CN114139410A - Electrostatic force applying method and system considering deformation of electrode surface and thin film reflecting surface - Google Patents
Electrostatic force applying method and system considering deformation of electrode surface and thin film reflecting surface Download PDFInfo
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Abstract
The invention belongs to the technical field of radar antenna simulation, and discloses an electrostatic force applying method and system considering deformation of an electrode surface and a thin film reflecting surface, which comprises the following steps: establishing a finite element model of the electrostatically formed film reflecting surface antenna, and applying boundary constraint; sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula; and applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis, and recalculating the electrostatic force according to the node positions of the deformed electrode surface and the deformed film reflecting surface by using the steps to continue the finite element structure deformation analysis of the electrostatic forming film reflecting surface antenna until the requirement of the deformation analysis precision is met. The invention can accurately calculate the electrostatic force when the electrode surface and the film reflecting surface deform, and provides a theoretical basis for high-precision deformation analysis and forming control of the electrostatic forming film reflecting surface antenna.
Description
Technical Field
The invention belongs to the technical field of radar antenna simulation, and particularly relates to an electrostatic force applying method and system considering deformation of an electrode surface and a thin film reflecting surface.
Background
At present, an electrostatic forming film reflecting surface antenna generally comprises a cable film electrode surface and a film reflecting surface, and a capacitor with a certain distance is formed between the cable film electrode surface and the film reflecting surface. When different voltages are applied to the electrode surface and the film reflection surface, electrostatic adsorption force is generated between the electrode surface and the film reflection surface. Because the cable membrane electrode surface and the thin film reflecting surface both belong to flexible structures, the electrode surface and the thin film reflecting surface can deform under the action of electrostatic force, and the deformation of the electrode surface and the thin film reflecting surface can change the distance between the thin film reflecting surface and the electrode surface, so as to change the size of the electrostatic force, thus solving the problem of how to calculate the electrostatic force after the electrode surface and the thin film reflecting surface deform.
However, the influence of the deformation of the electrode surface on the magnitude of the electrostatic force is mostly not considered in the industry, and Surya p. Liu super, millet permanent vibration etc. utilize finite element analysis software ANSYS to establish electrostatic field-film structure deformation field coupling model, and this method can solve the coupling problem between film deformation and the electrostatic field, but the modeling is more complicated, is not suitable for the complicated condition in boundary to do not consider the influence of electrode face deformation to the coupling model. Therefore, a new method of applying an electrostatic force considering the deformation of the electrode surface and the reflective surface of the thin film is required.
Through the above analysis, the problems and defects of the prior art are as follows:
(1) the influence of electrode surface deformation on the magnitude of electrostatic force is not considered in most of the industry.
(2) The existing method does not consider the problem of different position distances caused by different shapes of the thin film reflecting surface and the electrode surface, and also does not consider the influence of the deformation of the electrode surface on the size of the electrostatic force.
(3) In the existing method for solving the problems of film deformation and coupling between electrostatic fields through modeling, the modeling is complex, the method is not suitable for the condition of complex boundary, and the influence of electrode surface deformation on a coupling model is not considered.
The difficulty in solving the above problems and defects is: on one hand, considering the influence of the deformation of the thin film electrode surface on the size of the electrostatic force, an integral model of the electrostatic forming thin film reflecting surface antenna needs to be established, which relates to a complex finite element modeling process; on the other hand, the film electrode surface is laid on the supporting cable net and stretched on the supporting truss through the boundary cable, the boundary condition of the film electrode surface and the supporting truss is complex, and a coupling model is difficult to establish. The electrostatic force is calculated according to the relative position between the thin film reflecting surface unit and the electrode surface unit, so that the influence of the deformation of the thin film reflecting surface and the electrode surface on the electrostatic force is considered at the same time, and the difficulty lies in the problem of how to accurately calculate the electrostatic force and how to update the electrostatic force.
The significance of solving the problems and the defects is as follows: the invention considers the coupling problem between the deformation of the film reflecting surface and the electrode surface and the electrostatic field electrostatic force, and solves the problem that the existing coupling model modeling can not process the complex boundary, thus the realization of the integral deformation analysis of the electrostatic forming film reflecting surface antenna becomes possible. In addition, the electrostatically formed thin film reflecting surface antenna can be subjected to high and low temperature loads during the in-orbit operation, so that the thin film reflecting surface and the electrode surface are greatly deformed, and the method can also be applied to deformation analysis of the electrostatically formed thin film reflecting surface antenna under the large temperature difference temperature load.
