CN104123421B - A kind of Electrostatic deformation film reflector face form Design method based on machine field coupling - Google Patents
A kind of Electrostatic deformation film reflector face form Design method based on machine field coupling Download PDFInfo
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Abstract
The invention belongs to Radar Antenna System field, specifically a kind of Electrostatic deformation film reflector face form Design method based on machine field coupling, the stress uniformity and precision of film are placed in degree of equal importance by the present invention, the model based on the displacement field coupling of electrostatic field membrane structure is set up, solves optimum control voltage by optimisation strategy to realize that the shape generalization in Electrostatic deformation film reflector face is designed and shaping is controlled.It can not only take into account the performance requirement of film surface accuracy and stress uniformity, while compensate for the leakage that conventional method ignores structure and Electrostatic Field Coupling problem.
Description
Technical field
The invention belongs to Radar Antenna System field, specifically a kind of Electrostatic deformation film reflector based on machine field coupling
Face form Design method, it can be used for carrying out shape generalization design to Electrostatic deformation film reflector face, it may also be used for electrode is become
Influence of the factors such as shape, Different electrodes distribution form to film reflector face form carries out quantitative refinement analysis and evaluated, Yi Jijing
The shaping control of electrical forming film reflector face ground environment experiment.
Background technology
Electrostatic deformation film reflector face deployable antenna is by being distributed shape between high-field electrode and ground connection metal-coated films
Into electrostatic field, a kind of Active Reflector of film surface shape is controlled by electrostatic force.It is in surface density, expanding performance and in-orbit
In terms of face shape under thermal environment is kept, with prominent advantage, therefore the height of multiple international aerospace research structures is received
Pay close attention to and widely studied.2004, SRS.technologys companies of the U.S. and Northrop Grumman companies were carried out first
Action oriented research, and made bore 5m principle prototype.Antenna general structure, by astromesh structures, film support ring,
Lay the online high voltage control electrode of astromesh structure provinculums, ground connection film and multichannel electric power system composition.Electrostatic deformation
One of key technology of film reflector face deployable antenna design, is the form Design of film.Film morphology design is with shape face
Precision and film surface stress uniformity are target, and its design process includes initial configuration design and shaping voltage determines two aspects.
Initial configuration on film has two kinds of settings：One is that, using initial plane film as research object, two be with initial
Curved surface is research object.It is plane for primary face shape, it is possible to use " W " deviation from spherical form is effectively corrected in annular concentric distributed force,
Improve film shaped precision.But electrostatic force needed for oriented film is deformed into smaller focal length since the plane is very big, and due to first
The limitation of beginning configuration causes two targets of film surface stress uniformity and film surface accuracy to take into account.Therefore, initial configuration is flat
Face configuration, although analysis method is relatively simple, but shortcoming is also very prominent.SergeiA D point out that initial configuration can be parabola
Or sphere, can also be by even distributed force effect with unstressed curved surface, primary face shape being corrected using the method for inverse iteration, and tie
Close with distribution electrostatic force rectifying plane shape to improve the thought of film surface figure accuracy.But inverse iteration method is for the boundary portion of film
Divide and be often difficult to take into account, this influences whether the configuration of film, therefore it also has certain limitation.
Determination on shaping voltage, traditionally by high voltage control electrode fabrication into the shape parallel with film most end form face
Formula, the approximate transform of electrostatic field force and electrostatic pressure is realized by capacity plate antenna formula.However, firstly for preferable parallel song
Face, the relation between electrostatic field force and voltage not fully obeys capacity plate antenna formula, and curvature of curved surface is closely related；Second,
For engineering reality, placing can not keep being substantially parallel between the surface of high-field electrode and the profile surface of film；3rd,
Film reflector face is from process of the initial setting-out shape face by electrostatic force stretch forming to design curved surface, really film morphology-quiet
Electric Field Distribution replaces change procedure, and directly uses capacity plate antenna formula approximate transform electrostatic field force and voltage, often ignores this
One actual change process.So, traditionally directly utilize side of the capacity plate antenna formula to electrostatic force and control voltage approximate transform
There is significant limitation in method.
