Spacecraft micro-vibration suppression method and system based on key energy flow area

Abstract

The present invention discloses a method and system for suppressing spacecraft micro-vibration based on a critical energy flow zone, and relates to the field of spacecraft micro-vibration control technology. The steps of the method include: obtaining the parameters of a cabin and a flywheel in a spacecraft; establishing a coupled dynamics model of a flywheel-cabin, and calculating the node displacement response information of the cabin; establishing a power flow energy transfer model under a frequency domain steady-state response, and calculating the energy information of each node of the cabin; generating a visualized energy flow image based on the position information of each node of the cabin and the energy information of each node of the cabin; identifying a vortex zone based on the energy movement form, and determining the critical energy flow zone based on the energy flow vortex in the vortex zone; using the critical energy flow zone as the damping coating area to achieve cabin vibration suppression. The present invention can effectively improve the prediction accuracy of the vibration path and critical area of ​​the spacecraft flywheel-cabin coupling system, and the vibration suppression effect is significant when combined with the damping coating vibration suppression method.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft micro-vibration control, and in particular relates to a spacecraft micro-vibration suppression method and system based on a key energy flow area. Background Art

[0002] High-resolution spacecraft are extremely sensitive to micro-vibration disturbances when they are in orbit. The frequency of micro-vibration is generally distributed in the range of 1Hz~1000Hz, and the amplitude is small. The interference generated by the micro-vibration source stimulates the vibration of the structural cabin at its installation interface and is transmitted to the entire spacecraft, thereby affecting the working performance of the load. Therefore, it is very necessary to suppress the micro-vibration of the spacecraft structure.

[0003] Clarifying the main transmission paths of micro-vibrations and the locations where vibration reduction is implemented is the prerequisite for suppressing micro-vibrations in spacecraft structures. Because there are many components on a spacecraft, additional vibration isolation measures will bring about a large quality cost and also reduce the reliability of the spacecraft. At this time, if the vibration reduction or vibration suppression design is carried out in a targeted manner on the relevant vibration transmission paths, the vibration level at specific sensitive locations on the spacecraft can be more effectively reduced.

[0004] In the prior art, the vibration sensitive position can be determined by experimental testing means. For example, acoustic holography, laser vibrometer, etc. can give the maximum position of vibration energy, but the cost of structural testing is high, and it is impossible to predict the complete information of vibration energy flow and guide the structure preparation. Using prediction methods such as statistical energy method and transfer path analysis method, the main transmission path of vibration can be theoretically identified, and the vibration suppression design can be carried out accordingly according to the main transmission path of vibration. In the prior art, micro-vibration interference is usually equivalent to external excitation, ignoring the gyroscopic effect of the spacecraft excitation source and the coupling between the vibration source and the supporting structure, or it is only applicable to the case where the determination path is relatively simple or regular. However, there is a dynamic coupling between the micro-vibration source and the supporting structure in terms of inertia, stiffness, etc., especially the reaction flywheel, as the most important micro-vibration source on the satellite, is quite different from the general micro-vibration source, that is, the gyroscopic effect caused by the high-speed rotation of the flywheel. The gyroscopic effect will greatly change the dynamic characteristics of the coupled system, such as frequency and modal distribution, which in turn will lead to significant changes in the micro-vibration characteristics and transmission paths. The dynamic coupling effect between the micro-vibration source and its mounting cabin makes it difficult to accurately determine the vibration transmission path and key areas, and it is impossible to accurately determine which parts of the main transmission path need to be applied with vibration suppression measures, resulting in poor micro-vibration suppression effects on spacecraft. Summary of the invention

[0005] In view of the above-mentioned problems in the prior art, the present invention provides a spacecraft micro-vibration suppression method based on the energy flow key area, which has a simple implementation method, low cost, high vibration suppression accuracy and good effect. The method can solve the problems of complex micro-vibration energy transfer path of the spacecraft flywheel-cabin system and difficulty in determining the vibration suppression key area, thereby improving the spacecraft micro-vibration suppression effect.

[0006] The method for suppressing micro-vibration of a spacecraft based on a key energy flow zone of the present invention comprises the following steps:

[0007] Step S1, obtaining structural parameters of the cabin plate and flywheel in the target spacecraft and operating parameters of the flywheel;

[0008] Step S2, establishing a flywheel-deck coupling dynamic model, and substituting the structural parameters of the deck and the flywheel and the operating parameters of the flywheel obtained in step S1, to calculate the node displacement response information of the deck, wherein the flywheel-deck coupling dynamic model is a dynamic relationship model between the flywheel and the deck formed by dividing the deck into a plurality of nodes and a plurality of units and constructing the displacement of each node of the deck and the structural parameters of the deck and the flywheel and the operating parameters of the flywheel;

[0009] Step S3, establishing a power flow energy transfer model under a frequency domain steady-state response, and calculating the energy information of each node of the cabin board according to the power flow energy transfer model and the node displacement response information of the cabin board, wherein the power flow energy transfer model is an energy flow distribution model of each node of the cabin board in each direction formed based on the power flow method;

[0010] Step S4, generating a visualized energy flow image according to the position information of each node of the deck and the energy information of each node of the deck obtained in step S3;

[0011] Step S5, identifying a vortex area in the visualized energy flow image according to the movement form of energy in the visualized energy flow image, and determining an energy flow key area according to the energy flow vortex amount in the vortex area;

[0012] Step S6, using the energy flow key area as the damping coating area to achieve vibration suppression of the cabin plate.

[0013] Furthermore, in step S1, the structural parameters of the cabin include any one or more of cabin length, cabin width, cabin thickness, dissipation coefficient, cabin density, cabin Poisson's ratio, cabin elastic modulus and cabin shear modulus; the structural parameters of the flywheel include any one or more of mass, axial moment of inertia, radial moment of inertia and flywheel position; and the operating parameters of the flywheel include any one or more of static unbalance, dynamic unbalance and flywheel speed.

[0014] Furthermore, in step S2, the expression of the flywheel-nacelle coupling dynamic model is:

[0015]

[0016] In the formula, represents the nodal displacement of the flywheel-deck system, is the damping matrix of the flywheel-cabin system, is the stiffness matrix of the flywheel-deck system, is the disturbance excitation, is the mass matrix of the flywheel-deck system, ,in is the deck mass matrix, is the flywheel mass matrix, expressed as , is the radial moment of inertia of the flywheel, is the flywheel mass, is the flywheel gyro effect matrix, expressed as , is the axial moment of inertia of the flywheel, is the flywheel speed;

[0017] Disturbance Excitation The expression is:

[0018]

[0019] in, and are dynamic unbalance excitation and static unbalance excitation respectively, and They represent the initial phase angles of the static unbalance and dynamic unbalance distribution respectively.

