CN106295035A - The Electrostatic deformation film antenna shape adjustment method of optimization is worked in coordination with based on voltage and bitter end position - Google Patents
The Electrostatic deformation film antenna shape adjustment method of optimization is worked in coordination with based on voltage and bitter end position Download PDFInfo
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Abstract
本发明公开了一种基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法，首先基于已制作完成的静电成形薄膜天线实物测量信息建立静电成形薄膜天线有限元模型，给定初始电极电压值和索固定端节点初始位置；然后以电极电压值和索固定端节点位置作为优化设计变量并给定优化设计变量的上下限，以薄膜面节点拟合形面精度作为优化目标进行分析优化；最后得到优化结果，并将实物的电极电压和索端位置按优化得到的结果值进行调整，使之符合精度要求。本发明可以改善仅利用电极电压进行薄膜面形面调整的效果，并且索端位置调整相对于索力调整在实际工程中更容易实现，克服了利用有限元模型指导实物模型调整时各索力之间相互影响难以工程实现的问题。
The invention discloses a method for adjusting the shape and surface of an electrostatically formed film antenna based on the cooperative optimization of voltage and cable end position. First, the finite element model of the electrostatically formed film antenna is established based on the actual measurement information of the manufactured electrostatically formed film antenna, and the initial electrode is given. The voltage value and the initial position of the fixed end node of the cable; then the electrode voltage value and the fixed end node position of the cable are used as the optimal design variables and the upper and lower limits of the optimized design variables are given, and the film surface node fitting shape accuracy is used as the optimization target for analysis and optimization ; Finally, the optimization result is obtained, and the actual electrode voltage and cable end position are adjusted according to the optimized result value to make it meet the accuracy requirements. The invention can improve the effect of adjusting the surface shape of the film by using only the electrode voltage, and the adjustment of the position of the cable end is easier to realize in actual engineering than the adjustment of the cable force, and overcomes the difference between the cable forces when the finite element model is used to guide the adjustment of the physical model. Interaction among them is difficult to realize in engineering.
Description
技术领域technical field
本发明属于雷达天线技术领域，尤其涉及一种基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法。The invention belongs to the technical field of radar antennas, and in particular relates to a method for adjusting the shape and surface of an electrostatically formed film antenna based on collaborative optimization of voltage and cable end positions.
背景技术Background technique
静电成形薄膜天线(ECDMA)的工作原理是在镀有金属层的薄膜反射面和控制电极上施加不同的电压(一般薄膜为等效零势面，电极为高电势)，产生静电力对薄膜进行拉伸，从而使薄膜形成具有一定焦径比的反射面。电极电压通过电源进行实时调整，可以实现对反射面形面误差的及时补偿。此外，为了能够进一步提高对薄膜反射面形面精度的调整能力，薄膜边缘利用绳索张拉到支撑桁架上，可以通过电压与索对薄膜反射面进行协同调整。The working principle of the Electrostatic Forming Film Antenna (ECDMA) is to apply different voltages on the film reflective surface coated with a metal layer and the control electrode (generally the film is an equivalent zero potential surface, and the electrode is a high potential), and an electrostatic force is generated to move the film. Stretching, so that the film forms a reflective surface with a certain focal diameter ratio. The electrode voltage is adjusted in real time through the power supply, which can realize timely compensation for the shape error of the reflective surface. In addition, in order to further improve the ability to adjust the surface accuracy of the film reflective surface, the edge of the film is stretched to the support truss by ropes, and the film reflective surface can be adjusted cooperatively through voltage and cables.
然而业内普遍存在的问题是，仅仅利用电极电压对薄膜反射面形面精度进行调整的程度有限，而利用电压与索力共同调整时，在实际工程中很难将索力严格调整到规定值，如何利用有限元模型有效指导静电成形薄膜天线形面调整是目前亟待解决的问题。However, the common problem in the industry is that only using the electrode voltage to adjust the surface accuracy of the film reflective surface is limited, and it is difficult to strictly adjust the cable force to the specified value in actual engineering when the voltage and the cable force are used to adjust together. How to use the finite element model to effectively guide the adjustment of the shape and surface of the electrostatically formed film antenna is an urgent problem to be solved at present.
