Structural deformation calibration method for phased-array antenna under typical thermal load

Abstract

The invention discloses a method for calibrating structural deformation of a phased-array antenna under typical thermal load, and belongs to the field of electromechanical-thermal integrated lightweight of satellite-borne phased-array antennas. Determining a mechanical boundary condition, a temperature boundary condition, a geometric dimension, a mechanical parameter and a thermal parameter according to the actual temperature working condition and the antenna lamination structure; determining a temperature field function of the antenna laminated structure along the thickness direction according to the temperature boundary condition, the geometric dimension and the thermal parameters; obtaining an undetermined flexural surface function of the laminated structure of the antenna through the interoperability theorem of work; taking the deflection of the antenna laminated structure under the unit concentrated load as a basic solution, substituting the basic solution into an undetermined flexural surface function, and solving an undetermined coefficient in combination with a mechanical boundary condition to obtain an antenna laminated structure flexural surface function; and adjusting the mechanical parameters of the structure according to the flexural surface function until the structural deformation calibration of the phased-array antenna under the typical thermal load is realized. According to the invention, the structure deformation can be rapidly predicted in a preset precision range, and the method has the advantages of high calibration precision and high efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of electromechanical and thermal integration lightweight of satellite-borne phased array antennas, and relates to a method for calibrating the structural deformation of phased array antennas under typical thermal loads. Background Art

[0002] The working mode of active phased array antenna is extremely flexible, and its application is becoming more and more extensive. The requirements for electrical performance are getting higher and higher, which also leads to more and more demanding mechanical structure accuracy. The heat flux density of the antenna increases sharply, and the heat dissipation design becomes more and more difficult. The coupling relationship between the antenna mechanical structure, thermal and electromagnetic performance will be closer. Among them, the influence of thermal characteristics is particularly important. The temperature distribution generated by a large number of heating devices on the phased array array surface will cause the array surface structure to deform. At the same time, the change in the temperature distribution of the array surface will also cause the performance of T / R components that are particularly sensitive to temperature to degrade. These will cause the position of the antenna unit on the array surface to shift and deflect, as well as the fluctuation of the amplitude and phase of the excitation current, which will cause the direction of the antenna unit array to be distorted, and the mutual coupling effect between the units will change, which will eventually lead to the performance of the entire antenna deteriorating and failing to meet the requirements, or even failing to work normally.

[0003] The phased array antenna structure is a typical laminated structure. Generally, the antenna structure has a small thickness and a large side length, and can be regarded as a laminated thin plate structure. Under the action of the temperature field, the laminated thin plate structure will produce thermal stress and thermal torque under the constraints of boundary conditions due to the different thermal expansion coefficients of each layer of material, causing the antenna structure to bend and deform, thereby causing the position of the antenna array element to change, and the phase distribution of the antenna aperture to change. At the same time, it will also cause the deformation of the radiating unit, causing changes in the coupling between the units and the change in the radiation pattern, which will affect the comprehensive performance of the antenna.

[0004] By conducting flexural deformation analysis of phased array antennas under typical thermal loads, we can accurately understand the deformation of the antenna array surface under typical working conditions, and thus provide a basis for the debugging, calibration and optimization design of phased array antennas, which is of great significance in the field of lightweight electromechanical and thermal integration of satellite-borne phased array antennas.

[0005] At present, the structural deformation problem of phased array antennas under typical thermal loads is mainly solved through finite element numerical simulation methods, which consumes a lot of computing resources and time, and brings great time and resource costs to the structural optimization design of phased array antennas. Therefore, a structural deformation calibration method for phased array antennas under typical thermal loads is needed, which can quickly calculate the structural deformation within a certain accuracy range, so as to facilitate the rapid debugging, calibration and optimization design of antenna structure deformation. Summary of the invention

[0006] In view of the deficiencies in the above-mentioned prior art, an object of the present invention is to provide a method for calibrating the structural deformation of a phased array antenna under a typical thermal load. Based on the basic law of thermal conductivity and the reciprocity theorem of work, the structural deformation of the phased array antenna under a typical thermal load is evaluated and calibrated, thereby improving the accuracy and efficiency of the evaluation and calibration.