[0020] Furthermore, the steps of establishing the flywheel-nacelle coupling dynamic model include:

[0021] The three-degree-of-freedom four-node plate element is used to divide the cabin plate, forming a total of n nodes and m Unit, cabin j The displacement of the nodes for:

[0022]

[0023] In the formula, j Indicates the node number, ,in n is the total number of nodes, for z Direction translation displacement, For around x The rotation displacement in the axial direction, For around yRotational displacement in the axial direction;

[0024] Assume that the flywheel is fixed to the deck and installed at the node numbered f At the node of With the deck f The displacements of the nodes are the same, and the expression is ; Displacement of the flywheel-deck system It is composed of the displacement of each node of the cabin plate, that is, ;

[0025] Calculate the system kinetic energy of the flywheel-deck system 、System potential energy and system dissipated energy , where the system kinetic energy for:

[0026]

[0027] In the formula is the density of the deck, is the volume of the deck, is the radial moment of inertia of the flywheel rotor, is the axial moment of inertia of the flywheel rotor, is the flywheel mass, is the rotor speed, and the symbol · represents the time derivative;

[0028] System potential energy for:

[0029]

[0030] In the formula is the strain matrix, is the elastic coefficient matrix;

[0031] System dissipated energy for:

[0032]

[0033] In the formula is the dissipation coefficient;

[0034] The calculated system kinetic energy 、System potential energy and system dissipated energy Substituting into the Lagrange equation, the coupled dynamic model of flywheel-nacelle is obtained.

[0035] Furthermore, the energy information includes time-averaged energy density and energy flow components under frequency domain steady-state response; the detailed steps of calculating the energy information of each node of the cabin include:

[0036] According to the node displacement response information of the cabin plate, combined with the k The node number corresponding to the unit is obtained k The unit displacement response of the unit , k Indicates the unit number, ,in m is the total number of elements, and the element displacement response Converted into unit centroid displacement , the calculation formula is:

[0037]

[0038] in, is the plate element shape function matrix, where , denote the abscissa and ordinate of the unit centroid, respectively. The unit center of mass is z The translational displacement in the direction The unit centroid x The rotation displacement in the axial direction, The unit centroid y The rotation displacement in the axial direction, k is the unit number, k = ;

[0039] Based on the displacement response of the unit Calculate element centroid stress , the calculation formula is:

[0040]

[0041] in, The unit centroid is along x The bending moment in the direction The unit centroid is along y The bending moment in the direction is the unit center-of-mass torque, is the strain matrix, is the elastic coefficient matrix;

[0042] The unit power flow energy transfer model under the frequency domain steady-state response is established, and its expression is:

[0043]

[0044] in, Indicates k Units in x Directional energy flow component, Indicates k Units iny Directional energy flow component, is the excitation frequency, is the Poisson's ratio of the deck, Im represents the imaginary part, and * represents the complex conjugate;

[0045] Displace the unit centroid The three components and element centroid stress The three components Substituting into the unit power flow energy transfer model, we can obtain the frequency domain steady-state response x Directional unit energy flow component and y Directional unit energy flow component ;

[0046] According to the displacement of the unit centroid The three components Calculate the time average energy density of each unit of the cabin , the expression is:

[0047]

[0048] in, , The bending waves are x Direction and y The wave number of the direction, h is the deck thickness, D is the bending stiffness of the deck, is the density of the deck, t Indicates time, is Poisson's ratio.

[0049] Further, step S5 includes:

[0050] Determine the movement form of energy in the visualized energy flow image, wherein the movement forms of energy include source-sink flow and vortex flow, and the area enclosed by the streamlines of the vortex flow is the vortex area; the source-sink flow is a movement in which energy diffuses outward from the vibration source and finally converges to the flow, and the streamline deflection angle is less than 360°; the vortex flow is a movement in which there is local rotation in the transmission path and the streamline deflection angle exceeds 360°, wherein the vibration source is the starting point, the flow sink is the end point, and the line connecting the vibration source and the flow sink is the streamline;

[0051] Calculate the vortex energy flow in the vortex zone ω f If the energy flow vorticity value is greater than the reference vorticity, and the area of ​​the current vortex zone is greater than the specified proportion of the cabin area, then the vortex zone is determined to be the key area of ​​energy flow.

[0052] Furthermore, the energy flow vortex ωf The calculation formula is:

[0053]

[0054] in, is the unit response speed, Displacement of the centroid of each unit It is formed by combining units in order, and rot represents the curl.

[0055] Furthermore, in step S6, a viscoelastic material with a loss factor between 0.1 and 0.8 and a storage modulus between 1 and 5 MPa is selected as the damping coating, and the viscoelastic material is any one of butyl rubber, polysulfide rubber and polyurethane elastomer.

[0056] The present invention also proposes a system for implementing the above-mentioned spacecraft micro-vibration suppression method based on the key area of ​​energy flow, comprising:

[0057] A parameter acquisition unit, used to acquire the structural parameters of the cabin plate and flywheel in the target spacecraft and the operating parameters of the flywheel;

[0058] A deck response calculation unit is used to establish a flywheel-deck coupling dynamic model, and substitute the structural parameters of the deck and the flywheel obtained by the parameter acquisition unit, and the operating parameters of the flywheel, to calculate the response information of the node displacement of the deck. The flywheel-deck coupling dynamic model is a dynamic relationship model between the flywheel and the deck formed by dividing the deck into a plurality of nodes and a plurality of units, and according to the displacement of each node of the deck and the structural parameters of the deck and the flywheel, and the operating parameters of the flywheel;

[0059] An energy distribution calculation unit is used to establish a power flow energy transfer model under a frequency domain steady-state response, and calculate the energy information of each node of the cabin board according to the power flow energy transfer model and the node displacement response information of the cabin board. The power flow energy transfer model is an energy flow distribution model of each node of the cabin board in each direction formed based on the power flow method;

[0060] An energy flow image generating unit, used for generating a visualized energy flow image according to the position information of each node of the cabin and the energy information of each node of the cabin obtained by the energy distribution calculating unit;

[0061] An energy flow key area determination unit is used to identify the vortex area in the visualized energy flow image according to the movement form of energy in the visualized energy flow image, and determine the energy flow key area according to the energy flow vortex amount in the vortex area;

[0062] The damping coating area determination unit is used to use the energy flow key area as the damping coating application area to achieve vibration suppression of the cabin plate.

[0063] In addition, the present invention also proposes a computer device, including a processor and a memory, wherein the memory is used to store a computer program, and the processor is used to execute the computer program to execute the spacecraft micro-vibration suppression method based on the energy flow critical area.

