Electrostatic force application method and system considering deformation of electrode surface and thin film reflective surface

Abstract

The present invention belongs to the field of radar antenna simulation technology and discloses a method and system for applying electrostatic force that takes into account the deformation of electrode surfaces and thin film reflective surfaces. The method comprises: establishing a finite element model of an electrostatically formed thin film reflective surface antenna and applying boundary constraints; sequentially calculating the coordinates of the projection points of the midpoints of the thin film reflective surface units onto the electrode surface, calculating the distances between the midpoints of the thin film units and the projection points, and calculating the electrostatic force using a plate capacitor formula; applying the electrostatic force to the electrode surface and the thin film reflective surface to perform finite element structural deformation analysis, recalculating the electrostatic force using the above steps based on the node positions of the deformed electrode surface and the thin film reflective surface, and continuing the finite element structural deformation analysis of the electrostatically formed thin film reflective surface antenna until the deformation analysis accuracy requirements are met. The present invention can accurately calculate the magnitude of the electrostatic force when the electrode surface and the thin film reflective surface are deformed, providing a theoretical basis for high-precision deformation analysis and forming control of electrostatically formed thin film reflective surface antennas.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar antenna simulation, and in particular relates to an electrostatic force application method and system taking into account the deformation of an electrode surface and a thin film reflection surface. Background Art

[0002] Currently, electrostatically formed thin-film reflector antennas typically consist of a cable-membrane electrode surface and a thin-film reflector surface, forming a capacitor at a certain distance between them. When different voltages are applied to the electrode and thin-film reflector surfaces, an electrostatic attraction force is generated between them. Because both the cable-membrane electrode and thin-film reflector surfaces are flexible structures, they deform under the action of electrostatic forces. This deformation changes the distance between the thin-film reflector and the electrode surface, and thus the magnitude of the electrostatic force. This necessitates solving the problem of calculating the electrostatic force after the deformation of the electrode and thin-film reflector surfaces.

[0003] However, most researchers in the industry have not considered the effect of electrode surface deformation on the magnitude of the electrostatic force. Surya P. Chodimella, James D. Moore, and others assumed that the distance between the film's reflective surface and the electrode surface remained constant and used the plate capacitor formula to calculate the electrostatic force applied to the film's reflective surface. This method neither considers the difference in distance between the film's reflective surface and the electrode surface due to different shapes, nor the effect of electrode surface deformation on the magnitude of the electrostatic force. Liu Chao, Gu Yongzhen, and others used the finite element analysis software ANSYS to establish a coupled electrostatic field-film structure deformation field model. While this method can address the coupling between film deformation and the electrostatic field, the modeling is complex and unsuitable for complex boundary conditions. Furthermore, it does not consider the effect of electrode surface deformation on the coupled model. Therefore, a new electrostatic force application method that considers the deformation of the electrode and film's reflective surfaces is urgently needed.

[0004] Through the above analysis, the problems and defects of the existing technology are as follows:

[0005] (1) Most researchers in the industry have not considered the effect of electrode surface deformation on the magnitude of electrostatic force.

[0006] (2) The existing methods neither consider the problem of different distances at different positions caused by the different shapes of the film reflective surface and the electrode surface, nor consider the influence of the deformation of the electrode surface on the magnitude of the electrostatic force.

[0007] (3) The existing methods for solving the coupling problem between film deformation and electrostatic field through modeling are relatively complex and not suitable for situations with complex boundaries. In addition, the influence of electrode surface deformation on the coupling model is not considered.

[0008] The difficulty in solving the above problems and defects is as follows: on the one hand, considering the effect of thin film electrode surface deformation on the magnitude of the electrostatic force requires establishing an overall model of the electrostatically formed thin film reflector antenna, which involves a complex finite element modeling process; on the other hand, the thin film electrode surface is laid on a supporting cable net and is tensioned on the supporting truss by boundary cables. The boundary conditions between the two are relatively complex, making it difficult to establish a coupled model. The present invention calculates the electrostatic force by the relative position between the thin film reflector surface unit and the electrode surface unit, achieving the effect of the deformation of the thin film reflector surface and the electrode surface on the electrostatic force. The difficulty lies in how to accurately calculate the electrostatic force and how to update the electrostatic force.

