A Structural Optimization Design Method for Improving the Natural Frequency of Large Aperture Antenna Systems

Abstract

The present invention discloses a structural optimization design method for improving the natural frequency of a large-aperture antenna system. The method includes steps such as antenna structure state evaluation, conceptual design of the improved structure, and detailed design of the improved structure. Based on the structural material distribution obtained by topology optimization calculation, the present invention creates a parameter optimization model and performs parameter optimization calculation, so as to obtain an antenna structure that better conforms to engineering practice, and is applicable to fields such as structural optimization design sensitive to comparison stiffness or structural optimization design of large-aperture antenna systems with the goal of improving the natural frequency.

Description

Technical Field

[0001] The present invention belongs to the technical field of antenna structure design, and in particular relates to a structural optimization design method for improving the natural frequency of a large-aperture antenna system. The present invention mainly performs topology and parameter optimization on the antenna structure, thereby improving the natural frequency of the large-aperture antenna system and ensuring the stability and dynamic performance index requirements of the antenna system. Background Art

[0002] The antenna system usually includes an antenna, a mount, a drive system and a foundation. It is a complex elastic system with a certain natural frequency. When the frequency of the external interference force is close to or equal to the natural frequency of the system, the system will resonate and the amplitude will increase sharply, making the system unable to work normally, and even causing damage to the antenna system. In addition, with the development of radar, communication and radio astronomy technology, on the one hand, the aperture of the antenna needs to be further increased, so that the natural frequency of the antenna structure is further reduced; on the other hand, due to the increase in accuracy requirements, the bandwidth of the servo system needs to be further increased. In this way, the natural frequency of the structure gradually approaches the bandwidth of the servo system, and even falls within the bandwidth. In this case, various servo noises will excite the system to resonate, and the feedback will make the resonance continue, causing the servo system to be unstable, unable to work, and even structural damage.

[0003] In order to ensure the performance requirements of the antenna system and the stability of the servo system and avoid resonance, the antenna structure must be optimized so that the natural frequency of the structure avoids the frequency of various interference forces and is far away from the bandwidth of the servo system. The improvement of the natural frequency of the structure is mainly considered from two aspects: one is to improve the structural stiffness; the other is to reduce the inertia of the system. There are many factors that affect the structural stiffness, such as the torsion and bending stiffness of the motor and reducer shaft, the transmission ratio of the transmission system, the stiffness of the supporting structure, and the stiffness of various connectors and fasteners. Some of these factors have little effect on the natural frequency of the structure, while some factors have a greater impact, and increasing the structural stiffness often leads to an increase in inertia. Therefore, the stiffness of each part cannot be uniformly improved. The weak links in the load transfer path should be determined through structural analysis and targeted strengthening should be carried out. The influence of system inertia on the natural frequency of the structure is related to the structural materials used on the one hand, and to the antenna system structure and the layout of other equipment on the other hand. For structural materials, materials with higher elastic modulus and lower density can be selected, but such materials are usually more expensive. The layout of structures and other equipment is mainly to reduce the distance between the structure and the vibration nodes of related equipment, but this method has great limitations, mainly manifested in: the layout of the equipment is usually closely related to the overall indicators of the antenna, and changes in the layout are likely to have a great impact on other performance of the antenna (such as optical performance).

[0004] In summary, the improvement of the antenna natural frequency mainly focuses on enhancing the structural stiffness, and structural optimization (including topology optimization, shape optimization, parameter optimization, etc.) is the most common. At present, topology optimization is widely used in the improvement of the natural frequency of small-aperture antennas, but there are great limitations in the improvement of the overall structural modal frequency of large-aperture antennas. The main reasons are as follows: The premise of topology optimization is to first find a structure that meets the optimization model indicators, and then starting from this structure, gradually delete relevant materials to obtain a material layout that meets the requirements. For the large-aperture antenna structure, on the one hand, due to the influence of structural mass, the initial structure obtained by conventional methods cannot meet the natural frequency indicators. On the other hand, the structural mass parameters will also affect the convergence speed of the optimization goal in the topology optimization process and increase the amount of calculation data. Summary of the Invention

