Large reflector antenna active main reflector structure modeling and analysis method based on simplified actuator

Abstract

The invention relates to a large reflector antenna active main reflector structure modeling and analyzing method based on a simplified actuator, which comprises the following steps of: firstly, introducing the simplified actuator into an antenna structure model, and establishing an active main reflector structure model comprising the simplified actuator; secondly, the actual adjustment direction of the actuator can be obtained through a deformation result, caused by the environment load, of the model; finally, the actuator structure is assumed to be rigid, active adjustment structure analysis is simplified into a finite element constraint equation that panel supporting nodes adjust the specified displacement along the actual actuator direction, the equation is solved, and accurate structure deformation after panel adjustment is obtained.By means of the method, reference can be provided for accurate analysis of active adjustment of the large reflector antenna.

Description

Technical Field

[0001] This paper discloses a structural modeling and analysis method for the active main reflector of a large reflector antenna based on a simplified actuator. This method accurately calculates the deformation of the panel of a large reflector antenna after active adjustment along the actual orientation of the actuator. This method is applicable to the structural analysis of various large reflector antenna panels undergoing active adjustment. Background Art

[0002] With the advancement of deep space exploration, radio astronomy, and other fields, large reflector antennas are increasingly being developed towards larger apertures, higher precision, and higher frequency bands. Antennas are inevitably affected by natural loads such as gravity, wind load, and temperature, which can cause surface deformation, deteriorate precision, and significantly reduce antenna performance. For large, high-precision reflector antennas with diameters of tens of meters, thousands of panels, and weights of thousands of tons, achieving millimeter or even submillimeter surface accuracy is difficult. To ensure that reflector surfaces meet these precision requirements, active surface technology, as an effective method for compensating for antenna surface errors, is widely used in large reflector antennas with very high surface precision requirements.

[0003] Actuators play an adjustment role in active surface technology and are key components of the technology. However, the design of their mechanisms and control systems based on the actual needs of the antenna results in actuators being different and complex in actual projects, making it difficult to truly simulate their motion characteristics and adjustment functions in simulation calculations. For example, the Green Bank Telescope (GBT) in the United States has 2,209 precision actuators distributed across 2,004 panels. These actuators are driven by DC motors and use linear variable differential transformers to measure actuator positioning accuracy. When the panel is adjusted to the specified position, a self-locking device locks it. Mexico's Large The Millimeter Telescope (LMT) active surface system features 720 actuators, comprised of motors and reduction gear mechanisms. It uses a lever-driven screw for linear motion, with a maximum travel limit switch to restrict the stroke. The active surface system of the large reflector antenna also employs various sensors and control systems for real-time monitoring and control of the actuator adjustment panel, ensuring more precise and stable active adjustment. The active surface system's complex structure and numerous actuator types make it difficult to fully integrate it into a simulation model. The computational complexity and time complexity hinder optimization calculations. Therefore, it is necessary to simplify the actual actuator's motion characteristics and adjustment capabilities and incorporate them into the antenna model for structural simulation analysis.

[0004] In the structural analysis of active adjustment, most current research is based on the separation of the actuator and antenna structure. This simply extracts the panel deformation information for analysis, without considering the changes in actuator position and orientation after antenna structure deformation and their impact on panel adjustment. This limits the theoretical analysis capabilities of active surface theory. Summary of the Invention

[0005] The purpose of the present invention is to avoid the shortcomings of the background technology and provide a high-precision modeling and analysis method for the active main reflector structure of a large reflector antenna.

[0006] The technical solution of the present invention is: A method for simplifying an actuator with support and adjustment capabilities is provided. This method simplifies a complex actuator into a simple structure consisting of an adjustment beam, a support truss, and a support beam. Structural analysis of this simplified actuator within an active primary reflector model reveals changes in the actuator's position and orientation after gravity deformation. A simplified method for active adjustment analysis is presented. This method assumes the actuator is a rigid component, creates a separate panel model, and applies the gravity deformation of the panel support point of the main reflector to the model to approximate its deformation. The displacement of the adjustment point is then calculated based on the given adjustment amount and the orientation of the actuator after the main reflector is deformed. This displacement is then applied to the stiffness equation of the panel model. This active adjustment analysis method accounts for variations in actuator orientation and can accurately calculate the panel deformation after active adjustment.