发明内容Contents of the invention
本发明目的在于提供一种基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法，旨在解决利用有限元模型有效指导静电成形薄膜天线形面调整的问题。对于充气天线、平面薄膜天线等涉及柔性结构，利用面外力和边界索位置协同调整形面，本发明仍然适用。The purpose of the present invention is to provide a method for adjusting the shape and surface of an electrostatically formed thin film antenna based on the coordinated optimization of voltage and cable end position, aiming at solving the problem of using a finite element model to effectively guide the adjustment of the shape and surface of an electrostatically formed thin film antenna. For flexible structures such as inflatable antennas and planar film antennas, the present invention is still applicable to coordinate adjustment of the shape and surface by using external force and the position of the boundary cable.
本发明的技术方案是：基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法，包括以下步骤：The technical solution of the present invention is: a method for adjusting the shape and surface of an electrostatically formed film antenna based on the cooperative optimization of voltage and cable end position, including the following steps:
1)根据已制作完成的静电成形薄膜天线实物模型上测量的靶标点空间位置信息建立静电成形薄膜天线有限元模型；1) Establish the finite element model of the electrostatically formed film antenna according to the target point spatial position information measured on the manufactured electrostatically formed film antenna physical model;
2)给定静电成形薄膜天线有限元模型约束条件，即拉索最外端节点位移全部固定；2) The constraints of the finite element model of the electrostatically formed film antenna are given, that is, the displacements of the outermost nodes of the cables are all fixed;
3)以电极电压值和索端位置作为设计变量，给定设计变量初值和设计变量上下限；3) Taking the electrode voltage value and the position of the cable end as the design variables, the initial value of the design variable and the upper and lower limits of the design variable are given;
4)对设计变量进行归一化处理；4) Normalize the design variables;
5)给定静电成形薄膜天线在自重平衡态时的预应力；5) Given the prestress of the electrostatically formed film antenna in its self-weight equilibrium state;
6)以薄膜反射面节点拟合形面精度作为目标函数进行优化分析；6) The optimization analysis is carried out with the surface accuracy of the joint fitting shape of the film reflector as the objective function;
7)分析优化结果，完成基于电压与索端位置协同优化的静电成形薄膜天线形面调整。7) Analyze the optimization results, and complete the adjustment of the shape and surface of the electrostatically formed film antenna based on the collaborative optimization of the voltage and the position of the cable end.
上述步骤1)中所述的根据已制作完成的静电成形薄膜天线实物模型上测量的靶标点空间位置信息建立静电成形薄膜天线有限元模型，其具体步骤包括：According to the target point spatial position information measured on the electrostatically formed film antenna physical model that has been made as described in the above step 1), the electrostatically formed film antenna finite element model is established, and its specific steps include:
(1)在静电成形薄膜天线实物模型上贴置测量靶标点，要求薄膜反射面上贴置M1个靶标点，要求M1个靶标点布满整个薄膜反射面并且任意两个靶标点之间的距离在5-10cm范围内，拉索两端贴置M2＝2N2个靶标点，其中N2为拉索数目，；(1) Place measurement target points on the physical model of the electrostatically formed film antenna. It is required to place M 1 target points on the film reflective surface, and it is required that M 1 target points cover the entire film reflective surface and between any two target points The distance is within the range of 5-10cm, and M 2 =2N 2 target points are pasted on both ends of the cable, where N 2 is the number of cables;
(2)利用摄影测量技术得到所有靶标点的空间位置信息；(2) Obtain the spatial position information of all target points by using photogrammetry technology;
(3)利用测得的靶标点空间位置信息建立M＝M1+M2个节点，并根据薄膜反射面上的节点建立N1个薄膜三角形单元，根据拉索两端的节点建立N2个拉索单元。(3) Establish M=M 1 +M 2 nodes by using the measured spatial position information of the target point, and establish N 1 thin film triangular units based on the nodes on the thin film reflective surface, and establish N 2 pulley triangle units based on the nodes at both ends of the cable search unit.
