空间可展结构逆设计及宇航结构的装卡研究
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摘要
星载可展开构架式天线和空间光学摆镜都属于宇航结构,要求自身质量轻、体积小,同时达到完成各自科学任务所必须的技术指标。本文以星载可展开天线和空间光学摆镜的结构对各自表面精度的影响,进而影响各自的物理性能为主线,研究了以下六个方面;单元构架式可展开天线张拉反射面的形态特性,天线远场辐射特性,部分储能弹簧失效和空间热环境对远场的影响,构架式天线的赋形,空间光学摆镜装卡变形以及光学摆镜系统动力学分析。
可展开构架式天线反射面形态对其辐射特性影响显著,论文引入薄膜结构形态理论的分析方法(非线性有限元法和力密度法),对展开天线的反射面进行了形态分析。得到的结论是;当上弦节点位置全部落在设计抛物面上时,由上弦杆围成的三角平面所组成的曲面与标准抛物面的均方根误差最小。进而推导了三角平面组成曲面的最佳拟合抛物面的计算公式,编制了相应的程序。通过算例估算了Agrawal算法的误差大小。
所有对天线结构的研究都是以获得优良的电磁场性能为目的,因此精确的电磁场综合算法显得尤为重要。针对可展反射面形态的具体特点,基于几何光学原理,推导了可展天线远场的电场强度计算公式,再通过把口径面划分成矩形网格,用解析方法把远场进行积分,编制了相应程序。由于该程序同样适用于标准抛物面或者任何已知缺陷的反射面的辐射场计算,通过计算同一个标准抛物面天线在相同馈源激励下的辐射场,与Rahmat-Samii的经典算法进行比较,证明了本算法的准确性。本算法直接把结构和电性能相联系,省却了均方根误差这个中间值,使得设计更直观、准确。
空间可展天线进入轨道展开以后整个结构的形态会受到空间外热流和储能弹簧的影响,进而影响天线的电性能。本文计算了在夏至和冬至这两天天线运行时的瞬态温度场,及其带来的热弹性变形,和部分弹簧失效带来的结构变形,根据反射面与辐射特性的内在关系,求出了馈源的最佳安装位置。
赋形天线能够把有限的能量集中在感兴趣的敏感区域,因此受到普遍关注。构架式可展开天线由于其特殊的拓扑结构,不能照搬实体反射面天线的赋形方法。论文运用惩罚函数法构造了以反射面上法线方程的参数作为优化变量的目标函数,针对多变量复杂的目标函数,选择了直接搜索法进行优化计算。编制了相关赋形程序,结合算例进行了赋形计算,结果显示区域内得到的总辐射功率增加,功率分布更加均匀;如果节点可移动的范围越大,这种趋势越明显。
空间光学摆镜要求有极高的镜面质量,同时有相当的系统谐振频率,因此对摆镜的结构和装卡提出了苛刻的要求。论文设计了150mm摆镜的背架结构形式,把Zemike多项式引入到平板弹性力学方程,运用弹性地基理论建立了外圈力学方程,推导出两个等价的Bessel方程,根据特殊函数理论解出其通解。通过内外圈的变形协调条件,得到以Zemike多项式系数为变量求解外圈变形的方程组。利用广义逆求解出能够表征摆镜所有可能变形的一组零空间的基底向量。构造势能泛函,通过求解已知支臂装卡力作用下的最小势能,得到零空间基底函数的组合系数,进而求出每一个模态下的真实位移,各项系数对应的是各项Seidel像差;如果把所有位移叠加就得到了镜面误差。
对于复杂的摆镜结构,有效的办法是通过有限元求解,论文最后利用ANSYS中接触非线性模块对利用压板装卡的80mm摆镜系统进行建模计算,实验论证了本有限元模型的正确性,在此基础上设计了用螺栓直接装卡的150mm摆镜系统,进行了静力和动力分析,通过改变连接刚度计算了一系列系统基本频率,根据其变化规律找到最佳装卡力。此外还验算了150mm摆镜的理论计算结果。
The deployable truss antenna on the satellite and the space optical tilt mirror belong to the space structure, which require the light quality and small volume, and also meet the technology requirements of the task. This dissertation covers the following six fields based on the studies of surface precision of the antenna and the tilt mirror influenced by their structures, which affect their physical performance. These six fields include: the configuration of the tension reflector on the deployable element truss antenna; the far-field radiation of the antenna; the influence on the far-field by the partly spring invalidation and the space thermal environment; the shape design of the truss antenna; the stowing distortion of the space optical tilt mirror; and the dynamic analysis of the tilt mirror system.
The reflector configuration of the deployable truss antenna greatly influences its far-field radiation. The dissertation analyzes the configuration with the membrane configuration analytical method: nonlinear finite element method and force density method. The obtained conclusion is that: when the upper joints are all on the designing paraboloid, the RMS of the curved surface and the standard paraboloid is the least, which is composed by the triangular planes of the upper truss. In addition, the computing formula of the fitting paraboloid of the curved surface which is composed by the triangular plains is deduced. And the corresponding program is made. And the Agrawal error is analyzed.
