双环可展开桁架式天线动力学分析与优化设计
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摘要
随着航空技术和国防事业的发展,我国对大口径及超大口径天线的需求变得越来越迫切。然而,天线的口径不仅受到天线本身重量的约束,还受到火箭体积的限制。为了满足日益增长的需求,克服客观存在的限制与其之间的矛盾,大口径及超大口径天线就要求设计成轻质,并且在运输或未使用过程中保持小体积,而当在轨工作时便可展开成需要的形状。为了应对这样的现状,空间可展开结构作为天线周边支撑结构,越来越多地应用在天线上。本文对新型双环可展开桁架结构的方案设计和动力学分析、固有频率和模态分析、基于动力学约束的结构优化设计等问题进行了深入的研究。
在大量阅读国内外文献的基础上,总结了大口径及超大口径可展开天线的研究现状,对三种不同基本类型的可展开天线分别进行了介绍。说明了随着航天技术和国防事业的发展,对新型空间可展开桁架结构的需求和结构方案设计及展开分析的必要性。
从以往的单环可展开桁架结构出发,简要介绍了已被广泛应用的单环可展开桁架结构的优点。接着阐明了随着通信科学、地球勘测等日益发展,由于传统的单环可展开桁架结构的刚度低,已经不再满足大口径及超大口径天线的需要,从而揭示了设计新型可展开桁架结构方案的迫切需要。介绍了双环可展开桁架结构的几何拓扑关系及可展开的必要条件。基于天线的正常工作性能,从动力学特性的角度出发,推导并确定了该可展开桁架结构的最优高度和最佳划分边数。最后,分别介绍了双环可展开桁架结构内、外环的展开单元和内、外环之间的连系桁架的展开机理。
基于双环可展开桁架结构的动力学特性,基于Moore-Penrose广义逆方法,运用多体系统动力学理论来分析其展开的运动过程。在已有单环可展开桁架结构的基础上,添加了双环可展开桁架结构特有的约束方程：内、外环之间连系杆约束和扭簧连杆的约束。根据以上理论,采用C++Visual Studio2008自编计算仿真程序。为了验证该程序的可靠性,引入单摆模型和可展开桥梁模型,通过和理论计算值、ADAMS计算值的对比,可知两者在仿真结果上可以基本符合,并且自编仿真程序在建模过程和计算过程中能大大节约时间,提高效率。最后,通过数值仿真,获得该双环可展开桁架结构展开过程中的各个状态和各节点动力学参数,为之后的结构优化设计提供了依据。
基于Matlab对双环可展开桁架结构进行参数化建模,使得在计算不同口径、划分边数以及桁架高度的结构时建模更便捷。编制有限元动力学计算程序,以双环可展开桁架结构的初始尺寸为基准,计算该结构完全展开状态时的各阶模态以及在各个展开过程中的基频,从而分析该结构的动力学特性。通过和ANSYS计算结果对比,验证该程序的正确性。最后,实验室设计并制作了2m口径的双环可展开桁架结构的缩比模型,利用自编有限元程序计算了该模型的动力学特性并对其展开了测试试验。将计算结果和测试结果对比,可知上述自编程序所进行的有限元计算是比较符合实际的。
对少变量优化模型采用序列二次规划法和遗传算法分别进行优化并对比,为了显示双环可展开桁架结构在动力学特性方面的优势,建立了基于频率约束的最小质量优化模型。通过优化计算,获得了单、双环可展开桁架结构满足基频的最优质量。从优化结果分析可见,双环可展开桁架结构在保证刚度及减轻重量方面有明显的优势,并且随着口径的增大该优势更为明显。
双环可展开桁架结构的动力学特性不仅表现在完全展开状态时,它在初始收拢和各个展开过程中的动力学特性也至关重要。因此,可通过优化计算,获得了双环可展开桁架结构的最优截面和最小质量,并且计算了在该最优解的情况下,双环可展开桁架结构在初始收拢状态、展开过程中及完全展开状态时都满足动力学要求。
基于金属反射面的型面精度理论,对预应力索网反射面给出了型面精度计算公式。建立以最小质量为目标函数,双环可展开周边桁架的动力学特性、天线整体的动力学特性和型面精度、以及预应力拉索的最大应力为约束条件的优化模型。通过选择不同数量的设计变量获得了不同的最小质量最优解,结合实际模型加工、制作的情况,选择了适合该双环可展开桁架天线结构的最优设计变量数目,获得了双环可展开周边桁架式天线结构的最优解,因此,为天线结构的设计奠定了基础。
根据本文研究的最优计算方法,实验室研制了双环可展开天线的缩比模型,并对各类节点进行了机械设计。为了测试该缩比模型的可展开性和动力学特性,使得天线测试和试验结果更具有参考性,需要研制模拟太空失重环境的设备,对天线进行重力补偿,将重力的影响降到最低。本实验室与西安39所合作设计了一套无重力的试验吊架系统,为后续的试验做准备。
Demand for large-caliber and ultra-large-caliber antennas is increasing with the rapid development of the space science and astronautical technology. However, the caliber of antennas is severely restricted by weight and volume limitations of the launch vehicle such as the cowling for space use. Ultimately, this creates a design space governed by competing properties, where the antenna is desired to be as light and as small as possible during transportation, while as large as needed for effective operation when the antenna is fully deployed on the orbit. Foldable and deployable supporting structures have proven to be an effective system for addressing this challenging design problem. This paper emphasized on the design and dynamic analysis of the double-ring deployable truss antenna, and researched on the frequencies, modal analysis and structural optimization subjected to dynamic constraints.
On the basis of lots of domestic and foreign literatures, the current research situation of large-caliber and ultra-large-caliber antennas. Three basic different types of deployable antennas are introduced and it illustrates the necessity of the design and research of new kind of deployable truss antennas for space use. The design and manufacture of the scaled model and the tested results verified the numerical results. Therefore, the necessity and significance of the research of the double-ring deployable truss antenna are proved.