The content of the invention
The purpose of the present invention is only to focus on film surface accuracy in being designed for existing Electrostatic deformation film reflector face, neglect
Coupled relation slightly between electrostatic field and membrane structure displacement field, causes film shaped precision relatively low, film surface stress lack of homogeneity
Problem, it is proposed that a kind of Electrostatic deformation film reflector face form Design method based on machine field coupling, to realize Electrostatic deformation
The shape generalization design and accurately shaping control in film reflector face.
To achieve the above object, a kind of Electrostatic deformation film reflector face based on machine field coupling of technical scheme
Form Design method, it is characterized in that：At least comprise the following steps：
Step 101：According to the structural parameters in Electrostatic deformation film reflector face and the performance requirement of reflecting surface, high pressure is determined
The original geometric form and arrangement of coordination electrode；
Step 102：According to Electrostatic deformation film reflector face reflecting surface bore DaWith focal length fa, set up membrane structure displacement field
Analysis model, and load edge-restraint condition；
Step 103：Structural finite element model to film reflector face applies uniform prestressing force σd；
Step 104：Using the geometry of film reflector face and high voltage control electrode as the border of electrostatic field, Electrostatic deformation is set up
The electrostatic field analysis model of film reflector surface antenna；
Step 105：Electrostatic field analysis model Loading Control voltage is given, wherein film reflector face loads ground voltage, to height
Coordination electrode is pressed to press electrode lay-out mode Loading Control voltageWherein subscript 1 ..., n represents electrode channel
Number；
Step 106：The membrane structure analysis model and step 103 set up according to step 102 set up electrostatic field analysis model,
Set up electrostatic field-displacement structure field model of coupling of Electrostatic deformation film reflector surface antenna；
Step 107：Electrostatic field-displacement structure field model of coupling is solved, the performance parameter of antenna structure is calculated：It is thin
The root-mean-square error δ of the surface accuracy of film reflecting surfacermsWith the minimax stress ratio of filmWherein σ1And σ2Respectively
For first, second principal stress of film；
Step 108：Optimisation strategy is used to electrostatic field-displacement structure model of coupling, by high voltage control voltageAs design variable, analysis is optimized, when the performance parameter of antenna structure：Surface accuracy root mean square is missed
Poor δrmsWith the minimax stress ratio of filmWhen reaching design requirement, stop optimization analysis；Otherwise return to step
107；
Described step 106, comprises the following steps：
Step 401：Electrostatic field analysis model is solved, and preserves electrostatic energy resultMake k=1；
Step 402：By the solving result electrostatic force { F of electrostatic field analysis modele}kIt is loaded directly into membrane structure displacement field
On FEM model；
Step 403：Carry out displacement structure to solve, calculate membrane displacement { δ }k, and storage configuration deformation energy, it is designated as
Step 404：With displacement structure solving result { δ }kThe border of electrostatic field is updated, grid is repartitioned, gives birth to again
Into electrostatic field analysis model；
Step 405：Electrostatic field analysis is carried out, and preserves electrostatic energy result
Step 406：By the solving result electrostatic force { F of electrostatic field analysis modele}k+1Load on having for membrane structure analysis
Limit on meta-model；
Step 407：Carry out displacement structure and solve { δ }k+1, and storage configuration deformation energy, it is designated as
Step 408：Compare the result of electrostatic field twice and membrane structure displacement field analysis model, whenAndWhen, stop analysis, and the performance parameter of output film reflecting surface：Surface accuracy δrmsWith film it is maximum most
Small stress ratioOtherwise, make k=k+1 and return to 404 and proceed iterative.
