Carrier rocket vibration mode slope efficient prediction method based on model polycondensation

Abstract

The carrier rocket vibration mode slope efficient prediction method based on model condensation comprises the steps that 1, a three-dimensional finite element model of a cabin section where an inertial device is located is established; 2) performing model polycondensation on the three-dimensional finite element model of the cabin section where the inertial device is located; specifically, the degree of freedom of a cabin section structure is divided into a main degree of freedom and a secondary degree of freedom, a feature vector of the main degree of freedom participates in calculation of a physical model feature equation, order reduction of the physical model feature equation is achieved, a polycondensation model feature equation is obtained, and therefore a polycondensation model of a cabin section where the inertial device is located is obtained; and 3) applying the condensation model of the cabin section where the inertial device is located to whole-rocket dynamics analysis, and obtaining the vibration mode slope of the cabin section where the inertial device is located in a whole-rocket flight state by adopting a direct extraction method. The method solves the technical problem that an accurate and efficient prediction method for the vibration mode slope at the inertial device is lacked in the field at present.

Description

Technical Field

[0001] The present invention relates to the field of launch vehicles, and particularly to an efficient prediction method for the mode shape slope of a launch vehicle based on model condensation. Background Art

[0002] The mode shape slope at the inertial device in the flight state is an important parameter for the design of the attitude control system of a launch vehicle. The mode shape slope at the inertial device belongs to the local mode shape slope and is easily affected by factors such as skin (panel) wrinkling deformation, nearby opening deformation, and uncertainty in part connection. In the past, full-vehicle modal tests were generally used in engineering to obtain local mode shape slope data. The full-vehicle modal test has a long cycle and high cost, and in recent years, with the continuous improvement of the commercialization level of launch vehicles and simulation technology, it has gradually been cancelled. Using a three-dimensional finite element model can effectively improve the prediction accuracy of the mode shape slope at the inertial device, but the calculation efficiency of the three-dimensional model is relatively low, seriously affecting the development progress of the model. Therefore, it is necessary to carry out research on accurate and efficient prediction methods for local mode shape slopes. Summary of the Invention

[0003] The purpose of the present invention is to provide an efficient prediction method for the mode shape slope of a launch vehicle based on model condensation, so as to solve the technical problem that there is a lack of accurate and efficient prediction methods for the mode shape slope at the inertial device in the current field.

[0004] To achieve the above purpose, the present invention provides an efficient prediction method for the mode shape slope of a launch vehicle based on model condensation, including: Step 1, establishing a three-dimensional finite element model of the compartment where the inertial device is located; Step 2, performing model condensation on the three-dimensional finite element model of the compartment where the inertial device is located; specifically, dividing the degrees of freedom of the compartment structure into main degrees of freedom and secondary degrees of freedom, and using the eigenvectors of the main degrees of freedom to participate in the calculation of the characteristic equation of the physical model, realizing the reduction of the order of the characteristic equation of the physical model, obtaining the characteristic equation of the condensed model, and thus obtaining the condensed model of the compartment where the inertial device is located; Step 3, applying the condensed model of the compartment where the inertial device is located to the full-vehicle dynamics analysis, and using the direct extraction method to obtain the mode shape slope of the compartment where the inertial device is located under the full-vehicle flight state.

[0005] In the above-mentioned efficient prediction method for the mode shape slope of a launch vehicle based on model condensation, in Step 1, the modeling principle is: fully reflecting the dynamic characteristics of the inertial device; the modeling tool is based on commercial finite element preprocessing software; when modeling, the installation bracket of the inertial device and its nearby parts are simulated in three dimensions using shell elements and solid elements, and the inertial device is simulated using lumped mass elements, but the mass, inertia, and centroid position of the inertial device should be accurately reflected.

[0006] In the above-mentioned efficient prediction method for the mode shape slope of a launch vehicle based on model condensation, Step 2 includes:

[0007] 2-1) Divide the degrees of freedom \(n\) of the module structure into primary degrees of freedom and secondary degrees of freedom, and rewrite the physical model characteristic equation as:

[0008]

[0009] where \(m\) is the number of primary degrees of freedom, which are the first \(m\) of the total number of degrees of freedom \(n\) of the entire rocket; \(s\) is the number of secondary degrees of freedom, which are the last \(n - m\) of the total number of degrees of freedom \(n\) of the entire rocket; \(M\) is the structural mass matrix, and \(K\) is the structural stiffness matrix, both of which are \(n\times n\) square matrices, is the eigenvector, and \(\omega\) 2 is the eigenvalue; \(m\ll n\);

[0010] 2-2) Derive the relationship between and from Equation (1), specifically:

[0011] 2-2-1) Expand the second row in Equation (1) to obtain:

[0012]