[0009] The significance of resolving the above problems and deficiencies lies in the following: while considering the coupling between the deformation of the thin film reflector and electrode surfaces and the electrostatic field and electrostatic forces, the present invention also addresses the inability of existing coupled modeling models to handle complex boundary conditions, making it possible to perform overall deformation analysis of electrostatically formed thin film reflector antennas. Furthermore, during in-orbit operation, electrostatically formed thin film reflector antennas are subject to high and low temperature loads, which can cause significant deformation of the film reflector and electrode surfaces. Therefore, the present invention can also be applied to deformation analysis of electrostatically formed thin film reflector antennas under large temperature differentials. Summary of the Invention

[0010] In response to the problems existing in the prior art, the present invention provides a method and system for applying electrostatic force that takes into account the deformation of the electrode surface and the thin film reflective surface. In particular, it relates to a method for applying electrostatic force and a high-precision deformation analysis method for electrostatically formed thin film reflective surface antennas that takes into account the deformation of the electrode surface and the thin film reflective surface. The method aims to solve the problem of calculating the electrostatic force when the electrode surface and the thin film reflective surface are deformed at the same time.

[0011] The present invention is implemented as follows: a method for applying an electrostatic force taking into account the deformation of the electrode surface and the thin film reflective surface, the method comprising:

[0012] A finite element model of an electrostatically formed thin film reflector antenna is established, and boundary constraints are imposed. The coordinates of the projection points of the midpoints of the thin film reflector units onto the electrode surface are calculated in sequence, the distances between the midpoints of the thin film units and the projection points are calculated, and the electrostatic force is calculated using the flat plate capacitor formula. The electrostatic force is applied to the electrode surface and the thin film reflector surface to perform a finite element structural deformation analysis. The electrostatic force is recalculated using the above steps based on the node positions of the deformed electrode surface and the thin film reflector surface, and the finite element structural deformation analysis of the electrostatically formed thin film reflector antenna is continued until the deformation analysis accuracy requirements are met.

[0013] Furthermore, the electrostatic force application method considering the deformation of the electrode surface and the thin film reflective surface includes the following steps:

[0014] Step 1: Establish a finite element model of the electrostatically formed thin film reflector antenna and apply boundary constraints. This step realizes the overall finite element modeling of the electrostatically formed thin film reflector antenna and provides a model basis for considering the deformation of the thin film reflector surface and the electrode surface.

[0015] Step 2: Calculate the coordinates of the projection point of the midpoint of the thin film reflective surface unit onto the electrode surface, calculate the distance between the midpoint of the thin film unit and the projection point, and calculate the electrostatic force using the flat plate capacitor formula. This step realizes the calculation of the electrostatic force based on the relative position of the thin film reflective surface and the electrode surface, providing a theoretical basis for the high-precision calculation of the electrostatic force.

[0016] Step 3: Applying electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis. This step implements deformation analysis of the film reflective surface and the electrode surface under the action of electrostatic force, providing a basis for subsequent finite element model updates and electrostatic force updates.

[0017] Step 4: Extract the node displacements of the electrode surface and the thin film reflector surface, and analyze whether they meet the deformation accuracy requirements. If not, update the finite element model and return to step 2; if so, complete the deformation analysis of the electrostatically formed thin film reflector antenna. This step provides criteria for updating the finite element model and electrostatic force of the electrostatically formed thin film reflector surface to ensure that the deformation analysis of the electrode surface and the thin film reflector surface and the electrostatic force calculation can meet the accuracy requirements.

[0018] Furthermore, in step 1, establishing a finite element model of the electrostatically formed thin film reflector antenna and applying boundary constraints includes:

[0019] (1) Establishing the electrode surface support structure, including establishing a cable net structure based on the topological connection relationship between the front and rear cable nets and the vertical cable net, and meshing the cable net structure using cable units;

[0020] (2) establishing an electrode surface, including establishing an electrode surface on the front cable net triangular grid, meshing the electrode surface using triangular film units, and establishing N triangular film units on the electrode surface;

[0021] (3) Establishing a thin film reflective surface, including establishing boundary cables and paraboloids, meshing the paraboloids using triangular thin film units, establishing M triangular thin film units for the thin film reflective surface, and meshing the boundary cables using cable units;

[0022] (4) Assign material properties to the cable element and the membrane element; the cable element material property is set to: mass density 1685 kg / m 3 , elastic modulus 5.01 GPa, Poisson's ratio 0.30, cable cross-sectional diameter 1.1 mm, thermal expansion coefficient -2×10 -6 / ℃; the material properties of the membrane element are set to: mass density 1432kg / m3 , elastic modulus 1.67 GPa, Poisson's ratio 0.34, thickness 26.5 μm, thermal expansion coefficient 29×10 -6 / ℃;

[0023] (5) Apply boundary constraints, including constraining the displacement of the outermost ring nodes of the front and rear cable nets and the end points of the boundary cables of the thin film reflective surface in the X, T, and Z directions.

