天线结构位移场与电磁场耦合建模及分析研究
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摘要
电子装备作为机电结合的系统,其机电耦合问题已成为制约电子装备性能提高并影响下一代装备研制的一个瓶颈。本文在多个国家重点项目的支持下,以电子装备中典型案例—反射面天线和平板裂缝天线为研究对象,针对其在分析与设计过程中,存在的机械结构位移场与电磁场的场耦合问题进行了深入研究与探索,主要内容包括:
(1)针对反射面天线机电场耦合问题,综合考虑结构位移场引起的系统误差,以及制造和装配精度带来的随机误差,针对影响电磁场边界的主反射面变形、馈源位置和指向误差等主要误差,确定其与天线远场方向图的影响关系,建立反射面天线结构位移场与电磁场的场耦合理论模型。针对反射面天线结构和电磁网格不匹配的问题,采用结构和电磁网格矩阵转换的方法进行场耦合模型求解。经3.7米Ku频段卡塞格伦天线变形实验,验证了场耦合理论模型的正确性。
(2)为降低反射面天线结构变形对电性能影响,提出一种基于机电场耦合理论模型的馈源调整方法。在天线结构设计变量不变的情况下,构建以馈源位置和指向为设计变量,以天线电性能为目标函数的优化设计数学模型,弥补机电分离时馈源调整方法的不足。与最佳吻合面的馈源调整方法相比,可有效改善天线电性能。相关结论可为工程实践提供参考。
(3)针对平板裂缝天线机电场耦合问题,综合考虑系统误差和随机误差,从天线阵面平面度入手,针对影响电磁场边界的辐射单元(辐射缝)位置偏移、指向偏转,以及结构变形引起的缝电压幅相误差,确定其与天线远场方向图的影响关系,建立平板裂缝天线结构位移场与电磁场的场耦合理论模型。给出场耦合模型的顺序求解方法,并重点说明缝电压误差的计算方法。分别经Ku频段弹载和X频段机载平板裂缝天线的实物实验,验证了场耦合理论模型的正确性。
(4)就随机振动对机载雷达天线电性能的影响问题进行了研究。首先利用随机振动环境下天线结构响应的位移协方差矩阵,提出天线结构变形的随机样本生成方法,结合平板裂缝天线机电场耦合理论模型分析随机振动对天线电性能的影响。其次,根据天线结构响应的位移和应力分布信息,确定出天线结构的薄弱环节,提出结构改进方案,并分析随机振动对改进模型电性能的影响。数值结果表明改进模型可有效降低增益损失和指向误差,可为机载雷达天线工程设计人员提供参考。
(5)针对平板裂缝天线焊接后存在的结构变形对电性能影响问题,应用有限元方法和生死单元技术,对天线热加工过程进行数值模拟,分析材料物性参数和温度曲线与焊接后结构残余应力和变形的影响关系,并结合机电场耦合理论模型分析焊接变形对天线电性能的影响。着重讨论温度曲线与焊接变形及其电性能的影响关系,提出了焊接温度曲线的改进方案,降低焊接后的结构残余应力和变形,改善天线电性能。相关结论可为工程实践提供参考。
As a kind of electromechanical system, electronic equipments have serious electromechanical coupled problems, which constrain the improvement of the actual electromechanical equipments and the development of the next generation equipments. With the support of several national key projects, this paper studies the coupled problem between structural displacement field and electromagnetic field, which mainly takes place on the design and analysis period of reflector antennas and planar slotted waveguide array antennas. The modeling and synthesis analyses of the coupled problems are studied in detail. The author’s major contributions on the subject can be summarized as follows:
(1) The electromechanical coupled field problem of the reflector antenna is studied, and an electromechanical coupled model of the antenna is acquired to relate the structural displacement field with the electromagnetic field. In the model, the structural displacement field is a kind of system errors including the errors of main reflector, the position and orientation of the feed. The random errors from the process of manufacture and assembly of the antenna are considered in the model too. These errors change the amplitude and phase distribute of antenna aperture to affect the far electric field of antenna. For the non-matching grids problem of structure and electromagnetism in the solution of the coupled field model, the transformation matrix between two grids is used. The deformation experiment of a cassegrain reflector antenna with the diameter of 3.7m is accomplished to prove the correctness and effectiveness of the model.
