Deformation analysis method for super-long blade based on finite element simulation

Abstract

The application relates to a super-long blade deformation analysis method based on finite element simulation and belongs to the technical field of finite element product state simulation analysis, and solves the technical problem that the three-dimensional deformation analysis of the existing finite element analysis method cannot consider high precision, strong robustness and engineering practicability. The method steps are as follows: a finite element model of a fan super-long blade before deformation is established; a reference line of the fan super-long blade before deformation is determined; the fan super-long blade before deformation is discretized into a plurality of sectional blades on the reference line; based on modal analysis of the finite element model and local strain information of the fan super-long blade, the curvature of the reference line of the fan super-long blade after deformation is obtained; based on the curvature of the reference line, the position vector of each sectional blade after deformation is obtained; and the blade deformation vector is obtained according to the position vector of the blade after deformation and the position vector of the blade before deformation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of finite element product state simulation analysis, and particularly relates to a super-long blade deformation analysis method based on finite element simulation. BACKGROUND

[0002] As a powerful tool for structural performance analysis, the finite element analysis method has been widely used in the design and simulation stage of large flexible structures such as fan blades. This method can effectively predict the mechanical response of the structure under complex loads by establishing a high-precision model, providing a theoretical basis for optimization design.

[0003] The Chinese invention patent application with the publication number CN119272560A discloses a structure monitoring and abnormality identification method and system based on refined inverse finite elements in the full-size test process of a wind turbine blade. The three-dimensional strain field and displacement field of the wind turbine blade under torsional load are obtained by using finite element simulation and load mapping method. Each blade component is pre-classified to determine the corresponding monitoring scheme and perform full-size test experiment. Different inverse finite element calculation modules are used to process the monitoring data of the wind turbine blade to solve the three-dimensional strain field and displacement field of the wind turbine blade. The spatial correlation of the finite element analysis results and the inverse finite element monitoring results is combined to accurately identify and locate the specific damage position of the wind turbine blade by using numerical optimization method.

[0004] The Chinese invention patent application with the publication number CN120068521A discloses a blade disc finite element stress analysis method and system based on blade simplification. When simplifying the blade using lumped mass elements, part of the rim containing the rim at the web is extracted from the entire rim as a coupled rim. Then, the lumped mass elements and the coupled rim are coupled to eliminate the two end rims far from the web position, preventing the deformation of the two end rims from absorbing the centrifugal load. This allows more centrifugal load to be transmitted to the web and hub through the rim at the web, ensuring that the stress at the web and hub is close to the actual situation, reducing the error between the hub stress calculation result and the cylindrical cross-section radial stress calculation result, and improving the accuracy of finite element stress calculation and analysis.

[0005] The Chinese invention patent application with the publication number CN117332631A discloses a finite element analysis method for turbine blade with local thermal barrier coating peeling. A three-dimensional model of turbine blade with thermal barrier coating is established. Finite element meshing is performed on the three-dimensional model. Fluid-structure coupling calculation is performed on the divided finite element model using a turbulence model. The temperature field of the turbine blade with local thermal barrier coating peeling is obtained by post-processing.

[0006] However, direct application of finite element analysis method to real-time deformation monitoring and reconstruction of blade operating state still faces significant challenges. In actual operating conditions, the aerodynamic, inertial and gravitational loads borne by the blade are complex and variable, which are difficult to obtain and define accurately in real time. The unknownness and uncertainty of such loads make it difficult for forward analysis to work, so it is impossible to calculate the real-time deformation response from the load in online monitoring. Therefore, new technologies such as inverse finite element method (iFEM) are proposed, which reconstruct the full-field displacement through discrete measured strain. Although the inverse finite element method achieves high-precision reconstruction in theory, its method itself is still complex, and the solving process involves large-scale iterative calculation, which has a bottleneck in computational efficiency in actual engineering application, and the real-time performance is limited.

[0007] In addition, many existing deformation reconstruction methods, including some simplified finite element applications, are usually based on small deformation or linear assumption, which is difficult to accurately process the three-dimensional, large deflection, large torsion and other geometric nonlinear behaviors of super-long blades under strong wind and other loads, resulting in insufficient reconstruction accuracy in large deformation scenarios.

[0008] Therefore, there is an urgent need in the art for a new finite element simulation analysis method that can balance computational efficiency and reconstruction accuracy, especially for real-time analysis of three-dimensional large deformation of super-long blades. SUMMARY

[0009] In view of the prior art, in order to obtain the overall deformation of the structure, sensors need to be densely arranged, and in the case of large deformation and strong nonlinearity, the traditional finite element method cannot simultaneously consider computational efficiency, accuracy and engineering practicability, and cannot realize effective three-dimensional deformation real-time analysis. The present application provides a super-long blade deformation analysis method based on finite element simulation, thereby solving the technical problems that the prior art cannot simultaneously consider high accuracy, strong robustness and engineering practicability in large deformation conditions, and cannot reconstruct three-dimensional deformation in real time.