[0024] Furthermore, in step 2, the coordinates of the projection points of the midpoints of the thin film reflective surface units onto the electrode surface are calculated in sequence, the distance between the midpoints of the thin film units and the projection points is calculated, and the electrostatic force is calculated using the flat plate capacitor formula, including:

[0025] (1) Calculate the midpoint P of the i-th (i=1, 2, 3...M) thin film reflective surface unit i0 The coordinates of the three nodes of the triangular membrane element are x i1 ={x i1 y i1 z i1 ] T 、x i2 =[x i2 y i2 z i2 ] T 、x i3 =[x i3 y i3 z i3 ] T e then the midpoint coordinates are

[0026] (2) Determine whether the midpoint of the film unit is projected onto the j∈[1, N]th electrode surface unit, and calculate the projection point P of the midpoint onto the electrode surface. ij The coordinates of the three nodes of the j-th electrode surface unit are x j1 =[x j1 y j1 z j1 ] T 、x j2 =[x j2 y j2 z j2 ] T 、x j3 =[x j3 y j3 z j3 ] T , then the midpoint x of the membrane element i0 The coordinates of the projection point on the electrode surface are Where A=(y j3 -y j1)*(z j3 -z j1 )-(z j2 -z j1 )*(y j3 -y j1 ), B=(x j3 -x j1 )*(z j2 -z j1 )-(x j2 -x j1 )*(z j3 -z j1 ), C=(x j2 -x j1 )*(y j3 -y j1 )-(x j3 -x j1 )*(y j2 -y j1 )、D=-(A*x j1 +B*y j1 +C*z j1 );

[0027] (3) Calculate the distance between the midpoint of the membrane unit and the projection point as d ij =||x ij -x i0 ||;

[0028] (4) Using the flat plate capacitor formula, the electrostatic force on the thin film reflective surface unit and the electrode surface unit is calculated as follows: Among them, ε r is the relative dielectric constant, U j is the electrode voltage.

[0029] Furthermore, in step three, applying electrostatic force to the electrode surface and the thin film reflective surface to perform finite element structural deformation analysis includes:

[0030] (1) Apply an electrostatic force p in the form of a surface load to the i-th (i=1, 2, 3...M) thin film reflective surface unit and the j-th (j=1, 2, 3...N) electrode surface unit in turn. ij ;

[0031] (2) Given the initial pre-tension of the cable unit and the membrane unit, the nonlinear equilibrium equation (K L +K NL )δ=P;where K L is the linear stiffness matrix, K NL is the nonlinear stiffness matrix, δ is the node displacement matrix, and P is the node load matrix;

[0032] (3) Use the Newton-Raphson iterative method to solve nonlinear equilibrium equations.

[0033] Furthermore, in step 4, the node displacements of the electrode surface and the thin film reflective surface are extracted to analyze whether the deformation accuracy requirements are met, including:

[0034] (1) Extract the spatial coordinates X of the kth (k=1, 2, 3...NUM) node in sequence k =[X k Y k Z k ] T and displacement δ k =[u k v k w k ] T ; Among them, NUM is the total number of nodes, u k 、v k 、w k are the displacements of node k in the X, Y, and Z directions respectively;

[0035] (2) Calculate the root mean square error of node displacement

[0036] (3) If δ≤Δ, where Δ=0.01 is the upper limit of the node displacement error, the finite element deformation analysis of the electrostatically formed thin film reflector antenna is completed; otherwise, let X k =X k +δ k , return to step 2 and recalculate the electrostatic force and the deformation analysis of the finite element model of the electrostatically formed thin film reflector antenna.

[0037] Another object of the present invention is to provide an electrostatic force application system that considers the deformation of the electrode surface and the thin film reflective surface and applies the electrostatic force application method that considers the deformation of the electrode surface and the thin film reflective surface, the electrostatic force application system that considers the deformation of the electrode surface and the thin film reflective surface comprising:

[0038] Finite element model building module, used to build the finite element model of the electrostatically formed thin film reflector antenna and impose boundary constraints;

[0039] A calculation module is used to sequentially calculate the coordinates of the projection point of the midpoint of the thin film reflective surface unit projected onto the electrode surface, calculate the distance between the midpoint of the thin film unit and the projection point, and calculate the electrostatic force using a flat plate capacitor formula;

[0040] Finite element structural deformation analysis module, used to apply electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis;

[0041] The deformation accuracy requirement analysis module is used to extract the node displacements of the electrode surface and the thin film reflector surface and analyze whether the deformation accuracy requirements are met. If not, the finite element model is updated and the calculation module is returned; if so, the deformation analysis of the electrostatically formed thin film reflector antenna is completed.