Disclosure of Invention
The invention provides an electrostatic force application method and system considering deformation of an electrode surface and a thin film reflecting surface, and particularly relates to an electrostatic force application and electrostatic forming thin film reflecting surface antenna high-precision deformation analysis method considering deformation of the electrode surface and the thin film reflecting surface, aiming at solving the calculation problem of the electrostatic force when the electrode surface and the thin film reflecting surface deform simultaneously.
The present invention is achieved in that an electrostatic force application method taking into account deformations of an electrode surface and a thin film reflection surface, the electrostatic force application method taking into account deformations of the electrode surface and the thin film reflection surface includes:
establishing a finite element model of the electrostatically formed film reflecting surface antenna, and applying boundary constraint; sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula; and applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis, and recalculating the electrostatic force according to the node positions of the deformed electrode surface and the deformed film reflecting surface by using the steps to continue the finite element structure deformation analysis of the electrostatic forming film reflecting surface antenna until the requirement of the deformation analysis precision is met.
Further, the electrostatic force applying method considering the deformation of the electrode surface and the thin film reflecting surface includes the steps of:
establishing a finite element model of the electrostatically formed film reflecting surface antenna, and applying boundary constraint, wherein the step realizes integral finite element modeling of the electrostatically formed film reflecting surface antenna and provides a model foundation for considering deformation of a film reflecting surface and an electrode surface;
calculating coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface in sequence, calculating the distance between the middle points and the projection points of the thin film units, and calculating the electrostatic force by using a flat-plate capacitance formula, so that the electrostatic force is calculated according to the relative positions of the thin film reflecting surface and the electrode surface, and a theoretical basis is provided for high-precision calculation of the electrostatic force;
applying electrostatic force to the electrode surface and the thin film reflecting surface to perform finite element structure deformation analysis, wherein the deformation analysis of the thin film reflecting surface and the electrode surface under the action of the electrostatic force is realized, and a foundation is provided for the subsequent finite element model updating and electrostatic force updating;
step four, extracting node displacement of the electrode surface and the thin film reflecting surface, analyzing whether the node displacement meets the deformation precision requirement, if not, updating the finite element model, and returning to the step two; and if so, completing deformation analysis of the electrostatic forming film reflecting surface antenna, providing the updating criteria of the finite element model of the electrostatic forming film reflecting surface and the updating criteria of the electrostatic force, and ensuring that the deformation analysis of the electrode surface and the film reflecting surface and the calculation of the electrostatic force can meet the precision requirement.
Further, in the step one, the establishing a finite element model of the electrostatically formed film reflector antenna and applying a boundary constraint includes:
(1) establishing an electrode surface supporting structure, namely establishing a cable net structure according to the topological connection relation of the front cable net, the rear cable net and the vertical cable net, and performing grid division on the cable net structure by utilizing cable units;
(2) establishing electrode surfaces, namely establishing electrode surfaces on triangular meshes of the front cable net, and performing mesh division on the electrode surfaces by using triangular film units to establish N triangular film units with the electrode surfaces;
(3) establishing a film reflecting surface, including establishing boundary guy cables and a paraboloid, performing grid division on the paraboloid by utilizing triangular film units, establishing M film reflecting surface triangular film units, and performing grid division on the boundary guy cables by utilizing cable units;
(4) imparting material properties to the cord elements and the film elements; wherein the cable element material properties are set as: the mass density is 1685kg/m3Elastic modulus of 5.01GPa, Poisson's ratio of 0.30, cross-sectional diameter of the cable of 1.1mm, coefficient of thermal expansion of-2X 10-6/° c; the thin film unit material properties are set as: mass density 1432kg/m3Elastic modulus of 1.67GPa, Poisson's ratio of 0.34, thickness of 26.5 μm, and thermal expansion coefficient of 29X 10-6/℃；
(5) And applying boundary constraint, including constraining the displacement of the outermost ring nodes of the front and the back cable nets and the endpoint of the boundary cable of the film reflecting surface in X, T, Z three directions.