Described step 107, comprises the following steps：
Step 501：Determine design variable：By high voltage control voltageIt is used as design variable, wherein n tables
Show voltage channel number；
Step 502：Determine object function：By the surface accuracy of filmAs object function, its
Middle m represents the node total number of film reflector face structural finite element model, δiFor the position of i-th of node of structural finite element model
Move；For the Admissible displacement value of i-th of node；
Step 503：Determine constraints.Need the constraints met as follows：
To avoid overtension from bringing discharge breakdown problem, maximum controlling voltageIt is no more than
Critical voltage
Electrostatic field and displacement structure field analysis obey two model of coupling：
Wherein：The stiffness matrix [Κ (δ)] of membrane structure can be further written as：[Κ (δ)]=[ΚL+Κ(σd+Δ
σ)], [ΚL] be membrane structure finite element analysis linear stiffness matrix, [Κ (σd+ Δ σ)] it is nonlinear stiffness matrix, Δ σ is
The stress variation of membrane structure caused by malformation；Coefficient matrix [the Κ of electrostatic field finite element equationΕ(δ)] and film
Displacement { δ } is related；For the electrostatic field force suffered by film, it is related to the displacement of film to control voltage；Film
On i-th of node suffered by electrostatic force beWherein E represents electric-field intensity, NsRepresent
The sum of the construction unit related to node；AjRepresent the area of j-th of electrostatic structure unit；[BL] represent membrane structure unit
Geometric matrix, FiFor the panel load for the electrostatic face power formation being subject on unit i；{σM(E) electrostatic face power } is represented, can be by
Maxwell stress tensor equations are tried to achieve；
Step 504 sets up Optimized model：
Step 505：Iterative Optimized model, gives initial high pressure control voltage, into electrostatic field structure displacement field
Coupling model is solved, and calculates film performance parameter：Surface accuracy δrmsWith the minimax stress ratio of filmSatisfaction is set
Meter stops iteration when requiring；Otherwise, adjustment high voltage control voltage proceeds iteration.
Compared with prior art, its advantage is the present invention：The stress uniformity and precision of film are placed in of equal importance
Degree, sets up the model based on the displacement field coupling of electrostatic field-membrane structure, by optimisation strategy solve optimum control voltage come
Realize the shape generalization design and shaping control in Electrostatic deformation film reflector face.It can not only take into account film surface accuracy and should
The performance requirement of power uniformity, while compensate for the leakage that conventional method ignores structure and Electrostatic Field Coupling problem.
Brief description of the drawings
Fig. 1 Electrostatic deformation film reflectors face form Design overview flow chart；
Fig. 2 high-field electrodes geometry and layout type implementation process figure；
Fig. 3 Electrostatic deformation film reflectors face displacement structure field analysis model realization flow chart；
Fig. 4 electrostatic fields-displacement structure coupling model sets up implementation process figure；
The Optimized Iterative flow chart of Fig. 5 Electrostatic deformation film reflectors face form Design；
The schematic diagram of Fig. 6 electrode lay-outs mode 1；
The schematic diagram of Fig. 7 electrode lay-outs mode 2.