[0064] The beneficial effects achieved by the present invention are as follows:

[0065] 1) The present invention establishes a flywheel-cabin coupling dynamics model, calculates the response information of the node displacement of the cabin based on the flywheel-cabin coupling dynamics model, and simultaneously establishes a power flow energy transfer model under the frequency domain steady-state response, calculates the energy information of each node of the cabin, and generates a visualized energy flow image by combining the position information of each node of the cabin and the energy information of each node of the cabin. Then, the energy movement form and energy flow vortex in the visualized energy flow image are used to determine the key energy flow area, which can effectively improve the prediction accuracy of the vibration path and key area of ​​the spacecraft flywheel-cabin coupling system. Finally, the damping coating is applied to the key energy flow area as the damping coating application area, which can be combined with the damping coating vibration suppression method to achieve a significant vibration suppression effect;

[0066] 2) The present invention further considers the dynamic coupling effect between the micro-vibration source and the deck on which it is installed when constructing the flywheel-deck coupling dynamic model, which can improve the accuracy of the flywheel-deck coupling dynamic model. Combined with the power flow energy transfer model, a more realistic and accurate visualization image of the system energy flow can be obtained;

[0067] 3) The present invention further identifies the vortex area in the visualized energy flow image according to the movement form of energy in the visualized energy flow image, and determines the key area of ​​energy flow according to the energy flow vortex in the vortex area. The key position of vibration suppression of the flywheel-cabin system can be accurately found. Compared with traditional methods such as the cumulative transformation angle method, the accuracy of the judgment can be significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] FIG1 is a schematic diagram of the implementation process of the method for suppressing spacecraft micro-vibration based on the key area of ​​energy flow in this embodiment.

[0069] FIG. 2 is a schematic diagram of the implementation flow of energy flow calculation in this embodiment.

[0070] FIG3 is a schematic diagram showing the principle of the flywheel and cabin plate coupling system constructed in this embodiment.

[0071] FIG. 4 is a schematic diagram showing the principle of the coordinate system constructed in this embodiment.

[0072] FIG. 5 is a diagram showing the translation of the cabin plate at 600 rpm obtained in a specific application embodiment. w Schematic diagram of the response results.

[0073] FIG. 6 shows the rotation angle of the cabin plate at 600 rpm obtained in a specific application embodiment. Schematic diagram of the response results.

[0074] FIG. 7 shows the rotation angle of the cabin plate at 600 rpm obtained in a specific application embodiment. Schematic diagram of the response results.

[0075] FIG8 is a diagram showing the bending moment of the cabin plate at 600 rpm obtained in a specific application embodiment. Schematic diagram of the response results.

[0076] FIG. 9 shows the bending moment of the cabin plate at 600 rpm obtained in a specific application embodiment. Schematic diagram of the response results.

[0077] FIG. 10 is a diagram showing the torque of the cabin plate at 600 rpm obtained in a specific application embodiment. Schematic diagram of the response results.

[0078] FIG. 11 is a schematic diagram of the energy amplitude distribution characteristic results of the cabin plate at 600 rpm obtained in a specific application example.

[0079] Figure 12 is a schematic diagram of the basic motion forms of energy flow, where (a) is source-sink flow and (b) is vortex flow.

[0080] Figure 13 is a schematic diagram of the principle of energy flow mode division in a specific application embodiment, wherein (a) is a Class I energy flow mode (600-1200rpm), (b) is a Class II energy flow mode (1200-2400rpm), (c) is a Class III energy flow mode (2400-3600rpm), and (d) is a Class IV energy flow mode (3600-6000rpm).

[0081] FIG. 14 is a schematic diagram showing the principle of constructing a power transfer rate finite element model according to this embodiment.

[0082] Figure 15 is a schematic diagram of the key area position and vibration suppression effect obtained in a specific application embodiment, wherein the elliptical filled area in (a) is the key area of ​​the cumulative transition angle criterion, the framed area in (b) is the key area of ​​the vortex zone criterion, (c) is the energy flow distribution after damping vibration suppression based on the cumulative transition angle criterion, and (d) is the energy flow distribution after damping vibration suppression based on the vortex zone criterion.

[0083] FIG16 is a schematic diagram of the energy flow distribution and the location of the key energy flow area under the Class III working condition obtained in a specific application embodiment.

[0084] FIG17 is a schematic diagram of the energy flow distribution after vibration suppression under Class III working condition obtained in a specific application embodiment, where (a) is the damping coefficient of the application. = 0.01 after the damping coating, (b) is the damping coefficient of the coating = 0.1 after the damping coating, (c) is the damping coefficient of the coating =0.8 energy flux distribution after the damping coating.

[0085] FIG18 is a schematic diagram of the energy flow distribution and the location of the key energy flow area obtained under the Class I working condition in a specific application embodiment.

[0086] FIG19 is a schematic diagram of the energy flow distribution results after vibration suppression under the first type of working condition obtained in a specific application embodiment, where (a) is the damping coefficient of the application. = 0.01 after the damping coating, (b) is the damping coefficient of the coating = 0.1 after the damping coating, (c) is the damping coefficient of the coating =0.8 energy flux distribution after the damping coating. DETAILED DESCRIPTION

[0087] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0088] Below is a combination of Figures 1 to Fig.19 , and describes in detail the spacecraft micro-vibration suppression method based on the energy flow key area provided by the present invention and the beneficial effects achieved by using the method.

[0089] The present embodiment is based on a method for suppressing micro-vibration of a spacecraft in a critical energy flow zone. First, the parameters of a cabin and a flywheel in a spacecraft are obtained, and a coupled dynamic model of a flywheel and a cabin is input to obtain node displacement response information and model information of the cabin. The response information and model information are input into a power flow energy transfer model under a frequency domain steady-state response to obtain cabin energy flow information, a power transfer rate, and vorticity. The power transfer rate is used to evaluate the vibration suppression effect. The cabin model information and the energy flow information of each node of the cabin are input into Tecplot software to generate a visualized energy flow image. The vortex zone is identified according to the visualized energy flow image, and the critical energy flow zone is determined according to the energy flow vorticity of the vortex zone. The critical energy flow zone is used as the damping coating application area to achieve cabin vibration suppression.

[0090] like Figure 1 , 2 As shown, the detailed steps of the spacecraft micro-vibration suppression method based on the energy flow key area in this embodiment are:

[0091] Step S1, obtaining the structural parameters of the cabin plate and flywheel in the target spacecraft and the operating parameters of the flywheel.

[0092] In this embodiment, the structural parameters of the cabin include: cabin length, cabin width, cabin thickness, dissipation coefficient, cabin density, cabin Poisson's ratio, cabin elastic modulus, cabin shear modulus, etc.; the structural parameters of the flywheel include: mass, axial moment of inertia, radial moment of inertia, flywheel position, etc.; the operating parameters of the flywheel include: static unbalance, dynamic unbalance, flywheel speed, etc.

