Finite element dynamic analysis-based high-speed rotor blade model correction method
By combining finite element simulation and experimental modal analysis, the finite element model of high-speed rotor blades is corrected by using modal expansion method and correction factor calculation, which solves the problem of large model errors in the existing technology, and achieves more accurate blade dynamic analysis and improvement of calculation efficiency.
Patent Information
- Application Number
- CN202411824162.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-12
- Publication Date
- 2025-03-25
AI Technical Summary
The prior art inevitably introduces structural errors, parameter errors and order errors when establishing a finite element model of high-speed rotor blades, resulting in deviations from the actual dynamic responses and the failure to accurately reflect the actual working conditions of the blades.
By combining finite element simulation technology and experimental modal analysis methods, the simulation model and experimental model of rotor blades are established, and the simulation model is corrected to reduce errors through modal expansion method and correction factor calculation.
The problem of large errors in the rotor blade model at high speeds is effectively solved. The corrected model calculation results are more in line with the actual working conditions of the blade, the frequency error is reduced to less than 5%, the calculation efficiency is improved by 50%, and the degree of freedom is reduced by 80-90%.
Smart Images
Figure CN119691931A_ABST
Abstract
Description
Technical Field
[0001] The present specification relates to the field of simulation model correction, and in particular to a high-speed rotor blade model correction method based on finite element dynamic analysis. Background Art
[0002] Rotor blades are important components in aircraft engines. The integrity of high-speed rotating blades directly affects the safe operation of the overall structure of aircraft engines. Among them, blade vibration is often the main cause of high-cycle fatigue cracks or other damage to the blades. Once the rotor blades are damaged, the engine may be damaged at the least, and a flight accident may cause casualties at the worst. Therefore, the vibration problem of high-speed rotor blades directly affects the safe operation of the overall structure of aircraft engines.
[0003] At high speeds, existing measurement technologies cannot measure all vibration parameters of rotor blades during rotation. Theoretical calculation and simulation analysis of high-speed rotor dynamics are still the most economical and reliable research methods. However, due to various factors such as processing errors, actual rotor blades always have certain differences from the ideal structure, resulting in deviations between finite element simulation results and actual dynamic responses.
[0004] At present, finite element technology is mostly used in my country to simulate rotor blades at high speeds. The existing finite element technology will inevitably introduce errors when establishing models. Mainly including model structure error, parameter error and order error. If the error exceeds the allowable value, the finite element model will not reflect the actual structural characteristics, resulting in incorrect judgment of the actual blades. Summary of the invention
[0005] One of the embodiments of this specification provides a high-speed rotor blade model correction method based on finite element dynamic analysis. The method includes:
[0006] S1, establishing a rotor blade simulation model according to a research object using finite element simulation technology, and obtaining dynamic characteristic parameters of the research object structure, wherein the dynamic characteristic parameters include a simulation mode, a simulation frequency, a simulation mass matrix, and a simulation stiffness matrix;
[0007] S2, establishing an experimental model of the rotor blade of the research object based on an experimental modal analysis method, and obtaining experimental parameters of the research object, wherein the experimental parameters include an experimental mode, an experimental frequency, an experimental mass matrix, and an experimental stiffness matrix;
[0008] S3, according to the simulation mode and the experimental mode, expanding the rotor blade experimental model based on the rotor blade simulation model to obtain expanded experimental parameters;
[0009] S4, obtaining a correction factor according to the dynamic characteristic parameters and the expanded experimental parameters, and correcting the rotor blade simulation model.
[0010] In some embodiments, the S3 includes:
[0011] Determining the objective function of the factor matrix to be expanded according to the simulation mode and the experimental mode;
[0012] Determining the optimal factor matrix to be expanded through the objective function;
[0013] Based on the to-be-expanded factor matrix, the rotor blade experimental model is expanded so that the expanded rotor blade experimental model has the same degree of freedom as the rotor blade simulation model;
[0014] The expanded experimental parameters are obtained by calculation based on the expanded rotor blade experimental model.