[0042] Another object of the present invention is to provide a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the following steps:

[0043] (1) Establish a finite element model of the electrostatically formed thin film reflector antenna and apply boundary constraints;

[0044] (2) Calculate the coordinates of the projection point of the midpoint of the thin film reflective surface unit onto the electrode surface, calculate the distance between the midpoint of the thin film unit and the projection point, and calculate the electrostatic force using the flat plate capacitor formula;

[0045] (3) Applying electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis;

[0046] (4) Extract the node displacements of the electrode surface and the thin film reflector surface and analyze whether they meet the deformation accuracy requirements. If not, update the finite element model and return to step (2); if so, complete the deformation analysis of the electrostatically formed thin film reflector antenna.

[0047] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor performs the following steps:

[0048] (1) Establish a finite element model of the electrostatically formed thin film reflector antenna and apply boundary constraints;

[0049] (2) Calculate the coordinates of the projection point of the midpoint of the thin film reflective surface unit onto the electrode surface, calculate the distance between the midpoint of the thin film unit and the projection point, and calculate the electrostatic force using the flat plate capacitor formula;

[0050] (3) Applying electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis;

[0051] (4) Extract the node displacements of the electrode surface and the thin film reflector surface and analyze whether they meet the deformation accuracy requirements. If not, update the finite element model and return to step (2); if so, complete the deformation analysis of the electrostatically formed thin film reflector antenna.

[0052] Another object of the present invention is to provide an information data processing terminal, which is used to implement the electrostatic force application system that takes into account the deformation of the electrode surface and the thin film reflective surface.

[0053] Combining all the above-mentioned technical solutions, the advantages and positive effects of the present invention are as follows: the present invention provides an electrostatic force application method that takes into account the deformation of the electrode surface and the thin film reflective surface. The magnitude of the electrostatic force is calculated by the distance between the thin film reflective surface unit and the electrode surface unit. The electrostatic force is applied to the thin film reflective surface and the electrode surface respectively to perform finite element structural deformation analysis. While ensuring the accuracy of the electrostatic force calculation, the influence of the electrode surface deformation on the magnitude of the electrostatic force is considered. The present invention is also applicable to other types of electrostatically formed products that involve deformation of the electrode surface and the thin film surface, such as electrostatically formed thin film reflectors and electrostatically formed sunshades. In the field of satellite-borne electrostatically formed thin film reflective surface antenna technology, there is currently no electrostatic field calculation and application method that simultaneously considers the deformation of the electrode surface and the thin film reflective surface. Most methods assume that the deformation of the electrode surface is small relative to the deformation of the thin film reflective surface and the impact can be ignored. In fact, satellite-borne antennas face a complex load environment with constantly changing high and low temperatures during their on-orbit operation. Under the action of large temperature differences, both the electrode surface and the thin film reflective surface will undergo significant deformation. The method provided by the present invention also provides a basis for high-precision deformation analysis of satellite-borne electrostatically formed thin film reflective surface antennas during on-orbit operation.

[0054] The present invention provides an electrostatic force application method that takes into account the deformation of the electrode and thin-film reflector surfaces. This method accurately calculates the magnitude of the electrostatic force when the electrode and thin-film reflector surfaces deform, and by accounting for the effect of electrode surface deformation on the electrostatic force, it provides a theoretical basis for high-precision deformation analysis and shaping control of electrostatically formed thin-film reflector antennas. This method is applicable to radar antenna simulation, enabling high-precision finite element structural deformation analysis of electrostatically formed thin-film reflector antennas. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0056] Figure 1 This is a flow chart of an electrostatic force application method that takes into account the deformation of the electrode surface and the thin film reflective surface, provided by an embodiment of the present invention.

[0057] Figure 2 This is a schematic diagram of a method for applying an electrostatic force taking into account the deformation of the electrode surface and the thin film reflective surface provided by an embodiment of the present invention.

[0058] Figure 3 This is a structural block diagram of an electrostatic force application system that takes into account the deformation of the electrode surface and the thin film reflective surface provided by an embodiment of the present invention;

[0059] In the figure: 1. Finite element model construction module; 2. Calculation module; 3. Finite element structure deformation analysis module; 4. Deformation accuracy requirement analysis module.

[0060] Figure 4 This is a flow chart of applying boundary constraints to establish a finite element model of an electrostatically formed thin film reflector antenna provided by an embodiment of the present invention.

[0061] Figure 5 This is a flow chart for calculating the distance and electrostatic force between the midpoint and projection point of a thin film unit provided by an embodiment of the present invention.

[0062] Figure 6 Schematic diagram of the spatial relationship between the film midpoint and projection point provided by an embodiment of the present invention.