This paper starts with the general single-ring deployable truss antenna, and introduced the merits of the single-ring deployable truss antenna which is widely used nowadays. But the stiffness of the single-ring deployable truss antenna decreases sharply with the increasing caliber of the antennas when the space technology develops fast and fast. So the single-ring deployable truss antenna cannot satisfy the demand of the large-caliber and ultra-large-caliber antennas. It is necessary to design a new kind of antennas to satisfy this demand. This paper introduces the geometrical topology and the necessary conditions of the double-ring deployable truss. And due to the normal performances of the antenna, staring with the dynamic analysis, the best height and number of sides of the truss were obtained. Finally, the deploying mechanism of the inner ring and the outer ring of the double-ring deployable truss were introduced in details.
On the basis of the characteristics of the double-ring deployable truss and theory of Moore-Penrose, multi-body dynamic was utilized to analyze the deploying process. Some special constraints of the double-ring deployable truss were added on the basis of the formal single-ring deployable truss. Simulation was taken out in C++Visual2008. To verify the self-programmed procedure, the simple pendulum and deployable bridge were tested. And the results were compared with the calculated values by theory which gives the validity. Moreover, the self-programmed procedure can save much time when modeling and calculating. At last, each state and coordinates of all the nodes can be obtained by numerical simulation of the deploying process of the double-ring deployable truss.
Different models with different calibers and initial heights can be obtained by parameterization. By finite element method, modal analysis of the double-ring deployable truss and the first frequency of the double-ring deployable truss in each deploying state were obtained. By comparisons of the results with ANSYS, the validity of the self-programmed procedure was verified.
SQP method and GA were used for the few variables in the optimization. In order to show the advantages of the double-ring deployable truss, minimum weight optimization with frequencies constraints is established. By optimization, the minimum weight of the single-ring deployable truss and double-ring deployable truss were obtained separately. We can see that the double-ring deployable truss can save weight over the single-ring deployable truss with constraints satisfied.
Not only the characteristics of the double-ring deployable truss in the final deployed state were important, the characteristics of the double-ring deployable truss in the initial folded state and each deploying states were also important. Therefore, these dynamic constraints were added into to optimization model. By optimization, the minimum weight can be obtained with all the dynamic constraints in the initial folded state, each deploying states and the final deployed state satisfied.