Embodiment
As shown in figure 1, a kind of Electrostatic deformation film reflector face form Design method based on machine field coupling, its feature
It is：At least comprise the following steps：
Step 101：According to the structural parameters in Electrostatic deformation film reflector face and the performance requirement of reflecting surface, high pressure is determined
The original geometric form and arrangement of coordination electrode；
Step 102：According to Electrostatic deformation film reflector face reflecting surface bore DaWith focal length fa, set up membrane structure displacement field
Analysis model, and load edge-restraint condition；
Step 103：Structural finite element model to film reflector face applies uniform prestressing force σd；
Step 104：Using the geometry of film reflector face and high voltage control electrode as the border of electrostatic field, Electrostatic deformation is set up
The electrostatic field analysis model of film reflector surface antenna；
Step 105：Electrostatic field analysis model Loading Control voltage is given, wherein film reflector face loads ground voltage, to height
Coordination electrode is pressed to press electrode lay-out mode Loading Control voltageWherein subscript 1 ..., n represents electrode channel
Number；
Step 106：The membrane structure analysis model and step 103 set up according to step 102 set up electrostatic field analysis model,
Set up electrostatic field-displacement structure field model of coupling of Electrostatic deformation film reflector surface antenna；
Step 107：Electrostatic field-displacement structure field model of coupling is solved, the performance parameter of antenna structure is calculated：It is thin
The root-mean-square error δ of the surface accuracy of film reflecting surfacermsWith the minimax stress ratio of filmWherein σ1And σ2Respectively
For first, second principal stress of film；
Step 108：Optimisation strategy is used to electrostatic field-displacement structure model of coupling, by high voltage control voltageAs design variable, analysis is optimized, when the performance parameter of antenna structure：Surface accuracy root mean square is missed
Poor δrmsWith the minimax stress ratio of filmWhen reaching design requirement, stop optimization analysis；Otherwise return to step
107。
As shown in Fig. 2 described step 101, and in particular to following steps：
Step 201：High-field electrode is installed on astromesh structure provinculum nets, according to the reflecting surface in film reflector face
Bore DaWith focal length fa, it may be determined that its basic geometric parameters：The bore D in electrode supporting facefWith focal length Lf；
Step 202：The arrangement form of astromesh structure provinculum nets determines the fundamental form of the arrangement of high voltage control electrode
Formula, its conventional arrangement form mainly has three-way grid, two kinds of forms of quasi- geodesic curve, in order to increase the effective aperture in film reflector face
And enhancing preferentially chooses accurate geodesic grid distribution form to the control ability of thin film boundary；
Step 203：According to Agrawal formulaDetermine the segments n of provinculum net.Wherein,
δrmsfThe root-mean-square value of provinculum net admissible error is represented, film die opening d 1/10th is can use.LfRepresent astromesh provinculum rete cords
The maximum length of section.Film die opening d represents the minimum range between film and high-field electrode, usually more than 10mm；
Step 204：Each triangular mesh one high-field electrode of correspondence of astromesh structure provinculum net provinculum nets,
Each triangular-shaped electrodes may be connected to a supplying channels in theory.But in view of reduction Electrostatic deformation film reflector face
The requirement of antenna system complexity, on the premise of day system control requirement is met, can press adjacent some triangular-shaped electrodes
Ring-type or bulk are connected to same supplying channels.
As shown in figure 3, described step 102, and in particular to following steps：
Step 301：According to film reflector face bore DaWith focal length LaSet up the geometrical model in film reflector face；
Step 302：According to Agrawal formulaDetermine plane triangle film unit
Size of mesh opening.Wherein LaThe maximum admissible dimension of triangular mesh, δrmsmFor the root mean square of the errors of principles of Plane surface approximation curved surface
Value, no more than the 1/10 of film reflector face precision prescribed；
As shown in figure 4, described step 106, comprises the following steps：
Step 401：Electrostatic field analysis model is solved, and preserves electrostatic energy resultMake k=1；
Step 402：By the solving result electrostatic force { F of electrostatic field analysis modele}kIt is loaded directly into membrane structure displacement field
FEM model on；
Step 403：Carry out displacement structure to solve, calculate membrane displacement { δ }k, and storage configuration deformation energy, it is designated as
Step 404：With displacement structure solving result { δ }kThe border of electrostatic field is updated, grid is repartitioned, gives birth to again
Into electrostatic field analysis model；
Step 405：Electrostatic field analysis is carried out, and preserves electrostatic energy result
Step 406：By the solving result electrostatic force { F of electrostatic field analysis modele}k+1Load on having for membrane structure analysis
Limit on meta-model；
Step 407：Carry out displacement structure and solve { δ }k+1, and storage configuration deformation energy, it is designated as
Step 408：Compare the result of electrostatic field twice and membrane structure displacement field analysis model, whenAndWhen, stop analysis, and the performance parameter of output film reflecting surface：Surface accuracy δrmsWith the minimax of film
Stress ratioOtherwise, make k=k+1 and return to 404 and proceed iterative.