上述步骤3)中所述的以电极电压值和索端位置作为设计变量，给定设计变量初值和设计变量上下限具体包括：给定设计变量向量X＝[x1x2...xJ+K]T，其中前J个为电极电压值设计变量，后K个为拉索固定端Z向位置设计变量，给定设计变量初值X0＝[x10x20...x(J+K)0]T，给定设计变量上下限其中x i 和分别为第i个设计变量xi的下限值和上限值。The electrode voltage value and cable end position described in the above step 3) are used as the design variables, and the initial value of the given design variable and the upper and lower limits of the design variable specifically include: given design variable vector X=[x 1 x 2 ... x J+K ] T , where the first J are the design variables of the electrode voltage value, and the last K are the design variables of the Z-direction position of the fixed end of the cable, given the initial value of the design variable X 0 =[x 10 x 20 ... x ( J+K)0 ] T , given the upper and lower limits of design variables where x i and are the lower limit and upper limit of the i-th design variable x i , respectively.
上述步骤4)中所述的对设计变量进行归一化处理具体包括：将设计变量转换为其中第i个设计变量xi转换为设计变量初值转换为其中第i个设计变量初值xi0转换为 完成设计变量归一化处理。The normalization of the design variables described in the above step 4) specifically includes: converting the design variables into where the i-th design variable x i is converted to The initial value of the design variable is converted to Among them, the initial value x i0 of the i-th design variable is transformed into Complete the normalization process of the design variables.
上述步骤5)中所述的给定静电成形薄膜天线在自重平衡态时的预应力，其具体步骤包括：Above-mentioned step 5) the prestressing force of the given electrostatic forming film antenna described in self-weight equilibrium state, its specific steps include:
(1)给静电成形薄膜天线有限元模型施加初始预应力值PF0；(1) Apply the initial prestress value PF0 to the finite element model of the electrostatically formed film antenna;
(2)利用ANSYS有限元分析软件计算有限元模型在预应力PF0和重力载荷下薄膜面各节点位移和平衡预应力PF1；(2) Use ANSYS finite element analysis software to calculate the displacement of each node of the film surface and the balanced prestress PF1 of the finite element model under the prestress PF0 and gravity load;
(3)根据有限元分析位移收敛准则，判断薄膜面各节点位移均方根是否小于0.01，其中δi为各节点的位移值，M1为薄膜反射面节点数，若是，则求解得到所给定的静电成形薄膜天线在自重平衡状态时的预应力PF0；若否，令初始预应力值PF0＝PF1，转到给静电成形薄膜天线有限元模型施加初始预应力值PF0。(3) According to the displacement convergence criterion of finite element analysis, determine the root mean square displacement of each node on the membrane surface Is it less than 0.01, where δ i is the displacement value of each node, M 1 is the number of nodes on the film reflector, if so, then solve the prestress PF0 of the given electrostatically formed film antenna in the state of self-weight balance; if not, let The initial prestress value PF0=PF1, turn to apply the initial prestress value PF0 to the finite element model of the electrostatically formed film antenna.
上述步骤6)中所述的以薄膜反射面节点拟合形面精度作为目标函数进行优化分析，其具体步骤包括：In the above step 6), the optimization analysis is carried out with the film reflective surface node fitting surface accuracy as the objective function, and its specific steps include:
(1)给定目标函数其中，RMS为薄膜反射面节点拟合形面精度，zi为第i个薄膜反射面节点Z向实际位置，为最佳拟合抛物面上第i个节点Z向位置；(1) Given the objective function Among them, RMS is the shape accuracy of the film reflective surface node fitting, z i is the actual position of the i-th film reflective surface node in the Z direction, is the Z-direction position of the i-th node on the best fitting paraboloid;
(2)利用敏度优化方法求解具有设计变量上下限的优化模型，得到各设计变量的最优调整量ΔX＝[Δx1Δx2...ΔxJ+K]T，使得目标函数值RMS最小；(2) Use the sensitivity optimization method to solve the optimization model with the upper and lower limits of the design variables, and obtain the optimal adjustment amount of each design variable ΔX=[Δx 1 Δx 2 ...Δx J+K ] T , so that the objective function value RMS is the smallest ;
(3)得到最优的电极电压值和索端位置X'＝X0+ΔX，完成以薄膜反射面节点拟合形面精度作为目标函数的优化分析。(3) Obtain the optimal electrode voltage value and cable end position X'=X 0 +ΔX, and complete the optimization analysis with the surface accuracy of the node fitting shape of the thin film reflective surface as the objective function.