[0005] In view of the limitations and deficiencies of the above background technology, the present invention proposes a structural optimization design method for improving the natural frequency of large-aperture antennas based on the existing topology theory model. According to this optimization design method, the structural form and parameters that meet the natural frequency index requirements can be calculated, and during the optimization process, the calculation convergence speed of the optimization model can be improved, laying a technical foundation for meeting the dynamic characteristics and optical performance indicators of large-aperture antennas.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A structural optimization design method for improving the natural frequency of a large-aperture antenna system, comprising the following steps:

[0008] (1) Antenna structure state evaluation: Create a finite element model of the antenna structure according to the geometric model, calculate the distribution of the modal strain energy of the antenna structure, and determine the priority of the antenna structure improvement based on the magnitude of the modal strain energy of the antenna structure;

[0009] (2) Conceptual design of the improved structure: Create a topology optimization model, conduct a conceptual design on the structure to be improved, and calculate the optimal force transmission path of the antenna structure;

[0010] (3) Detailed design of the improved structure: Based on the optimal force transmission path, use a parameter optimization model to conduct a detailed design on the improved structure.

[0011] Further, the topology optimization model is:

[0012] Optimization goal: min(V)

[0013] Constraint conditions:

[0014] Optimization variables: x = {x1, x2, …, x N}T ∈Ω1

[0015] Among them, V represents the volume of the design space structure; f1 and f2 respectively represent the first-order and second-order modal frequencies; x is the design variable of each discrete region, that is, the element density, and its value is 0 or 1, where 0 represents the absence of material and 1 represents the presence.

[0016] The relationship between the design variable and the material properties is established through the following equation, so as to realize the goal and constraints of the optimization variable affecting the optimization model:

[0017]

[0018] Among them, x i is the element density; E i (x i ) and ρ i (x i ) are the material elastic modulus and material density weighted by the element density x i respectively; E0 is the unweighted elastic modulus of the solid material; E min and ρ min are the elastic modulus and material density of the material structure region that needs to be deleted; p is the penalty coefficient, which is used to make the element density x i distributed at both ends of the interval [0,1].

[0019] Furthermore, the parameter optimization model is:

[0020] Optimization goal: min(V)

[0021] Constraint conditions:

[0022] Optimization variables: D = {D1, D2, D3, …, D m}

[0023] Among them, D is the key parameter of the structure; m is the number of key parameters of the structure.

[0024] The beneficial effects of the present invention are as follows:

[0025] 1. Based on the existing topology theory model, the present invention improves the natural frequency of the large-aperture antenna and has a faster calculation convergence speed.

[0026] 2. The method of the present invention can calculate the structural form and parameters that meet the requirements of the natural frequency index, and during the optimization process, it can improve the calculation convergence speed of the optimization model, laying a technical foundation for meeting the dynamic characteristics and optical performance index of the large-aperture antenna.

[0027] 3. The present invention realizes the purpose of simplifying the structural optimization design space setting, accelerating the convergence speed of topology optimization, and making the structural boundary of the topology optimization result clearer by decoupling the relationship between the unit density and the material density.

[0028] 4. Based on the structural material distribution obtained from the topology optimization calculation, the present invention creates a parameter optimization model and performs parameter optimization calculation, so as to obtain an antenna structure that better conforms to the engineering practice, and is applicable to fields such as the structural optimization design sensitive to comparison stiffness or the structural optimization design of large-aperture antenna systems aiming at improving the natural frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram of the overall appearance of the SKA-P antenna structure in the embodiment of the present invention.

[0030] Figure 2 It is a finite element modeling scheme of the pedestal cylinder.

[0031] Figure 3 It is a schematic diagram of the finite element modeling of the flange and bolt connection of the pedestal cylinder.

[0032] Figure 4 It is a schematic diagram of the finite element modeling of the azimuth steering box assembly.

[0033] Figure 5 It is a schematic diagram of the finite element modeling of the central body assembly.

[0034] Figure 6 It is a schematic diagram of the first-order (left) and second-order (right) modal strain energy distribution of the azimuth steering box.

[0035] Figure 7 It is a schematic diagram of the first-order (left) and second-order (right) modal strain energy distribution of the central body structure.