[0007] The objective of the present invention is achieved through the following technical solutions:

[0008] The present invention discloses a method for calibrating the structural deformation of a phased array antenna under a typical thermal load, comprising the following steps:

[0009] Step 1: Determine the mechanical boundary conditions, temperature boundary conditions, geometric dimensions, mechanical parameters and thermal parameters according to the actual temperature conditions and the antenna laminate structure;

[0010] The actual temperature condition refers to the typical thermal load of the phased array antenna in the low-Earth orbit environment; the antenna laminate structure is mainly composed of the antenna array surface, chip layer, network layer, and cold plate, which are sequentially numbered 1, 2, ..., k, ..., l from the antenna array surface to the cold plate. The antenna laminate structure is regarded as a laminate structure in which the main direction of the material coincides with the coordinate axis x and y directions, and the number of structural layers is recorded as l; the temperature boundary conditions include the antenna array surface temperature T1, the heat source intensity q in each layer vk (k=1,2,…,l), coolant temperature T f and the convection heat transfer coefficient h f , the mechanical boundary conditions include the deflection w at the boundary | x＝0,a and w| y＝0,b , corner at the boundary and In the antenna laminate structure, the mechanical boundary condition is a fixed support mechanical boundary condition, in which the deflection and rotation at the boundary are both equal to 0; the geometric dimensions include the length a along the x-axis, the width b along the y-axis, and the thickness δ of each layer along the height direction. k (k=1,2,…,l); Mechanical parameters include the equivalent Young's modulus E of each layer structure k (k=1,2,…,l), equivalent shear modulus G k (k=1,2,…,l) and equivalent Poisson's ratio v k (k=1,2,…,l); thermal parameters include the thermal expansion coefficient of each layer [α xx ,α yy ,α xy ] k (k=1,2,…,l) and thermal conductivity κ k (k=1,2,…,l).

[0011] Step 2: Determine the temperature field function of the antenna laminate structure along the thickness direction according to the temperature boundary conditions, geometric dimensions and thermal parameters;

[0012] The solution of the temperature field function of the antenna laminate structure along the thickness direction comprises the following steps:

[0013] Step 2.1. Under typical thermal loads, the temperature field of each layer of the antenna laminate structure satisfies the one-dimensional steady-state thermal conduction differential equation, which is expressed as follows:

[0014]

[0015] Where: T k (z,T k1 ,T k2 ) represents the undetermined temperature field function segment of the kth layer, z is the coordinate along the thickness direction, T k1 and T k2 Represent the upper and lower surface temperatures of the kth layer respectively, which are unknown quantities. The undetermined temperature field function of the kth layer can be derived from the one-dimensional steady-state heat conduction differential equation, and the expression is:

[0016]

[0017] Where: C k1 and C k2 is the coefficient, z k1 is the z coordinate of the upper surface of the kth layer, z k2 is the z coordinate of the lower surface of the kth layer;

[0018] Step 2.2: According to Fourier's law, the temperature field function of the kth layer is divided into segments T k (z,T k1 ,T k2 ) is substituted into the heat flux density q of the kth layer. k (z,T k1 ,T k2 );

[0019]

[0020] Step 2.3: Calculate the heat flux density q of convective heat transfer by Newton's law of cooling f , the expression is:

[0021]

[0022] Step 2.4: Under steady-state heat transfer, when the heat source layer is at layer r, due to the internal heat source intensity q vk When it is zero, the heat flux is a constant function and its value is independent of z, so the heat flux should be written as q k (T k1 ,T k2 ), and the heat source intensity q in the heat source layer vkis not zero, the value of heat flux changes with z, so the heat flux is still written as q k (z,T k1 ,T k2 );

[0023] According to the first law of thermodynamics, the boundary on one side of the heat source layer is selected. When the boundary is at z r1 At the position, the heat flux density q in the continuous area outside the boundary k (T k1 ,T k2 ) is equal everywhere and equal to the heat source layer z r1 The heat flux at position q r (z r1 ,T r1 ,T r2 ), the other side of the heat source layer is the same, and when there is a convection heat transfer boundary condition, the heat flux density q k (T k1 ,T k2 ) and the convective heat flux q f Also equal, and then the linear equations are listed to solve the temperature T on the upper surface of the kth layer k1 and the lower surface temperature T k2 :

[0024]

[0025] Where: q1(T 11 ,T 12 ) is the heat flux density of the first layer, q2(T 21 ,T 22 ) is the heat flux density of the second layer, q r+1 (T (r+1)1 ,T (r+1)2 ) is the heat flux density of the (r+1)th layer, q l (T l1 ,T l2 ) is the heat flux density of the first layer, q r (z r1 ,T r1 ,T r2 ) is the heat flux density on the upper surface of the heat source layer, q r (z r2 ,T r1 ,T r2 ) is the heat flux density on the lower surface of the heat source layer;

[0026] Step 2.5: The upper surface temperature T k1 and the lower surface temperature T k2 Substituting into formula (2), we can get the temperature field function segment T of the kth layer of the antenna laminate structure: k (z):