Further, in the second step, the calculating coordinates of the projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, the calculating distance between the middle points of the thin film units and the projection points, and the calculating electrostatic force by using a plate capacitance formula includes:
(1) calculating a midpoint P of an i (i-1, 2, 3.. M) th thin film reflecting surface uniti0The coordinates of (a); the coordinates of three nodes of the triangular film unit are x respectivelyi1＝{xi1 yi1 zi1]T、xi2＝[xi2 yi2 zi2]T、xi3＝[xi3 yi3 zi3]Te is the midpoint coordinate
(2) Judging whether the middle point of the film unit projects on the jth Ee [1, N ]]Calculating a projection point P of the midpoint projected onto the electrode surface on each electrode surface unitijThe coordinates of (a); the coordinates of three nodes of the jth electrode surface unit are x respectivelyj1＝[xj1 yj1 zj1]T、xj2＝[xj2 yj2 zj2]T、xj3＝[xj3 yj3 zj3]TThen the film unit midpoint xi0The coordinates of the projection point on the electrode surface are
Wherein A ═ yj3-yj1)*(zj3-zj1)-(zj2-zj1)*(yj3-yj1)、B＝(xj3-xj1)*(zj2-zj1)-(xj2-xj1)*(zj3-zj1)、C＝(xj2-xj1)*(yj3-yj1)-(xj3-xj1)*(yj2-yj1)、D＝-(A*xj1+B*yj1+C*zj1)；
(3) Calculating the distance d between the midpoint of the film unit and the projection pointij＝||xij-xi0||；
(4) The electrostatic force borne by the thin film reflecting surface unit and the electrode surface unit is calculated by using a plate capacitance formula
Wherein epsilonrIs relative dielectric constant, UjIs the electrode voltage.
Further, in step three, applying electrostatic force to the electrode surface and the thin film reflection surface to perform finite element structural deformation analysis, including:
(1) sequentially applying electrostatic force p in the form of surface load on the ith (i is 1, 2, 3.. M) thin film reflecting surface unit and the jth (j is 1, 2, 3.. N) electrode surface unitij；
(2) Given the initial pre-tension of the cord and film elements, a non-linear equilibrium equation (K) is establishedL+KNL) δ ═ P; wherein KLIs a linear stiffness matrix, KNLThe matrix is a nonlinear stiffness matrix, delta is a node displacement matrix, and P is a node load matrix;
(3) and solving the nonlinear equilibrium equation by using a Newton-Raphson iterative method.
Further, in the fourth step, the extracting node displacement of the electrode surface and the film reflecting surface, and analyzing whether the requirement of deformation precision is met or not includes:
(1) sequentially extracting spatial coordinates X of a k (k ═ 1, 2, 3.. NUM) th nodek＝[Xk Yk Zk]TAnd a displacement deltak＝[uk vk wk]T(ii) a Wherein NUM is the total number of nodes, uk、vk、wkX, Y, Z displacement of the node k in three directions;
(2) calculating root mean square error of node displacement
(3) If delta is less than or equal to delta, wherein delta is 0.01 which is the upper limit value of the node displacement error, completing finite element deformation analysis of the electrostatic forming film reflecting surface antenna; otherwise, let Xk＝Xk+δkAnd returning to the step two, and carrying out electrostatic force calculation and electrostatic forming film reflecting surface antenna finite element model deformation analysis again.
Another object of the present invention is to provide an electrostatic force application system considering deformation of an electrode surface and a thin film reflective surface, to which the electrostatic force application method considering deformation of an electrode surface and a thin film reflective surface is applied, the electrostatic force application system considering deformation of an electrode surface and a thin film reflective surface including:
the finite element model building module is used for building a finite element model of the electrostatic forming film reflecting surface antenna and applying boundary constraint;
the calculation module is used for calculating the coordinates of projection points projected from the middle points of the thin film reflecting surface units to the electrode surface in sequence, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula;
the finite element structure deformation analysis module is used for applying electrostatic force to the electrode surface and the film reflecting surface to carry out finite element structure deformation analysis;
the deformation precision requirement analysis module is used for extracting node displacement of the electrode surface and the film reflecting surface, analyzing whether the node displacement meets the deformation precision requirement, if not, updating the finite element model, and returning to the calculation module; if yes, the deformation analysis of the electrostatic forming film reflecting surface antenna is completed.
It is a further object of the invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of:
(1) establishing a finite element model of the electrostatically formed film reflecting surface antenna, and applying boundary constraint;
(2) sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula;
(3) applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis;
(4) extracting node displacement of the electrode surface and the thin film reflecting surface, analyzing whether the node displacement meets the requirement of deformation precision, if not, updating the finite element model, and returning to the step (2); if yes, the deformation analysis of the electrostatic forming film reflecting surface antenna is completed.
