displacement field model of antenna is made. By the phase distribution of distorted antenna aperture, physical optics (PO) method and Fourier transform are used to calculation far electric field of antennas. Then an electromechanical coupling model of reflector antennas is developed. Aimed at the separated status of structural and EM design in antenna engineering, an integrated synthesis analysis system for large reflector antenna was developed by use of acquired electromechanical coupling model. The analysis platform testing has been made with two antenna engineering cases. Furthermore, based on the electromechanical coupling theory of reflector antennas, a mechatronic synthesis optimization design model is developed, which directly uses the electrical performance as the optimization object.
A correlation factor consisting of focal length and diameter is introduced used in EM computation to develop a novel modified formula for antenna gainloss. And the corresponding mathematic expressions based on normal and radial error of reflector surface are presented respectively. By using the relationship among the transient wind pressure and speed and structural distortion, the mathematic expression of antenna gainloss under transient and average wind load is developed.
To obtain an extremely high accurate surface precision and the EM performances, an electromechanical synthesis optimization analysis model of space antenna structures is developed, which adopts the axial gain of antenna and power consumption of actuators as the objective functions, the material strength of bars and actuator's mechanical capability and active travel of actuator as constraint conditions. Based on the synthesis optimization model, a new coupled structural-electromagnetic-thermal optimization model is also given. The applications of coupling optimization model demonstrate the potential for the significant improvement of performances and for less necessary effort for shape control of space antenna.
The influence of position error of radiation element in rectangular planar active phased array antenna (APAA) on the electrical field intensity and directivity of antenna is studied. And the corresponding probability formula of field intensity is deduced. The characteristic of two basic deformations of APAA planar is analyzed. Then the mathematic model of thermal distortion error in planar of APAA is generated. Whereafter, the influence of rectangular planar distortion on the radiation pattern of APAA is studied. The analysis process of CMFP is also determined. According to the error model of antenna structural distortion, a coupled model involving displacement-electromagnetic-temperature field in rectangular planar APAA is established. The flow of coupled multifield analysis is drawn.
提出了基于最小二乘原理的拟合抛物面方法，并分别给出了精确计算天线表面轴向、法向和径向误差的方法。基于反映变形天线反射面的形状的目的，提出了一种不同于传统最佳吻合方法的分块拟合变形反射面的方法(DFM)，利用周向函数与径向函数来确定每个块域的边界曲线，同时利用Coons曲面拟合每个块域。这里边界拟合函数包括三角函数、多项式函数以及B样条函数等。同时也给出了变形反射面精度的可靠性模型以及两种探索性的变形反射面拟合方法。
基于天线结构的变形分析，建立了天线的结构位移场模型。利用变形天线口径面的相位分布，根据PO法和傅立叶变换得到天线远区电场分布，建立了面天线机电两场耦合模型。针对天线工程中机电设计分离的现状，利用所建立的面天线机电耦合模型，研制了面天线机电性能综合分析系统，并结合工程案例对平台系统进行了实际测试。同时根据面天线机电耦合理论，直接以天线电性能为优化目标，建立了面天线机电综合优化设计模型。
通过引入天线电磁计算中包含天线焦距和口径的相关因子，提出了一种新的计算天线增益损失的数学公式，并分别给出了利用表面法向误差和径向误差进行计算的具体公式。利用脉动风荷的风压、风速与反射面结构变形之间的关系，建立了瞬态风荷下与平均风荷下的天线增益损失之间的关系式。
结合大型空间桁架天线结构的特点，基于提高空间天线电磁性能以及降低作动器能耗的目的，利用拟合变形反射面，建立了一种以天线轴向增益和作动器能耗为目标函数的空间桁架天线机电耦合优化模型，以用较低的作动器能耗，满足天线结构精度控制与电磁性能要求。耦合模型的约束条件主要包括杆件结构强度(应力)、作动器结构强度(轴力)和作动器的行程(变形)。把热载荷作为外载荷，通过智能桁架天线的结构——电磁耦合优化模型，建立了其机电热耦合优化分析模型，从而实现空间智能桁架天线反射面的准静态与动态形状调整与控制。
分析了矩形阵面APAA辐射单元位置误差对天线电场和方向性的影响，推导出了场强概率公式。针对APAA阵面的两种基本变形，建立了天线阵面热变形误差的数学模型。分析了结构误差对天线副瓣电平和增益的影响，并给出了一个可应用于工程实践的确定公差指标的方法。基于APAA的结构变形分析、热功耗分析，以及相位误差的引入，建立了矩形栅格APAA的机电热三场耦合模型，给出了多场耦合分析的流程，并对阵面弯曲变形和碗状双曲变形下的APAA电性能讲行了仿真分析。