[0015] In some embodiments, the S4 includes:
[0016] Based on the dynamic characteristic parameters and the expanded experimental parameters, a characteristic equation group of the rotor blade simulation model and the rotor blade experimental model is established;
[0017] Based on the characteristic equation group, a difference equation of the rotor blade simulation model and the rotor blade experimental model with respect to the correction factor is established;
[0018] The correction factor is solved by the least square solution to correct the rotor blade simulation model.
[0019] One of the embodiments of this specification provides a high-speed rotor blade model correction system based on finite element dynamic analysis,
[0020] A simulation model building module is used to build a rotor blade simulation model according to the research object using finite element simulation technology to obtain dynamic characteristic parameters of the research object structure, wherein the dynamic characteristic parameters include simulation mode, simulation frequency, simulation mass matrix, and simulation stiffness matrix;
[0021] An experimental model building module, used to build an experimental model of the rotor blade of the research object based on an experimental modal analysis method, and obtain experimental parameters of the research object, wherein the experimental parameters include experimental mode, experimental frequency, experimental mass matrix, and experimental stiffness matrix;
[0022] An experimental model expansion module, used for expanding the rotor blade experimental model based on the rotor blade simulation model according to the simulation mode and the experimental mode, to obtain expanded experimental parameters;
[0023] The simulation model correction module is used to obtain a correction factor according to the dynamic characteristic parameters and the expanded experimental parameters, and to correct the rotor blade simulation model.
[0024] One of the embodiments of the present specification provides a high-speed rotor blade model correction device based on finite element dynamic analysis, including a processor, wherein the processor is used to execute a high-speed rotor blade model correction method based on finite element dynamic analysis.
[0025] One of the embodiments of the present specification provides a computer-readable storage medium, wherein the storage medium stores computer instructions. When a computer reads the computer instructions in the storage medium, the computer executes a high-speed rotor blade model correction method based on finite element dynamic analysis.
[0026] The beneficial effects of the present invention include:
[0027] 1. By using the modal expansion method, the problem of difficulty in matching the rotor blade experimental model and the rotor blade simulation model due to different nodes is solved.
[0028] 2. Use the correction method to correct the original rotor blade simulation model so that the calculation results of the corrected model are more consistent with the actual working conditions of the blade. Compared with the experimental results, when the speed is lower than 5000 rpm, the correction method can reduce the corrected frequency error to less than 5%. The frequency error of the 5000-15000 speed model is less than 10% using the low speed correction.
[0029] 3. Use the submodal synthesis method and introduce super units to accelerate the finite element correction process of the rotor blade simulation model, which increases the model correction calculation efficiency by 50% and reduces the calculation freedom by 80-90%. This solves the problem of too large matrix dimensions and difficulty in calculation caused by too many degrees of freedom in the finite element correction process. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] This specification will be further described in the form of exemplary embodiments, which will be described in detail by the accompanying drawings. These embodiments are not restrictive, and in these embodiments, the same number represents the same structure, wherein:
[0031] Figure 1 is an exemplary flow chart of a high-speed rotor blade model correction method based on finite element dynamic analysis according to some embodiments of this specification;
[0032] Figure 2 It is an exemplary structural diagram of a high-speed rotor blade model correction method system based on finite element dynamic analysis according to some embodiments of this specification. DETAILED DESCRIPTION
[0033] In order to more clearly illustrate the technical solutions of the embodiments of this specification, the following is a brief introduction to the drawings required for the description of the embodiments. Obviously, the drawings described below are only some examples or embodiments of this specification. For ordinary technicians in this field, this specification can also be applied to other similar scenarios based on these drawings without creative work. Unless it is obvious from the language environment or otherwise explained, the same reference numerals in the figures represent the same structure or operation.
[0034] It should be understood that the "system", "device", "unit" and / or "module" used herein are a method for distinguishing different components, elements, parts, portions or assemblies at different levels. However, if other words can achieve the same purpose, the words can be replaced by other expressions.
[0035] As shown in this specification and claims, unless the context clearly indicates an exception, the words "a", "an", "an" and / or "the" do not refer to the singular and may also include the plural. Generally speaking, the terms "comprise" and "include" only indicate the inclusion of the steps and elements that have been clearly identified, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements.