It is another object of the present invention to provide a computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
(1) establishing a finite element model of the electrostatically formed film reflecting surface antenna, and applying boundary constraint;
(2) sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula;
(3) applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis;
(4) extracting node displacement of the electrode surface and the thin film reflecting surface, analyzing whether the node displacement meets the requirement of deformation precision, if not, updating the finite element model, and returning to the step (2); if yes, the deformation analysis of the electrostatic forming film reflecting surface antenna is completed.
Another object of the present invention is to provide an information data processing terminal for realizing the electrostatic force applying system in consideration of the deformation of the electrode surface and the thin film reflecting surface.
By combining all the technical schemes, the invention has the advantages and positive effects that: according to the electrostatic force applying method considering the deformation of the electrode surface and the thin film reflecting surface, the size of the electrostatic force is calculated through the distance between the thin film reflecting surface unit and the electrode surface unit, the electrostatic force is respectively applied to the thin film reflecting surface and the electrode surface to carry out finite element structure deformation analysis, and the influence of the deformation of the electrode surface on the size of the electrostatic force is considered while the calculation accuracy of the electrostatic force is ensured. The invention is still applicable to other types of electrostatically formed products involving deformation of the electrode and film surfaces, such as electrostatically formed film mirrors and electrostatically formed light shields. In the technical field of satellite-borne electrostatic forming film reflecting surface antennas, no electrostatic field calculation and application method considering deformation of an electrode surface and a film reflecting surface simultaneously exists at present, and most of the method is to assume that the deformation of the electrode surface is smaller than that of the film reflecting surface, so that the influence can be ignored. In fact, the satellite-borne antenna faces a complex load environment with constantly changing high and low temperatures in the in-orbit operation process, the electrode surface and the film reflecting surface can deform greatly under the action of large temperature difference, and the method provided by the invention also provides a basis for high-precision deformation analysis of the satellite-borne electrostatically-formed film reflecting surface antenna in the in-orbit operation process.
The electrostatic force applying method considering the deformation of the electrode surface and the thin film reflecting surface can accurately calculate the size of the electrostatic force when the electrode surface and the thin film reflecting surface deform, considers the influence of the deformation of the electrode surface on the electrostatic force, and provides a theoretical basis for high-precision deformation analysis and forming control of the electrostatic forming thin film reflecting surface antenna. The method is applied to the field of radar antenna simulation, and can be used for carrying out high-precision finite element structure deformation analysis on the electrostatically formed film reflecting surface antenna.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of an electrostatic force application method considering deformation of an electrode surface and a thin film reflective surface according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of an electrostatic force applying method considering the deformation of the electrode surface and the thin film reflecting surface according to an embodiment of the present invention.
FIG. 3 is a block diagram of an electrostatic force application system in accordance with an embodiment of the present invention, which considers the deformation of the electrode surface and the reflective surface of the thin film;
in the figure: 1. a finite element model building module; 2. a calculation module; 3. a finite element structure deformation analysis module; 4. and a deformation precision requirement analysis module.
FIG. 4 is a flow chart of applying boundary constraints for establishing a finite element model of an electrostatically formed thin film reflector antenna according to an embodiment of the present invention.
Fig. 5 is a flowchart for calculating the distance between the midpoint and the projected point of the thin film unit and the electrostatic force according to the embodiment of the present invention.
FIG. 6 is a schematic diagram of a spatial relationship between a midpoint and a projected point of a film according to an embodiment of the present invention.
Fig. 7 is a flow chart for electrostatic force application and nonlinear equilibrium equation solution provided by an embodiment of the present invention.
Fig. 8 is a flowchart for extracting node displacement of the electrode surface and the thin film reflection surface and analyzing whether the node displacement meets the requirement of deformation accuracy according to the embodiment of the present invention.
FIG. 9 is a schematic diagram of an integral finite element model of an electrostatic formed film antenna according to an embodiment of the present invention.
Fig. 10 is a schematic diagram of the deformation of the electrode surface and the reflective surface of the thin film without considering the deformation of the electrode surface according to the embodiment of the present invention.