The precise Electro Magnetic Field synthetical method is especially important because all the antenna studies aim to obtain the best electro magnetic field performance. According to the features of the deployable reflector configuration and the geometry optical theory, the computing formula of the electro-field intensity of the truss antenna is inferred. Then, the integral of the far-field is conducted with the analytical method, and the corresponding program is designed when the paraboloid is separated to form rectangular grid on the aperture plane. Because this program also applies to the computation of the reflector radiation field of the standard paraboloid or
any paraboloid whose distortion is already described, the method is proved to be correct by comparing with the result of Rahmat-Samii. This method directly related the structure with the electro magnetic field, which improves the design by leaving out the RMS value.
When the deployable antenna deploys after orbiting, the configuration of the whole structure will be influenced by the outer space heat current and the spring. This dissertation provides the instant temperature field when the antenna runs on the Summer Solstice and the midwinter, as well as the thermal flexibility and the structure distortion caused by the partly spring invalidation. Furthermore, the best installing position of the feed is obtained based on the internal relationship between the reflector and the radiation features.
The shape designing of the antenna can focus the limited energy on the sensitive area, so much attention has been paid to it. Because the topology structure of the deployable truss antenna is very special, the shape designing method can not copy that of the solid reflector. This dissertation applies the penalty function to construct the target function when the parameters in the normal equation of the reflector are used as the optimized variables. The direct searching method is used to optimize the computation considering the complicated target function with multi variables. The corresponding shape designing program is made and an example is given to illustrate that the total power in the target area improves and the distribution of the power is more smooth. If the moving range of the joints is enlarged, such direction becomes more evident.
The space tilt mirror requires the least surface error and the high system resonance frequency, so the structure and the stowing of the mirror become more crucial. The dissertation designs the structure of the 150mm mirror. The Zernike polynomial is used in the elastic plane equation. The equation of the out loop is presented based on the elasticity groundsill. Two equivalent Bessel equations are deduced. And the general solution is obtained by use of the special function. An equation group of Zernike polynomial coefficients is obtained based on the harmony between the deformations of the outer and the inside loops. A group of null space vectors which indicate all the possible distortions of the mirror is gained by means of inverse matrix. The energy functional is established and a group of composed coefficients of the null space function is obtained by gaining the least energy when the load on the mirror's arms is specified. So the actual displacement under each model is obtained. And each coefficient corresponds to each Seidel aberration coefficient. And the mirror surface error is gained by adding all the displacements.
As to the complicated tilt mirror structure, the effective way is to apply the finite element method to solve the problem. The dissertation analyzes the 80mm tilt mirror system stowed with pressing board by means of contact nonlinear model in ANSYS. The experiment proves the validity of the model. And 150mm system is designed. In addition, the static and dynamic analysis is conducted. As a result, a series of systematic frequency is obtained by changing the joint stiffness and the optimized load can be found. At last, the theoretical result of the 150mm tilt mirror is checked.
可展开构架式天线反射面形态对其辐射特性影响显著,论文引入薄膜结构形态理论的分析方法(非线性有限元法和力密度法),对展开天线的反射面进行了形态分析。得到的结论是;当上弦节点位置全部落在设计抛物面上时,由上弦杆围成的三角平面所组成的曲面与标准抛物面的均方根误差最小。进而推导了三角平面组成曲面的最佳拟合抛物面的计算公式,编制了相应的程序。通过算例估算了Agrawal算法的误差大小。
所有对天线结构的研究都是以获得优良的电磁场性能为目的,因此精确的电磁场综合算法显得尤为重要。针对可展反射面形态的具体特点,基于几何光学原理,推导了可展天线远场的电场强度计算公式,再通过把口径面划分成矩形网格,用解析方法把远场进行积分,编制了相应程序。由于该程序同样适用于标准抛物面或者任何已知缺陷的反射面的辐射场计算,通过计算同一个标准抛物面天线在相同馈源激励下的辐射场,与Rahmat-Samii的经典算法进行比较,证明了本算法的准确性。本算法直接把结构和电性能相联系,省却了均方根误差这个中间值,使得设计更直观、准确。
空间可展天线进入轨道展开以后整个结构的形态会受到空间外热流和储能弹簧的影响,进而影响天线的电性能。本文计算了在夏至和冬至这两天天线运行时的瞬态温度场,及其带来的热弹性变形,和部分弹簧失效带来的结构变形,根据反射面与辐射特性的内在关系,求出了馈源的最佳安装位置。
赋形天线能够把有限的能量集中在感兴趣的敏感区域,因此受到普遍关注。构架式可展开天线由于其特殊的拓扑结构,不能照搬实体反射面天线的赋形方法。论文运用惩罚函数法构造了以反射面上法线方程的参数作为优化变量的目标函数,针对多变量复杂的目标函数,选择了直接搜索法进行优化计算。编制了相关赋形程序,结合算例进行了赋形计算,结果显示区域内得到的总辐射功率增加,功率分布更加均匀;如果节点可移动的范围越大,这种趋势越明显。
空间光学摆镜要求有极高的镜面质量,同时有相当的系统谐振频率,因此对摆镜的结构和装卡提出了苛刻的要求。论文设计了150mm摆镜的背架结构形式,把Zemike多项式引入到平板弹性力学方程,运用弹性地基理论建立了外圈力学方程,推导出两个等价的Bessel方程,根据特殊函数理论解出其通解。通过内外圈的变形协调条件,得到以Zemike多项式系数为变量求解外圈变形的方程组。利用广义逆求解出能够表征摆镜所有可能变形的一组零空间的基底向量。构造势能泛函,通过求解已知支臂装卡力作用下的最小势能,得到零空间基底函数的组合系数,进而求出每一个模态下的真实位移,各项系数对应的是各项Seidel像差;如果把所有位移叠加就得到了镜面误差。
对于复杂的摆镜结构,有效的办法是通过有限元求解,论文最后利用ANSYS中接触非线性模块对利用压板装卡的80mm摆镜系统进行建模计算,实验论证了本有限元模型的正确性,在此基础上设计了用螺栓直接装卡的150mm摆镜系统,进行了静力和动力分析,通过改变连接刚度计算了一系列系统基本频率,根据其变化规律找到最佳装卡力。此外还验算了150mm摆镜的理论计算结果。