上述步骤7)中所述的分析优化结果，完成基于电压与索端位置协同优化的静电成形薄膜天线形面调整，其具体步骤包括：Based on the analysis and optimization results described in the above step 7), the shape and surface adjustment of the electrostatically formed film antenna based on the collaborative optimization of the voltage and the position of the cable end is completed, and the specific steps include:
(1)将静电成形薄膜天线实物模型的电极电压值和索端位置调整到优化值X'；(1) Adjust the electrode voltage value and cable end position of the physical model of the electrostatically formed film antenna to the optimal value X';
(2)利用摄影测量技术测量调整后的薄膜反射面各靶标点位置信息，计算薄膜反射面节点拟合形面精度 (2) Use photogrammetry technology to measure the position information of each target point on the adjusted film reflective surface, and calculate the surface accuracy of the node fitting shape of the film reflective surface
(3)判断调整后薄膜反射面节点拟合形面精度RMS是否符合设计要求，是，则完成基于电压与索端位置协同优化的静电成形薄膜天线形面调整；否，则改变初始预应力值PF0，返回步骤5)。(3) Judging whether the RMS surface accuracy RMS of the adjusted film reflective surface node fitting meets the design requirements, if yes, then complete the electrostatically formed film antenna shape adjustment based on the collaborative optimization of voltage and cable end position; if not, change the initial prestress value PF0, return to step 5).
本发明的有益效果：本发明提供的基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法，能够实现有限元模型指导静电成形薄膜天线实物形面调整，并且利用电压和索端位置协同优化可以更好地调整薄膜反射面形面精度。Beneficial effects of the present invention: the method for adjusting the shape and surface of the electrostatically formed film antenna based on the cooperative optimization of voltage and cable end position provided by the present invention can realize the adjustment of the physical shape of the electrostatically formed film antenna guided by the finite element model, and utilize the voltage and the position of the cable end Collaborative optimization can better adjust the shape precision of the thin film reflective surface.
附图说明Description of drawings
图1是本发明实施例提供的基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法总体流程图；Fig. 1 is an overall flow chart of the method for adjusting the shape and surface of an electrostatically formed film antenna based on the cooperative optimization of voltage and cable end position provided by an embodiment of the present invention;
图2是本发明实施例提供的根据已制作完成的静电成形薄膜天线实物模型上测量的靶标点空间位置信息建立静电成形薄膜天线有限元模型流程图；Fig. 2 is a flow chart of establishing a finite element model of an electrostatically formed film antenna according to the target point spatial position information measured on the manufactured electrostatically formed film antenna physical model provided by the embodiment of the present invention;
图3是本发明实施例提供的给定静电成形薄膜天线在自重平衡态时的预应力流程图；Fig. 3 is a flow chart of prestressing of a given electrostatically formed film antenna provided in an embodiment of the present invention in a self-weight equilibrium state;
图4是本发明实施例提供的以薄膜面节点拟合形面精度作为目标函数进行优化分析流程图；Fig. 4 is a flow chart of optimization analysis provided by an embodiment of the present invention with the film surface node fitting surface accuracy as the objective function;
图5是本发明实施例提供的分析优化结果，完成基于电压与索端位置协同优化的静电成形薄膜天线形面调整流程图；Fig. 5 is the analysis and optimization result provided by the embodiment of the present invention, and the flow chart of completing the adjustment of the shape and surface of the electrostatically formed film antenna based on the cooperative optimization of the voltage and the position of the cable end;
图6是本发明实施例提供的静电成形薄膜天线节点与单元示意图；Fig. 6 is a schematic diagram of nodes and units of an electrostatically formed film antenna provided by an embodiment of the present invention;
图7是本发明实施例提供的静电成形薄膜天线调整前节点位置误差分布图；Fig. 7 is a distribution diagram of node position errors before adjustment of the electrostatic forming film antenna provided by the embodiment of the present invention;
图8是本发明实施例提供的静电成形薄膜天线调整后节点位置误差分布图。FIG. 8 is a distribution diagram of node position errors after adjustment of the electrostatically formed film antenna provided by the embodiment of the present invention.