As shown in figure 5, described step 107, comprises the following steps：
Step 501：Determine design variable：By high voltage control voltageIt is used as design variable, wherein n tables
Show voltage channel number；
Step 502：Determine object function：By the surface accuracy of filmAs object function, its
Middle m represents the node total number of film reflector face structural finite element model, δiFor the position of i-th of node of structural finite element model
Move；For the Admissible displacement value of i-th of node；
Step 503：Determine constraints.Need the constraints met as follows：
1) it is to avoid overtension from bringing discharge breakdown problem, maximum controlling voltageNo more than critical voltage
2) electrostatic field and displacement structure field analysis obey two model of coupling：
Wherein：The stiffness matrix [Κ (δ)] of membrane structure can be further written as：[Κ (δ)]=[ΚL+Κ(σd+Δ
σ)], [ΚL] be membrane structure finite element analysis linear stiffness matrix, [Κ (σd+ Δ σ)] it is nonlinear stiffness matrix, Δ σ is
The stress variation of membrane structure caused by malformation；Coefficient matrix [the Κ of electrostatic field finite element equationΕ(δ)] and film
Displacement { δ } is related；For the electrostatic field force suffered by film, it is related to the displacement of film to control voltage；Film
On i-th of node suffered by electrostatic force beWherein E represents electric-field intensity, NsRepresent
The sum of the construction unit related to node；AjRepresent the area of j-th of electrostatic structure unit；[BL] represent membrane structure unit
Geometric matrix, FiFor the panel load for the electrostatic face power formation being subject on unit i；{σM(E) electrostatic face power } is represented, can be by
Maxwell stress tensor equations are tried to achieve；
Step 504 sets up Optimized model：
On the stress uniformity condition of film, i.e. minimax stress ratio, do not enter Optimized model explicitly herein.
This is due to that uniform design stress is loaded on film ideal position, then by optimizing and revising voltage so that film keeps essence
Degree.The uniform prestressing force σ of designing load in the design geometries of film requirementd, by the optimization of lateral load, make outer load
Lotus matches as far as possible with design stress, i.e., stress variation is minimum.Because the form of membrane structure has height coupling：If thin
Membrane equilibrium state stress σ deviates uniform prestressing force σdVery little, then the deflection of film also should very little；If instead deflection is very
Small, then stress variation also can very little.Therefore ensure that membrane structure should while guarantee surface accuracy is implied in Optimized model
The design requirement of power uniformity.
Step 505：Iterative Optimized model.Given initial high pressure control voltage, into electrostatic field structure displacement field
Coupling model is solved, and calculates film performance parameter：Surface accuracy δrmsWith the minimax stress ratio of filmSatisfaction is set
Meter stops iteration when requiring；Otherwise, adjustment high voltage control voltage proceeds iteration；
Iterative Optimized model described in step 505, comprises the following steps：
On optimized algorithm, herein from gradient type optimization method.Due to object function δrmsIt is all modal displacements of structure
The function of { δ }, therefore basis of sensitivity analysis method is relatively more suitable for this solution.Specific calculation procedure is as follows：
Step 601 solves film modal displacement to the sensitivity of voltage according to following formula, formed the sensitivity of each design variable to
Amount, and write as matrix form：
WhereinIn the column vector only withCorresponding i-th of element is 1, its
It is remaining to be all zero.
Face shape error { Δ δ } can be expressed as the adjustment amount of each spread voltage by step 602With the linear combination of sensitivity
Form
Being write as matrix form then can table
Step 603 is solved with least square methodIt can obtain
If step 604 adjustment amountMeet designated precision, then it is assumed that voltage reaches requirement, iteration can be stopped；Otherwise,
The first step is returned to proceed.