[0007] The modeling and analysis method of the active main reflector structure of a large reflector antenna based on a simplified actuator includes the following steps: (1) The complex actuator mechanism is simplified into a simple structure consisting of an adjustment beam, a support truss, and a support beam. The simplified actuator is introduced into the antenna structure model, and the finite element method is used to establish a finite element structure model of the antenna active main reflector including the simplified actuator (hereinafter referred to as the antenna structure model); (2) Apply gravity load to the model and perform structural analysis to obtain the gravity deformation of the antenna structure model and the simplified actuator pointing direction; (3) Assuming that the actuator is a rigid component, the antenna active adjustment structural analysis is simplified to constraining the displacement of the panel support point under gravity load to make the panel deformation approximate the active main reflector model. Then, the panel support node adjusts the specified displacement along the direction of the actuator, thereby realizing the accurate structural analysis of the panel active adjustment. The specific calculation method is as follows: (4) Extract the coordinates and unit information of each node of the antenna structure model back frame, actuator and panel, construct the stiffness matrix K of the overall model according to the order of the degree of freedom of each node, calculate the gravity equivalent node load column vector P, and form the overall stiffness equation with the model node displacement column vector: . According to different model structures, it can be expressed as: [ K bus K sp K sa K sp K panel K pa K sa K pa K actuator ] [ u bus u panel u actuator ] = [ P bus P panel P actuator ] . where K bus , Kpanel , K actuator etc. are the stiffness matrices corresponding to the connection between the back frame, panel and actuator, u bus is the displacement of the unit node in the back frame, u panel is the displacement of the unit node in the panel, u actuator is the displacement of the unit node in the actuator, P bus is the nodal load of the unit in the back frame, P panel is the nodal load of the element in the panel, P actuator is the nodal load of the element in the actuator. Since the antenna structure model introduces a simplified actuator and is convenient for subsequent calculations, the above equation is expressed as: [ K od K oc K dd K oc K ua K uc K dd K uc K dc ] [ u od u ua u dc ] = [ P od P ua P dc ] . where K od , K ua , K dc etc. are the stiffness matrices corresponding to the connection relationship between other unit nodes in the antenna structure except the adjustment beam and the nodes at the upper and lower ends of the adjustment beam, u od is the displacement of other structural nodes except the adjustment beam, u ua To adjust the displacement of the upper end node of the beam, u dc To adjust the displacement of the lower end node of the beam, P od 、P ua 、P dc is the node load of the corresponding structure. Solving this equation and summing the original coordinates of the adjusted beam nodes with the displacements of the adjusted beam nodes, we can obtain the gravity deformation of the model and the simplified actuator orientation, which can be expressed as the direction cosines in the global coordinate system: . Where L is the length of the simplified actuator after adjusting the beam deformation, x ua 、y ua 、z ua etc. are the coordinates of the nodes at both ends after adjusting the beam deformation. (5) A model with only the panel in the antenna structure model (hereinafter referred to as the panel model) is established, and its structural deformation can be expressed as: [ K op K oc K co K cp ] [ u op u cp ] = [ P op P cp ] . where K op , K oc , K cp is the stiffness matrix corresponding to other nodes and support points in the panel, u op is the node displacement of the panel except the support point, u cp is the node displacement of the support point, P op 、P cp is the corresponding node load. The displacement of the panel support point of the antenna structure model under gravity load is applied to the corresponding node of the panel model. The gravity load is applied to the panel model for structural analysis, and the approximate deformation of the panel and the panel model in the antenna structure model is obtained. (6) Assuming the actuator adjustment amount u adjust is known, then the adjustment amount is equivalent to adjusting the displacement of the upper end node of the beam: . Extract the node displacement u of the panel support point in the antenna structure model under gravity load G , then the displacement u applied to the support point of the panel model under gravity load is actively adjusted cp It can be expressed as: . Therefore, the deformation of the panel model after active adjustment is: . The calculated panel model deformation approximates the panel deformation after active adjustment in the antenna structure model. The correctness and effectiveness of this method were determined by comparing it with the calculation results from finite element software. This method can accurately analyze the structural deformation of large reflector antennas after active adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 This is a flow chart of the present invention.

[0009] Figure 2 The active adjustment of the antenna active surface is simplified to a schematic diagram of adjusting the specified displacement of the panel support point along the direction of the actuator.

[0010] Figure 3 This is a schematic diagram of the correspondence between the simplified actuator and the actual actuator.