[0027]

[0028] In the formula, all parameters except the independent variable z are known. The temperature field function of each layer of the antenna laminate structure is divided into segments T k (z) is summarized, that is, the temperature field function T(z) of the antenna laminate structure along the thickness direction is obtained:

[0029]

[0030] Step 3: Obtain the undetermined flexure surface function of the antenna laminate structure through the reciprocal theorem of work;

[0031] The solution of the undetermined deflection surface function of the antenna laminate structure comprises the following steps:

[0032] Step 3.1. Consider the antenna laminate structure subjected to typical thermal load as laminate A, and there is a laminate B with exactly the same mechanical boundary conditions as the antenna laminate structure. Apply a unit concentrated load P at point (ξ,η) on plate B, where P = 1. Calculate the work W(σ',ε') done by the stress of plate A on the deformation of plate B and the work W(σ',ε') done by the stress of plate B on the deformation of plate A. The corresponding expressions are:

[0033]

[0034] In the formula: σ' and ε' are the stress and strain of plate A, σ" and ε" are the stress and strain of plate B, and the superscript ij is the dummy index of the Einstein summation convention. In the calculation of this formula, ij takes three groups of superscripts: xx, yy, and xy, and k is the layer number;

[0035] Step 3.2: When considering temperature changes, the stress-strain relationship of the kth layer of the laminate is expressed as:

[0036]

[0037] Where: [σ xx σ yy σ xy ] k T is the stress matrix of the kth layer, [ε xx ε yy ε xy ] k T is the strain matrix of the kth layer, [α xx α yy α xy ] k T is the thermal expansion coefficient array of the kth layer. Since the main direction of the material coincides with the x and y coordinate axes, temperature changes do not cause shear strain, so αxy =0, T k (z) is the temperature field function segment of the kth layer of the antenna laminate structure, T0 is the initial temperature value, is the transformation matrix of the two-dimensional stiffness matrix Q in the main direction of the kth layer, and the corresponding expression is:

[0038]

[0039] Where: E is Young's modulus, G is shear modulus, v is Poisson's ratio, and subscripts 1 and 2 represent the main directions of the material. Since the main directions of the material coincide with the x and y directions of the coordinate axes, Q 16 =Q 26 =0;

[0040] Step 3.3: Transform the two-dimensional stiffness matrix Q into Substituting into formula (9) we get:

[0041]

[0042] Substituting formula (11) into formula (8), we get:

[0043]

[0044] Where: T k '(z) is the temperature field function segment of the kth layer of plate A, T0' is the initial temperature value of plate A, T k "(z) is the temperature field function segment of the kth layer of plate B, T0" is the initial temperature value of plate B, and k is the layer number;

[0045] According to the reciprocal theorem of work, an equation relationship is established, and the corresponding expression is:

[0046]

[0047] Step 3.4: Integrate both sides of equation (13) at the same time, and the corresponding expression is:

[0048]

[0049] Where: P' is the surface force acting on plate A, P" is the surface force acting on plate B, Q' is the volume force acting on plate A, Q" is the volume force acting on plate B, U' is the displacement vector of plate A, U" is the displacement vector of plate B, Ω is the surface area of ​​plate A, the area of ​​plate B is the same as that of plate A, V is the volume of plate A, the volume of plate B is the same as that of plate A;

[0050] Step 3.5: Since plate B is an isothermal structure, the temperature field function T”(z) of plate B is always equal to the initial temperature value T0”, so the temperature field function of each layer of plate B is segmented into T k"(z) are equal to the initial temperature value T0 of plate B", and equation (14) is rewritten as equation (15), which gives the undetermined flexure surface function w(ξ,η,M m ,M n ):

[0051]

[0052] Where: w*(ξ,η,x,y) refers to the deflection of plate B when it is subjected to a unit concentrated load P at point (ξ,η), which is called the basic solution, M m and M n are all unknown coefficients related to the mechanical boundary conditions of plate A, m and n are summation parameters, a is the length in the x direction, and b is the width in the y direction;

[0053] The mechanical boundary condition of plate A is a fixed support boundary condition, which is converted into a simply supported boundary condition with bending moment. The expression of the bending moment of plate A after conversion is:

[0054]

[0055] Where: Parameter M m and M n The meaning of the parameters is consistent with that in formula (15).

[0056] The deflection of the antenna laminate structure under unit concentrated load is taken as the basic solution, substituted into the undetermined flexure surface function of step three, and the undetermined coefficient is solved in combination with the mechanical boundary conditions of step one to obtain the flexure surface function of the antenna laminate structure.