The electromechanical coupling problem has been an important bottleneck of many factors influencing the performances of military electronic fumishments, which have a typical multidisciplinary characteristic. Using the advantage and research achievements of Xidian University in antenna structural design, the dissertation discusses the coupled multifield problems (CMFP) involving the mechanical structural displacement field, electromagnetic (EM) field and temperature field, which mainly take place in design and analysis period of parabolic antenna and phased array antenna. The modeling theory and synthesis analysis method of CMFP are studied in detail.
The least squared criterion based paraboloid fitting method is proposed. And the accurate calculation method for errors in axial, normal and radial direction of reflector surface is submitted. Based on the actual shape of distorted reflector and according to antenna mechanical structural analysis, a new divided-fitting method (DFM) is presented which is quite different from the traditional best-fit paraboloid method. It determines the boundary condition of each zone by first dividing the distorted reflector into many zones, then adopting Coons surface to fit each zone and combining the hoop function and radial function fitting methods. The boundary fitting functions include a trigonometric, polynomial and B spline functions etc. The reliability model of distorted surface precision and other two explored fitting methods are also introduced.
Based on the analysis of distorted antenna structure, an accurate structural displacement field model of antenna is made. By the phase distribution of distorted antenna aperture, physical optics (PO) method and Fourier transform are used to calculation far electric field of antennas. Then an electromechanical coupling model of reflector antennas is developed. Aimed at the separated status of structural and EM design in antenna engineering, an integrated synthesis analysis system for large reflector antenna was developed by use of acquired electromechanical coupling model. The analysis platform testing has been made with two antenna engineering cases. Furthermore, based on the electromechanical coupling theory of reflector antennas, a mechatronic synthesis optimization design model is developed, which directly uses the electrical performance as the optimization object.
A correlation factor consisting of focal length and diameter is introduced used in EM computation to develop a novel modified formula for antenna gainloss. And the corresponding mathematic expressions based on normal and radial error of reflector surface are presented respectively. By using the relationship among the transient wind pressure and speed and structural distortion, the mathematic expression of antenna gainloss under transient and average wind load is developed.
To obtain an extremely high accurate surface precision and the EM performances, an electromechanical synthesis optimization analysis model of space antenna structures is developed, which adopts the axial gain of antenna and power consumption of actuators as the objective functions, the material strength of bars and actuator's mechanical capability and active travel of actuator as constraint conditions. Based on the synthesis optimization model, a new coupled structural-electromagnetic-thermal optimization model is also given. The applications of coupling optimization model demonstrate the potential for the significant improvement of performances and for less necessary effort for shape control of space antenna.
The influence of position error of radiation element in rectangular planar active phased array antenna (APAA) on the electrical field intensity and directivity of antenna is studied. And the corresponding probability formula of field intensity is deduced. The characteristic of two basic deformations of APAA planar is analyzed. Then the mathematic model of thermal distortion error in planar of APAA is generated. Whereafter, the influence of rectangular planar distortion on the radiation pattern of APAA is studied. The analysis process of CMFP is also determined. According to the error model of antenna structural distortion, a coupled model involving displacement-electromagnetic-temperature field in rectangular planar APAA is established. The flow of coupled multifield analysis is drawn.
引文
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