[0011] Figure 4 This is the finite element structural model diagram of the antenna's active main reflector.

[0012] Figure 5 This is the displacement distribution diagram of the antenna active main reflector model under different working conditions.

[0013] Figure 6 Displacement distribution diagram of the antenna panel model after active adjustment under different working conditions. DETAILED DESCRIPTION

[0014] Reference Figures 1 - 6 A method for modeling and analyzing the active main reflector structure of a large reflector antenna based on a simplified actuator includes the following steps:

[0015] The actuator structure is simplified into three parts: support beam, support truss and adjustment beam, all of which are composed of short beams. ANSYS is used to establish a finite element structural model of the antenna active main reflector containing a simplified actuator and to perform triangular meshing on the panel. The model consists of three parts: panel, back frame and simplified actuator. The upper node of the support beam in the simplified actuator is connected to the panel support point, and the upper chord node of the back frame is connected to the lower node of the actuator adjustment beam. The back frame and actuator use Beam4 units, and the panel uses Shell63 units. The density, Young's modulus, Poisson's ratio and thickness of the panel of this model are 2.73×10 -6 kg / mm 3 , 7.17×10 4 MPa, 0.3 and 20 mm. The density, Young's modulus, Poisson's ratio, cross-sectional area and moment of inertia of the simplified actuator are 7.85×10 -6 kg / mm 3 , 2.1×10 5 MPa, 0.3, 400πmm 2 and 4000πmm. The density, Young's modulus and Poisson's ratio of the back frame are 7.85×10 -6 kg / mm 3 , 2.1×10 5 MPa and 0.3.