[0057] Substituting the basic solution into the undetermined flexure surface function and solving the flexure surface function of the antenna laminate structure in combination with the mechanical boundary conditions comprises the following steps:

[0058] Step 4.1: For the basic solution w * (ξ,η,x,y), since the mechanical boundary condition of plate A has been transformed from a fixed support boundary condition to a simply supported boundary condition with bending moment, the mechanical boundary condition of plate B is also a simply supported boundary condition, and the deflection surface function w of plate B is * The corresponding expressions of the laminate differential equation and the four-sided simply supported boundary conditions corresponding to (x, y) are:

[0059]

[0060] Where: q(x,y) is the lateral load on plate B, D 11 , D 12 , D 22 , D 66 is the stiffness coefficient in the bending stiffness matrix D, and the corresponding expression of the bending stiffness matrix D is:

[0061]

[0062] Where: Q ij is the transformation matrix of the two-dimensional stiffness matrix Q The stiffness coefficient in k1 is the z coordinate of the upper surface of the kth layer, z k2 is the z coordinate of the lower surface of the kth layer, k is the layer number;

[0063] Step 4.2: Plate B deflection surface function w * (x, y) and the lateral distributed load q(x, y) are both in the form of double trigonometric series, and the corresponding expressions are:

[0064]

[0065] Where: w mn is an undetermined coefficient. Since the lateral distributed load q(x,y) is known, it is a unit concentrated load applied at the point (ξ,η). The coefficient q mn Directly calculated from the following formula:

[0066]

[0067] Step 4.3: Change the deflection surface function w of plate B to * Substitute (x, y) and the lateral distributed load q(x, y) into both sides of the differential equation (17) and solve for the coefficient w mn The expression is:

[0068]

[0069] Since plate B is subjected to a unit concentrated load, the uniformly distributed load 1 / dxdy on the differential area dxdy is used to replace the lateral distributed load q(x,y). At this time, q(x,y) is equal to 1 / dxdy in the differential area at the point (ξ,η), and all other positions are equal to zero, so the coefficient w mn The expression is rewritten as:

[0070]

[0071] Step 4.4: Substitute equation (22) into equation (19) to obtain the deflection surface function w of plate B: * (x,y), that is, the basic solution w is obtained * (ξ,η,x,y), the expression is:

[0072]

[0073] Step 4.5: Substitute the basic solution w obtained from equation (23) *Substituting (ξ,η,x,y) into equation (15), we can obtain the deflection surface function w(ξ,η) of the antenna laminate structure. The corresponding expression is:

[0074]

[0075] Where: Undetermined coefficient M m and M n Solve the equations using the fixed boundary conditions, the equations and the coefficients M m and M n The corresponding expression is:

[0076]

[0077]

[0078] Step 5: Use the deflection surface function obtained in step 4 to determine whether the degree of structural deformation meets the preset requirements. If so, output the result to achieve structural deformation calibration; if not, modify the mechanical parameters of the structure and return to step 2.

[0079] Beneficial effects:

[0080] 1. The present invention discloses a method for calibrating the structural deformation of a phased array antenna under a typical thermal load. According to actual temperature boundary conditions, geometric dimensions and thermal parameters, the temperature field function of the antenna laminate structure along the thickness direction can be determined, which can effectively prevent the deterioration of the electromagnetic performance of the antenna due to the temperature drift of the performance of heat-sensitive electronic components (such as phase shifters).

[0081] 2. The present invention can accurately obtain the deflection deformation of the antenna laminate structure under typical thermal loads through theoretical calculations based only on temperature boundary conditions, mechanical boundary conditions, relevant geometric dimensions of the laminate, mechanical parameters and thermal parameters. It can quickly predict the structural deformation within a predetermined accuracy range, facilitate the rapid debugging, calibration and optimization of the antenna structure deformation, and save a lot of manpower and material resources.

[0082] 3. The present invention discloses a method for calibrating the structural deformation of a phased array antenna under a typical thermal load. Based on the basic law of thermal conductivity and the reciprocity theorem of work, the method can evaluate and calibrate the structural deformation of the phased array antenna under a typical thermal load, thereby improving the accuracy and efficiency of the evaluation and calibration and providing a basis for guiding the assembly optimization design of heat-releasing components.