[0036] Flowcharts are used in this specification to illustrate the operations performed by the system according to the embodiments of this specification. It should be understood that the preceding or following operations are not necessarily performed precisely in order. Instead, the steps may be processed in reverse order or simultaneously. At the same time, other operations may also be added to these processes, or one or more operations may be removed from these processes.
[0037] Figure 1 FIG. 1 is an exemplary flow chart of a high-speed rotor blade model correction method based on finite element dynamic analysis according to some embodiments of this specification. Figure 1 As shown, the method includes:
[0038] S1, establishing a rotor blade simulation model according to a research object using finite element simulation technology, and obtaining dynamic characteristic parameters of the research object structure, wherein the dynamic characteristic parameters include simulation mode, simulation frequency, simulation mass matrix, and simulation stiffness matrix.
[0039] In some embodiments, the rotor blade simulation model uses the finite element analysis method to establish a finite element model of a specific engineering structure in a computer, and uses computer simulation technology to obtain the dynamic characteristics of the research object structure.
[0040] Finite element method is a numerical method that divides a complex continuum into a number of finite small units, establishes local simple equations on each unit, and then combines these local equations into the global equation of the whole system, so as to approximately solve complex engineering problems. The main purpose of finite element method is to simulate complex real-world working conditions through computers.
[0041] In some embodiments, the dynamic characteristic parameters extracted from the finite element modeling results of the rotor blade simulation model include: mass matrix Mn, stiffness matrix Kn, simulation frequency w, and simulation mode Ψ.
[0042] S2, establishing an experimental model of the rotor blade of the research object based on an experimental modal analysis method, and obtaining experimental parameters of the research object, wherein the experimental parameters include experimental mode, experimental frequency, experimental mass matrix, and experimental stiffness matrix.
[0043] In some embodiments, the rotor blade experimental model is based on the experimental modal analysis method, and the structure is experimentally tested on the premise of having a real object or prototype of the engineering object. Specifically, laser vibration measurement technology can be used to measure the experimental parameters of the model, and the experimental frequency w*, experimental mode Φ*, and experimental mass matrix M of the model can be extracted according to the experimental measurement results. * , experimental stiffness matrix K * .
[0044] S3, according to the simulation mode and the experimental mode, the rotor blade experimental model is expanded based on the rotor blade simulation model to obtain expanded experimental parameters.
[0045] In some embodiments, step S3 specifically includes:
[0046] Firstly, according to the simulation mode and the experimental mode, an objective function of the factor matrix to be expanded is determined, and an optimal factor matrix to be expanded is determined through the objective function.
[0047] Specifically, as shown in formula (1):
[0048]
[0049] Where L(Q) is the objective function, Q is the factor matrix to be expanded, simulation frequency w, simulation mode Ψ, and mode Ф*.
[0050] By taking the derivative of the objective function L(Q) and setting the reciprocal to zero, the optimal solution of the factor matrix Q to be expanded is calculated.
[0051] Then, based on the factor matrix to be expanded, the rotor blade experimental model is expanded so that the expanded rotor blade experimental model has the same degree of freedom as the rotor blade simulation model, and the expanded experimental parameters are obtained by calculation according to the expanded rotor blade experimental model.
[0052] Specifically, in order to ensure that the experimental data and the simulation data are physically consistent, the experimental modal matrix is expanded to have the same dimension as the simulation modal result. Here, the optimal fitting method is used to expand the experimental mode. This method represents the rotor experimental mode as a linear combination of the simulation mode to form an expanded experimental modal matrix, as shown in formula (2):
[0053]
[0054] In the formula, represents the experimental mode after expansion, and Q is the factor matrix to be expanded.
[0055] In some embodiments, the rotor blade simulation model may be reduced in order by using a substructure modal analysis method.
[0056] Specifically, for complex rotor blades, the finite element model has a large number of nodes, which leads to a large dimension of the correction matrix and high computational requirements, so the model needs to be reduced in order. The substructure modal synthesis method (CMS) is an effective method for dynamic analysis of large structures. CMS decomposes the entire structure into several smaller substructures, performs modal analysis on each substructure independently, and then synthesizes the modal information of these substructures in the global coordinate system to form the dynamic characteristics of the overall system.