[0013] 2-2-2) Solve for in Equation (2) to get:

[0014]

[0015] 2-2-3) Considering that in engineering, the mass matrix is usually a lumped mass matrix, i.e., a diagonal matrix, then \(M\) sm = \(M\) ms = 0, and further simplify Equation (3) to:

[0016]

[0017] 2-2-4) Ignore the inertial effect of the secondary degrees of freedom, i.e., \(M\) ss = 0, then Equation (4) simplifies to:

[0018]

[0019] 2-2-5) Combine Equation (5) to obtain the eigenvector of the physical model characteristic equation as:

[0020]

[0021] 2-2-6) Denote as the degrees of freedom transformation matrix, then Equation (6) simplifies to:

[0022]

[0023] Equation (7) is and relationship;

[0024] 2 - 3) Utilize and relationship to achieve the reduction of order of the physical model characteristic equation to obtain the reduced - order model characteristic equation;

[0025] Utilize and relationship, use with fewer degrees of freedom to participate in the calculation of the physical model characteristic equation, and achieve the reduction of order of the equation. Specifically:

[0026] 2 - 3 - 1) Combining Equation (7), the physical model characteristic equation can be written as:

[0027]

[0028] 2 - 3 - 2) Multiply both sides of Equation (8) on the left by T T to obtain:

[0029]

[0030] 2 - 3 - 3) Denote K R = T T KT, M R = T T MT as the condensed stiffness matrix and the condensed mass matrix respectively, then Equation (9) can be written as:

[0031]

[0032] Equation (10) is the reduced - order model characteristic equation;

[0033] 2 - 4) Solving the reduced - order model characteristic equation can obtain the approximate solution of the characteristic value ω 2 of the physical model characteristic equation and the eigenvectors of the main degrees of freedom

[0034] The above - mentioned method for efficiently predicting the mode - shape slope of a launch vehicle based on model condensation, wherein in step 2, model condensation is performed by programming or through commercial finite - element software.

[0035] Compared with the prior art, the beneficial technical effects of the present invention are:

[0036] An efficient prediction method for the mode shape slope of a launch vehicle based on model condensation, which is proposed by the present invention, is based on the model condensation technology and the direct extraction method of the mode shape slope, and can be applied to the field of launch vehicle dynamics analysis. While ensuring the calculation accuracy of the slope at the inertial device, this method greatly improves the calculation efficiency, enhances the reliability and safety of the launch vehicle, shortens the development cycle of the launch vehicle, and can effectively solve the technical problem that there is a lack of an accurate and efficient prediction method for the mode shape slope at the inertial device in the flight state in this field. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The efficient prediction method for the mode shape slope of a launch vehicle based on model condensation of the present invention is given by the following embodiments and drawings.

[0038] Figure 1 It is a flowchart of the efficient prediction method for the mode shape slope of a launch vehicle based on model condensation according to an embodiment of the present invention.

[0039] Figure 2 It is a schematic diagram of a three-dimensional finite element model of the section where the inertial device is located in an embodiment of the present invention.

[0040] Figure 3 It is a matching diagram of the test results and modal simulation results of the breathing order mode shape of the local skin of a rate gyro in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] The following will combine Figures 1 to 3 to further describe in detail the efficient prediction method for the mode shape slope of a launch vehicle based on model condensation of the present invention.

[0042] Figure 1 Shown is a flowchart of the efficient prediction method for the mode shape slope of a launch vehicle based on model condensation according to an embodiment of the present invention.

[0043] Refer to Figure 1 , the efficient prediction method for the mode shape slope of a launch vehicle based on model condensation in this embodiment includes:

[0044] Step 1: Establish a three-dimensional finite element model of the section where the inertial device is located;

[0045] The modeling principle is: to fully reflect the dynamic characteristics of the inertial device as much as possible; the modeling tool is based on commercial finite element preprocessing software, such as HyperMesh, MSC.Patran;

[0046] Taking the rate gyro as an example, in this embodiment, MSC.Patran is used to establish a three-dimensional finite element model of the compartment where the inertial device (rate gyro) is located. When modeling, the installation bracket of the inertial device and its nearby parts are simulated in three dimensions using shell elements, solid elements, etc., and the inertial device is simulated using lumped mass elements, but the mass, inertia, and centroid position of the inertial device should be accurately reflected. The three-dimensional finite element model of the compartment where the inertial device is located established in this embodiment is as shown in Figure 2 shown;

[0047] Step 2: Condense the three-dimensional finite element model of the compartment where the inertial device is located to obtain a condensed model of the compartment where the inertial device is located;