(2) Basing on the coupled field model, a kind of feed adjusting method is presented to decrease the effect of the distorted reflector antenna on the electrical performances. The method determines the position and orientation of feed by the optimization model with the object of electrical performances in changeless structural design variables, and make up for the methods of feed adjusting when structure and electromagnetic are separate. Compared with the best-fitting parabolic method, this method is good for improving the electrical performances. These results could be referenced in engineering practice.
(3) The electromechanical coupled field problem of planar slotted waveguide array antenna is studied, and an electromechanical coupled model of the antenna is acquired to relate the structural displacement field with the electromagnetic field. In the model, the structural displacement field includes the errors of the position and orientation of radiating slots. The errors of the slots voltages in the model are from the distorted slotted waveguide array and the process of manufacture and assembly of the antenna. These errors change the amplitude and phase distribute of radiating slots, a simple vectorial superposition is used to calculate far electric field of antenna. The coupled field model can be solved in the sequence way, the computational method of slots voltages is studies in detail. The deformation experiments of two prototype antennas with frequency bands of Ku and X are accomplished to certify the correctness and effectiveness of the model separately.
(4) The effect of random vibration on the electrical performances in the air-bone antenna is addressed. Firstly, the displacement covariance matrix of the responded antenna structure from random vibration is calculated, the method of making the random samples of the distorted antenna is given according to the matrix, the electrical performances is obtained by the coupled field model of planar slotted waveguide antenna. Secondly, the weak regions are found by the responded distribution of the displacement and stress of the antenna and improved subsequently. Finally, numerical results indicate that the improved model decreases the effect of random vibration on the gain loss and pointing error, and can be referenced in engineering practice.
(5) The effect of the deformation of antenna structure from the braze welding on the antenna electrical performances is carried out. Firstly, the deformation is analyzed by the finite element method and the technology of birth and death element, the effect of the physical properties of materials and temperature curves in the braze welding on the residual stress and deformation is obtained, the electrical performances are given by the coupled field model of planar slotted waveguide antenna. By analyzing the relations among temperature curves, the deformation and electrical performances, the temperature curve is improved to decrease the residual stress, the deformation and the influence on electrical performances. These results can be referenced in engineering practice.
(1)针对反射面天线机电场耦合问题,综合考虑结构位移场引起的系统误差,以及制造和装配精度带来的随机误差,针对影响电磁场边界的主反射面变形、馈源位置和指向误差等主要误差,确定其与天线远场方向图的影响关系,建立反射面天线结构位移场与电磁场的场耦合理论模型。针对反射面天线结构和电磁网格不匹配的问题,采用结构和电磁网格矩阵转换的方法进行场耦合模型求解。经3.7米Ku频段卡塞格伦天线变形实验,验证了场耦合理论模型的正确性。
(2)为降低反射面天线结构变形对电性能影响,提出一种基于机电场耦合理论模型的馈源调整方法。在天线结构设计变量不变的情况下,构建以馈源位置和指向为设计变量,以天线电性能为目标函数的优化设计数学模型,弥补机电分离时馈源调整方法的不足。与最佳吻合面的馈源调整方法相比,可有效改善天线电性能。相关结论可为工程实践提供参考。
(3)针对平板裂缝天线机电场耦合问题,综合考虑系统误差和随机误差,从天线阵面平面度入手,针对影响电磁场边界的辐射单元(辐射缝)位置偏移、指向偏转,以及结构变形引起的缝电压幅相误差,确定其与天线远场方向图的影响关系,建立平板裂缝天线结构位移场与电磁场的场耦合理论模型。给出场耦合模型的顺序求解方法,并重点说明缝电压误差的计算方法。分别经Ku频段弹载和X频段机载平板裂缝天线的实物实验,验证了场耦合理论模型的正确性。
(4)就随机振动对机载雷达天线电性能的影响问题进行了研究。首先利用随机振动环境下天线结构响应的位移协方差矩阵,提出天线结构变形的随机样本生成方法,结合平板裂缝天线机电场耦合理论模型分析随机振动对天线电性能的影响。其次,根据天线结构响应的位移和应力分布信息,确定出天线结构的薄弱环节,提出结构改进方案,并分析随机振动对改进模型电性能的影响。数值结果表明改进模型可有效降低增益损失和指向误差,可为机载雷达天线工程设计人员提供参考。
(5)针对平板裂缝天线焊接后存在的结构变形对电性能影响问题,应用有限元方法和生死单元技术,对天线热加工过程进行数值模拟,分析材料物性参数和温度曲线与焊接后结构残余应力和变形的影响关系,并结合机电场耦合理论模型分析焊接变形对天线电性能的影响。着重讨论温度曲线与焊接变形及其电性能的影响关系,提出了焊接温度曲线的改进方案,降低焊接后的结构残余应力和变形,改善天线电性能。相关结论可为工程实践提供参考。
As a kind of electromechanical system, electronic equipments have serious electromechanical coupled problems, which constrain the improvement of the actual electromechanical equipments and the development of the next generation equipments. With the support of several national key projects, this paper studies the coupled problem between structural displacement field and electromagnetic field, which mainly takes place on the design and analysis period of reflector antennas and planar slotted waveguide array antennas. The modeling and synthesis analyses of the coupled problems are studied in detail. The author’s major contributions on the subject can be summarized as follows:
(1) The electromechanical coupled field problem of the reflector antenna is studied, and an electromechanical coupled model of the antenna is acquired to relate the structural displacement field with the electromagnetic field. In the model, the structural displacement field is a kind of system errors including the errors of main reflector, the position and orientation of the feed. The random errors from the process of manufacture and assembly of the antenna are considered in the model too. These errors change the amplitude and phase distribute of antenna aperture to affect the far electric field of antenna. For the non-matching grids problem of structure and electromagnetism in the solution of the coupled field model, the transformation matrix between two grids is used. The deformation experiment of a cassegrain reflector antenna with the diameter of 3.7m is accomplished to prove the correctness and effectiveness of the model.
(2) Basing on the coupled field model, a kind of feed adjusting method is presented to decrease the effect of the distorted reflector antenna on the electrical performances. The method determines the position and orientation of feed by the optimization model with the object of electrical performances in changeless structural design variables, and make up for the methods of feed adjusting when structure and electromagnetic are separate. Compared with the best-fitting parabolic method, this method is good for improving the electrical performances. These results could be referenced in engineering practice.
(3) The electromechanical coupled field problem of planar slotted waveguide array antenna is studied, and an electromechanical coupled model of the antenna is acquired to relate the structural displacement field with the electromagnetic field. In the model, the structural displacement field includes the errors of the position and orientation of radiating slots. The errors of the slots voltages in the model are from the distorted slotted waveguide array and the process of manufacture and assembly of the antenna. These errors change the amplitude and phase distribute of radiating slots, a simple vectorial superposition is used to calculate far electric field of antenna. The coupled field model can be solved in the sequence way, the computational method of slots voltages is studies in detail. The deformation experiments of two prototype antennas with frequency bands of Ku and X are accomplished to certify the correctness and effectiveness of the model separately.
(4) The effect of random vibration on the electrical performances in the air-bone antenna is addressed. Firstly, the displacement covariance matrix of the responded antenna structure from random vibration is calculated, the method of making the random samples of the distorted antenna is given according to the matrix, the electrical performances is obtained by the coupled field model of planar slotted waveguide antenna. Secondly, the weak regions are found by the responded distribution of the displacement and stress of the antenna and improved subsequently. Finally, numerical results indicate that the improved model decreases the effect of random vibration on the gain loss and pointing error, and can be referenced in engineering practice.
(5) The effect of the deformation of antenna structure from the braze welding on the antenna electrical performances is carried out. Firstly, the deformation is analyzed by the finite element method and the technology of birth and death element, the effect of the physical properties of materials and temperature curves in the braze welding on the residual stress and deformation is obtained, the electrical performances are given by the coupled field model of planar slotted waveguide antenna. By analyzing the relations among temperature curves, the deformation and electrical performances, the temperature curve is improved to decrease the residual stress, the deformation and the influence on electrical performances. These results can be referenced in engineering practice.
引文
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