Fig. 11 is a schematic diagram of deformation of the electrode surface and the reflective surface of the thin film in consideration of deformation of the electrode surface according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In view of the problems of the prior art, the present invention provides an electrostatic force application method considering the deformation of an electrode surface and a thin film reflecting surface, and the present invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, the electrostatic force application method considering the deformation of the electrode surface and the thin film reflective surface according to the embodiment of the present invention includes the following steps:
s101, establishing a finite element model of the electrostatic forming film reflecting surface antenna, and applying boundary constraint;
s102, sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula;
s103, applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis;
s104, extracting node displacement of the electrode surface and the thin film reflecting surface, analyzing whether the node displacement meets the requirement of deformation precision, if not, updating the finite element model, and returning to S102; if yes, the deformation analysis of the electrostatic forming film reflecting surface antenna is completed.
Fig. 2 shows a schematic diagram of an electrostatic force applying method considering the deformation of the electrode surface and the thin film reflective surface according to an embodiment of the present invention.
As shown in fig. 3, an electrostatic force application system considering deformation of an electrode surface and a thin film reflective surface according to an embodiment of the present invention includes:
the finite element model building module 1 is used for building a finite element model of the electrostatic forming film reflecting surface antenna and applying boundary constraint;
the calculation module 2 is used for calculating the projection point coordinates of the middle point of the thin film reflecting surface unit projected onto the electrode surface in sequence, calculating the distance between the middle point of the thin film unit and the projection point, and calculating the electrostatic force by using a flat capacitor formula;
the finite element structure deformation analysis module 3 is used for applying electrostatic force to the electrode surface and the film reflecting surface to carry out finite element structure deformation analysis;
the deformation precision requirement analysis module 4 is used for extracting node displacement of the electrode surface and the film reflecting surface, analyzing whether the node displacement meets the deformation precision requirement, if not, updating the finite element model, and returning to the calculation module; if yes, the deformation analysis of the electrostatic forming film reflecting surface antenna is completed.
The technical solution of the present invention is further described below with reference to specific examples.
The electrostatic force applying method considering the deformation of the electrode surface and the thin film reflecting surface provided by the embodiment of the invention comprises the following steps:
1) establishing a finite element model of the electrostatically formed film reflecting surface antenna, and applying boundary constraint;
2) sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula;
3) applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis;
4) extracting node displacement of the electrode surface and the film reflecting surface, and analyzing whether the requirement of deformation precision is met: if not, updating the finite element model, and returning to the step 2); if yes, the antenna deformation analysis of the electrostatic forming film reflecting surface is completed.
Fig. 2 is a general flowchart of an electrostatic force application method considering the deformation of the electrode surface and the thin film reflecting surface according to an embodiment of the present invention.
As shown in fig. 4, the step 1) described above specifically involves the following steps:
(1) establishing an electrode surface supporting structure, namely establishing a cable net structure according to the topological connection relation of the front cable net, the rear cable net and the vertical cable net, and performing grid division on the cable net structure by utilizing cable units;
(2) establishing electrode surfaces, namely establishing electrode surfaces on triangular meshes of the front cable net, and performing mesh division on the electrode surfaces by using triangular film units to establish N triangular film units with the electrode surfaces;
(3) establishing a film reflecting surface, including establishing boundary guy cables and a paraboloid, performing grid division on the paraboloid by utilizing triangular film units, establishing M film reflecting surface triangular film units, and performing grid division on the boundary guy cables by utilizing cable units;
(4) and (c) imparting material properties to the cord elements and the film elements, wherein the cord element material properties are set to: the mass density is 1685kg/m3Elastic modulus of 5.01GPa, Poisson's ratio of 0.30, cross-sectional diameter of the cable of 1.1mm, coefficient of thermal expansion of-2X 10-6/° c, the film unit material properties are set as: mass density 1432kg/m3Modulus of elasticity 1.67GPa, Poisson's ratio 0.34, thickness 26.5 μm, coefficient of thermal expansion 29X 10-6/℃；
(5) And applying boundary constraint, including constraining the displacement of the outermost ring nodes of the front and the back cable nets and the endpoint of the boundary cable of the film reflecting surface in X, Y, Z three directions.