[0083] 4. The present invention discloses a method for calibrating the structural deformation of a phased array antenna under a typical thermal load. A laminated thin plate structure model is used to analyze the flexural deformation of the antenna under a typical thermal load. Based on the structural deformation calibration results of the present invention, structural optimization of the phased array antenna under a typical thermal load is achieved. Based on the optimization results, the electromechanical and thermal integration and lightweight of the satellite-borne phased array antenna are achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0085] Figure 1 A flow chart of a method for calibrating structural deformation of a phased array antenna under typical thermal loads of the present invention;

[0086] Figure 2 A schematic diagram of the laminated structure of a phased array antenna transmitting array in an embodiment of the method of the present invention;

[0087] Figure 3 Schematic diagram of equivalent mechanical boundary conditions in an embodiment of the method of the present invention. DETAILED DESCRIPTION

[0088] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0089] refer to Figure 2 A simplified case in which the overall structure of a phased array antenna transmitting array is deformed under a typical working condition thermal load is selected as an example for specific description. This embodiment discloses a method for calibrating the structural deformation of a phased array antenna under a typical thermal load. The specific implementation steps are as follows:

[0090] Step 1. Determine the mechanical boundary conditions, temperature boundary conditions, geometric dimensions, mechanical parameters and thermal parameters according to the actual temperature conditions and the antenna laminate structure. The actual temperature conditions refer to the typical thermal loads that the phased array antenna is subjected to in the low-Earth orbit environment. The antenna laminate structure is mainly composed of the antenna array face, chip layer, network layer and cold plate. They are arranged in sequence from the antenna array face to the cold plate using the serial numbers 1, 2, ..., k, ..., l. The antenna laminate structure is regarded as a laminate structure in which the main direction of the material coincides with the coordinate axis x and y directions, and the number of structural layers is recorded as l. The temperature boundary conditions include the antenna array face temperature T1, the heat source intensity q in each layer vk (k=1,2,…,l), coolant temperature T f and the convection heat transfer coefficient h f , the mechanical boundary conditions include the deflection w at the boundary | x＝0,a and w| y＝0,b , corner at the boundary and In the antenna laminate structure, the mechanical boundary condition is a fixed support mechanical boundary condition, in which the deflection and rotation at the boundary are both equal to 0; the geometric dimensions include the length a along the x-axis, the width b along the y-axis, and the thickness δ of each layer along the height direction. k (k=1,2,…,l); Mechanical parameters include the equivalent Young's modulus E of each layer structure k (k=1,2,…,l), equivalent shear modulus G k (k=1,2,…,l) and equivalent Poisson's ratio v k (k=1,2,…,l); thermal parameters include the thermal expansion coefficient of each layer [α xx ,α yy ,α xy ] k (k=1,2,…,l) and thermal conductivity κ k (k=1,2,…,l).

[0091] In this embodiment, the maximum deflection is required to be no more than 0.5 mm. The mechanical boundary conditions, temperature boundary conditions, geometric dimensions, mechanical parameters and thermal parameters are shown in Table 1 below.

[0092] Table 1 Mechanical boundary conditions, temperature boundary conditions, geometric dimensions, mechanical parameters and thermal parameters

[0093]

[0094]

[0095] Step 2: Determine the temperature field function of the antenna laminate structure along the thickness direction. According to the conditions in step 1, the expression of the temperature field function is:

[0096]

[0097] Step 3: Obtain the undetermined flexure surface function of the antenna laminate structure through the reciprocal theorem of work;

[0098] In the first step, the antenna laminate structure subjected to a typical thermal load is regarded as a laminate A, and there is a laminate B with exactly the same mechanical boundary conditions as the antenna laminate structure. A unit concentrated load P is applied at point (ξ,η) on plate B, and obviously P = 1; the work W(σ',ε') done by the stress of plate A on the deformation of plate B and the work W(σ',ε') done by the stress of plate B on the deformation of plate A are calculated, and the corresponding expressions are:

[0099]

[0100] in:

[0101]

[0102] In the second step, according to the reciprocal theorem of work, the two equations are established as an equation. After integrating both ends of the equation, since plate B is an isothermal structure, the temperature field function T" (z) of plate B is always equal to the initial temperature value T0", then the temperature field function of each layer of plate B is segmented T k "(z) are all equal to the initial temperature value T0 of plate B", from which the undetermined flexure surface function w(ξ,η,M m ,M n ):

[0103]

[0104] Where: w*(ξ,η,x,y) refers to the deflection of plate B when it is subjected to a unit concentrated load P at point (ξ,η), which is called the basic solution, M m and M n are all unknown coefficients related to the mechanical boundary conditions of plate A, m and n are summation parameters, a is the length in the x direction, and b is the width in the y direction;

[0105] The mechanical boundary condition of plate A is a fixed support boundary condition, which is converted into a simply supported boundary condition with bending moment. The expression of the bending moment of plate A after conversion is:

[0106]

[0107] Among them: parameter M m and M n The meaning of the parameters is consistent with that in formula (5).