[0057] Furthermore, the specific process of reducing the order of the rotor blade simulation model is as follows:
[0058] 1) Structural division: Divide the complex structure into several substructures. Each substructure is a component of the overall structure, which is convenient for independent analysis.
[0059] 2) Substructure modal analysis: Perform modal analysis on each substructure to obtain its low-order modes and interface modes. These modal information are used to describe the dynamic characteristics inside the substructure and the connection characteristics with other substructures.
[0060] 3) Superelement generation: compress the modal information of each substructure into an equivalent superelement. The superelement retains the interface degrees of freedom and important internal modes, greatly reducing the number of degrees of freedom, thereby simplifying the calculation.
[0061] 4) Superunit combination: Combine the generated superunits into the overall structural model. Connect adjacent superunits through interface degrees of freedom to form an overall superunit model.
[0062] 5) Modal synthesis: Perform modal synthesis on the entire super-unit model to construct a complete system mode. Through this process, the modal information of each super-unit can be integrated into the modal characteristics of the overall system.
[0063] 6) Overall analysis: Perform dynamic analysis on the integrated overall model to solve its natural frequency and modal vibration shape, and obtain the dynamic response and vibration characteristics of the entire structure.
[0064] S4, obtaining a correction factor according to the dynamic characteristic parameters and the expanded experimental parameters, and correcting the rotor blade simulation model.
[0065] In some embodiments, step S4 specifically includes:
[0066] S41, based on the dynamic characteristic parameters and the expanded experimental parameters, establishing a set of characteristic equations for the rotor blade simulation model and the rotor blade experimental model.
[0067] In some embodiments, the correction factor can be obtained by using an improved orthogonal model-orthogonal mode method. The improved orthogonal model-orthogonal mode method is a parameter modification method that does not rely on sensitivity analysis. By using the above method, it is assumed that there is a relationship between the rotor blade simulation model and the rotor blade experimental model, and a characteristic equation group is established, as shown in formula (3):
[0068]
[0069] Among them, K* is the experimental stiffness matrix, M* is the experimental mass matrix, K and M are the simulation stiffness matrix and simulation mass matrix of the rotor blade simulation model, respectively, and Kn and Mn are the contributions of the simulation stiffness matrix and simulation mass matrix of the nth subunit of the rotor blade simulation model to the overall matrix of the system: α n , β n is the stiffness correction factor and mass correction factor of the nth sub-unit, and Ne represents the number of units.
[0070] S42, based on the characteristic equation group, establishing a difference equation of the rotor blade simulation model and the rotor blade experimental model with respect to the correction factor.
[0071] Specifically, the improved orthogonal model-orthogonal modal method process establishes the difference equation between the experimental mode and the finite element modal characteristic equation by substituting the two. For the i-th order simulation mode and the j-th order experimental mode, the following relationship is obtained, as shown in equation (4):
[0072]
[0073] Among them, C ij，n and E ij，nrepresents the stiffness and mass contribution of the nth element, f ij is the error between the experimental and simulated modes. Writing the equation system in matrix form gives equation (5):
[0074] [CE]p=Gp=f (5),
[0075] Where p is the correction factor.
[0076] S43, solving the correction factor through the least square solution, and correcting the rotor blade simulation model.
[0077] It should be noted that the above description of the relevant process is only for example and explanation, and does not limit the scope of application of this specification. For those skilled in the art, various modifications and changes can be made to the process under the guidance of this specification. However, these modifications and changes are still within the scope of this specification.