As shown in fig. 5, the step 2) above specifically involves the following steps:
(1) calculating a midpoint P of an i (i-1, 2, 3.. M) th thin film reflecting surface uniti0Specifically, the coordinates of three nodes of the triangular film unit are xi1＝[xi1 yi1 zi1]T、xi2＝[xi2 yi2 zi2]T、xi3＝[xi3 yi3 zi3]TThen the midpoint coordinate is
(2) Judging whether the middle point of the film unit projects on the jth Ee [1, N ]]On the electrode surface unit, calculating the projection point P of the midpoint projected onto the electrode surfaceijSpecifically, the coordinates of three nodes of the jth electrode surface unit are x respectivelyj1＝[xj1 yj1 zj1]T、xj2＝[xj2 yj2 zj2]T、xj3＝[xj3 yj3 zj3]TThen the film unit midpoint xi0The coordinates of the projection point on the electrode surface are
Wherein A ═ yj3-yj1)(zj3-zj1)-(zj2-zj1)*(yj3-yj1)、B＝(xj3-xjj)*(zj2-zj1)-(xj2-xj1)*(zj3-zj1)、C＝(xj2-xj1)*(yj3-yj1)-(xj3-xj1)*(yj2-yj1)、D＝-(A*xj1+B*yj1+C*zj1)；
(3) Calculating the distance d between the midpoint of the film unit and the projection pointij＝||xij-xi0The spatial position relationship between the middle point of the film reflecting surface and the projection point coordinate is shown in figure 6;
(4) the electrostatic force borne by the thin film reflecting surface unit and the electrode surface unit is calculated by using a plate capacitance formula
Wherein epsilonrIs relative dielectric constant, UjIs the electrode voltage.
As shown in fig. 7, the step 3) above specifically involves the following steps:
(1) sequentially applying electrostatic force p in the form of surface load on the ith (i is 1, 2, 3.. M) thin film reflecting surface unit and the jth (j is 1, 2, 3.. N) electrode surface unitij；
(2) Given the initial pre-tension of the cord and film elements, a non-linear equilibrium equation (K) is establishedL+KNL) δ ═ P, where KLIs a linear stiffness matrix, KNLThe matrix is a nonlinear stiffness matrix, delta is a node displacement matrix, and P is a node load matrix;
(3) and solving the nonlinear equilibrium equation by using a Newton-Raphson iterative method.
As shown in fig. 8, the step 4) above specifically involves the following steps:
(1) sequentially extracting spatial coordinates X of a k (k ═ 1, 2, 3.. NUM) th nodek＝[Xk Yk Zk]TAnd a displacement deltak＝[uk vk wk]TWherein NUM is the total number of nodes, uk、vk、wkX, Y, Z displacement of the node k in three directions;
(2) calculating root mean square error of node displacement
(3) If delta is less than or equal to delta,if delta is 0.01, the upper limit value of the node displacement error is obtained, and finite element deformation analysis of the electrostatic forming film reflecting surface antenna is completed; otherwise, let Xk＝Xk+δkAnd returning to the step 2) to calculate the electrostatic force and analyze the deformation of the finite element model of the electrostatic forming film reflecting surface antenna again.
The application effect of the present invention will be described in detail with reference to simulation experiments.
Simulation conditions are as follows:
taking an electrostatic forming film reflecting surface antenna with the aperture of 5M as an example, an established integral finite element model is shown in fig. 9, wherein the finite element model comprises N204 electrode surface triangular film units and M864 film reflecting surface triangular film units, the electrostatic force applying method is used for load application and finite element deformation analysis of the film reflecting surface and the electrode surface, and finally, the deformation conditions of the film reflecting surface and the film electrode surface before and after the electrode surface deformation are considered, as shown in fig. 10 and fig. 11, the film reflecting surface and the film electrode surface are obviously deformed under the action of electrostatic force, and the deformation cannot be ignored for the deformation analysis of the high-precision electrostatic forming film reflecting surface antenna. The simulation experiment is only carried out on the electrostatic forming film reflecting surface antenna with the characteristic caliber, and the invention is still applicable to other systems which are controlled by electrostatic force, such as electrostatic forming film reflecting mirrors, updating calculation of electrostatic force in a micro-electro-mechanical system and the like.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When used in whole or in part, can be implemented in a computer program product that includes one or more computer instructions. When loaded or executed on a computer, cause the flow or functions according to embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL), or wireless (e.g., infrared, wireless, microwave, etc.)). 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, a data center, etc., that includes one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid state disk (ssd)), among others.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. An electrostatic force application method in consideration of deformation of an electrode surface and a thin film reflecting surface, characterized by comprising: establishing a finite element model of the electrostatically formed film reflecting surface antenna, and applying boundary constraint; sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula; and applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis, and recalculating the electrostatic force according to the node positions of the deformed electrode surface and the deformed film reflecting surface by using the steps to continue the finite element structure deformation analysis of the electrostatic forming film reflecting surface antenna until the requirement of the deformation analysis precision is met.