Advantages of the present invention can be further illustrated by following emulation experiment：
Simulated conditions：
Film is used uniformly isotropism Kapton polyimide materials, and parameter is：Elastic modulus E=2.17Gpa, membrane material
Thickness t=0.025mm, thermalexpansioncoefficientα=8.0e-6, Poisson's ratio ν=0.30.Take reflecting surface structural parameters：Bore Da=
3000.0mm, focal length fa=3000.0mm, using cooling -20.0oC apply uniform design stress, film die opening d=13.0mm,
Electrode surface scrapping off film surface P axial minimum distance is about 10.0mm；It is preceding to net place parabola bore Df=2980.0mm,
Focal length ff=3000.0mm.Arrange that the provinculum net of high-field electrode uses quasi- geodesic curve grid configuration, horizontal plane radial direction etc. compares
It is divided into 6 sections, forms 6 ring, 216 triangular-shaped electrodes.Electrode lay-out mode, using following two forms：
(1) all nodes of the provinculum net of arrangement electrode are on parabola, and electrode surface is paraboloidal relative to ideal
Optimal sync error is 0.33mm.The triangular-shaped electrodes UNICOM per ring is to a supplying channels from the inside to the outside, totally 6 high voltage supplies
Passage, electrode lay-out mode is as shown in Figure 6；
(2) root-mean-square value rms1=0.8mm deformation, electrode occur from preferable parabola for the provinculum net node of arrangement electrode
Relative ideal paraboloidal optimal sync error in face is 0.92mm.By three ring electrodes in from the inside to the outside per ring in triangle electricity
Pole divides equally 3 parts, and simultaneously adjacent electrode UNICOM is to a supplying channels, i.e., per 3 high voltage supply passages of ring；Outer three ring from the inside to the outside
Triangular-shaped electrodes in the every ring of electrode divide equally 6 parts of adjacent UNICOMs to a supplying channels, i.e., per 6 high voltage supply passages of ring.It is high
Press supplying channels number：3 × 3+6 × 3=27 supplying channels, electrode lay-out mode is as shown in Figure 7.
Form Design is carried out to the film reflector face using the method for the present invention.
Simulation result：
(1) simulation result of electrode lay-out mode 1：
Film shaped morphological index and control voltage result is as shown in table 1.
The film morphology design result of the electrode lay-out mode 1 of table 1
Explanation：With respect to the improvement rate of the optimal identical precision in the surface accuracy comparative electrode face that improvement rate refers to film；
Pv represents film maximum displacement value.
1. table 1 lists the morphological analysis result of film：Surface accuracy is 0.0503mm, and the stress of film entirety film surface is equal
Even property index minimax stress ratio is 1.17, and the shape face and stress uniformity for illustrating film realize largely simultaneous
Turn round and look at；
2. the maximum max (E) of electric-field intensity is 1080v/mm, within the breakdown strength scope of ground experiment
(3000.0v/mm)；
(2) simulation result of electrode lay-out mode 2：
Shown in film shaped morphological index and control voltage result such as table (2).
The film morphology design result of the electrode lay-out mode 1 of table 2
Explanation：With respect to the improvement rate of the optimal identical precision in the surface accuracy comparative electrode face that improvement rate refers to film；
1. table 2 lists the morphological analysis result of film：Surface accuracy is 0.159mm, and the stress of film entirety film surface is equal
Even property index minimax stress ratio is 1.7, illustrates electrode lay-out mode and electrode deformation to the form of film to a certain degree
Influence；
Even if 2. electrode deforms, the forming accuracy of Electrostatic deformation film can also have largely compared with the precision of electrode surface
Raising；
Above-mentioned simulation numerical experiment is proved, rationally and effectively it can be used for Electrostatic deformation film using the present invention
Reflecting surface carries out shape generalization design, it may also be used for anti-to film to many factors such as electrode deformation, Different electrodes distribution forms
The influence for penetrating face form carries out quantitative refinement analysis and evaluated, and Electrostatic deformation film reflector face ground environment experiment into
Shape is controlled.