[0016] Extract the coordinates of each node of the simplified model of ANSYS and calculate the stiffness matrix of each unit. Among them, the stiffness matrix of the beam unit is calculated according to the standard finite element process as follows: (1) The spatial beam element in the local coordinate system has two nodes i and j, each with 6 degrees of freedom, and its node displacement vector U e and the node load vector P e for: U e = [ u i v i w i θ xi θ yi θ zi u j v j w j θ xj θ yj θ zj ] T P e = [ P ui P vi P wi M xi M yi M zi P uj P vj P wj M xj M yj M zj ] T The stiffness matrices of the spatial beam elements corresponding to the node displacements are given below based on the local coordinate system. For axial displacement, the stiffness matrix is ​​similar to that of the rod element: K u 1 u 2 e = EA ij l ij [ 1 − 1 − 1 1 ] Where, is the Young's modulus of the spatial beam, A ij is the cross-sectional area of ​​the beam containing nodes i and j, l ij is the length of the beam containing nodes i and j. When the beam is subjected to torsion, the torsion angle θ can be x1 and θ x2 Analogous to the axial displacement of a beam, the stiffness matrix is ​​obtained: K θ x 1 θ x 2 e = GJ ij l ij [ 1 − 1 − 1 1 ] Where G is the shear modulus, J is the ij is the rotational moment of inertia of beam ij. When the beam bends in the plane, the corresponding stiffness matrix is: K v i θ zi v j θ zj e = EI ijZ l ij 3 [ 12 6 l ij − 12 6 l ij 6 l ij 4 l ij 2 − 6 l ij 2 l ij 2 − 12 − 6 l ij 12 − 6 l ij 6 l ij 2 l ij 2 − 6 l ij 4 l ij 2 ] K ω i θ yi ω j θ yj e = EI ijY l ij 3 [ 12 − 6 l ij − 12 − 6 l ij − 6 l ij 4 l ij 2 6 l [[ID=1og]]ij 2 l ij 2 − 12 6 l ij 12 6 l ij − 6 l ij 2 l ij 2 6 l ij 4 l ij 2 ] Among them, I ijZ , I ijY is the moment of inertia of beam ij. Combine the above stiffness matrices in the order of degrees of freedom to obtain the complete element stiffness matrix K in the local coordinate system e for: K e = [ K beam ei K beam eij K beam eji K beam ej ] K beam ei = [ EA ij l ij 0 0 0 0 0 0 12 EI ijZ l ij 3 0 0 0 6 EI ijZ l ij 2 0 0 12 EI ijY l ij 3 0 − 6 EI ijY l ij 2 0 0 0 0 GJ l ij 0 0 0 0 − 6 EI [[ID=1y5]]ijY l ij 2 0 4 EI ijY l ij 0 0 6 EI ijZ l ij 2 0 0 0 4 EI ijZ l ij ] K beam eij = [ − EA ij l ij 0 0 0 0 0 0 − 12 EI ijZ l ij 3 0 0 0 6 EI ijZ l ij 2 0 0 − 12 EI ijY l ij 3 0 − 6 EI ijY l ij 2 0 0 0 0 − GJ l ij 0 0 0 0 6 EI ijY l ij 2 0 2 EI ijY l ij 0 0 − 6 EI ijZ l ij 2 0 0 0 2 EI ijZ l ij ] K beam eji = [ − EA ij l ij 0 0 0 0 0 0 − 12 EI ijZ l ij 3 0 0 0 − 6 EI ijZ l ij 2 0 0 − 12 EI ​ l ​ 3 0 − 6 ​ ​ l ​ 2 0 0 0 0 ​ ​ l ​ 0 0 0 0 − 6 ​ ​ l ​ 2 0 2 ​ ​ l ​ 0 0 6 ​ ​ l ​ 2 0 0 0 2 ​ ​ l ​ ] K ​ ​ = [ ​ ​ l ​ 0 0 0 0 0 0 12 ​ ​ l ​ 3 0 0 0 − 6 ​ ​ l ​ 2 0 0 12 ​ ​ l ​ 3 0 6 ​ ​ l ​ 2 0 0 0 0 ​ l ​ 0 0 0 0 6 ​ ​ l ​ 2 0 4 ​ ​ l ​ 0 0 − 6 ​ ​ l ​ 2 0 0 0 4 ​ ​ l ​ ] Considering the shear effect, add the shear effect coefficient ɸ in the y-axis direction y and the shear influence coefficient ɸ in the z-axis direction z . E is the elastic modulus, I z is the moment of inertia about the z axis, G is the shear modulus, A z is the effective shear area of ​​the section along the z-axis, and L is the unit length. z =A / F z , is the unit cross-sectional area, F z is the shear deformation coefficient along the z-axis.ɸ z The same applies. To calculate the stiffness equation, the element's nodal loads and nodal displacements must be transformed from the local coordinate system to the global coordinate system, and the element's stiffness matrix must also undergo a corresponding coordinate transformation. Only then can the element's global stiffness matrix and nodal loads be directly added together according to the superposition rule to form the global stiffness equation. The following describes the coordinate system transformation calculation method. Let K, U and P be the stiffness matrix, node displacement vector and node load vector in the global coordinate system, K e 、U e and P eis the stiffness matrix, node displacement vector and node load vector in the local coordinate system, and T is the coordinate transformation matrix between the local coordinate system and the global coordinate system. Then we have According to the stiffness equation, we can get So there