2. The electrostatic force application method taking into account the deformation of the electrode surface and the thin film reflecting surface as set forth in claim 1, wherein the electrostatic force application method taking into account the deformation of the electrode surface and the thin film reflecting surface comprises the steps of:
establishing a finite element model of an electrostatic forming film reflecting surface antenna, and applying boundary constraint;
sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film reflecting surface units and the projection points, and calculating the electrostatic force by using a flat capacitor formula;
applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis;
step four, extracting node displacement of the electrode surface and the thin film reflecting surface, analyzing whether the node displacement meets the deformation precision requirement, if not, updating the finite element model, and returning to the step two; if yes, the deformation analysis of the electrostatic forming film reflecting surface antenna is completed.
3. The method for applying an electrostatic force considering the deformation of the electrode surface and the thin film reflecting surface according to claim 2, wherein in the step one, the establishing of the finite element model of the electrostatically formed thin film reflecting surface antenna and the applying of the boundary constraint comprise:
(1) establishing an electrode surface supporting structure, namely establishing a cable net structure according to the topological connection relation of the front cable net, the rear cable net and the vertical cable net, and performing grid division on the cable net structure by utilizing cable units;
(2) establishing an electrode surface, namely establishing the electrode surface on a front cable mesh triangular grid, and performing grid division on the electrode surface by utilizing triangular film units to establish N electrode surface triangular film units, wherein N is the total number of the electrode surface divided units;
(3) establishing a film reflecting surface, including establishing boundary guy cables and a paraboloid, performing grid division on the paraboloid by utilizing triangular film units, establishing M triangular film units of the film reflecting surface, wherein M is the total number of the units divided by the film reflecting surface, and performing grid division on the boundary guy cables by utilizing cable units;
(4) imparting material properties to the cord elements and the film elements; wherein the cable element material properties are set as: the mass density is 1685kg/m3Elastic modulus 5.01GPa, Poisson's ratio0.30, a cross-sectional diameter of the cord of 1.1mm, a coefficient of thermal expansion of-2X 10-6/° c; the thin film unit material properties are set as: mass density 1432kg/m3Elastic modulus of 1.67GPa, Poisson's ratio of 0.34, thickness of 26.5 μm, and thermal expansion coefficient of 29X 10-6/℃；
(5) And applying boundary constraint, namely constraining the displacement of the outermost ring nodes of the front and rear cable nets and the displacement of the boundary cable endpoints of the film reflecting surface in X, Y, Z three directions, wherein X, Y, Z is three coordinate axes of a Cartesian three-dimensional coordinate system.
4. The method for applying an electrostatic force considering the deformation of the electrode surface and the thin film reflecting surface as claimed in claim 2, wherein in the second step, the coordinates of the projected points of the middle points of the thin film reflecting surface units projected onto the electrode surface are sequentially calculated, the distance between the middle points of the thin film units and the projected points is calculated, and the electrostatic force is calculated by using a plate capacitance formula, comprising:
(1) calculating a midpoint P of an i (i-1, 2, 3.. M) th thin film reflecting surface uniti0The coordinates of (a); the coordinates of three nodes of the triangular film unit are x respectivelyi1＝[xi1 yi1 zi1]T、xi2＝[xi2 yi2 zi2]T、xi3＝[xi3 yi3 zi3]TThen the midpoint coordinate is
(2) Judging whether the middle point of the film unit projects on the jth Ee [1, N ]]Calculating a projection point P of the midpoint projected onto the electrode surface on each electrode surface unitijThe coordinates of (a); the coordinates of three nodes of the jth electrode surface unit are x respectivelyj1＝[xj1 yj1 zj1]T、xj2＝[xj2 yj2 zj2]T、xj3＝[xj3 yj3 zj3]TThen the film unit midpoint xi0The coordinates of the projection point on the electrode surface are
Wherein A ═ yj3-yj1)*(zj3-zj1)-(zj2-zj1)*(yj3-yj1)、B＝(xj3-xj1)*(zj2-zj1)-(xj2-xj1)*(zj3-zj1)、C＝(xj2-xj1)*(yj3-yj1)-(xj3-xj1)*(yj2-yj1)、D＝-(A*xj1+B*yj1+C*zj1)；
(3) Calculating the distance d between the midpoint of the film unit and the projection pointij＝||xij-xi0||；
(4) The electrostatic force borne by the thin film reflecting surface unit and the electrode surface unit is calculated by using a plate capacitance formula
Wherein epsilonrIs relative dielectric constant, UjIs the electrode voltage.