[0063] Figure 7 This is a flow chart of applying electrostatic force and solving nonlinear equilibrium equations provided by an embodiment of the present invention.

[0064] Figure 8 This is a flow chart for extracting the node displacements of the electrode surface and the thin film reflective surface and analyzing whether the deformation accuracy requirements are met, provided by an embodiment of the present invention.

[0065] Figure 9 This is a diagram of the overall finite element model of the electrostatically formed film antenna provided by an embodiment of the present invention.

[0066] Figure 10 This is a schematic diagram of the deformation of the electrode surface and the thin film reflective surface when the deformation of the electrode surface is not considered, provided by an embodiment of the present invention.

[0067] Figure 11 This is a schematic diagram of the deformation of the electrode surface and the thin film reflective surface when the electrode surface deformation is considered, provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0069] In order to solve the problems existing in the prior art, the present invention provides an electrostatic force application method that takes into account the deformation of the electrode surface and the thin film reflective surface. The present invention is described in detail below with reference to the accompanying drawings.

[0070] like Figure 1 As shown, the electrostatic force application method provided by the embodiment of the present invention taking into account the deformation of the electrode surface and the thin film reflective surface includes the following steps:

[0071] S101, establish a finite element model of the electrostatically formed thin film reflector antenna and apply boundary constraints;

[0072] S102, sequentially calculating the coordinates of the projection point of the midpoint of the thin film reflective surface unit onto the electrode surface, calculating the distance between the midpoint of the thin film unit and the projection point, and calculating the electrostatic force using the flat plate capacitor formula;

[0073] S103, applying electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis;

[0074] S104, extracting the node displacements of the electrode surface and the thin film reflector surface, analyzing whether they meet the deformation accuracy requirements, if not, updating the finite element model and returning to S102; if so, completing the deformation analysis of the electrostatically formed thin film reflector antenna.

[0075] The principle diagram of the electrostatic force application method considering the deformation of the electrode surface and the film reflective surface provided by the embodiment of the present invention is as follows: Figure 2 shown.

[0076] like Figure 3 As shown, the electrostatic force application system provided by the embodiment of the present invention taking into account the deformation of the electrode surface and the thin film reflective surface includes:

[0077] Finite element model building module 1, used to establish a finite element model of an electrostatically formed thin film reflector antenna and impose boundary constraints;

[0078] Calculation module 2, used to sequentially calculate the coordinates of the projection point of the midpoint of the thin film reflective surface unit projected onto the electrode surface, calculate the distance between the midpoint of the thin film unit and the projection point, and calculate the electrostatic force using the flat plate capacitor formula;

[0079] Finite element structural deformation analysis module 3, used for applying electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis;

[0080] The deformation accuracy requirement analysis module 4 is used to extract the node displacements of the electrode surface and the thin film reflector surface, and analyze whether the deformation accuracy requirements are met. If not, the finite element model is updated and the calculation module is returned to. If so, the deformation analysis of the electrostatically formed thin film reflector antenna is completed.

[0081] The technical solution of the present invention is further described below in conjunction with specific embodiments.

[0082] The electrostatic force application method provided by an embodiment of the present invention taking into account the deformation of the electrode surface and the thin film reflective surface includes the following steps:

[0083] 1) Establish a finite element model of the electrostatically formed thin film reflector antenna and apply boundary constraints;

[0084] 2) Calculate the coordinates of the projection point of the midpoint of the thin film reflective surface unit onto the electrode surface, calculate the distance between the midpoint of the thin film unit and the projection point, and calculate the electrostatic force using the flat plate capacitor formula;

[0085] 3) Applying electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis;

[0086] 4) Extract the node displacements of the electrode surface and the thin film reflector surface and analyze whether they meet the deformation accuracy requirements: if not, update the finite element model and return to step 2); if yes, complete the deformation analysis of the electrostatically formed thin film reflector antenna.

[0087] in Figure 2 This is a general flow chart of an electrostatic force application method that takes into account the deformation of the electrode surface and the thin film reflective surface, provided by an embodiment of the present invention.