The deployable truss antenna on the satellite and the space optical tilt mirror belong to the space structure, which require the light quality and small volume, and also meet the technology requirements of the task. This dissertation covers the following six fields based on the studies of surface precision of the antenna and the tilt mirror influenced by their structures, which affect their physical performance. These six fields include: the configuration of the tension reflector on the deployable element truss antenna; the far-field radiation of the antenna; the influence on the far-field by the partly spring invalidation and the space thermal environment; the shape design of the truss antenna; the stowing distortion of the space optical tilt mirror; and the dynamic analysis of the tilt mirror system.
The reflector configuration of the deployable truss antenna greatly influences its far-field radiation. The dissertation analyzes the configuration with the membrane configuration analytical method: nonlinear finite element method and force density method. The obtained conclusion is that: when the upper joints are all on the designing paraboloid, the RMS of the curved surface and the standard paraboloid is the least, which is composed by the triangular planes of the upper truss. In addition, the computing formula of the fitting paraboloid of the curved surface which is composed by the triangular plains is deduced. And the corresponding program is made. And the Agrawal error is analyzed.
The precise Electro Magnetic Field synthetical method is especially important because all the antenna studies aim to obtain the best electro magnetic field performance. According to the features of the deployable reflector configuration and the geometry optical theory, the computing formula of the electro-field intensity of the truss antenna is inferred. Then, the integral of the far-field is conducted with the analytical method, and the corresponding program is designed when the paraboloid is separated to form rectangular grid on the aperture plane. Because this program also applies to the computation of the reflector radiation field of the standard paraboloid or
any paraboloid whose distortion is already described, the method is proved to be correct by comparing with the result of Rahmat-Samii. This method directly related the structure with the electro magnetic field, which improves the design by leaving out the RMS value.
When the deployable antenna deploys after orbiting, the configuration of the whole structure will be influenced by the outer space heat current and the spring. This dissertation provides the instant temperature field when the antenna runs on the Summer Solstice and the midwinter, as well as the thermal flexibility and the structure distortion caused by the partly spring invalidation. Furthermore, the best installing position of the feed is obtained based on the internal relationship between the reflector and the radiation features.
The shape designing of the antenna can focus the limited energy on the sensitive area, so much attention has been paid to it. Because the topology structure of the deployable truss antenna is very special, the shape designing method can not copy that of the solid reflector. This dissertation applies the penalty function to construct the target function when the parameters in the normal equation of the reflector are used as the optimized variables. The direct searching method is used to optimize the computation considering the complicated target function with multi variables. The corresponding shape designing program is made and an example is given to illustrate that the total power in the target area improves and the distribution of the power is more smooth. If the moving range of the joints is enlarged, such direction becomes more evident.
The space tilt mirror requires the least surface error and the high system resonance frequency, so the structure and the stowing of the mirror become more crucial. The dissertation designs the structure of the 150mm mirror. The Zernike polynomial is used in the elastic plane equation. The equation of the out loop is presented based on the elasticity groundsill. Two equivalent Bessel equations are deduced. And the general solution is obtained by use of the special function. An equation group of Zernike polynomial coefficients is obtained based on the harmony between the deformations of the outer and the inside loops. A group of null space vectors which indicate all the possible distortions of the mirror is gained by means of inverse matrix. The energy functional is established and a group of composed coefficients of the null space function is obtained by gaining the least energy when the load on the mirror's arms is specified. So the actual displacement under each model is obtained. And each coefficient corresponds to each Seidel aberration coefficient. And the mirror surface error is gained by adding all the displacements.
As to the complicated tilt mirror structure, the effective way is to apply the finite element method to solve the problem. The dissertation analyzes the 80mm tilt mirror system stowed with pressing board by means of contact nonlinear model in ANSYS. The experiment proves the validity of the model. And 150mm system is designed. In addition, the static and dynamic analysis is conducted. As a result, a series of systematic frequency is obtained by changing the joint stiffness and the optimized load can be found. At last, the theoretical result of the 150mm tilt mirror is checked.
引文
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