5. The electrostatic force application method considering the deformation of the electrode surface and the thin film reflective surface as claimed in claim 2, wherein in step three, the applying of the electrostatic force to the electrode surface and the thin film reflective surface to perform finite element structure deformation analysis comprises:
(1) sequentially applying electrostatic force p in the form of surface load on the ith (i is 1, 2, 3.. M) thin film reflecting surface unit and the jth (j is 1, 2, 3.. N) electrode surface unitij；
(2) Given the initial pre-tension of the cord and film elements, a non-linear equilibrium equation (K) is establishedL+KNL) δ ═ P; wherein KLIs a linear stiffness matrix, KNLThe matrix is a nonlinear stiffness matrix, delta is a node displacement matrix, and P is a node load matrix;
(3) and solving the nonlinear equilibrium equation by using a Newton-Raphson iterative method.
6. The method for applying electrostatic force considering the deformation of the electrode surface and the thin film reflecting surface according to claim 2, wherein the step four of extracting the node displacement of the electrode surface and the thin film reflecting surface and analyzing whether the deformation accuracy requirement is satisfied includes:
(1) sequentially extracting spatial coordinates X of a k (k ═ 1, 2, 3.. NUM) th nodek＝[Xk Yk Zk]TAnd a displacement deltak＝[ukvk wk]T(ii) a Wherein NUM is the total number of nodes, uk、vk、wkX, Y, Z displacement of the node k in three directions;
(2) calculating root mean square error of node displacement
(3) If delta is less than or equal to delta, wherein delta is 0.01 which is the upper limit value of the node displacement error, completing finite element deformation analysis of the electrostatic forming film reflecting surface antenna; otherwise, let Xk＝Xk+δkAnd returning to the step two, and carrying out electrostatic force calculation and electrostatic forming film reflecting surface antenna finite element model deformation analysis again.
7. An electrostatic force application system considering deformation of an electrode surface and a thin film reflecting surface, which implements the electrostatic force application method considering deformation of an electrode surface and a thin film reflecting surface according to any one of claims 1 to 6, wherein the electrostatic force application system considering deformation of an electrode surface and a thin film reflecting surface comprises:
the finite element model building module is used for building a finite element model of the electrostatic forming film reflecting surface antenna and applying boundary constraint;
the calculation module is used for calculating the coordinates of projection points projected from the middle points of the thin film reflecting surface units to the electrode surface in sequence, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula;
the finite element structure deformation analysis module is used for applying electrostatic force to the electrode surface and the film reflecting surface to carry out finite element structure deformation analysis;
the deformation precision requirement analysis module is used for extracting node displacement of the electrode surface and the film reflecting surface, analyzing whether the node displacement meets the deformation precision requirement, if not, updating the finite element model, and returning to the calculation module; if yes, the deformation analysis of the electrostatic forming film reflecting surface antenna is completed.
8. A computer device, characterized in that the computer device comprises a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of:
(1) establishing a finite element model of the electrostatically formed film reflecting surface antenna, and applying boundary constraint;
(2) sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula;
(3) applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis;
(4) extracting node displacement of the electrode surface and the thin film reflecting surface, analyzing whether the node displacement meets the requirement of deformation precision, if not, updating the finite element model, and returning to the step (2); if yes, the deformation analysis of the electrostatic forming film reflecting surface antenna is completed.
9. A computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
(1) establishing a finite element model of the electrostatically formed film reflecting surface antenna, and applying boundary constraint;
(2) sequentially calculating the coordinates of projection points of the middle points of the thin film reflecting surface units projected onto the electrode surface, calculating the distance between the middle points of the thin film units and the projection points, and calculating the electrostatic force by using a flat capacitor formula;
(3) applying electrostatic force to the electrode surface and the film reflecting surface to perform finite element structure deformation analysis;
(4) extracting node displacement of the electrode surface and the thin film reflecting surface, analyzing whether the node displacement meets the requirement of deformation precision, if not, updating the finite element model, and returning to the step (2); if yes, the deformation analysis of the electrostatic forming film reflecting surface antenna is completed.
10. An information data processing terminal characterized by being used to realize the electrostatic force application system taking into account the deformation of the electrode face and the thin film reflecting face as set forth in claim 7.
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