[0048] The prediction of the mode shape slope is essentially to solve the generalized eigenvalue problem of the undamped free vibration of the entire launch vehicle, that is, the solution problem of the characteristic equation of the physical model where M is the structural mass matrix and K is the structural stiffness matrix, both of which are n-order square matrices, is the eigenvector, and ω 2 is the eigenvalue; when the number of degrees of freedom of the entire rocket is very large or the virtual mass method is used to simulate the liquid in the structure, the orders of the M matrix and the K matrix are very high (that is, n takes a large value), and the computational cost of directly solving the characteristic equation of the above physical model is very large;

[0049] In engineering, often only the eigenvalues of some of the first few orders and the eigenvectors of some degrees of freedom are concerned. Based on the above idea, the model condensation reduces the matrix order and improves the computational efficiency through modal truncation;

[0050] Specifically, it includes:

[0051] 2-1) Divide the degrees of freedom (n, a large number) of the compartment structure into main degrees of freedom (also called retained degrees of freedom, the first m, a small number) and secondary degrees of freedom (also called reduced degrees of freedom, the last n-m), then the characteristic equation of the physical model can be written as:

[0052]

[0053] where the subscripts m and s represent the number of main degrees of freedom and the number of secondary degrees of freedom, respectively;

[0054] 2-2) Derive the relationship between and from Equation (1), specifically:

[0055] 2-2-1) Expand the second row in Equation (1) to obtain:

[0056]

[0057] 2-2-2) Solve in Equation (2) to obtain:

[0058]

[0059] 2-2-3) Considering that the mass matrix in engineering is usually a lumped mass matrix, i.e., a diagonal matrix, then M sm = M ms = 0. Thus, equation (3) is simplified to:

[0060]

[0061] 2-2-4) Ignoring the inertial effect of the secondary degrees of freedom, i.e., M ss = 0, then equation (4) is simplified to:

[0062]

[0063] 2-2-5) Combining equation (5), the eigenvector of the characteristic equation of the physical model is obtained as:

[0064]

[0065] 2-2-6) Denote as the degree-of-freedom transformation matrix. Then equation (6) is simplified to:

[0066]

[0067] Equation (7) is the relationship between and ;

[0068] 2-3) Using the relationship between and to reduce the order of the characteristic equation of the physical model, and obtaining the reduced-order model characteristic equation;

[0069] Using the relationship between and , using the with fewer degrees of freedom to participate in the calculation of the characteristic equation of the physical model to achieve the reduction of the equation order. Specifically:

[0070] 2-3-1) Combining equation (7), the characteristic equation of the physical model can be written as:

[0071]

[0072] 2-3-2) Multiply both sides of equation (8) on the left by T T to obtain:

[0073]

[0074] 2-3-3) Denote K R = T T KT, MR = T T Let \(K\) and \(M\) be the stiffness matrix and mass matrix after condensation respectively. Then Equation (9) can be written as:

[0075]

[0076] Equation (10) is the characteristic equation of the condensed model;

[0077] The condensed stiffness matrix \(K\) R and the condensed mass matrix \(M\) R are the condensed models of the section where the inertial device is located; \(\omega\) 2 and can characterize the dynamic characteristics of the section where the inertial device is located;

[0078] The characteristic equation of the condensed model is an \(m\)-order equation. The main degrees of freedom \(m\) can be selected as needed. Generally, \(m\) is small (i.e., \(m\ll n\)). Therefore, compared with the characteristic equation of the physical model, the computational amount of the characteristic equation of the condensed model is greatly reduced;

[0079] 2 - 4) Solving the characteristic equation of the condensed model can obtain the approximate solutions of the eigenvalues \(\omega\) 2 of the physical model characteristic equation and the eigenvectors \(\varphi\) m of the main degrees of freedom (retained degrees of freedom);

[0080] By comparing the \(\omega\) R and \(\varphi\) 2 obtained by solving the characteristic equation of the condensed model \((K R -\omega m M)\varphi 2 = 0 with the \(\omega\) m and \(\varphi\) obtained by solving the physical model characteristic equation \((K - \omega 2 M)\varphi = 0, the reliability of the condensed model of the section where the inertial device is located can be verified; 2 2

[0081] Model condensation can be carried out by writing a program or using commercial finite element software (such as MSC.Nastran);

[0082] Based on the three - dimensional finite element model of the section where the inertial device is located established in step 1), the structural mass matrix \(M\) and structural stiffness matrix \(K\) in the physical model characteristic equation \((K - \omega 2 M)\varphi = 0 can be obtained. At this time, the orders of the \(M\) matrix and \(K\) matrix are very high (usually the value of \(n\) is in the tens of thousands). In this embodiment, \(m = 200\) is selected. According to step 2, the reduced - order stiffness matrix and mass matrix, that is, the condensed stiffness matrix \(K R and the condensed mass matrix \(M R can be calculated, and then the characteristic equation of the condensed model is obtained; solving the characteristic equation of the condensed model to obtain the approximate solution of \(\omega 2 and \(\varphi\)m ;

[0083] Step 3: Apply the lumped model of the section where the inertial device is located to the full-rocket dynamics analysis, and use the direct extraction method to obtain the mode shape slope of the section where the inertial device is located under the full-rocket flight state;

[0084] In this embodiment, the lumped model of the section where the inertial device is located obtained in Step 2 is subjected to the full-rocket vertical state modal analysis. The absolute deviation between the simulation result and the test result of the mode shape slope at the rate gyro is less than 0.002, and the result consistency is very good, as Figure 3 shown.