具体实施方式detailed description
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。In order to make the object, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.
本发明提供了一种基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法，用于利用有限元模型中的电极电压与索端位置协同优化指导静电成形薄膜天线形面调整。下面结合附图对本发明的应用原理作详细的描述。The invention provides an electrostatically formed thin film antenna shape adjustment method based on collaborative optimization of voltage and cable end position, which is used to guide the adjustment of the electrostatically formed thin film antenna shape by utilizing the coordinated optimization of electrode voltage and cable end position in a finite element model. The application principle of the present invention will be described in detail below in conjunction with the accompanying drawings.
本发明实施例的基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法包括以下步骤：The method for adjusting the shape and surface of an electrostatically formed film antenna based on the cooperative optimization of voltage and cable end position in the embodiment of the present invention includes the following steps:
1)根据已制作完成的静电成形薄膜天线实物模型上测量的靶标点空间位置信息建立静电成形薄膜天线有限元模型；1) Establish the finite element model of the electrostatically formed film antenna according to the target point spatial position information measured on the finished electrostatically formed film antenna physical model;
2)给定静电成形薄膜天线有限元模型约束条件，即拉索最外端节点位移全部固定；2) The constraints of the finite element model of the electrostatically formed film antenna are given, that is, the displacements of the outermost nodes of the cables are all fixed;
3)以电极电压值和索端位置作为设计变量，给定设计变量初值和设计变量上下限；3) Taking the electrode voltage value and the position of the cable end as the design variables, the initial value of the design variable and the upper and lower limits of the design variable are given;
4)对设计变量进行归一化处理；4) Normalize the design variables;
5)给定静电成形薄膜天线在自重平衡态时的预应力；5) Given the prestress of the electrostatically formed film antenna in its self-weight equilibrium state;
6)以薄膜反射面节点拟合形面精度作为目标函数进行优化分析；6) The optimization analysis is carried out with the surface accuracy of the joint fitting shape of the film reflector as the objective function;
7)分析优化结果，完成基于电压与索端位置协同优化的静电成形薄膜天线形面调整。7) Analyze the optimization results, and complete the adjustment of the shape and surface of the electrostatically formed film antenna based on the collaborative optimization of the voltage and the position of the cable end.
其中图1是本发明实施例提供的基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法总体流程图。1 is an overall flow chart of an electrostatically formed film antenna profile adjustment method based on collaborative optimization of voltage and cable end positions provided by an embodiment of the present invention.
如图2所示，上述的步骤1)，具体涉及如下步骤：As shown in Figure 2, the above-mentioned step 1) specifically involves the following steps:
(1)在静电成形薄膜天线实物模型上贴置测量靶标点，要求薄膜反射面上贴置M1个靶标点，要求M1个靶标点布满整个薄膜反射面并且任意两个靶标点之间的距离在5-10cm范围内，拉索两端贴置M2＝2N2个靶标点，其中N2为拉索数目，；(1) Place measurement target points on the physical model of the electrostatically formed film antenna. It is required to place M 1 target points on the film reflective surface, and it is required that M 1 target points cover the entire film reflective surface and between any two target points The distance is within the range of 5-10cm, and M 2 =2N 2 target points are pasted on both ends of the cable, where N 2 is the number of cables;
(2)利用摄影测量技术得到所有靶标点的空间位置信息；(2) Obtain the spatial position information of all target points by using photogrammetry technology;
(3)利用测得的靶标点空间位置信息建立M＝M1+M2个节点，并根据薄膜反射面上的节点建立N1个薄膜三角形单元，根据拉索两端的节点建立N2个拉索单元。(3) Establish M=M 1 +M 2 nodes by using the measured spatial position information of the target point, and establish N 1 thin film triangular units based on the nodes on the thin film reflective surface, and establish N 2 pulley triangle units based on the nodes at both ends of the cable search unit.