[0088] like Figure 4 As shown, the above step 1) specifically involves the following steps:

[0089] (1) Establishing the electrode surface support structure, including establishing a cable net structure based on the topological connection relationship between the front and rear cable nets and the vertical cable net, and meshing the cable net structure using cable units;

[0090] (2) establishing an electrode surface, including establishing an electrode surface on the front cable net triangular grid, meshing the electrode surface using triangular film units, and establishing N triangular film units on the electrode surface;

[0091] (3) Establishing a thin film reflective surface, including establishing boundary cables and paraboloids, meshing the paraboloids using triangular thin film units, establishing M triangular thin film units for the thin film reflective surface, and meshing the boundary cables using cable units;

[0092] (4) Assign material properties to the cable unit and membrane unit, where the cable unit material property is set to: mass density 1685kg / m 3 , elastic modulus 5.01 GPa, Poisson's ratio 0.30, cable cross-sectional diameter 1.1 mm, thermal expansion coefficient -2×10 -6 / ℃, the material properties of the membrane element are set to: mass density 1432kg / m 3 , elastic modulus 1.67 GPa, Poisson's ratio 0.34, thickness 26.5 μm, thermal expansion coefficient 29×10 -6 / ℃;

[0093] (5) Apply boundary constraints, including constraining the displacement of the outermost ring nodes of the front and rear cable nets and the end points of the boundary cables of the film reflective surface in the X, Y, and Z directions.

[0094] like Figure 5 As shown, the above step 2) specifically involves the following steps:

[0095] (1) Calculate the midpoint P of the i-th (i=1, 2, 3...M) thin film reflective surface unit i0Specifically, the coordinates of the three nodes of the triangular membrane element are x i1 =[x i1 y i1 z i1 ] T 、x i2 =[x i2 y i2 z i2 ] T 、x i3 =[x i3 y i3 z i3 ] T , then the midpoint coordinates are

[0096] (2) Determine whether the midpoint of the film unit is projected on the j∈[1, N]th electrode surface unit, and then calculate the projection point P of the midpoint projected onto the electrode surface ij Specifically, the coordinates of the three nodes of the j-th electrode surface unit are x j1 =[x j1 y j1 z j1 ] T 、x j2 =[x j2 y j2 z j2 ] T 、x j3 =[x j3 y j3 z j3 ] T , then the midpoint x of the membrane element i0 The coordinates of the projection point on the electrode surface are Where A=(y j3 -y j1 )(z j3 -z j1 )-(z j2 -z j1 )*(y j3 -y j1 ), B=(x j3 -x jj )*(z j2 -z j1 )-(x j2 -x j1 )*(z j3 -z j1 ), C=(x j2 -x j1 )*(y j3 -y j1 )-(x j3 -xj1 )*(y j2 -y j1 )、D=-(A*x j1 +B*y j1 +C*z j1 );

[0097] (3) Calculate the distance between the midpoint of the membrane unit and the projection point as d ij =||x ij -x i0 ||, the spatial position relationship between the coordinates of the midpoint of the film reflection surface and the projection point is shown in Figure 6 ;

[0098] (4) Using the flat plate capacitor formula, the electrostatic force on the thin film reflective surface unit and the electrode surface unit is calculated as follows: Among them, ε r is the relative dielectric constant, U j is the electrode voltage.

[0099] like Figure 7 As shown, the above step 3) specifically involves the following steps:

[0100] (1) Apply an electrostatic force p in the form of a surface load to the i-th (i=1, 2, 3...M) thin film reflective surface unit and the j-th (j=1, 2, 3...N) electrode surface unit in turn. ij ;

[0101] (2) Given the initial pre-tension of the cable unit and the membrane unit, the nonlinear equilibrium equation (K L +K NL )δ=P,where K L is the linear stiffness matrix, K NL is the nonlinear stiffness matrix, δ is the node displacement matrix, and P is the node load matrix;

[0102] (3) Use the Newton-Raphson iterative method to solve nonlinear equilibrium equations.

[0103] like Figure 8 As shown, the above step 4) specifically involves the following steps:

[0104] (1) Extract the spatial coordinates X of the kth (k=1, 2, 3...NUM) node in sequence k =[X k Y k Z k ] T and displacement δ k =[u k v k w k ] T, where NUM is the total number of nodes, u k 、v k 、w k are the displacements of node k in the X, Y, and Z directions respectively;

[0105] (2) Calculate the root mean square error of node displacement

[0106] (3) If δ≤Δ, where Δ=0.01 is the upper limit of the node displacement error, the finite element deformation analysis of the electrostatically formed thin film reflector antenna is completed; otherwise, let X k =X k +δ k , return to step 2) and recalculate the electrostatic force and the deformation analysis of the finite element model of the electrostatically formed thin film reflector antenna.

[0107] The application effect of the present invention is described in detail below in conjunction with simulation experiments.