Claims (1)
1. a kind of Electrostatic deformation film reflector face form Design method based on machine field coupling, it is characterized in that：At least include such as
Lower step：
Step 101：According to the structural parameters in Electrostatic deformation film reflector face and the performance requirement of reflecting surface, high voltage control is determined
The original geometric form and arrangement of electrode；
Step 102：According to Electrostatic deformation film reflector face reflecting surface bore DaWith focal length fa, set up membrane structure displacement field analysis
Model, and load edge-restraint condition；
Step 103：Structural finite element model to film reflector face applies uniform prestressing force σd；
Step 104：Using the geometry of film reflector face and high voltage control electrode as the border of electrostatic field, Electrostatic deformation film is set up
The electrostatic field analysis model of reflector antenna；
Step 105：Electrostatic field analysis model Loading Control voltage, wherein film reflector face loading ground voltage are given, it is voltage-controlled to height
Electrode processed presses electrode lay-out mode Loading Control voltageWherein subscript 1 ..., n represents electrode channel number；
Step 106：The membrane structure analysis model and step 104 set up according to step 102 set up electrostatic field analysis model, set up
The electrostatic field of Electrostatic deformation film reflector surface antenna-displacement structure field model of coupling；
Step 107：Electrostatic field-displacement structure field model of coupling is solved, the performance parameter of antenna structure is calculated：Film is anti-
Penetrate the root-mean-square error δ of the surface accuracy in facermsWith the minimax stress ratio of filmWherein σ1And σ2It is respectively thin
First, second principal stress of film；
Step 108：Optimisation strategy is used to electrostatic field-displacement structure model of coupling, by high voltage control voltageAs design variable, analysis is optimized, when the performance parameter of antenna structure：Surface accuracy root mean square is missed
Poor δrmsWith the minimax stress ratio of filmWhen reaching design requirement, stop optimization analysis；Otherwise return to step 105；
Described step 107, comprises the following steps：
Step 401：Electrostatic field analysis model is solved, and preserves electrostatic energy result We k, make k=1；
Step 402：By the solving result electrostatic force { F of electrostatic field analysis modele}kIt is loaded directly into limited in membrane structure displacement field
On meta-model；
Step 403：Carry out displacement structure to solve, calculate membrane displacement { δ }k, and storage configuration deformation energy, it is designated as Ws k；
Step 404：With displacement structure solving result { δ }kThe border of electrostatic field is updated, grid is repartitioned, regenerates electrostatic
Field analysis model；
Step 405：Electrostatic field analysis is carried out, and preserves electrostatic energy result We k+1；
Step 406：By the solving result electrostatic force { F of electrostatic field analysis modele}k+1Load on the finite element mould of membrane structure analysis
On type；
Step 407：Carry out displacement structure and solve { δ }k+1, and storage configuration deformation energy, it is designated as Ws k+1；
Step 408：Compare the result of electrostatic field twice and membrane structure displacement field analysis model, when | Ws k+1-Ws k| ＜ εs, and |
We k+1-We k| ＜ εeWhen, stop analysis, and the performance parameter of output film reflecting surface：Surface accuracy δrmsWith film it is maximum most
Small stress ratioOtherwise, make k=k+1 and return to 404 and proceed iterative；Wherein, εsRepresent electrostatic force direction
The strain of length direction produced by the normal stress being distributed on section, εeIt is distributed on the section for representing membrane displacement direction
Normal stress produced by length direction strain；
Described step 108, comprises the following steps：
Step 501：Determine design variable：By high voltage control voltageAs design variable, wherein n represents electricity