is From the above formula, we can get the displacement transformation relationship of node i (the same applies to node j), and the coordinate transformation matrix T is: [ u i v i w i ] = [ u i e ​ e ) + v i e ​ e ) + w i ​ e ) u i e ​ e ) + v i e ​ e ) + w i ​ e ) u i e ​ e ) + v i e ​ e ) + w i ​ e ) ] = ​ [ u i e v i e w i e ] [ ​ ​ ​ ​ ​ ​ ] = [ ​ ​ e ​ e ) + ​ ​ e ​ e ) + ​ ​ e ​ e ) ​ ​ e ​ e ) + ​ ​ e ​ e ) + ​ ​ e ​ e ) ​ ​ e ​ e ) + ​ ​ e ​ z ,y e ) + ​ ​ e ​ z ,z e ) ] = ​ [ ​ ​ e ​ ​ e ​ ​ e ] ​ = [ ​ e ) ​ e ) ​ e ) ​ e ) ​ e ) ​ e ) ​ e ) ​ z ,y e ) ​ z ,z e ) ] Where λ is the node coordinate transformation matrix, cos(x,x e ),cos(x,y e )…cos(z,z e ) is the direction cosine of the local coordinate axis and the global coordinate axis. From the above, we can get: T = [ ​ 0 0 0 0 ​ 0 0 0 0 ​ 0 0 0 0 ​ ] Based on the above, the stiffness matrix, node load vector and node displacement vector in the global coordinate system of the spatial beam element can be obtained. (2) Shell elements consist of membrane elements and bending elements. The triangular bending element is composed of Discrete Kirchhoff Theory (DKT) elements, with a total of 3 nodes, and the degrees of freedom of each node are ω, θ, x and θ y , its stiffness matrix is ​​expressed as: Where D is the elastic coefficient matrix, B is the strain-displacement conversion matrix, η and ξ represent the components of the area coordinate, h is the panel thickness, μ is the Poisson's ratio, and A is the area of ​​the panel. DKT It can be obtained by three-point Gaussian integral method. The parameters are expressed as: D = ​ 3 12 ( 1 − ​ 2 ) [ 1 ​ 0 ​ 1 0 0 0 1 − ​ 2 ] B ( ​ , ​ ) = 1 2 A [ y 31 H x , ​ T + y 12 H x , ​ T − x 31 H y, ​ T − x 12 H y, ​ T − x 31 H x, ​ T − x 12 H x, ​ T + y 31 H y , ​ T + y 12 H y , ​ T ] H x , ​ = [ − P 5 ( 1 − 2 ​ ) − ​ (P 6 − P 5 ) q 5 ( 1 − 2 ​ ) − ​ (q 5 + q 6 ) − 4 + 6 ( ​ + ​ ) + r 5 ( 1 − 2 ​ ) − ​ (r 5 + r 6 ) ​ (P 4 + P 6 ) ​ (P 4 − P 6 ) − ​ ( r 6 − r 4 ) P 5 ( 1 − 2 ​ ) − ​ (P 4 + P 5 ) q 5 ( 1 − 2 ​ ) + ​ (q 4 − q 5 ) − 2 + 6 ​ + r 5 ( 1 − 2 ​ ) + ​ (r 4 − r 5 ) ] H y , ​ = [ − t 5 ( 1 − 2 ​ ) − ​ (t 6 − t 5 ) 1 + r 5 ( 1 − 2 ​ ) − ​ (r 5 + r 6 ) − q 5 ( 1 − 2 ​ ) − ​ (r 5 + r 6 ) ​ (t 4 + t 6 ) ​ ( r 4 − r 6 ) − ​ ( q 4 − q 6 ) t 5 ( 1 − 2 ​ ) − ​ (t 4 + t 5 ) − 1 + r 5 ( 1 − 2 ​ ) + ​ (r 4 − r 5 ) − q 5 ( 1 − 2 ​ ) − ​ ( q 4 − q 5 ) ] H x , ​ = [ P 6 ( 1 − 2 ​ ) + ​ ( P 5 − P 6 ) q 6 ( 1 − 2 ​ ) − ​ ( q 5 + q 6 ) − 4 + 6 ( ​ + ​ ) + r 6 ( 1 − 2 ​ ) − ​ (r 5 + r 6 ) − P 6 ( 1 − 2 ​ ) + ​ ( P 4 + P 6 ) q 6 ( 1 − 2 ​ ) − ​ ( q 6 − q 4 ) − 2 + 6 ​ + r 6 ( 1 − 2 ​ ) + ​ ( q 4 − q 6 ) − ​ ( P 4 + P 5 ) ​ ( q 4 − q 5 ) − ​ ( r 5 − r 4 ) ] H y , ​ = [ t 6 ( 1 − 2 ​ ) − ​ (t 5 − t 6 ) 1 + r 6 ( 1 − 2 ​ ) − ​ (r 5 + r 6 ) − q 6 ( 1 − 2 ​ ) − ​ ( q 5 + q 6 ) − t 6 ( 1 − 2 ​ ) + ​ (t 4 + t 6 ) − 1 + r 6 ( 1 − 2 ​ ) + ​ (r 4 − r 6 ) − q 6 ( 1 − 2 ​ ) − ​ ( q 4 − q 6 ) − ​ (t 4 + t 5 ) ​ ( r 4 − r 5 ) − q 5 ( 1 − 2 ​ ) − ​ ( q 4 − q 5 ) ] in: , , (Same for y) , i and j are 1, 2, and 3 respectively When ij = 23, 32, or 12, k is 4, 5, or 6. η and ξ represent the L2 and L3 of the area coordinates, respectively. Perform three-point integration, and the stiffness matrix of the DKT element can be obtained as follows: Since the Allman rotational freedom can enhance the convergence of shell structures during large rotations and can be used for large deformation analysis of structures, the improved triangular membrane element with Allman rotational stiffness (SHELL63 element with KEYOPT(3)=2) is used for calculation. Each node has three degrees of freedom, u, v, and w (w is the rotational freedom), which are the displacement in the x and y directions and the rotational freedom in the vertical plane. The specific derivation is as follows: The normal and tangential displacement modes of one side of the triangular membrane element are defined as Where s is the distance from any point on one side of the triangular membrane element to one end node, and the coefficients a1…a5 are unknowns. Let the side length be l, then we have So the node displacement u,v can be expressed as Where γ is the angle between the outward normal of each edge and the x-axis. Define the difference of the terminal