The equation of the RMS of the reflecting surface was established according to the theory of the metallic reflector. Therefore the RMS constraint was also added into the optimization model and the optimal result was obtained. Then different numbers of the design variables were chosen to obtain the different minimum weights. The best number of the design variables was chosen to design and manufacture the model, which gives some foundations for the design of antenna. A scaled model was designed by the optimization method researched in this paper, and a set of systems which can eliminate the gravity of the antenna was also designed for the experiments in the future.
在大量阅读国内外文献的基础上,总结了大口径及超大口径可展开天线的研究现状,对三种不同基本类型的可展开天线分别进行了介绍。说明了随着航天技术和国防事业的发展,对新型空间可展开桁架结构的需求和结构方案设计及展开分析的必要性。
从以往的单环可展开桁架结构出发,简要介绍了已被广泛应用的单环可展开桁架结构的优点。接着阐明了随着通信科学、地球勘测等日益发展,由于传统的单环可展开桁架结构的刚度低,已经不再满足大口径及超大口径天线的需要,从而揭示了设计新型可展开桁架结构方案的迫切需要。介绍了双环可展开桁架结构的几何拓扑关系及可展开的必要条件。基于天线的正常工作性能,从动力学特性的角度出发,推导并确定了该可展开桁架结构的最优高度和最佳划分边数。最后,分别介绍了双环可展开桁架结构内、外环的展开单元和内、外环之间的连系桁架的展开机理。
基于双环可展开桁架结构的动力学特性,基于Moore-Penrose广义逆方法,运用多体系统动力学理论来分析其展开的运动过程。在已有单环可展开桁架结构的基础上,添加了双环可展开桁架结构特有的约束方程：内、外环之间连系杆约束和扭簧连杆的约束。根据以上理论,采用C++Visual Studio2008自编计算仿真程序。为了验证该程序的可靠性,引入单摆模型和可展开桥梁模型,通过和理论计算值、ADAMS计算值的对比,可知两者在仿真结果上可以基本符合,并且自编仿真程序在建模过程和计算过程中能大大节约时间,提高效率。最后,通过数值仿真,获得该双环可展开桁架结构展开过程中的各个状态和各节点动力学参数,为之后的结构优化设计提供了依据。
基于Matlab对双环可展开桁架结构进行参数化建模,使得在计算不同口径、划分边数以及桁架高度的结构时建模更便捷。编制有限元动力学计算程序,以双环可展开桁架结构的初始尺寸为基准,计算该结构完全展开状态时的各阶模态以及在各个展开过程中的基频,从而分析该结构的动力学特性。通过和ANSYS计算结果对比,验证该程序的正确性。最后,实验室设计并制作了2m口径的双环可展开桁架结构的缩比模型,利用自编有限元程序计算了该模型的动力学特性并对其展开了测试试验。将计算结果和测试结果对比,可知上述自编程序所进行的有限元计算是比较符合实际的。
对少变量优化模型采用序列二次规划法和遗传算法分别进行优化并对比,为了显示双环可展开桁架结构在动力学特性方面的优势,建立了基于频率约束的最小质量优化模型。通过优化计算,获得了单、双环可展开桁架结构满足基频的最优质量。从优化结果分析可见,双环可展开桁架结构在保证刚度及减轻重量方面有明显的优势,并且随着口径的增大该优势更为明显。
双环可展开桁架结构的动力学特性不仅表现在完全展开状态时,它在初始收拢和各个展开过程中的动力学特性也至关重要。因此,可通过优化计算,获得了双环可展开桁架结构的最优截面和最小质量,并且计算了在该最优解的情况下,双环可展开桁架结构在初始收拢状态、展开过程中及完全展开状态时都满足动力学要求。
基于金属反射面的型面精度理论,对预应力索网反射面给出了型面精度计算公式。建立以最小质量为目标函数,双环可展开周边桁架的动力学特性、天线整体的动力学特性和型面精度、以及预应力拉索的最大应力为约束条件的优化模型。通过选择不同数量的设计变量获得了不同的最小质量最优解,结合实际模型加工、制作的情况,选择了适合该双环可展开桁架天线结构的最优设计变量数目,获得了双环可展开周边桁架式天线结构的最优解,因此,为天线结构的设计奠定了基础。
根据本文研究的最优计算方法,实验室研制了双环可展开天线的缩比模型,并对各类节点进行了机械设计。为了测试该缩比模型的可展开性和动力学特性,使得天线测试和试验结果更具有参考性,需要研制模拟太空失重环境的设备,对天线进行重力补偿,将重力的影响降到最低。本实验室与西安39所合作设计了一套无重力的试验吊架系统,为后续的试验做准备。
Demand for large-caliber and ultra-large-caliber antennas is increasing with the rapid development of the space science and astronautical technology. However, the caliber of antennas is severely restricted by weight and volume limitations of the launch vehicle such as the cowling for space use. Ultimately, this creates a design space governed by competing properties, where the antenna is desired to be as light and as small as possible during transportation, while as large as needed for effective operation when the antenna is fully deployed on the orbit. Foldable and deployable supporting structures have proven to be an effective system for addressing this challenging design problem. This paper emphasized on the design and dynamic analysis of the double-ring deployable truss antenna, and researched on the frequencies, modal analysis and structural optimization subjected to dynamic constraints.