[0093] Specifically, the parameters of this embodiment are shown in Table 1 and Table 2.

[0094] Table 1: Cabin parameters

[0095]

[0096] Table 2: Flywheel parameters

[0097]

[0098] Step S2, establishing a coupled dynamic model of the flywheel and the deck, and substituting the structural parameters of the deck and the flywheel and the operating parameters of the flywheel obtained in step S1, and calculating the response information of the node displacement of the deck. The coupled dynamic model of the flywheel and the deck is a dynamic relationship model between the flywheel and the deck formed by dividing the deck into multiple nodes and multiple units and constructing the model according to the displacement of each node of the deck and the structural parameters of the deck and the flywheel and the operating parameters of the flywheel.

[0099] This embodiment specifically uses the finite element power flow method to calculate the energy distribution of each node of the cabin plate, and the detailed steps include the following steps:

[0100] Step S2.1, constructing a flywheel-deck coupling dynamics model, and calculating the displacement response of each node of the deck based on the flywheel-deck coupling dynamics model.

[0101] Step S2.1.1, construct the physical model.

[0102] In this embodiment, the physical model is constructed as a system in which a reaction flywheel is fixed at the center of the spacecraft structure cabin, such as Figure 3 As shown in the figure, the basic assumptions of the physical model are: the mass of the spacecraft is large enough, and the influence of rigid body motion on the system coupling during flight is ignored; the flywheel rotor is rigid and rotates steadily, and the steering dynamics of the rotor and the relative motion between the stator and rotor are ignored, and the flywheel stator and rotor have the same center of mass; during the rotation of the flywheel, due to the influence of the unbalanced amount, vibration is generated and transmitted to the cabin; the amplitude of the microvibration is very small, and the deformation nonlinearity is ignored; the cabin mainly vibrates laterally, and only the bending deformation is considered, and the in-plane deformation is ignored.

[0103] Step S2.1.2, define the coordinate system used to describe the cabin vibration and the flywheel rotor motion, including the space inertial coordinate system, the flywheel fixed coordinate system, the swing coordinate system and the rotor fixed coordinate system.

[0104] like Figure 4 As shown, including the space inertial coordinate system , describing the overall motion of the flywheel-deck system, the origin is located at the corner point of the deck, The axis is parallel to the positive normal of the deck plane. , The axis is parallel to the length and width of the deck. Flywheel fixed coordinate system , describing the motion of the flywheel stator, with the origin located at the inertial coordinate system of the deck point, by Pan Get. Intermediate auxiliary coordinate system and swing coordinate system , used to describe the translation and rocking vibration of the rotor. Intermediate auxiliary coordinate system , the flywheel fixed coordinate system Around y Axis rotation Get. Swing coordinate system , by the flywheel intermediate auxiliary coordinate system Around Axis rotation We get that the origin is located at the center of mass of the rotor and swings along with the rotor. Axis and The axes coincide with the principal axis of radial inertia of the rotor. Coincident with the main axis of rotor pole inertia. Rotor fixed coordinate system , the origin is at the rotor mass center, Axis and Axis coincidence, , Shaft winding Axis speed sports.

[0105] Step S2.1.3, dividing the deck after determining the displacement of the deck and the flywheel.

[0106] First, divide the deck into n nodes and m units. One unit has four nodes and one unit number. k Corresponding to four node numbers j , the displacement of each node of the cabin for:

[0107] (1)

[0108] in, for zAxial translation displacement, for x The rotation displacement in the axial direction, for y The rotation displacement in the axial direction, j is the node number, .

[0109] Since the flywheel is fixed to the deck, the flywheel is fixed to the deck at the installation point (node At the same time, the flywheel is considered to be in steady rotation and the speed is constant. , at this time, the flywheel displacement is:

[0110] (2)

[0111] Flywheel-deck system displacement It is assembled by displacement of each node of the cabin plate. .

[0112] Step S2.1.4, calculate the system energy of the flywheel-deck system, including the system kinetic energy of the flywheel-deck system 、System potential energy and system dissipated energy .

[0113] Alternatively, the system kinetic energy expression is:

[0114] (3)

[0115] in, is the density of the deck, is the volume of the deck, is the radial moment of inertia of the flywheel rotor, is the axial moment of inertia of the flywheel rotor, is the flywheel mass, is the rotor speed, represents the time derivative.

[0116] The potential energy expression of the system is:

[0117] (4)

[0118] in, is the strain matrix, is the elastic coefficient matrix.

[0119] The expression of system dissipated energy is:

[0120] (5)

[0121] in, is the dissipation coefficient.

[0122] Step S2.1.5, the system kinetic energy calculated in step S2.1.4 、System potential energy and system dissipated energy Substituting into the Lagrange equation, the flywheel-cabin coupling dynamic model is established to calculate the system response:

[0123] (6)

[0124] in, represents the system displacement, is the damping matrix of the system, is the system stiffness matrix, is the disturbance excitation, , is the system mass matrix, is the mass matrix of the deck, is the flywheel mass matrix, expressed as , is the flywheel gyro effect matrix, expressed as , is the axial moment of inertia of the flywheel, is the radial moment of inertia of the flywheel, is the flywheel mass, is the flywheel speed.

[0125] excitation The dynamic and static unbalanced excitation disturbance from the flywheel is expressed as:

[0126] (7)

[0127] in, and are dynamic and static unbalanced excitations, and They represent the initial phase angles of the static unbalance and dynamic unbalance distribution respectively.

[0128] Step 2.1.6, substitute the structural parameters of the target spacecraft cabin and flywheel and the operating parameters of the flywheel obtained in step S1 into the flywheel-cabin coupling dynamic model to calculate the system displacement The value of k The node number corresponding to each unit is obtained k Displacement response of each unit .

[0129] In the specific application examples, the above method of this embodiment is used to perform simulations and compared with the theoretical calculation results to obtain the following results: Figures 5 to 10As shown, it can be seen from the figure that in terms of displacement and internal force distribution, the results obtained by the above method of this embodiment are basically consistent with those obtained by theoretical calculation, which verifies the correctness of the dynamic analysis model of this embodiment.

[0130] Step S3, establish a power flow energy transfer model under frequency domain steady-state response, and calculate the energy information of each node of the cabin board according to the power flow energy transfer model and the node displacement response information of the cabin board. The power flow energy transfer model is an energy flow distribution model of each node of the cabin board in each direction constructed based on the power flow method.

[0131] In this embodiment, the energy information specifically includes the time-averaged energy density and the energy flow component under the frequency domain steady-state response. The detailed steps for calculating the energy information of each node of the cabin are:

[0132] Step S3.1, exporting the node displacement response information and node position information in the form of a data file.