[0108] Simulation conditions:

[0109] Taking the 5m diameter electrostatically formed thin film reflector antenna as an example, the overall finite element model is established as shown in Figure 9 In the finite element model, there are N = 204 triangular thin film units on the electrode surface and M = 864 triangular thin film units on the thin film reflective surface. The electrostatic force application method of the present invention is used to apply loads on the thin film reflective surface and the electrode surface and perform finite element deformation analysis. The final deformation of the thin film reflective surface and the thin film electrode surface before and after the electrode surface deformation is considered is as follows: Figure 10 and Figure 11 As shown, the electrostatic force significantly deforms both the thin film reflective surface and the thin film electrode surface. This deformation cannot be ignored for the deformation analysis of high-precision electrostatically formed thin film reflector antennas. This simulation experiment was conducted only for an electrostatically formed thin film reflector antenna with a characteristic aperture. The present invention is also applicable to other systems controlled by electrostatic forces, such as electrostatically formed thin film mirrors and electrostatic force update calculations in micro-electromechanical systems.

[0110] In the above embodiments, all or part of the embodiments can be implemented by software, hardware, firmware, or any combination thereof. When implemented in whole or in part in the form of a computer program product, the computer program product includes one or more computer instructions. When the computer program instructions are loaded or executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL) or wireless (e.g., infrared, wireless, microwave, etc.)) method. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that includes one or more available media. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0111] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for applying electrostatic force taking into account the deformation of the electrode surface and the thin film reflective surface, characterized in that: The electrostatic force application method considering the deformation of the electrode surface and the thin film reflective surface includes: establishing a finite element model of an electrostatically formed thin film reflective surface antenna and applying boundary constraints; sequentially calculating the coordinates of the projection points of the midpoints of the thin film reflective surface units onto the electrode surface, calculating the distances between the midpoints of the thin film units and the projection points, and calculating the electrostatic force using a flat plate capacitor formula; applying the electrostatic force to the electrode surface and the thin film reflective surface to perform a finite element structural deformation analysis, recalculating the electrostatic force using the above steps based on the node positions of the deformed electrode surface and the thin film reflective surface, and continuing the finite element structural deformation analysis of the electrostatically formed thin film reflective surface antenna until the deformation analysis accuracy requirements are met; The electrostatic force application method considering the deformation of the electrode surface and the thin film reflective surface comprises the following steps: Step 1: Establish a finite element model of the electrostatically formed thin film reflector antenna and apply boundary constraints; Step 2: Calculate the coordinates of the projection point of the midpoint of the thin film reflective surface unit onto the electrode surface, calculate the distance between the midpoint of the thin film unit and the projection point, and calculate the electrostatic force using the flat plate capacitor formula; Step 3: Apply electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis; Step 4: Extract the node displacements of the electrode surface and the thin film reflector surface to analyze whether they meet the deformation accuracy requirements. If not, update the finite element model and return to step 2; if so, complete the deformation analysis of the electrostatically formed thin film reflector antenna; In step 4, the node displacements of the electrode surface and the thin film reflective surface are extracted to analyze whether the deformation accuracy requirements are met, including: (1) Extract the spatial coordinates X of the kth (k=1, 2, 3...NUM) node in sequence k =[X k Y k Z k ] T and displacement δ k =[u k v k w k ] T ; Among them, NUM is the total number of nodes, u k 、v k 、w k are the displacements of node k in the X, Y, and Z directions respectively; (2) Calculate the root mean square error of node displacement (3) If δ≤Δ, where Δ=0.01 is the upper limit of the node displacement error, the finite element deformation analysis of the electrostatically formed thin film reflector antenna is completed; otherwise, let X k =X k +δ k , return to step 2, and recalculate the electrostatic force and the deformation analysis of the finite element model of the electrostatically formed thin film reflector antenna; In step 1, the finite element model of the electrostatically formed thin film reflector antenna is established and boundary constraints are imposed, including: (1) Establishing the electrode surface support structure, including establishing a cable net structure based on the topological connection relationship between the front and rear cable nets and the vertical cable net, and meshing the cable net structure using cable units; (2) establishing an electrode surface, including establishing an electrode surface on the front cable net triangular grid, meshing the electrode surface using triangular thin film units, and establishing N triangular thin film units of the electrode surface, where N is the total number of units divided into the electrode surface; (3) Establishing a thin film reflective surface, including establishing boundary cables and paraboloids, meshing the paraboloids using triangular thin film units, establishing M triangular thin film units for the thin film reflective surface, where M is the total number of units for the thin film reflective surface, and meshing the boundary cables using cable units; (4) Assign material properties to the cable element and the membrane element; the cable element material property is set to: mass density 1685 kg / m 3 , elastic modulus 5.01 GPa, Poisson's ratio 0.30, cable cross-sectional diameter 1.1 mm, thermal expansion coefficient -2×10 -6 / ℃; the material properties of the membrane element are set to: mass density 1432kg / m 3 , elastic modulus 1.67 GPa, Poisson's ratio 0.34, thickness 26.5 μm, thermal expansion coefficient 29×10 -6 / ℃; (5) Imposing boundary constraints, including constraining the displacement of the outermost nodes of the front and rear cable nets and the endpoints of the boundary cables of the film reflective surface in the X, Y, and Z directions, where X, Y, and Z are the three coordinate axes of the Cartesian three-dimensional coordinate system; In step 2, the coordinates of the projection points of the midpoint of the thin film reflective surface unit projected onto the electrode surface are calculated in sequence, the distance between the midpoint of the thin film unit and the projection point is calculated, and the electrostatic force is calculated using the flat plate capacitor formula, including: (1) Calculate the midpoint P of the i-th (i=1, 2, 3...M) thin film reflective surface unit i0 The coordinates of the three nodes of the triangular membrane element are x i1 =[x i1 y i1 z i1 ] T 、x i2 =[x i2 y i2 z i2 ] T 、x i3 =[x i3 y i3 z i3 ] T , then the midpoint coordinates are (2) Determine whether the midpoint of the film unit is projected onto the j∈[1, N]th electrode surface unit, and calculate the projection point P of the midpoint onto the electrode surface. ij The coordinates of the three nodes of the j-th electrode surface unit are x j1 =[x j1 y j1 z j1 ] T 、x j2 =[x j2 y j2 z j2 ] T 、x j3 =[x j3 y j3 z j3 ] T , then the midpoint x of the membrane element i0 The coordinates of the projection point on the electrode surface are Where A=(y j3 -y j1 )*(z j3 -z j1 )-(z j2 -z j1 )*(y j3 -y j1 ), B=(x j3 -x j1 )*(z j2 -z j1 )-(x j2 -x j1 )*(z j3 -z j1 ), C=(x j2 -x j1 )*(y j3 -y j1 )-(x j3 -x j1 )*(y j2 -y j1 )、D=-(A*x j1 +B*y j1 +C*z j1 ); (3) Calculate the distance between the midpoint of the membrane unit and the projection point as d ij =||x ij -x i0 ||; (4) Using the flat plate capacitor formula, the electrostatic force on the thin film reflective surface unit and the electrode surface unit is calculated as follows: Among them, ε r is the relative dielectric constant, U j is the electrode voltage; In step three, applying electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis includes: (1) Apply an electrostatic force p in the form of a surface load to the i-th (i=1, 2, 3...M) thin film reflective surface unit and the j-th (j=1, 2, 3...N) electrode surface unit in sequence. ij ; (2) Given the initial pre-tension of the cable unit and the membrane unit, the nonlinear equilibrium equation (K L +K NL )δ=P;where K L is the linear stiffness matrix, K NL is the nonlinear stiffness matrix, δ is the node displacement matrix, and P is the node load matrix; (3) Use the Newton-Raphson iterative method to solve nonlinear equilibrium equations.