[0108] Step 4: Taking the deflection of the antenna laminated structure under the unit concentrated load as the basic solution, substituting it into the undetermined flexure surface function of step 3, solving the undetermined coefficients in combination with the mechanical boundary conditions of step 1, and obtaining the flexure surface function of the antenna laminated structure;

[0109] The first step is to write the deflection surface function w of plate B * The laminate differential equation corresponding to (x, y) and the four-sided simply supported boundary conditions are as follows:

[0110]

[0111] Where: q(x,y) is the lateral load on plate B, that is, the unit concentrated load P, and the expression of the bending stiffness matrix D is as follows:

[0112]

[0113] The second step is to solve the differential equation to obtain the deflection surface function of plate B, that is, the basic solution w * (ξ,η,x,y), the expression is:

[0114]

[0115] The third step is to convert the basic solution w obtained from equation (9) * Substituting (ξ,η,x,y) into equation (5), we can obtain the deflection surface function w(ξ,η) of the antenna laminate structure. The corresponding expression is:

[0116]

[0117] in:

[0118]

[0119] Step 5: Determine whether the degree of structural deformation meets the preset requirements. The maximum deflection occurs at the point (127.5, 127.5). Substituting the coordinates of this point into the maximum deflection is 0.289 mm. After verification, the error of the prediction result is within the allowable range of the project and is less than 0.5 mm. The degree of deformation meets the preset requirements. The structural deformation calibration result is output to realize the structural deformation calibration of the phased array antenna under typical thermal load.

[0120] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calibrating the structural deformation of a phased array antenna under typical thermal loads, characterized in that: The following steps are included: Step 1: Determine the mechanical boundary conditions, temperature boundary conditions, geometric dimensions, mechanical parameters and thermal parameters according to the actual temperature conditions and the antenna laminate structure; Step 2: Determine the temperature field function of the antenna laminate structure along the thickness direction according to the temperature boundary conditions, geometric dimensions and thermal parameters; Step 3: Obtain the undetermined flexure surface function of the antenna laminate structure through the reciprocal theorem of work; Step 4: Taking the deflection of the antenna laminated structure under the unit concentrated load as the basic solution, substituting it into the undetermined flexure surface function of step 3, solving the undetermined coefficients in combination with the mechanical boundary conditions of step 1, and obtaining the flexure surface function of the antenna laminated structure; Step 5: Use the deflection surface function obtained in step 4 to determine whether the degree of structural deformation meets the preset requirements. If so, output the result to achieve structural deformation calibration; if not, modify the mechanical parameters of the structure and return to step 2.

2. The method for calibrating the structural deformation of a phased array antenna under typical thermal loads according to claim 1, characterized in that: The actual temperature condition described in step 1 refers to the typical thermal load of the phased array antenna in the low-Earth orbit environment; the antenna laminate structure is mainly composed of the antenna array surface, chip layer, network layer, and cold plate, which are sequentially numbered 1, 2, ..., k, ..., l from the antenna array surface to the cold plate. The antenna laminate structure is regarded as a laminate structure in which the main direction of the material coincides with the coordinate axis x and y directions, and the number of structural layers is recorded as l; the temperature boundary conditions include the antenna array surface temperature T1, the heat source intensity q in each layer vk (k=1,2,…,l), coolant temperature T f and the convection heat transfer coefficient h f , the mechanical boundary conditions include the deflection w at the boundary | x＝0,a and w| y＝0,b , corner at the boundary and In the antenna laminate structure, the mechanical boundary condition is a fixed support mechanical boundary condition, in which the deflection and rotation at the boundary are both equal to 0; the geometric dimensions include the length a along the x-axis, the width b along the y-axis, and the thickness δ of each layer along the height direction. k (k=1,2,…,l); Mechanical parameters include the equivalent Young's modulus E of each layer structure k (k=1,2,…,l), equivalent shear modulus G k (k=1,2,…,l) and equivalent Poisson's ratio v k (k=1,2,…,l); thermal parameters include the thermal expansion coefficient of each layer [α xx ,α yy ,α xy ] k (k=1,2,…,l) and thermal conductivity κ k (k=1,2,…,l).

3. The method for calibrating the structural deformation of a phased array antenna under typical thermal loads according to claim 2, characterized in that: The specific implementation method of step 2 includes the following steps: Step 2.