其中上述步骤3)，具体包括：给定设计变量向量X＝[x1x2...xJ+K]T，其中前J个为电极电压值设计变量，后K个为拉索固定端Z向位置设计变量，给定设计变量初值X0＝[x10x20...x(J+K)0]T，给定设计变量上下限其中x i 和分别为第i个设计变量xi的下限值和上限值。The above step 3) specifically includes: given design variable vector X=[x 1 x 2 ... x J+K ] T , wherein the first J are the design variables of the electrode voltage value, and the last K are the fixed ends of the cables Z direction position design variable, given the initial value of the design variable X 0 = [x 10 x 20 ... x (J+K)0 ] T , given the upper and lower limits of the design variable where x i and are the lower limit and upper limit of the i-th design variable x i , respectively.
其中上述步骤4)，具体包括：将设计变量转换为其中第i个设计变量xi转换为设计变量初值转换为其中第i个设计变量初值xi0转换为完成设计变量归一化处理。Wherein the above-mentioned step 4) specifically includes: converting the design variable into where the i-th design variable x i is converted to The initial value of the design variable is converted to Among them, the initial value x i0 of the i-th design variable is transformed into Complete the normalization process of the design variables.
如图3所示，上述的步骤5)，具体涉及如下步骤：As shown in Figure 3, the above-mentioned step 5) specifically involves the following steps:
(1)给静电成形薄膜天线有限元模型施加初始预应力值PF0；(1) Apply the initial prestress value PF0 to the finite element model of the electrostatically formed film antenna;
(2)利用ANSYS有限元分析软件计算有限元模型在预应力PF0和重力载荷下薄膜面各节点位移和平衡预应力PF1；(2) Use ANSYS finite element analysis software to calculate the displacement of each node of the film surface and the balanced prestress PF1 of the finite element model under the prestress PF0 and gravity load;
(3)根据有限元分析位移收敛准则，判断薄膜面各节点位移均方根是否小于0.01，其中δi为各节点的位移值，M1为薄膜反射面节点数，若是，则求解得到所给定的静电成形薄膜天线在自重平衡状态时的预应力PF0；若否，令初始预应力值PF0＝PF1，转到给静电成形薄膜天线有限元模型施加初始预应力值PF0。(3) According to the displacement convergence criterion of finite element analysis, determine the root mean square displacement of each node on the membrane surface Is it less than 0.01, where δ i is the displacement value of each node, M 1 is the number of nodes on the film reflector, if so, then solve the prestress PF0 of the given electrostatically formed film antenna in the state of self-weight balance; if not, let The initial prestress value PF0=PF1, turn to apply the initial prestress value PF0 to the finite element model of the electrostatically formed film antenna.
如图4所示，上述的步骤6)，具体涉及如下步骤：As shown in Figure 4, the above-mentioned step 6) specifically involves the following steps:
(1)给定目标函数其中，RMS为薄膜反射面节点拟合形面精度，zi为第i个薄膜反射面节点Z向实际位置，为最佳拟合抛物面上第i个节点Z向位置；(1) Given the objective function Among them, RMS is the shape accuracy of the film reflective surface node fitting, z i is the actual position of the i-th film reflective surface node in the Z direction, is the Z-direction position of the i-th node on the best fitting paraboloid;
(2)利用敏度优化方法求解具有设计变量上下限的优化模型，得到各设计变量的最优调整量ΔX＝[Δx1Δx2...ΔxJ+K]T，使得目标函数值RMS最小；(2) Use the sensitivity optimization method to solve the optimization model with the upper and lower limits of the design variables, and obtain the optimal adjustment amount of each design variable ΔX=[Δx 1 Δx 2 ...Δx J+K ] T , so that the objective function value RMS is the smallest ;
(3)得到最优的电极电压值和索端位置X'＝X0+ΔX，完成以薄膜反射面节点拟合形面精度作为目标函数的优化分析。(3) Obtain the optimal electrode voltage value and cable end position X'=X 0 +ΔX, and complete the optimization analysis with the surface accuracy of the node fitting shape of the thin film reflective surface as the objective function.