2. An electrostatic force application system considering deformation of an electrode surface and a thin film reflective surface for implementing the electrostatic force application method considering deformation of an electrode surface and a thin film reflective surface according to claim 1, characterized in that: The electrostatic force application system considering the deformation of the electrode surface and the thin film reflective surface includes: Finite element model building module, used to build the finite element model of the electrostatically formed thin film reflector antenna and impose boundary constraints; A calculation module is used to sequentially calculate the coordinates of the projection point of the midpoint of the thin film reflective surface unit projected onto the electrode surface, calculate the distance between the midpoint of the thin film unit and the projection point, and calculate the electrostatic force using a flat plate capacitor formula; Finite element structural deformation analysis module, used to apply electrostatic force to the electrode surface and the film reflective surface to perform finite element structural deformation analysis; The deformation accuracy requirement analysis module is used to extract the node displacements of the electrode surface and the thin film reflector surface and analyze whether the deformation accuracy requirements are met. If not, the finite element model is updated and the calculation module is returned; if so, the deformation analysis of the electrostatically formed thin film reflector antenna is completed.

3. A computer device, characterized in that: The computer device includes a memory and a processor, wherein the memory stores a computer program. When the computer program is executed by the processor, the processor performs the steps of the electrostatic force application method considering the deformation of the electrode surface and the thin film reflective surface as claimed in claim 1.

4. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of the electrostatic force application method considering deformation of an electrode surface and a thin film reflective surface as claimed in claim 1.

5. An information data processing terminal, characterized in that: The information data processing terminal is used to implement the electrostatic force application system according to claim 2 that takes into account the deformation of the electrode surface and the thin film reflective surface.

Images