[0078] Figure 2 2 is an exemplary structural diagram of a high-speed rotor blade model correction method system based on finite element dynamic analysis according to some embodiments of this specification. Specifically, the high-speed rotor blade model correction system 200 includes:
[0079] A simulation model building module 210 is used to build a rotor blade simulation model according to a research object using finite element simulation technology to obtain dynamic characteristic parameters of the research object structure, wherein the dynamic characteristic parameters include simulation mode, simulation frequency, simulation mass matrix, and simulation stiffness matrix;
[0080] An experimental model building module 220 is used to build an experimental model of the rotor blade of the research object based on an experimental modal analysis method, and obtain experimental parameters of the research object, wherein the experimental parameters include experimental mode, experimental frequency, experimental mass matrix, and experimental stiffness matrix;
[0081] The experimental model expansion module 230 is used to expand the rotor blade experimental model based on the rotor blade simulation model according to the simulation mode and the experimental mode, and obtain the expanded experimental parameters;
[0082] The simulation model correction module 240 is used to obtain a correction factor through an improved orthogonal model-orthogonal modal calculation unit matrix to correct the rotor blade simulation model.
[0083] One of the embodiments of the present specification provides a high-speed rotor blade model correction device based on finite element dynamic analysis, including a processor, wherein the processor is used to execute a high-speed rotor blade model correction method based on finite element dynamic analysis.
[0084] One of the embodiments of the present specification provides a computer-readable storage medium, wherein the storage medium stores computer instructions. When a computer reads the computer instructions in the storage medium, the computer executes a high-speed rotor blade model correction method based on finite element dynamic analysis.
[0085] The basic concepts have been described above. Obviously, for those skilled in the art, the above detailed disclosure is only for example and does not constitute a limitation of this specification. Although not explicitly stated here, those skilled in the art may make various modifications, improvements and corrections to this specification. Such modifications, improvements and corrections are suggested in this specification, so such modifications, improvements and corrections still belong to the spirit and scope of the exemplary embodiments of this specification.
[0086] At the same time, this specification uses specific words to describe the embodiments of this specification. For example, "one embodiment", "an embodiment", and / or "some embodiments" refer to a certain feature, structure or characteristic related to at least one embodiment of this specification. Therefore, it should be emphasized and noted that "one embodiment" or "an embodiment" or "an alternative embodiment" mentioned twice or more in different positions in this specification does not necessarily refer to the same embodiment. In addition, certain features, structures or characteristics in one or more embodiments of this specification can be appropriately combined.
[0087] In addition, unless explicitly stated in the claims, the order of the processing elements and sequences described in this specification, the use of alphanumeric characters, or the use of other names are not intended to limit the order of the processes and methods of this specification. Although the above disclosure discusses some invention embodiments that are currently considered useful through various examples, it should be understood that such details are only for illustrative purposes, and the attached claims are not limited to the disclosed embodiments. On the contrary, the claims are intended to cover all modifications and equivalent combinations that are consistent with the essence and scope of the embodiments of this specification. For example, although the system components described above can be implemented by hardware devices, they can also be implemented only by software solutions, such as installing the described system on an existing server or mobile device.
[0088] Similarly, it should be noted that in order to simplify the description disclosed in this specification and thus help understand one or more embodiments of the invention, in the above description of the embodiments of this specification, multiple features are sometimes combined into one embodiment, figure or description thereof. However, this disclosure method does not mean that the features required by the subject matter of this specification are more than the features mentioned in the claims. In fact, the features of the embodiments are less than all the features of the single embodiment disclosed above.
[0089] In some embodiments, numbers describing the number of components and attributes are used. It should be understood that such numbers used in the description of the embodiments are modified by the modifiers "about", "approximately" or "substantially" in some examples. Unless otherwise specified, "about", "approximately" or "substantially" indicate that the numbers are allowed to vary by ±20%. Accordingly, in some embodiments, the numerical parameters used in the specification and claims are approximate values, which may change according to the required features of individual embodiments. In some embodiments, the numerical parameters should take into account the specified significant digits and adopt the general method of retaining digits. Although the numerical domains and parameters used to confirm the breadth of their range in some embodiments of this specification are approximate values, in specific embodiments, the setting of such numerical values is as accurate as possible within the feasible range.
[0090] Each patent, patent application, patent application publication, and other materials, such as articles, books, specifications, publications, documents, etc., cited in this specification are hereby incorporated by reference in their entirety. Except for application history documents that are inconsistent with or conflicting with the contents of this specification, documents that limit the broadest scope of the claims of this specification (currently or later attached to this specification) are also excluded. It should be noted that if the descriptions, definitions, and / or use of terms in the materials attached to this specification are inconsistent or conflicting with the contents described in this specification, the descriptions, definitions, and / or use of terms in this specification shall prevail.