displacement derivatives as the fifth boundary condition, so that Where w1 and w2 are the rotational degrees of freedom of the nodes at both ends. Obviously, these two rotations are not real in plane elastic analysis, but they are closely related to nodal rotations. Furthermore, the use of the above formula neither prevents displacement compatibility nor restricts the vertex angles of triangular elements. Therefore, all constant strain states can be accurately represented by this formula, guaranteeing convergence to an exact solution with consistent mesh optimization. According to the above formula, we can get The boundary displacement expression of one side of the triangular membrane element is obtained as: The boundary displacement expressions on the other two sides are similar. Therefore, u and v can be expressed as: Among them, the relationship between the triangle area coordinates ξ1, ξ2, ξ3 and the triangle vertices is: [ ​ 1 ​ 2 ​ 3 ] = 1 2 ​ [ ( x 2 y 3 − x 3 y 2 ) ( y 2 − y 3 ) ( x 3 − x 2 ) ( x 3 y 1 − x 3 y 2 ) ( y 3 − y 1 ) ( x 1 − x 3 ) ( x 1 y 2 − x 2 y 1 ) ( y 1 − y 2 ) ( x 2 − x 1 ) ] [ 1 x y ] This unit has only 5 independent strain coefficients, so the strain matrix can be obtained from the above formula and the strain expression: B = [ 1 y 0 0 0 0 0 1 x 0 0 − x 0 − y 1 ] Therefore, the strain matrix in the local coordinate system can be obtained. According to the finite element calculation process, the stiffness matrix of the Allman unit can be expressed as: C = 1 2 ​ [ y 23 0 1 2 y 1 y 23 y 31 0 1 2 y 2 y 31 y 12 0 1 2 y 3 y 12 0 0 − 1 2 y 23 0 0 − 1 2 y 31 0 0 − 1 2 y 12 0 x 32 1 2 x 1 x 23 0 x 13 1 2 x 2 x 31 0 x 21 1 2 x 3 x 12 0 0 − 1 2 x 23 0 0 − 1 2 x 31 0 0 − 1 2 x 12 x 32 y 23 1 2 ( x 1 y 32 + y 1 x 32 ) x 13 y 31 1 2 ( x 2 y 13 + y 2 x 13 ) x 21 y 12 1 2 ( x 3 y 21 + y 3 x 21 ) ] Where D is the elastic coefficient matrix and t is the element thickness. The Allman triangle element is extended and improved by constructing a linear strain triangle element (LST). This eliminates the translational displacement of the midpoint of each edge and is more conducive to calculating the rotational degrees of freedom of the corner points. The node coordinates of the three corner points are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). Its stiffness matrix can be expressed as: T = [ 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 2 0 b 3 1 2 0 − b 3 0 0 0 0 1 2 a 3 0 1 2 − a 3 0 0 0 0 0 0 1 2 0 b 1 1 2 0 − b 1 0 0 0 0 1 2 a 1 0 1 2 − a 1 1 2 0 − b 2 0 0 0 1 2 0 b 2 0 1 2 − a 2 0 0 0 0 1 2 a 2 ] K LST is the stiffness matrix of the linear strain triangular element. V is the volume of the membrane element. K AI is the modified Allman triangle element stiffness matrix, T is the transformation K LST With K AI The transformation matrix of . At this time, the unit still has a zero energy mode. This is because the unit has only one integration point. When bending, this integration point has no strain energy. At this time, the unit has no stiffness and cannot resist deformation. A penalty stiffness needs to be defined as: K s = ( ​ ​ ) Q T Q Q = [ x 2 − x 3 4 A y 2 − y 3 4 A − 1 3 x 3 − x 1 4 A y 3 − y 2 4 A − 1 3 x 1 − x 2 4 A y 1 − y 2 4 A − 1 3 ] Where δ is the penalty parameter, which is set to 0.01. V is the volume, G is the shear modulus, and Q is the relative rotation matrix. Therefore, the complete membrane element stiffness matrix can be obtained: The membrane element (degrees of freedom are u, v, θ z ) and bending elements (degrees of freedom w, θ x ,θ y ) are combined in the order of degrees of freedom to obtain the stiffness matrix of the SHELL63 element in the local coordinate system. At this point, the stiffness matrix also needs to be converted to the global coordinate system. Similar to the beam element, the coordinate transformation matrix is ​​obtained by calculating the direction cosines of the local coordinate system and the global coordinate system, thereby obtaining the stiffness matrix in the global coordinate system. After the above shell and beam elements are transformed into spatial coordinates, the coordinates of each node are inserted and integrated according to the node number to obtain the overall stiffness matrix K.