[0133] Step S3.2, the derived node displacement information is converted into unit centroid displacement through post-processing, and the expression is:

[0134] (8)

[0135] in, is the plate element shape function matrix, , is the coordinate of the unit centroid, is the translation of the unit mass center in the z-axis direction, is the rotation of the unit center of mass about the x-axis, is the rotation of the unit center of mass about the y-axis, k is the unit number, k = .

[0136] Step S3.3, according to the unit displacement response Calculate the element centroid stress using the expression:

[0137] (9)

[0138] in, , is the deck bending moment, is the deck torque, k is the unit number, k = .

[0139] Step S3.4, establish a unit power flow energy transfer model under frequency domain steady-state response, the calculation formula is:

[0140] (10)

[0141] in, represents the energy flow component in the x-axis direction, represents the energy flow component in the y-axis direction, is the excitation frequency, is the Poisson's ratio of the deck, Im represents the imaginary part, * represents the complex conjugate, k is the unit number, k = ;

[0142] Step S3.5, calculate the time average energy density at each position of the cabin board, the expression is:

[0143] (11)

[0144] in, , is the bending wave number, h is the deck thickness, D is the bending stiffness of the deck, is the density of the deck, t Indicates time, x express x Axis position variables, y express y Axis position variable.

[0145] Step S3.6, calculating the power transfer rate;

[0146] In this embodiment, the finite element is defined as follows: Fig.11 As shown, the expression is:

[0147] (12)

[0148] in, is the power at the boundary, , o Number the selected boundary elements. is the power at the flywheel excitation point, , i Mounting point for flywheel f The corresponding four unit numbers, , the power of each unit .

[0149] In a specific application example, the result calculated by the above method is as follows: Fig.12 As shown in the figure, it can be seen that the energy amplitude is symmetrically distributed about the center of the cabin (excitation point), and gradually weakens from the center to the surroundings, which is in line with the law of energy transfer.

[0150] Step S4, generating a visualized energy flow image according to the position information of each node of the deck and the energy information of each node of the deck obtained in step S3.

[0151] In this embodiment, the visualized energy flow image can be obtained by importing the node position information and the node energy information into the Tecplot software. Specifically, the node position information and the node energy information are organized into a dat file in the Tecplot format, and the dat file is loaded into the Tecplot software. The software automatically calculates the energy direction of each node through the dat file information, and then draws a visualized energy flow image. The specific setting steps include:

[0152] 1. Load the dat file through the "Tecplot Data Loader" data reading module;

[0153] 2. Select the graphics category "2D Cartesian";

[0154] 3. Use the "Zone layers" module to set the coordinate system and grid of the visualization graphics;

[0155] 4. Generate streamlines using the "Streamtraces" module;

[0156] 5. Export the image in .jpg or .png format to get a visualized energy flow image.

[0157] In a specific application embodiment, the visualized energy flow image and the energy flow distribution characteristic results of the cabin board obtained by the above method are as follows: Fig.13 shown.

[0158] Step S5, identifying the vortex area in the visualized energy flow image according to the movement form of energy in the visualized energy flow image, and determining the energy flow key area according to the energy flow vortex amount in the vortex area.

[0159] Under the influence of the flywheel gyroscopic effect, the energy movement form is transformed from source-sink motion to vortex motion, and from sub-step S2.2.5, it can be seen that the power flow is obtained by path integration. The vortex zone has dense streamlines and long flow paths, and the dissipated power will be higher than other areas. Therefore, the critical area judgment criteria for the vibration transmission path of the flywheel-cabin system are defined, and the vortex zone with an energy flow vortex greater than the reference vortex and an area greater than 1 / 10 of the cabin area is defined as the energy flow critical area, that is, the vibration suppression effect is best in this area.

[0160] Step S5.1, determine the movement form of energy in the visualized energy flow image, where the movement forms of energy include source-sink flow and vortex flow, and the area enclosed by the streamlines of the vortex flow is the vortex area; source-sink flow is a movement in which energy diffuses outward from the vibration source and finally converges to the flow, and the streamline deflection angle is less than 360°; vortex flow is a movement in which there is local rotation in the transmission path, and the streamline deflection angle exceeds 360°, wherein the vibration source is the starting point, the flow sink is the end point, and the line connecting the vibration source and the flow sink is the streamline.

[0161] Step S5.1.1, define the basic motion forms of energy flow.

[0162] Vibration energy has the law of flowing from high energy density area to low energy density area, where the starting point of energy is the vibration source, the end point is the flow confluence, the area connecting the vibration source and the flow confluence is the transmission path, and the line connecting the vibration source and the flow confluence is the streamline. A vibration energy transmission path consists of a vibration source, a flow confluence and countless streamlines. The envelope area of ​​the streamlines between the same vibration source and flow confluence is a transmission path.

[0163] First, the vibration source is defined as the local peak value of the vibration energy density, which is represented by the starting point or area of ​​the transfer path streamline. The generalized vibration source includes the following three categories: (1) Excitation source: refers to the local vibration energy peak generated by the continuous action of the external excitation force; (2) Boundary source: the energy flow input generated by boundary conditions such as simple support and fixed support; (3) Induced source: the local peak value of vibration energy generated inside the plate and shell components by the combined action of the excitation force and boundary conditions. In addition, in some cases, the position of the excitation source does not completely coincide with the excitation point. In this case, the divergent source closest to the excitation point is also considered to be the excitation source.

[0164] Secondly, flow sinks can be broadly defined as local troughs of structural vibration energy, which are represented as the end points or termination areas of the transfer path streamlines. Similarly, generalized flow sinks include the following two categories: (1) internal flow sinks: local vibration energy minima caused by structural damping or external dampers; (2) boundary flow sinks: due to the influence of structural damping and boundary shape, some streamlines terminate at the structural boundary.

[0165] Finally, the transfer path can be broadly defined as a continuous channel of energy flow composed of related transfer path streamlines. Considering the complex transfer path situation in the cabin, the transfer path can be further defined as a continuous area composed of all adjacent streamlines between the same vibration source and flow sink. The boundary of the transfer path is the intersection line formed by the streamlines of different vibration sources or flow sinks. In some cases, there are other vibration sources or flow sinks in the streamline field of the vibration source and flow sink. In this case, the transfer area between the vibration source and flow sink is divided into multiple transfer paths.

[0166] Based on the above definition, the energy flow in the cabin has two basic motion forms: source-sink flow and vortex flow. Fig.14 As shown in the figure, the energy diffuses outward from the vibration source and finally converges to the flow. The movement with a streamline deflection angle less than 360° is a source-sink flow, as shown in the figure. Fig.14 As shown in (a). There is local rotation in the transfer path, and the flow line deflection angle exceeds 360°, which is a vortex flow, as shown in Fig.14 As shown in (b).