1. Under typical thermal loads, the temperature field of each layer of the antenna laminate structure satisfies the one-dimensional steady-state thermal conduction differential equation, which is expressed as follows: Where: T k (z,T k1 ,T k2 ) represents the undetermined temperature field function segment of the kth layer, z is the coordinate along the thickness direction, T k1 and T k2 Represent the upper and lower surface temperatures of the kth layer respectively, which are unknown quantities. The undetermined temperature field function of the kth layer is derived from the one-dimensional steady-state heat conduction differential equation, and the expression is: Where: C k1 and C k2 is the coefficient, z k1 is the z coordinate of the upper surface of the kth layer, z k2 is the z coordinate of the lower surface of the kth layer; Step 2.2: According to Fourier's law, the temperature field function of the kth layer is divided into segments T k (z,T k1 ,T k2 ) is substituted into the heat flux density q of the kth layer. k (z,T k1 ,T k2 ); Step 2.3: Calculate the heat flux density q of convective heat transfer by Newton's law of cooling f , the expression is: Step 2.4: Under steady-state heat transfer, when the heat source layer is at layer r, due to the internal heat source intensity q vk When it is zero, the heat flux is a constant function and its value is independent of z, so the heat flux should be written as q k (T k1 ,T k2 ), and the heat source intensity q in the heat source layer vk is not zero, the value of heat flux changes with z, so the heat flux is still written as q k (z,T k1 ,T k2 ); According to the first law of thermodynamics, the boundary on one side of the heat source layer is selected. When the boundary is at z r1 At the position, the heat flux density q in the continuous area outside the boundary k (T k1 ,T k2 ) is equal everywhere and equal to the heat source layer z r1 The heat flux at position q r (z r1 ,T r1 ,T r2 ), the other side of the heat source layer is the same, and when there is a convection heat transfer boundary condition, the heat flux density q k (T k1 ,T k2 ) and the convective heat flux q f Also equal, and then the linear equations are listed to solve the temperature T on the upper surface of the kth layer k1 and the lower surface temperature T k2 : Where: q1(T 11 ,T 12 ) is the heat flux density of the first layer, q2(T 21 ,T 22 ) is the heat flux density of the second layer, q r+1 (T (r+1)1 ,T (r+1)2 ) is the heat flux density of the (r+1)th layer, q l (T l1 ,T l2 ) is the heat flux density of the first layer, q r (z r1 ,T r1 ,T r2 ) is the heat flux density on the upper surface of the heat source layer, q r (z r2 ,T r1 ,T r2 ) is the heat flux density on the lower surface of the heat source layer; Step 2.5: The upper surface temperature T k1 and the lower surface temperature T k2 Substituting into formula (2), we can get the temperature field function segment T of the kth layer of the antenna laminate structure: k (z): In the formula, all parameters except the independent variable z are known. The temperature field function of each layer of the antenna laminate structure is divided into segments T k (z) is summarized, that is, the temperature field function T(z) of the antenna laminate structure along the thickness direction is obtained:

4. The method for calibrating the structural deformation of a phased array antenna under typical thermal loads according to claim 3, characterized in that: The specific implementation method of step three includes the following steps: Step 3.