[0017] Since this case only analyzes gravity loads, the equivalent loads of the nodes of the antenna structure model under gravity are calculated for both the upward and horizontal working conditions and integrated into the load column vector P according to the node order. The overall stiffness equation is then used: The displacement of each node in the antenna structure model can be calculated.

[0018] By summing the original coordinates of the adjustment beam node and the displacement of the adjustment beam node, the gravity deformation of the model can be obtained, and the simplified actuator orientation can be expressed as the direction cosine in the global coordinate system: Where L is the length of the simplified actuator-adjusted beam after deformation, x ua 、y ua 、z ua etc. are the coordinates of the nodes at both ends after adjusting the beam deformation.

[0019] The antenna structure model consists of only the panel (hereinafter referred to as the panel model), and its structural deformation can be expressed as: [ K ​ K ​ K ​ K ​ ] [ u ​ u ​ ] = [ P ​ P ​ ] where K op , K oc , K cp is the stiffness matrix corresponding to other nodes and support points in the panel, u op is the node displacement of the panel except the support point, u cp is the node displacement of the support point, P op 、P cp is the corresponding node load. The displacement of the panel support point of the antenna structure model under gravity load is applied to the corresponding node of the panel model. The gravity load is applied to the panel model for structural analysis, and the approximate deformation of the panel and the panel model in the antenna structure model is obtained.

[0020] Given actuator adjustment u adjust is a known quantity, then the adjustment amount is equivalent to adjusting the displacement of the upper node of the beam: Extract the node displacement u of the panel support point in the antenna structure model under gravity load G , then the displacement u applied to the support point of the panel model under gravity load is actively adjusted cp It can be expressed as: Therefore, the deformation of the panel model after active adjustment is:

[0021] In this case, the adjustment range of each actuator was set to ±5 mm. The active adjustment structure analysis was calculated based on an ideal antenna main reflector under gravity deformation conditions. The actuators were given random adjustments, which were then converted to adjustments to the corresponding panel support points on the adjustment beam, imposing displacement constraints on the model.

[0022] The displacement constraints are input into the ANSYS antenna panel simulation model to obtain the displacement of each node and related data of the antenna panel model after active adjustment.

[0023] By comparing the results, the node displacement of the antenna panel model after active adjustment can be calculated and compared with the results calculated by ANSYS. The maximum node displacement error under the upward working condition is 3.14×10 -10 mm, the maximum node displacement error under the horizontal working condition is 1.28×10 -9 mm, meeting the calculation accuracy requirements.

[0024] Through this simulation example, it can be seen that the method adopted in the present invention can realize the simulation analysis of active adjustment of large-scale reflective surface antennas, and can be used for the optimization design of actuator distribution for active adjustment in the antenna structure design stage, to solve the problem of insufficient precision of the reflective surface shape, and to improve the electrical performance efficiency of the overall antenna.