On the basis of lots of domestic and foreign literatures, the current research situation of large-caliber and ultra-large-caliber antennas. Three basic different types of deployable antennas are introduced and it illustrates the necessity of the design and research of new kind of deployable truss antennas for space use. The design and manufacture of the scaled model and the tested results verified the numerical results. Therefore, the necessity and significance of the research of the double-ring deployable truss antenna are proved.
This paper starts with the general single-ring deployable truss antenna, and introduced the merits of the single-ring deployable truss antenna which is widely used nowadays. But the stiffness of the single-ring deployable truss antenna decreases sharply with the increasing caliber of the antennas when the space technology develops fast and fast. So the single-ring deployable truss antenna cannot satisfy the demand of the large-caliber and ultra-large-caliber antennas. It is necessary to design a new kind of antennas to satisfy this demand. This paper introduces the geometrical topology and the necessary conditions of the double-ring deployable truss. And due to the normal performances of the antenna, staring with the dynamic analysis, the best height and number of sides of the truss were obtained. Finally, the deploying mechanism of the inner ring and the outer ring of the double-ring deployable truss were introduced in details.
On the basis of the characteristics of the double-ring deployable truss and theory of Moore-Penrose, multi-body dynamic was utilized to analyze the deploying process. Some special constraints of the double-ring deployable truss were added on the basis of the formal single-ring deployable truss. Simulation was taken out in C++Visual2008. To verify the self-programmed procedure, the simple pendulum and deployable bridge were tested. And the results were compared with the calculated values by theory which gives the validity. Moreover, the self-programmed procedure can save much time when modeling and calculating. At last, each state and coordinates of all the nodes can be obtained by numerical simulation of the deploying process of the double-ring deployable truss.
Different models with different calibers and initial heights can be obtained by parameterization. By finite element method, modal analysis of the double-ring deployable truss and the first frequency of the double-ring deployable truss in each deploying state were obtained. By comparisons of the results with ANSYS, the validity of the self-programmed procedure was verified.
SQP method and GA were used for the few variables in the optimization. In order to show the advantages of the double-ring deployable truss, minimum weight optimization with frequencies constraints is established. By optimization, the minimum weight of the single-ring deployable truss and double-ring deployable truss were obtained separately. We can see that the double-ring deployable truss can save weight over the single-ring deployable truss with constraints satisfied.
Not only the characteristics of the double-ring deployable truss in the final deployed state were important, the characteristics of the double-ring deployable truss in the initial folded state and each deploying states were also important. Therefore, these dynamic constraints were added into to optimization model. By optimization, the minimum weight can be obtained with all the dynamic constraints in the initial folded state, each deploying states and the final deployed state satisfied.
The equation of the RMS of the reflecting surface was established according to the theory of the metallic reflector. Therefore the RMS constraint was also added into the optimization model and the optimal result was obtained. Then different numbers of the design variables were chosen to obtain the different minimum weights. The best number of the design variables was chosen to design and manufacture the model, which gives some foundations for the design of antenna. A scaled model was designed by the optimization method researched in this paper, and a set of systems which can eliminate the gravity of the antenna was also designed for the experiments in the future.
引文
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