如图5所示，上述的步骤7)，具体涉及如下步骤：As shown in Figure 5, the above-mentioned step 7) specifically involves the following steps:
(1)将静电成形薄膜天线实物模型的电极电压值和索端位置调整到优化值X'；(1) Adjust the electrode voltage value and cable end position of the physical model of the electrostatically formed film antenna to the optimal value X';
(2)利用摄影测量技术测量调整后的薄膜反射面各靶标点位置信息，计算薄膜反射面节点拟合形面精度 (2) Use photogrammetry technology to measure the position information of each target point on the adjusted film reflective surface, and calculate the surface accuracy of the node fitting shape of the film reflective surface
(3)判断调整后薄膜反射面节点拟合形面精度RMS是否符合设计要求，是，则完成基于电压与索端位置协同优化的静电成形薄膜天线形面调整；否，则改变初始预应力值PF0，返回步骤5)。(3) Judging whether the RMS surface accuracy RMS of the adjusted film reflective surface node fitting meets the design requirements, if yes, then complete the electrostatically formed film antenna shape adjustment based on the collaborative optimization of voltage and cable end position; if not, change the initial prestress value PF0, return to step 5).
下面结合仿真实验对本发明的应用效果作详细的描述。The application effects of the present invention will be described in detail below in combination with simulation experiments.
仿真条件：Simulation conditions:
在已经制作完成的静电成形薄膜天线样机上贴置M＝691个测量靶标点，利用摄影测量技术得到靶标点的坐标然后建立相应的有限元节点和单元如图6，共有N1＝1128个薄膜三角形单元，N2＝36个索单元，索外端节点全固定。为了体现本发明的准确性，这里给出了利用电压与索端位置调整前后的薄膜反射面形面精度，如图7为初始薄膜反射面节点位置误差分布云图，初始形面精度RMS0＝0.7066mm；如图8，为施加优化得到的电极电压与索端位置后薄膜反射面节点位置误差分布云图，调整后形面精度RMS＝0.5207mm。可知根据本发明进行静电成形薄膜反射面形面精度调整可以获得很好的效果。Place M=691 measurement target points on the finished electrostatically formed film antenna prototype, use photogrammetry technology to obtain the coordinates of the target points, and then establish the corresponding finite element nodes and units as shown in Figure 6, with a total of N 1 =1128 films For triangular elements, N 2 =36 cable elements, and the outer end nodes of the cables are all fixed. In order to reflect the accuracy of the present invention, the surface accuracy of the film reflection surface before and after the adjustment of the voltage and the cable end position is provided here, as shown in Figure 7, which is the cloud diagram of the node position error distribution of the initial film reflection surface, and the initial surface accuracy RMS 0 =0.7066 mm; as shown in Figure 8, it is the cloud diagram of the error distribution of the node position of the film reflective surface after applying the optimized electrode voltage and the position of the cable end, and the adjusted surface accuracy RMS=0.5207mm. It can be seen that the adjustment of the surface precision of the reflective surface of the electrostatically formed film according to the present invention can obtain very good results.
综上，本发明提供的基于电压与索端位置协同优化的静电成形薄膜天线形面调整方法，能够实现有限元模型指导静电成形薄膜天线实物形面调整，并且利用电压和索端位置协同优化可以更好地调整薄膜反射面形面精度。In summary, the method for adjusting the shape and surface of the electrostatically formed film antenna based on the collaborative optimization of the voltage and the position of the cable end provided by the present invention can realize the adjustment of the physical shape of the electrostatically formed film antenna guided by the finite element model, and the collaborative optimization of the voltage and the position of the cable end can realize Better adjust the shape accuracy of the thin film reflective surface.
以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。本实施例没有详细叙述的部分和英文缩写属本行业的公知常识，在网上可以搜索到，这里不一一叙述。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. within range. The parts and English abbreviations that are not described in detail in this embodiment belong to the common knowledge in this industry and can be searched on the Internet, so they will not be described one by one here.
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