Pressure passageway number；
Step 502：Determine object function：By the surface accuracy of filmAs object function, wherein
M represents the node total number of film reflector face structural finite element model, δiFor the displacement of i-th of node of structural finite element model；
For the Admissible displacement value of i-th of node；
Step 503：Constraints is determined, it is necessary to which the constraints met is as follows：
To avoid overtension from bringing discharge breakdown problem, maximum controlling voltageNo more than critical voltage
Electrostatic field and displacement structure field analysis obey two model of coupling：
Wherein：The stiffness matrix [K (δ)] of membrane structure can be further written as：[K (δ)]=[KL+K(σd+ Δ σ)], [KL] be
The linear stiffness matrix of membrane structure finite element analysis, [K (σd+ Δ σ)] it is nonlinear stiffness matrix, Δ σ leads for malformation
The stress variation of the membrane structure of cause；Coefficient matrix [the K of electrostatic field finite element equationE(δ)] and film displacement { δ } phase
Close；For the electrostatic field force suffered by film, it is related to the displacement of film to control voltage；I-th on film
Electrostatic force suffered by node isWherein E represents electric-field intensity, NsRepresent and node phase
The sum of the construction unit of pass；AjRepresent the area of j-th of electrostatic structure unit；[BL] represent membrane structure unit geometric moment
Battle array；{σM(E) electrostatic face power } is represented, can be tried to achieve by Maxwell stress tensor equations；
Step 504 sets up Optimized model：
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Step 505：Iterative Optimized model, gives initial high pressure control voltage, into electrostatic field structure displacement field coupling
Model solution, calculates film performance parameter：Surface accuracy δrmsWith the minimax stress ratio of filmMeeting design will
Stop iteration when asking；Otherwise, adjustment high voltage control voltage proceeds iteration.
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| CN201410372864.6A CN104123421B (en) | 2014-07-31 | 2014-07-31 | A kind of Electrostatic deformation film reflector face form Design method based on machine field coupling |
Applications Claiming Priority (1)
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| CN105160115B (en) * | 2015-09-14 | 2018-01-26 | 西安电子科技大学 | Based on the approximate reflector antenna electromechanics Integrated Optimal Design method with sensitivity analysis |
| CN105426592B (en) * | 2015-11-06 | 2018-10-12 | 西安电子科技大学 | A kind of Electrostatic deformation film reflector surface antenna analysis method |
| CN105510881B (en) * | 2015-11-20 | 2018-02-06 | 西安电子科技大学 | A kind of Electrostatic deformation film antenna radial cable length adjuster and method of adjustment |
| CN106055902B (en) * | 2016-06-03 | 2018-10-30 | 西安电子科技大学 | The Novel Interval Methods of reflector antenna electrical property under panel is random and systematic error |
| CN106126922B (en) * | 2016-06-23 | 2018-12-11 | 西安电子科技大学 | Radio astronomical telescope track unevenness Reverse Design towards pointing accuracy |
| CN106295035B (en) * | 2016-08-16 | 2019-04-30 | 西安电子科技大学 | The Electrostatic deformation film antenna shape adjustment method of optimization is cooperateed with bitter end position based on voltage |
| CN106989694B (en) * | 2017-05-17 | 2020-01-14 | 西安电子科技大学 | Estimation method for surface shape and surface precision of cable membrane electrode by considering membrane wrinkles |
| CN112069736A (en) * | 2020-09-11 | 2020-12-11 | 北京理工大学 | Quasi-electrostatic field coupling communication model optimization method based on improved immune algorithm |
| CN114139410A (en) * | 2021-10-19 | 2022-03-04 | 青岛科技大学 | Electrostatic force applying method and system considering deformation of electrode surface and thin film reflecting surface |
| CN114065434B (en) * | 2021-11-22 | 2024-02-13 | 青岛科技大学 | Method for analyzing deformation of film reflecting surface of electrostatically formed film antenna |
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