[0091] Finally, it should be understood that the embodiments described in this specification are only used to illustrate the principles of the embodiments of this specification. Other variations may also fall within the scope of this specification. Therefore, as an example and not a limitation, alternative configurations of the embodiments of this specification may be considered consistent with the teachings of this specification. Accordingly, the embodiments of this specification are not limited to the embodiments explicitly introduced and described in this specification.
Claims
1. A high-speed rotor blade model correction method based on finite element dynamic analysis, characterized in that: include: S1, establishing a rotor blade simulation model according to a research object using finite element simulation technology, and obtaining dynamic characteristic parameters of the research object structure, wherein the dynamic characteristic parameters include a simulation mode, a simulation frequency, a simulation mass matrix, and a simulation stiffness matrix; S2, establishing an experimental model of the rotor blade of the research object based on an experimental modal analysis method, and obtaining experimental parameters of the research object, wherein the experimental parameters include an experimental mode, an experimental frequency, an experimental mass matrix, and an experimental stiffness matrix; S3, according to the simulation mode and the experimental mode, expanding the rotor blade experimental model based on the rotor blade simulation model to obtain expanded experimental parameters; S4, obtaining a correction factor according to the dynamic characteristic parameters and the expanded experimental parameters, and correcting the rotor blade simulation model.
2. The high-speed rotor blade model correction method based on finite element dynamic analysis according to claim 1 is characterized in that: The S3 includes: Determining the objective function of the factor matrix to be expanded according to the simulation mode and the experimental mode; Determining the optimal factor matrix to be expanded through the objective function; Based on the to-be-expanded factor matrix, the rotor blade experimental model is expanded so that the expanded rotor blade experimental model has the same degree of freedom as the rotor blade simulation model; The expanded experimental parameters are obtained by calculation based on the expanded rotor blade experimental model.
3. The high-speed rotor blade model correction method based on finite element dynamic analysis according to claim 2 is characterized in that: Before the step of determining the objective function of the factor matrix to be expanded according to the simulation mode and the experimental mode, the method further includes: The simulation modes of the rotor blade simulation model are reduced in order by using a substructure modal analysis method.
4. The high-speed rotor blade model correction method based on finite element dynamic analysis according to claim 1 is characterized in that: The S4 includes: Based on the dynamic characteristic parameters and the expanded experimental parameters, a characteristic equation group of the rotor blade simulation model and the rotor blade experimental model is established; Based on the characteristic equation group, a difference equation of the rotor blade simulation model and the rotor blade experimental model with respect to the correction factor is established; The correction factor is solved by the least square solution to correct the rotor blade simulation model.
5. A high-speed rotor blade model correction system based on finite element dynamic analysis, characterized in that: include: A simulation model building module is used to build a rotor blade simulation model according to the research object using finite element simulation technology to obtain dynamic characteristic parameters of the research object structure, wherein the dynamic characteristic parameters include simulation mode, simulation frequency, simulation mass matrix, and simulation stiffness matrix; An experimental model building module, used to build an experimental model of the rotor blade of the research object based on an experimental modal analysis method, and obtain experimental parameters of the research object, wherein the experimental parameters include experimental mode, experimental frequency, experimental mass matrix, and experimental stiffness matrix; An experimental model expansion module, used for expanding the rotor blade experimental model based on the rotor blade simulation model according to the simulation mode and the experimental mode, to obtain expanded experimental parameters; The simulation model correction module is used to obtain a correction factor according to the dynamic characteristic parameters and the expanded experimental parameters, and to correct the rotor blade simulation model.
6. A high-speed rotor blade model correction device based on finite element dynamic analysis, comprising a processor, wherein the processor is used to execute the high-speed rotor blade model correction method based on finite element dynamic analysis according to any one of claims 1 to 4.
7. A computer-readable storage medium, wherein the storage medium stores computer instructions. When a computer reads the computer instructions in the storage medium, the computer executes the high-speed rotor blade model correction method based on finite element dynamic analysis as described in any one of claims 1 to 4.