[0010] The present application provides a super-long blade deformation analysis method based on finite element simulation, the specific steps are as follows:

[0011] Step 1. Establish a finite element model of the fan super-long blade before deformation; determine the reference line of the fan super-long blade before deformation; and divide the fan super-long blade before deformation into a plurality of segmented blades on the reference line.

[0012] Step 2. Based on the modal analysis of the finite element model of the fan super-long blade before deformation and the local strain information of the fan super-long blade, the curvature of the reference line of the deformed fan super-long blade is obtained, and the specific steps are as follows:

[0013] extracting, by modal analysis, a strain mode and a rotation angle mode of each finite element grid unit of the finite element model of the fan over-length blade in an undeformed state; obtaining a strain mode matrix based on the strain mode of each finite element grid unit; and obtaining a rotation angle mode matrix based on the rotation angle mode;

[0014] obtaining local strain information of the fan over-length blade, and obtaining a modal coordinate vector based on the strain mode matrix;

[0015] obtaining a rotation angle vector on a reference line of the fan over-length blade by superposition using the rotation angle mode matrix based on the modal coordinate vector;

[0016] interpolating the rotation angle vector on the reference line of the fan over-length blade into a continuous function vector of the rotation angle vector;

[0017] obtaining a reference line curvature of the deformed fan over-length blade based on the continuous function vector of the rotation angle vector and the reference line arc length coordinate of the fan over-length blade in the undeformed state;

[0018] Step 3. Obtaining a position vector of each segmented blade in a deformed state based on the reference line curvature of the deformed fan over-length blade;

[0019] Step 4. Obtaining a blade deformation vector according to the position vector of each segmented blade in the deformed state and the position vector in the undeformed state.

[0020] Optionally, the method further comprises Step 5, blade quality assessment based on the blade deformation vector.

[0021] Optionally, the specific steps of establishing the finite element model of the fan over-length blade in the undeformed state are as follows: performing grid division on the fan over-length blade in the undeformed state to obtain a plurality of finite element grid units; determining element attributes and material properties of each finite element grid unit; setting boundary conditions; and obtaining the finite element model of the fan over-length blade in the undeformed state based on the finite element grid units, the element attributes, the material properties and the boundary conditions.

[0022] Optionally, the specific steps of Step 3 are as follows:

[0023] obtaining a local rotation matrix of each segmented blade relative to a previous segmented blade in a global coordinate system based on the reference line curvature of the deformed fan over-length blade;

[0024] obtaining a composite rotation matrix of each segmented blade in the global coordinate system based on the local rotation matrix;

[0025] obtaining a geometric shape vector of each segmented blade in the undeformed state;

[0026] Based on the composite rotation matrix of each segment blade in the global coordinate system and the geometric shape vector before deformation, the deformation is summed from the root of the ultra-long blade of the wind turbine outward to obtain the position vector of each segment blade after deformation.

[0027] Optionally, based on the curvature of the reference line of the deformed wind turbine's ultra-long blades, the specific steps for obtaining the local rotation matrix of each segment blade relative to the previous segment blade in the global coordinate system are as follows:

[0028] The reference arc length coordinates of the undeformed wind turbine blade and the reference curvature of the deformed wind turbine blade are segmented according to the discrete method of multiple segmented blades obtained in step 1 to obtain the segmented arc length coordinates and segmented reference curvature.

[0029] Based on the segmented arc length coordinates and the curvature of the segmented reference line, the rotation angle change on each segmented blade is obtained.

[0030] Based on the change in rotation angle on each segment blade, the local rotation matrix of each segment blade relative to the previous segment blade in the global coordinate system is obtained.

[0031] Optionally, based on the local rotation matrix, the composite rotation matrix of each segmented blade in the global coordinate system is obtained, and its expression is:

[0032]

[0033] In the formula: For the first i The composite rotation matrix of segmented blades in the global coordinate system; Indicates the first i -1 Composite rotation matrix of segmented blades in global coordinate system; Indicates the first i Segmented blades relative to the first i -1 Local rotation matrix of the segmented blade in the global coordinate system.

[0034] Optionally, the position vector of each segmented blade after deformation is expressed as:

[0035]

[0036] in, It is the first i Position vector of the segmented blade after deformation; It is the first i -1 The position vector of the segmented blade after deformation; Indicates the first i The geometric shape vector of the segmented blade when it is not deformed.

[0037] Optionally, the local strain information of the fan overlength blade is acquired by a strain sensor, and a modal coordinate vector is obtained based on a strain modal matrix and by using a least square method.

[0038] Optionally, the expression of the modal coordinate vector is:

[0039]

[0040] wherein, is the modal coordinate vector; denotes the strain modal matrix; denotes the local strain information inside the finite element grid unit in the finite element model of the fan overlength blade.

[0041] Optionally, the expression of the rotation angle vector on the reference line of the fan overlength blade is:

[0042]

[0043] wherein, denotes the rotation angle vector on the reference line of the fan overlength blade; denotes the rotation angle modal matrix.