[0167] Under the influence of the gyroscopic effect G, the system produces two swing modes, positive precession and reverse precession, which are coupled with other modes of the system at the flywheel speeds of 624rpm, 1600rpm, 2853rpm, and 3275rpm. The swing mode generated by the gyroscopic effect affects the mode of the system, causing the energy flow distribution type to change. Type I mode, such as Fig.13 As shown in (a), the main distribution is 600rpm~1200rpm, there are more excitation sources and flow sinks, the energy is concentrated at the center, but the energy transfer paths on both sides are relatively scattered; Type II mode, such as Fig.13 As shown in (b), it is mainly distributed in the range of 1800rpm to 2400rpm, the energy flows on both sides merge with the central vortex, and the number of sources and sinks and the transfer path are reduced; Type III mode, such as Fig.13 As shown in (c), the distribution is at 3000rpm, forming the prototype of the overall vortex energy flow distribution pattern. The energy moves mainly in the form of a vortex in the plate, with two obvious internal vortices; the type IV mode, such as Fig.13 As shown in (d), the distribution is 3600-6000rpm, showing a vortex energy flow distribution. Among them, the energy flow distribution modes of types I and II are affected by the first-order vibration mode of the flywheel-cabin system. The first-order frequency of the system is 23Hz, which is 27Hz different from the second-order natural frequency. Therefore, when the speed is less than the second-order frequency speed of 3000rpm, the first-order vibration mode of the system is mainly excited, resulting in unclear vortex energy flow distribution.

[0168] Step S5.1.2, identifying the vortex area based on the obtained visualized energy flow image and combining it with the basic movement form of energy flow. The vortex area is the area enclosed by the vortex flow streamlines.

[0169] Step S5.2, determining the key energy flow area.

[0170] For incompressible fluid motion with constant density, constant kinematic viscosity, and potential through the body, the general form of the vorticity transport equation is:

[0171] (13)

[0172] in, is the kinematic viscosity coefficient, which can be compared to the damping of energy flow The left side of the equation represents the rate of change of the vorticity of the micro-group along the streamline. The first term on the right side of the equation is the vortex extension and torsion term, which reflects the deformation and displacement of the vortex. The second term is the viscous diffusion term, which reflects the dissipation of the vortex. For energy flow motion, when there is damping on the cabin, the energy of the vortex will be weakened. When the local flow velocity changes, the shape and position of the vortex will change.

[0173] In the vortex zone, the precise position of the vortex zone is further determined by visualizing the image and the energy vorticity. The expression of the energy flow vorticity is:

[0174] (14)

[0175] in, is the unit response speed, Depend on Assembled in unit order, rot represents the curl. When the vorticity is greater than the reference vorticity (can be 1), the area can be considered as the key area of ​​vortex energy flow. When the area of ​​the vortex is less than 1 / 10 of the area of ​​the cabin, the vortex flow flowing here can be ignored, and the point is regarded as a source-sink flow.

[0176] Step S6, applying the damping coating to the key area of ​​energy flow as the damping coating application area to achieve vibration suppression of the cabin plate.

[0177] In this embodiment, a suitable viscoelastic material is selected as the damping coating, such as butyl rubber, polysulfide rubber or polyurethane elastomer, etc. These materials should have a high loss factor and a suitable storage modulus. The loss factor of butyl rubber can vary between 0.1 and 0.8 in the temperature range of -50 to 70°C, showing good damping performance, so it is selected as an alternative material.

[0178] In this embodiment, the geometry and size of the damping coating are determined according to the critical energy flow area to ensure that it can completely cover the critical energy flow area. Preferably, its thickness is not greater than 1 / 5 of the thickness of the cabin plate so as not to affect the function of the spacecraft.

[0179] When applying the damping coating, first clean the surface of the cabin, evenly apply cyanoacrylate adhesive in the key area of ​​energy flow, lay the butyl rubber coating on it and press it flat to ensure there are no bubbles and wrinkles. Wait one minute for the adhesive to cure and the damping coating can be applied.

[0180] In order to verify the effective effect of the present invention, the following experiment is conducted to evaluate the vibration suppression effect using the above method of the present invention. The specific process is as follows:

[0181] 1) The cumulative transformation angle criterion and the vortex zone criterion are used to determine the key areas of energy flow and analyze the vibration suppression effect.

[0182] The cumulative transition angle criterion is used to determine the critical area, and the expression is:

[0183] (15)

[0184] in, is the position variable, and are the starting and ending positions on the streamline, is the integration step along the streamline, and is the energy flow vector at two adjacent points on the streamline. The threshold of the streamline cumulative change angle is generally set to When the cumulative change angle between the direct vibration source and the target point is greater than , the area is determined to be the main influence area of ​​the target point.

[0185] In a specific application embodiment, based on the energy flow distribution diagram and vorticity information, a judgment criterion is used to determine the energy flow critical area, as shown in (a) and (b) in Figure 15, where the lower left corner square is the target point, and the wireframe is the energy flow critical area obtained by different criteria.

[0186] By adding a damping with a dissipation coefficient of 1 in the key area of ​​energy flow and ensuring that the damping added area is equal, the power transfer rates at the target points are 3.50% and 1.61% respectively. Using the vortex zone criterion for path judgment reduces the power transfer rate of the target point by 54%. Obviously, using the vortex zone judgment criterion for determining the key position of the vibration path has higher accuracy and better vibration suppression effect.

[0187] The energy flow distribution after vibration suppression is obtained as Fig.15 As shown in (c) and (d), the shaded area is the main energy flow path affecting the target point. Fig.15 From (d), we can see that after using the vortex zone criterion to suppress vibration, the vortex on one side of the target point is dissipated, which is given by Fig.15 As shown in (c), after using the cumulative transformation angle to suppress vibration, the vortices on both sides are affected, and the energy flow on the right side of the cabin converges to the damping addition area. Therefore, there are two reasons why the vortex area has a better effect of suppressing vibration: (1) The energy flow in the vortex area is dense and has a long flow path, which improves the efficiency of damping dissipation; (2) Adding damping in the vortex area will not attract energy flows in other areas to the vicinity of the target point.

[0188] 2) Change the flywheel speed and determine the key energy flow area for the third type of energy flow distribution condition. The results are as follows: Fig.16 shown.

[0189] 3) Add different dissipation coefficients in key areas The damping coating is used to obtain the energy flow distribution diagram after vibration suppression. The results are as follows: Fig.17As shown in the figure, as the dissipation coefficient increases, the vortex is gradually dissipated, the streamline length and density decrease, and it turns into source-sink motion when the dissipation coefficient is 0.1.

[0190] 4) Change the flywheel speed and determine the key area of ​​energy flow for the first type of energy flow distribution condition. The result is shown in Figure 18.