[0085] The present invention has been successfully applied to the elastic design and coupling analysis of the first flight state of a certain domestic new-generation launch vehicle. The present invention can fully reflect the local dynamic characteristics of the inertial device and improve the prediction accuracy of the mode shape slope of the inertial device under the flight state of the launch vehicle.

[0086] Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. An efficient prediction method for the slope of a launch vehicle vibration mode based on model condensation, characterized in that: include: Step 1: Establish a three-dimensional finite element model of the compartment where the inertial device is located; Step 2, performing model reduction on the three-dimensional finite element model of the compartment where the inertial device is located to obtain a reduced model of the compartment where the inertial device is located; The degrees of freedom of the cabin structure are divided into primary degrees of freedom and secondary degrees of freedom, and the eigenvectors of the primary degrees of freedom are used to participate in the calculation of the characteristic equation of the physical model, so as to reduce the order of the characteristic equation of the physical model and obtain the characteristic equation of the condensed model, thereby obtaining the condensed model of the cabin where the inertial device is located; Step 3: Apply the condensed model of the compartment where the inertial device is located to the dynamic analysis of the entire rocket, and use the direct extraction method to obtain the vibration mode slope of the compartment where the inertial device is located under the flight state of the entire rocket.

2. The method for efficiently predicting the slope of a launch vehicle mode based on model condensation according to claim 1, characterized in that: In the step 1, the modeling principle is: fully reflect the dynamic characteristics of the inertial device; the modeling tool is based on commercial finite element pre-processing software; when modeling, the inertial device mounting bracket and its surrounding parts are simulated in three-dimensional form using shell units and solid units, and the inertial device is simulated using concentrated mass units, but the mass, inertia and center of mass position of the inertial device should be accurately reflected.

3. The method for efficiently predicting the slope of a launch vehicle mode based on model condensation according to claim 1, characterized in that: The step 2 comprises: 2-1) The degrees of freedom n of the cabin structure are divided into primary degrees of freedom and secondary degrees of freedom. The characteristic equation of the physical model is Rewrite it as: In the formula, m is the number of primary degrees of freedom, which is the first m of the total number of degrees of freedom n; s is the number of secondary degrees of freedom, which is the last nm of the total number of degrees of freedom n; M is the structural mass matrix, and K is the structural stiffness matrix, both of which are n-order square matrices. is the eigenvector, ω 2 is the eigenvalue; m<<n; 2-2) According to formula (1), we can deduce and The relationship is as follows: 2-2-1) Expand the second line in formula (1) to obtain: 2-2-2) Solve the equation (2) get: 2-2-3) Considering that the mass matrix in engineering is usually a clustered mass matrix, that is, a diagonal matrix, then M sm =M ms =0, and then simplify formula (3) to: 2-2-4) Ignore the inertial effect of the secondary degrees of freedom, that is, M ss =0, then formula (4) is simplified to: 2-2-5) Combining formula (5), the characteristic vector of the characteristic equation of the physical model is obtained as: 2-2-6) Note is called the degree of freedom conversion matrix, then equation (6) is simplified to: Formula (7) is and relationship; 2-3)Use and The relationship between the physical model characteristic equation is realized by The order of is reduced to obtain the characteristic equation of the polycondensation model; use and The relationship between Participate in the calculation of the characteristic equation of the physical model and realize the order reduction of the equation, specifically: 2-3-1) Combined with formula (7), the characteristic equation of the physical model can be written as: 2-3-2) Multiply both sides of equation (8) by T T get: 2-3-3) Remember K R =T T KT, M R =T T MT are the stiffness matrix and mass matrix after polycondensation, respectively. Then equation (9) can be written as: Formula (10) is the characteristic equation of the polycondensation model; 2-4) Solving the characteristic equation of the polycondensation model can obtain the characteristic value ω of the characteristic equation of the physical model 2 The approximate solution and the eigenvectors of the main degrees of freedom 4. The method for efficiently predicting the slope of a launch vehicle mode based on model condensation according to claim 1, characterized in that: In step 2, the model is condensed by writing a program or using commercial finite element software.

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