1. Consider the antenna laminate structure subjected to typical thermal load as laminate A, and there is a laminate B with exactly the same mechanical boundary conditions as the antenna laminate structure. Apply a unit concentrated load P at point (ξ,η) on plate B, where P = 1. Calculate the work W(σ',ε') done by the stress of plate A on the deformation of plate B and the work W(σ',ε') done by the stress of plate B on the deformation of plate A. The corresponding expressions are: In the formula: σ' and ε' are the stress and strain of plate A, σ" and ε" are the stress and strain of plate B, and the superscript ij is the dummy index of the Einstein summation convention. In the calculation of this formula, ij takes three groups of superscripts: xx, yy, and xy, and k is the layer number; Step 3.2: When considering temperature changes, the stress-strain relationship of the kth layer of the laminate is expressed as: Where: [σ xx σ yy σ xy ] k T is the stress matrix of the kth layer, [ε xx ε yy ε xy ] k T is the strain matrix of the kth layer, [α xx α yy α xy ] k T is the thermal expansion coefficient array of the kth layer. Since the main direction of the material coincides with the x and y coordinate axes, temperature changes do not cause shear strain, so α xy =0, T k (z) is the temperature field function segment of the kth layer of the antenna laminate structure, T0 is the initial temperature value, is the transformation matrix of the two-dimensional stiffness matrix Q in the main direction of the kth layer, and the corresponding expression is: Where: E is Young's modulus, G is shear modulus, v is Poisson's ratio, and subscripts 1 and 2 represent the main directions of the material. Since the main directions of the material coincide with the x and y directions of the coordinate axes, Q 16 =Q 26 =0; Step 3.3: Transform the two-dimensional stiffness matrix Q into Substituting into formula (9) we get: Substituting formula (11) into formula (8), we get: Where: T k '(z) is the temperature field function segment of the kth layer of plate A, T0' is the initial temperature value of plate A, T k "(z) is the temperature field function segment of the kth layer of plate B, T0" is the initial temperature value of plate B, and k is the layer number; According to the reciprocal theorem of work, an equation relationship is established, and the corresponding expression is: Step 3.4: Integrate both sides of equation (13) at the same time, and the corresponding expression is: Where: P' is the surface force acting on plate A, P" is the surface force acting on plate B, Q' is the volume force acting on plate A, Q" is the volume force acting on plate B, U' is the displacement vector of plate A, U" is the displacement vector of plate B, Ω is the surface area of ​​plate A, the area of ​​plate B is the same as that of plate A, V is the volume of plate A, the volume of plate B is the same as that of plate A; Step 3.5: Since plate B is an isothermal structure, the temperature field function T”(z) of plate B is always equal to the initial temperature value T0”, so the temperature field function of each layer of plate B is segmented into T k "(z) are equal to the initial temperature value T0 of plate B", and equation (14) is rewritten as equation (15), which gives the undetermined flexure surface function w(ξ,η,M m ,M n ): Where: w*(ξ,η,x,y) refers to the deflection of plate B when it is subjected to a unit concentrated load P at point (ξ,η), which is called the basic solution, M m and M n are all undetermined coefficients related to the mechanical boundary conditions of plate A, m and n are summation parameters, a is the length in the x direction, and b is the width in the y direction; The mechanical boundary condition of plate A is a fixed support boundary condition, which is converted into a simply supported boundary condition with bending moment. The expression of the bending moment of plate A after conversion is: Where: Parameter M m and M n The meaning of the parameters is consistent with that in formula (15).

5. The method for calibrating the structural deformation of a phased array antenna under typical thermal loads according to claim 4, characterized in that: The specific implementation method of step 4 includes the following steps: Step 4.1: For the basic solution w * (ξ,η,x,y), since the mechanical boundary condition of plate A has been transformed from a fixed support boundary condition to a simply supported boundary condition with bending moment, the mechanical boundary condition of plate B is also a simply supported boundary condition, and the deflection surface function w of plate B is * The corresponding expressions of the laminate differential equation and the four-sided simply supported boundary conditions corresponding to (x, y) are: Where: q(x,y) is the lateral load on plate B, D 11 , D 12 , D 22 , D 66 is the stiffness coefficient in the bending stiffness matrix D, and the corresponding expression of the bending stiffness matrix D is: Where: Q ij is the transformation matrix of the two-dimensional stiffness matrix Q The stiffness coefficient in k1 is the z coordinate of the upper surface of the kth layer, z k2 is the z coordinate of the lower surface of the kth layer, k is the layer number; Step 4.2: Plate B deflection surface function w * (x, y) and the lateral distributed load q(x, y) are both in the form of double trigonometric series, and the corresponding expressions are: Where: w mn is an undetermined coefficient. Since the lateral distributed load q(x,y) is known, it is a unit concentrated load applied at the point (ξ,η). The coefficient q mn Directly calculated from the following formula: Step 4.3: Change the deflection surface function w of plate B to * Substitute (x, y) and the lateral distributed load q(x, y) into both sides of the differential equation (17) and solve for the coefficient w mn The expression is: Since plate B is subjected to a unit concentrated load, the uniformly distributed load 1 / dxdy on the differential area dxdy is used to replace the lateral distributed load q(x,y). At this time, q(x,y) is equal to 1 / dxdy in the differential area at the point (ξ,η), and all other positions are equal to zero, so the coefficient w mn The expression is rewritten as: Step 4.4: Substitute equation (22) into equation (19) to obtain the deflection surface function w of plate B: * (x,y), that is, the basic solution w is obtained * (ξ,η,x,y), the expression is: Step 4.5: Substitute the basic solution w obtained from equation (23) * Substituting (ξ,η,x,y) into equation (15), we can obtain the deflection surface function w(ξ,η) of the antenna laminate structure. The corresponding expression is: Where: Undetermined coefficient M m and M n Solve the equations using the fixed boundary conditions, the equations and the coefficients M m and M n The corresponding expression is:

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