[0191] 5) Add different dissipation coefficients in key areas The damping coating is used to obtain the energy flow distribution diagram after vibration suppression, as shown in Fig.19 As shown, the vortex motion mode is destroyed by adding the damping cladding, and when the dissipation coefficient is greater than 0.1, the vortices on both sides are dissipated first.

[0192] 6) Calculate the power transfer rate of the damping coating applied in the critical area and the entire body.

[0193] The results are shown in Table 3. The power transfer rate of adding damping in the vortex zone is lower than that of adding damping as a whole. It can be verified that damping vibration suppression in the vortex zone is the optimal vibration suppression position.

[0194] Table 3: Power transfer ratio of local added damping and overall added damping ( )

[0195]

[0196] 7) Evaluate the vibration suppression effect of the method proposed in this invention.

[0197] In summary, the present invention can have the following effects:

[0198] (1) The damping vibration suppression effect in the vortex zone is better than that in the source-sink zone, and is better than the overall vibration suppression. Therefore, the vortex zone criterion determination method is accurate and effective.

[0199] (2) After adding damping to the cabin, the energy flow will be attracted by the damping, forming more flow sinks in the damping area, and the original vortex motion pattern will be destroyed, transforming into source-sink motion.

[0200] This embodiment also provides a system for implementing the above-mentioned method for suppressing spacecraft micro-vibration based on the key area of ​​energy flow, including:

[0201] A parameter acquisition unit, used to acquire the structural parameters of the cabin plate and flywheel in the target spacecraft and the operating parameters of the flywheel;

[0202] A deck response calculation unit is used to establish a flywheel-deck coupling dynamic model, and substitute the structural parameters of the deck and the flywheel obtained by the parameter acquisition unit, and the operating parameters of the flywheel, to calculate the response information of the node displacement of the deck. The flywheel-deck coupling dynamic model is a dynamic relationship model between the flywheel and the deck formed by dividing the deck into a plurality of nodes and a plurality of units, and according to the displacement of each node of the deck and the structural parameters of the deck and the flywheel, and the operating parameters of the flywheel;

[0203] An energy distribution calculation unit is used to establish a power flow energy transfer model under a frequency domain steady-state response, and calculate the energy information of each node of the cabin board according to the power flow energy transfer model and the node displacement response information of the cabin board. The power flow energy transfer model is an energy flow distribution model of each node of the cabin board in each direction formed based on the power flow method;

[0204] An energy flow image generating unit, used for generating a visualized energy flow image according to the position information of each node of the cabin and the energy information of each node of the cabin obtained by the energy distribution calculating unit;

[0205] An energy flow key area determination unit is used to identify the vortex area in the visualized energy flow image according to the movement form of energy in the visualized energy flow image, and determine the energy flow key area according to the energy flow vortex amount in the vortex area;

[0206] The damping coating area determination unit is used to use the energy flow key area as the damping coating application area to achieve vibration suppression of the cabin plate.

[0207] The system of this embodiment corresponds one-to-one with the above-mentioned method for suppressing spacecraft micro-vibration based on the key area of ​​energy flow, and will not be described in detail here.

[0208] This embodiment further provides a computer device, including a processor and a memory, wherein the memory is used to store a computer program, and the processor is used to execute the computer program to perform the above method.

[0209] The above is only a preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment, it is not intended to limit the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for suppressing micro-vibration of spacecraft based on key energy flow areas, characterized in that: The following steps are involved: Step S1, obtaining structural parameters of the cabin plate and flywheel in the target spacecraft and operating parameters of the flywheel; Step S2, establishing a flywheel-deck coupling dynamic model, and substituting the structural parameters of the deck and the flywheel and the operating parameters of the flywheel obtained in step S1, to calculate the node displacement response information of the deck, wherein the flywheel-deck coupling dynamic model is a dynamic relationship model between the flywheel and the deck formed by dividing the deck into a plurality of nodes and a plurality of units and constructing the displacement of each node of the deck and the structural parameters of the deck and the flywheel and the operating parameters of the flywheel; Step S3, establishing a power flow energy transfer model under a frequency domain steady-state response, and calculating the energy information of each node of the cabin board according to the power flow energy transfer model and the node displacement response information of the cabin board, wherein the power flow energy transfer model is an energy flow distribution model of each node of the cabin board in each direction formed based on the power flow method; Step S4, generating a visualized energy flow image according to the position information of each node of the deck and the energy information of each node of the deck obtained in step S3; Step S5, identifying a vortex area in the visualized energy flow image according to the movement form of energy in the visualized energy flow image, and determining an energy flow key area according to the energy flow vortex amount in the vortex area; Step S6, using the energy flow key area as the damping coating area to achieve vibration suppression of the cabin plate; In step S2, the expression of the flywheel-nacelle coupling dynamic model is: Where δ represents the node displacement of the flywheel-deck system, C c is the damping matrix of the flywheel-cabin system, K c is the stiffness matrix of the flywheel-deck system, Q is the disturbance excitation, M c is the mass matrix of the flywheel-deck system, M c =M d +M r , where M d is the deck mass matrix, M r is the flywheel mass matrix, expressed as M r =diag{m r ,I r ,I r }, I r is the radial moment of inertia of the flywheel, m r is the flywheel mass, G r is the flywheel gyro effect matrix, expressed as I p is the axial moment of inertia of the flywheel, Ω is the speed of the flywheel; The expression of disturbance excitation Q is: Among them, T u and F u are dynamic unbalance excitation and static unbalance excitation respectively, and They represent the initial phase angles of the static unbalance and dynamic unbalance distribution respectively.

2. The method for suppressing spacecraft micro-vibration based on the key area of ​​energy flow according to claim 1 is characterized in that: In step S1, the structural parameters of the deck include any one or more of the deck length, the deck width, the deck thickness, the dissipation coefficient, the deck density, the deck Poisson's ratio, the deck elastic modulus and the deck shear modulus; the structural parameters of the flywheel include any one or more of the mass, the axial moment of inertia, the radial moment of inertia and the flywheel position; the operating parameters of the flywheel include any one or more of the static unbalance, the dynamic unbalance and the flywheel speed.