[0036] Figure 8 It is the topology optimization design space of the central body structure.

[0037] Figure 9 It is the topology optimization design space of the azimuth steering box.

[0038] Figure 10 It is the change of the optimization objective of the topology optimization model with the number of iterations.

[0039] Figure 11 It is the change of the optimization constraints of the topology optimization model with the number of iterations.

[0040] Figure 12 It is the topology optimization calculation result of the central body.

[0041] Figure 13 It is the topology optimization calculation result of the azimuth steering box.

[0042] Figure 14 The structural parametric finite element model reconstructed based on the topological optimization calculation results.

[0043] Figure 15 The structural diagram after parameter optimization. Specific implementation manners

[0044] The present invention will be further described below in conjunction with the accompanying drawings and specific implementation manners.

[0045] A structural optimization design method for improving the natural frequency of a large-aperture antenna system. This method is based on the existing topological theory model, combines the structural load transfer path, dynamic characteristics, and strain energy state of the large-aperture antenna structure, and gives the key structural components that have a greater impact on the antenna natural frequency and the structural optimization design method. The main technical solutions of this method are as follows:

[0046] 1. Evaluation of the antenna structure state

[0047] Evaluate the antenna structure state based on the antenna modal strain energy distribution. Sort the antenna structure according to the numerical value of the structural modal strain energy from high to low, and comprehensively consider factors such as the functional requirements of the structure, the manufacturability of structure modification, and economy to determine the priority of antenna structure improvement.

[0048] 2. Conceptual design of the improved structure

[0049] Establish a topological optimization model with the minimum volume of the design space structure as the optimization goal and the first two-order modal frequencies as the optimization constraints, and calculate the conceptual design of the improved structure. The optimization model is as follows:

[0050]

[0051] Wherein, V represents the volume of the design space structure; f1 and f2 respectively represent the first-order and second-order modal frequencies; x is the design variable of each discrete region, also known as the element density, and the value is 0 or 1, where 0 represents the absence of material and 1 represents the existence.

[0052] The design variable of the optimization model (1) establishes the relationship with the material properties through the following equation, thereby realizing that the optimization variable affects the objective and constraints of the optimization model:

[0053]

[0054] In the formula: x i is the element density; E i (x i ) and ρ i (x i ) are respectively the material modulus of elasticity and density after passing through the element density x iThe weighted elastic modulus and material density of the material; E0 and ρ0 are the unweighted elastic modulus and material density of the solid material; E min and ρ min are the elastic modulus and material density of the material structure region to be deleted. In the actual structure, the E min and ρ min should be 0. However, to avoid singularity of the matrix during model solution, E min and ρ min need to be set to E0 / 10 6 and ρ0 / 10 6 ; p is the penalty coefficient, and its main function is to make the element density x i distribute at both ends of the interval [0,1]. Generally, the p value with the best penalty effect needs to be obtained through numerical experiments according to the actual situation. Usually, in most cases, p = 3.

[0055] It can be seen from Equation (2) that during the process of taking the modal frequency improvement as the optimization goal, as the optimization variable x i changes, the elastic modulus and material density of the design area will both change, increasing the difficulty of solving the optimization model (1); in addition, due to the existence of the parameter ρ0, it is also difficult to determine the topological optimization design space. In view of this, Equation (2) is changed to the form of Equation (3):

[0056]

[0057] 3. Detailed design of the improved structure

[0058] Combining Equations (1), (2) and (3), in the final result calculated by the topological optimization model, there will be a region with a certain intermediate element density, making the boundary between the materials to be retained and the materials to be deleted not particularly clear. Therefore, directly using the calculation result of topological optimization for structural design often fails to meet the set optimization constraints and optimization goals.

[0059] In addition, the main purpose of the modified Equation (3) proposed by the present invention is to calculate the best force transmission path of the structure, reduce the iteration times of the optimization model, and reduce the difficulty of determining the design space, which has obvious effects in the optimization design of large-aperture antenna structures. And, since all material densities in the design space are set to very small values, the modal frequencies calculated by the optimization model are not accurate, and it is necessary to use parameter optimization technology based on the force transmission path calculated by the optimization model to finally determine the parameters of the structure. The corresponding parameter optimization model is as follows:

[0060]

[0061] In the formula: D is the key parameter of the structure; m is the number of key parameters of the structure.