Claims

1. Modeling and analysis method of active main reflector structure of large reflector antenna based on simplified actuator, characterized by The steps include: (1) The complex actuator mechanism is simplified into a simple structure consisting of an adjustment beam, a support truss and a support beam, the simplified actuator is introduced into the antenna structure model, and the finite element structure model of the antenna active main reflector including the simplified actuator is established using the finite element method (hereinafter referred to as the antenna structure model); (2) Apply gravity load to the model and perform structural analysis to obtain the gravity deformation of the antenna structure model and the simplified actuator pointing direction; (3) Assuming that the actuator is a rigid component, the antenna active adjustment structural analysis is simplified to constraining the displacement of the panel support point under gravity load to make the panel deformation approximate the active main reflector model, and then the panel support node adjusts the specified displacement along the direction of the actuator, thereby realizing the precise structural analysis of the panel active adjustment. The specific calculation method is as follows: (4) Extract the coordinates and unit information of each node of the antenna structure model back frame, actuator and panel, construct the stiffness matrix K of the overall model according to the order of the degree of freedom of each node, calculate the gravity equivalent node load column vector P, and form the overall stiffness equation with the model node displacement column vector: ， According to different model structures, it can be expressed as: ， Where K bus , K panel , K actuator etc. are the stiffness matrices corresponding to the connection between the back frame, panel and actuator, u bus is the displacement of the unit node in the back frame, u panel is the displacement of the unit node in the panel, u actuator is the displacement of the unit node in the actuator, P bus is the nodal load of the unit in the back frame, P panel is the nodal load of the element in the panel, P actuator is the nodal load of the element in the actuator; Since the antenna structure model introduces a simplified actuator and is convenient for subsequent calculations, the above equation is expressed as: ， Where K od , K ua , K dc etc. are the stiffness matrices corresponding to the connection relationship between other unit nodes in the antenna structure except the adjustment beam and the nodes at the upper and lower ends of the adjustment beam, u od is the displacement of other structural nodes except the adjustment beam, u ua To adjust the displacement of the upper node of the beam, u dc To adjust the displacement of the lower node of the beam, P od , P ua , P dc is the node load of the corresponding structure; Solving this equation and summing the original coordinates of the adjustment beam node and the displacement of the adjustment beam node, we can get the gravity deformation of the model and the simplified actuator orientation can be expressed as the direction cosine in the global coordinate system: ， Where L is the length of the simplified actuator-adjusted beam after deformation, x ua ,y ua 、z ua etc. are the coordinates of the nodes at both ends after adjusting the beam deformation; (5) A model with only the panel in the antenna structure model (hereinafter referred to as the panel model) is established, and its structural deformation can be expressed as: ， Where K op , K oc , K cp is the stiffness matrix corresponding to other nodes and support points in the panel, u op is the node displacement of the panel except the support point, u cp is the node displacement of the support point, P op , P cp is the corresponding node load; The displacement of the panel support point of the antenna structure model under the gravity load is applied to the corresponding node of the panel model, and the gravity load is applied to the panel model for structural analysis to obtain the approximate deformation of the panel and the panel model in the antenna structure model; (6) Assuming the actuator adjustment amount u adjust is known, then the adjustment amount is equivalent to adjusting the displacement of the node at the upper end of the beam: ， Extract the node displacement u of the panel support point in the antenna structure model under gravity load G , then the displacement u applied to the support point of the panel model under gravity load is cp It can be expressed as: ， Therefore, the deformation of the panel model after active adjustment is: ， The calculated deformation of the panel model can approximate the deformation of the panel after active adjustment in the antenna structure model. The correctness and effectiveness of this method are judged by comparing the calculation results of this method with those of the finite element software. This method can accurately analyze the structural deformation of large reflector antennas after active adjustment.

2. The method for modeling and analyzing the active main reflector structure of a large reflector antenna based on a simplified actuator according to claim 1, characterized in that: The large reflector antenna structure includes a back frame, a simplified actuator and a panel.

3. The method for modeling and analyzing the active main reflector structure of a large reflector antenna based on a simplified actuator according to claim 1, characterized in that: The simplified actuator structure in the large reflector antenna includes an adjustment beam, a support truss and a support beam.

4. The method for modeling and analyzing the active main reflector structure of a large reflector antenna based on a simplified actuator according to claim 1, characterized in that: This method can obtain the actual orientation of the actuator after the structure is deformed.

5. The method for modeling and analyzing the active main reflector structure of a large reflector antenna based on a simplified actuator according to claim 1, characterized in that: The active adjustment analysis of the antenna structure model can be simplified into the finite element constraint equation for adjusting the specified displacement of the panel support point along the actuator direction.

6. The method for modeling and analyzing the active main reflector structure of a large reflector antenna based on a simplified actuator according to claim 1, characterized in that: The panel deformation in the antenna structure model can be approximated by using the panel model to perform node constraints.

7. The method for modeling and analyzing the active main reflector structure of a large reflector antenna based on a simplified actuator according to claim 1, characterized in that: The structural analysis of the antenna structure model and the panel model can be calculated using the stiffness equation.

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