3. The method for suppressing spacecraft micro-vibration based on the key area of ​​energy flow according to claim 1 is characterized in that: The steps to establish the flywheel-nacelle coupled dynamic model include: The cabin plate is divided by a three-degree-of-freedom four-node plate element, forming a total of n nodes and m units. The displacement δ of the jth node of the cabin plate is j for: d j =[w j i jx i jy ] T In the formula, j represents the node number, j = 1, 2, ..., n, where n is the total number of nodes, w j is the translational displacement in the z direction, θ jx is the rotation displacement around the x-axis, θ jy is the rotation displacement around the y-axis; Assume that the flywheel is fixed to the deck and installed at the node numbered f, then the displacement δ of the flywheel is f The same as the displacement of the fth node of the cabin, the expression is δ f =[w f θ fx θ fy ] T The displacement δ of the flywheel-deck system is composed of the displacements of each node of the deck, that is, δ = [δ1…δ n ] T ; Calculate the system kinetic energy T of the flywheel-deck system c 、System potential energy Π c and system dissipated energy R c , where the system kinetic energy T c for: Where ρ is the density of the deck, V d is the volume of the deck, I r is the radial moment of inertia of the flywheel rotor, I p is the axial moment of inertia of the flywheel rotor, m r is the mass of the flywheel, Ω is the speed of the rotor, and the symbol · represents the derivative with respect to time; The system potential energy Πc is: Where B is the strain matrix and D is the elastic coefficient matrix; System dissipated energy R c for: Where η is the dissipation coefficient; The calculated system kinetic energy T c 、System potential energy Π c and system dissipated energy R c Substituting into the Lagrange equation, the coupled dynamic model of flywheel-nacelle is obtained.

4. The method for suppressing spacecraft micro-vibration based on the key area of ​​energy flow according to claim 1 is characterized in that: The energy information includes time-averaged energy density and energy flow components under frequency domain steady-state response; The detailed steps of calculating the energy information of each node of the cabin board include: According to the node displacement response information of the cabin plate and the node number corresponding to the kth unit, the unit displacement response of the kth unit is obtained: k represents the unit number, k = 1, 2, ..., m, where m is the total number of units, and the unit displacement response Converted into unit centroid displacement δ ck , the calculation formula is: Among them, N(x c ,y c ) is the plate element shape function matrix, where x c ,y c denote the horizontal and vertical coordinates of the unit centroid, respectively, w ck is the translational displacement of the unit mass center in the z direction, θ cxk is the rotational displacement of the unit mass center around the x-axis, θ cyk is the rotation displacement of the unit mass center around the y-axis, k is the unit number, k = 1, ..., m; Based on the displacement response of the unit Calculate the unit centroid stress M c , the calculation formula is: Among them, M cxk is the bending moment generated by the unit mass center along the x direction, M cyk is the bending moment generated by the unit centroid along the y direction, M cxyk is the unit center of mass torque, B is the strain matrix, and D is the elastic coefficient matrix; The unit power flow energy transfer model under the frequency domain steady-state response is established, and its expression is: Among them, p xk represents the energy flow component of the kth unit in the x direction, p yk represents the energy flow component of the kth unit in the y direction, ω is the excitation frequency, μ is the Poisson's ratio of the cabin, Im represents the imaginary part, and * represents the complex conjugate; Displace the unit centroid by δ ck The three components w ck ,θ cxk ,θ cyk and the element centroid stress M ck The three components M cxk 、M cyk 、M cxyk Substituting into the unit power flow energy transfer model, the x-direction unit energy flow component p in the frequency domain steady-state response is obtained. xk and the y-direction unit energy flow component p yk ; According to the unit centroid displacement δ ck The three components w ck ,θ cxk ,θ cyk Calculate the time average energy density of each unit of the cabin The expression is: Among them, k x , k y are the wave numbers of the bending wave in the x and y directions respectively, h is the thickness of the deck, D is the bending stiffness of the deck, ρ is the density of the deck, t represents the time, and μ is the Poisson's ratio.

5. The method for suppressing spacecraft micro-vibration based on the key area of ​​energy flow according to claim 1, characterized in that: Step S5 includes: Determine the movement form of energy in the visualized energy flow image, wherein the movement forms of energy include source-sink flow and vortex flow, and the area enclosed by the streamlines of the vortex flow is the vortex area; the source-sink flow is a movement in which energy diffuses outward from the vibration source and finally converges to the flow, and the streamline deflection angle is less than 360°; the vortex flow is a movement in which there is local rotation in the transmission path and the streamline deflection angle exceeds 360°, wherein the vibration source is the starting point, the flow sink is the end point, and the line connecting the vibration source and the flow sink is the streamline; Calculate the vortex energy flow ω in the vortex zone f If the energy flow vorticity value is greater than the reference vorticity, and the area of ​​the current vortex zone is greater than the specified proportion of the cabin area, then the vortex zone is determined to be the key area of ​​energy flow.

6. The method for suppressing spacecraft micro-vibration based on the key area of ​​energy flow according to claim 5 is characterized in that: Energy flow vortex ω f The calculation formula is: in, is the unit response speed, δ c The displacement of the centroid of each unit δ ck It is formed by combining units in order, and rot represents the curl.

7. The method for suppressing micro-vibration of a spacecraft based on a critical energy flow area according to any one of claims 1 to 6, characterized in that: In step S6, a viscoelastic material with a loss factor between 0.1 and 0.8 and a storage modulus between 1 and 5 MPa is selected as the damping coating, and the viscoelastic material is any one of butyl rubber, polysulfide rubber and polyurethane elastomer.

8. A system for implementing the method for suppressing spacecraft micro-vibration based on the energy flow key area as described in any one of claims 1 to 7, characterized in that: include: A parameter acquisition unit, used to acquire the structural parameters of the cabin plate and flywheel in the target spacecraft and the operating parameters of the flywheel; A deck response calculation unit is used to establish a flywheel-deck coupling dynamic model, and substitute the structural parameters of the deck and the flywheel obtained by the parameter acquisition unit, and the operating parameters of the flywheel, to calculate the response information of the node displacement of the deck. The flywheel-deck coupling dynamic model is a dynamic relationship model between the flywheel and the deck formed by dividing the deck into a plurality of nodes and a plurality of units, and according to the displacement of each node of the deck and the structural parameters of the deck and the flywheel, and the operating parameters of the flywheel; An energy distribution calculation unit is used to establish a power flow energy transfer model under a frequency domain steady-state response, and calculate the energy information of each node of the cabin board according to the power flow energy transfer model and the node displacement response information of the cabin board. The power flow energy transfer model is an energy flow distribution model of each node of the cabin board in each direction formed based on the power flow method; An energy flow image generating unit, used for generating a visualized energy flow image according to the position information of each node of the cabin and the energy information of each node of the cabin obtained by the energy distribution calculating unit; An energy flow key area determination unit is used to identify the vortex area in the visualized energy flow image according to the movement form of energy in the visualized energy flow image, and determine the energy flow key area according to the energy flow vortex amount in the vortex area; The damping coating area determination unit is used to use the energy flow key area as the damping coating application area to achieve vibration suppression of the cabin plate.

9. A computer device comprising a processor and a memory, wherein the memory is used to store a computer program, wherein: The processor is configured to execute the computer program to perform the method according to any one of claims 1 to 7.

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