[0062] In the parameter optimization model (4), the material density parameter is the density without weighting and correction. Therefore, the final result calculated by the model can be directly used for structural design.

[0063] The following details this method in combination with the SKA-P antenna:

[0064] In this embodiment, the SKA-P antenna mainly consists of the bottom cylinder 1 of the pedestal barrel, the middle cylinder 2 of the pedestal barrel, the upper cylinder 3 of the pedestal barrel, the azimuth steering box 4, the central body V-beam 5, the central body U-frame 6, the central body A-frame 7, the main surface back frame 8, the main surface assembly 9, the sub-reflector support 10, and the sub-reflector assembly 11, etc.

[0065] From Figure 1 it can be seen that the large-aperture antenna structure in this embodiment is mainly of the truss and thin-walled types. If the design space of topological optimization is set at any position from Figure 1 4 to 11 as shown, it will not only not increase the initial modal calculation result of topological optimization, but will further reduce the modal frequency of the structure, increasing the optimization difficulty of the optimization model.

[0066] This method corrects the material density of the topological optimization design space through Equation (3), enabling the initial modal calculation result of the topological optimization model to meet the optimization constraints. Moreover, this method also reduces the influence of the change in the mass matrix of the design region on the modal frequency during the topological optimization process, making the structural boundary calculated by the topological optimization model clearer and accelerating the convergence speed of the optimization model.

[0067] The structural optimization design method used to improve the natural frequency of the antenna structure in this embodiment is mainly achieved through the following steps:

[0068] 1) Create a finite element model based on the geometric model. During the model creation process, it is necessary to reflect the original topological form of the structure as much as possible so that the weak positions of the structure can be more clearly shown when calculating the strain energy. The modeling scheme adopted in this embodiment is as follows:

[0069] a) The finite element modeling scheme for the three parts of the pedestal barrel is to adopt a technical scheme combining quadrilateral and triangular elements. As Figure 2 shown, the finite element model 12 of the bottom cylinder, the finite element model 13 of the middle cylinder, and the finite element model 14 of the top circle;

[0070] b) The finite element modeling scheme for the flange 15 and bolt 16 connections between the three parts of the pedestal barrel is to adopt a technical scheme combining hexahedron, triangular prism, beam elements, and multi-point constraint elements. As Figure 3 shown;

[0071] c) The finite element modeling scheme of the azimuth steering box assembly is as follows Figure 4 As shown, it mainly includes the finite element model 17 of the pitch axis ear (mainly modeled with triangular prisms and hexahedrons), the finite element model 18 of the azimuth steering box (in the form of a thin-walled structure, mainly modeled with quadrilaterals and triangles), the finite element model 19 of the lower support of the pitch drive (mainly modeled with triangular prisms and hexahedrons), and the upper support plate 20 of the azimuth bearing (mainly modeled with triangular prisms and hexahedrons);

[0072] d) The finite element modeling scheme of the central body assembly is as follows Figure 5 As shown, it mainly includes the finite element model 21 of the U-shaped frame (mainly modeled with triangles and quadrilaterals), the finite element model 22 of the V-shaped beam (mainly modeled with triangles and quadrilaterals), and the finite element model 23 of the A-shaped frame (mainly modeled with triangles and quadrilaterals).

[0073] 2) Based on the finite element models created in step 1), apply displacement constraints in the six degrees of freedom directions at the bottom of the bottom cylinder 1 of the pedestal tube. When outputting the results, select the strain energy and vibration mode vectors, and calculate and output the modal frequencies, vibration modes, and strain energy distributions of the antenna structure before optimization. According to the distribution of the strain energy, screen out two regions with relatively high values, namely the central body structure assembly and the azimuth steering box assembly, as shown in Figure 6 and Figure 7 As shown, where 24, 26 and 25, 27 are the modal strain energy distributions of the first-order and second-order modal vibration modes, that is, the dark regions in the figure. It can be seen from the strain energy distribution that in the first-order mode, the weak links of the azimuth steering box mainly appear in the connection regions between the lower support 19 of the pitch drive and the box 18 and the upper support plate 20 of the azimuth bearing; in the second-order mode, the weak links of the azimuth steering box mainly appear in the connection regions between the lower support 19 of the pitch drive and the pitch axis ear 17; the weak links of the central body structure are mainly concentrated in the A-shaped frame 23 and the V-shaped beam region 22.

[0074] 3) Based on the analysis results of the strain energy in step 2), set the design space for the structural topology optimization calculation. The structural optimization design space is mainly realized by filling elements within the structurally designable region (mainly referring to the three-dimensional space that does not interfere with other structures). The optimized design space 28 of the central body is as shown in Figure 8 As shown, some square empty regions in the middle are mainly the interference regions with the azimuth steering box 4 during the antenna pitch movement; the optimized design space 29 of the azimuth steering box is as shown in Figure 9 As shown, some empty regions are mainly interfering with the installation spaces of related equipment.

[0075] 4) Topology optimization calculations are performed based on the created topology optimization model, the improved material model, and the antenna structure finite element model with optimized design spaces 28 and 29. The changes in the topology optimization objectives and constraints during the calculation process are as shown in Figure 10 and Figure 11 . It can be seen from the change curves shown in the figure that the final optimization objective region is stable and the optimization constraints are also met. The material distribution of the design space is as shown in Figure 12 and Figure 13 . It can be known from the topology optimization calculation results that: the distribution and connection positions of the V-shaped beam 5 in the central body structure are changed, and the shape of the original A-shaped frame 7 is also redesigned; the azimuth steering box enhances the connection with the pitch lug 17 and the connection between the lower pitch drive lug 19 and the upper support plate 20 of the azimuth bearing.

[0076] 5) Create a parameter optimization model. The creation of the parameter optimization model is mainly achieved through the relevant parameters of the existing elements. As shown in Figures 12 - 15 , in this embodiment, the distribution 30 of the central body material mainly simulates the load transfer path through the beam element 32, and the distribution 31 of the azimuth steering box material mainly simulates the load transfer path through the shell element 33. Among them, the cross-section parameters of the beam element and the thickness parameter of the shell element are the design variables of the parameter optimization model. The created parametric finite element model is as shown in Figure 14 . The structure after parameter optimization is as shown in Figure 15 . Among them, the central body structure 34 and the azimuth steering box 35 are rebuilt according to the parameter optimization results, and the model meets the requirements of the modal frequency improvement index after reconstruction.

Claims

1. A structural optimization design method for improving the natural frequency of a large-aperture antenna system, characterized in that, Including the following steps: (1) Antenna structure state evaluation: Create a finite element model of the antenna structure according to the geometric model, calculate the distribution of the modal strain energy of the antenna structure, and determine the priority of the improvement of the antenna structure based on the magnitude of the modal strain energy of the antenna structure; (2) Conceptual design of the improved structure: Create a topology optimization model, conduct a conceptual design on the structure to be improved, and calculate the optimal force transmission path of the antenna structure; The topology optimization model is: Optimization objective: min(V) Constraints: Optimized variables: x = {x1, x2, …, x N} T ∈ Ω1 where V represents the volume of the structure in the design space; f1 and f2 represent the first-order and second-order modal frequencies respectively; x is the design variable of each discrete region, that is, the element density, taking values of 0 or 1, where 0 represents the absence of material and 1 represents the presence; The design variable establishes the relationship with the material properties through the following equation, thereby realizing the goal that the optimization variable affects the objective and constraints of the optimization model: Among them, x i is the unit density; E i (x i ) and ρ i (x i ) are the elastic modulus and material density of the material weighted by the unit density x i respectively; E0 is the unweighted elastic modulus of the solid material; E min and ρ min are the elastic modulus and material density of the material structure area to be deleted; p is the penalty coefficient used to make the unit density x i distribute at both ends of the interval [0, 1]; (3) Detailed design of the improved structure: Based on the optimal force transmission path, use the parameter optimization model to conduct a detailed design on the improved structure; The parameter optimization model is: Optimization objective: min(V) Constraints: Optimized variables: D = {D1, D2, D3, …, D m} where D is the key parameter of the structure; m is the number of key parameters of the structure.

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