[0044] Compared with the prior art, the present application has at least the following beneficial effects: based on the finite element simulation, the strain modal and the rotation angle modal of the structure are acquired, only a limited number of measured strain data are needed, and the curvature distribution of the reference line required to represent the overall deformation of the beam body can be efficiently calculated; further combined with the strategy of segmenting the rotation matrix, the deformation reconstruction problem of the overlength blade under the condition of strong geometric nonlinearity and large deformation is effectively solved, so that the accurate and real-time analysis of the three-dimensional large deformation of the structure is realized. BRIEF DESCRIPTION OF DRAWINGS

[0045] The accompanying drawings are included to provide a further understanding of the present application, and are incorporated herein and constitute a part of this application.

[0046] Figure 1 is a flowchart of the overlength blade deformation analysis method based on finite element simulation of the present application. DETAILED DESCRIPTION

[0047] In order to enable the above-mentioned objects, features and advantages of the present application to be more clearly understood, the present application will be further described below with reference to the drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict. In addition, the present application can also be implemented in other ways different from those described herein, and therefore, the protection scope of the present application is not limited by the specific embodiments disclosed below.

[0048] One specific embodiment of the present application is as follows: Figure 1, discloses a long blade deformation analysis method based on finite element simulation, the specific steps are as follows:

[0049] Step 1: Establish a finite element model of the fan super-long blade before deformation; determine the reference line of the fan super-long blade before deformation; and divide the fan super-long blade before deformation into multiple segmented blades on the reference line.

[0050] Further, the fan super-long blade before deformation is meshed to obtain a plurality of finite element grid units; the unit properties and material characteristics of each finite element grid unit are determined; the boundary conditions are set; and the finite element model of the fan super-long blade before deformation is obtained based on the finite element grid units, the unit properties, the material characteristics and the boundary conditions.

[0051] Further, the blade with a length exceeding 60 meters is a super-long blade; and the boundary condition is a six-degree-of-freedom fixed support at the blade root.

[0052] Further, the reference line is the center line or elastic axis of the fan super-long blade.

[0053] Step 2: Based on the modal analysis of the finite element model of the fan super-long blade before deformation and the local strain information of the fan super-long blade, the curvature of the reference line after deformation of the fan super-long blade is obtained.

[0054] Specifically, the finite element model of the fan super-long blade (including its unit properties, material characteristics and boundary conditions) is taken as the analysis object, the strain modal and the rotation modal of each finite element grid unit in the finite element model of the fan super-long blade are extracted through modal analysis; the strain modal matrix is obtained based on the strain modal of each finite element grid unit; and the rotation modal matrix is obtained based on the rotation modal.

[0055] The local strain information of the fan super-long blade is obtained through a strain sensor, the modal coordinate vector is obtained using the least square method based on the strain modal matrix, and the expression is as follows:

[0056]

[0057] Wherein, is the modal coordinate vector; represents the strain modal matrix; represents the local strain information inside the finite element grid unit in the finite element model of the fan super-long blade.

[0058] Further, based on the modal coordinate vector, the rotation vector is obtained by superposition using the rotation modal matrix, and the expression is as follows:

[0059]

[0060] Wherein, a rotation angle vector on a reference line of the fan over-length blade; a rotation angle modal matrix.

[0061] Further, the rotation angle vector on the reference line of the fan over-length blade is interpolated into a continuous function vector of the rotation angle vector, expressed as:

[0062]

[0063] wherein, a continuous function vector of the rotation angle vector; , , are rotation angle continuous functions around the x, y and z axes respectively; s a reference line arc length coordinate of the fan over-length blade when not deformed.

[0064] Further, the reference line curvature of the deformed fan over-length blade is obtained based on the continuous function vector of the rotation angle vector and the reference line arc length coordinate of the fan over-length blade when not deformed, expressed as:

[0065]

[0066] wherein, a reference line curvature of the deformed fan over-length blade.

[0067] Step 3: based on the reference line curvature of the deformed fan over-length blade, the position vector of each segmented blade after deformation is obtained.

[0068] Step 31: based on the reference line curvature of the deformed fan over-length blade, the local rotation matrix of the first i segmented blade relative to the first i -1 segmented blade in the global coordinate system is obtained.

[0069] Specifically,

[0070] the reference line arc length coordinate of the fan over-length blade when not deformed and the reference line curvature of the deformed fan over-length blade are segmented according to the segmentation manner of the plurality of segmented blades obtained in step 1 to obtain segmented arc length coordinates and segmented reference line curvatures .

[0071] based on the segmented arc length coordinates and the segmented reference line curvatures , the rotation angle change amount on each segmented blade is obtained, expressed as:

[0072]

[0073] wherein, is the i segmented blade relative to the i -1stsegmented blade in the change of the rotation angle, , , and is the i segmented blade relative to the i -1stsegmented blade in the change of the rotation angle is the component of the z axis, y axis and x axis; is the i segmented blade relative to the i -1stsegmented blade in the change of the arc length, , denotes the segmented arc length coordinate of the i -1stsegmented blade.

[0074] Based on the change of the rotation angle on each segmented blade, the local rotation matrix of the i segmented blade relative to the i -1stsegmented blade in the global coordinate system is obtained , and the expression is:

[0075]

[0076]

[0077] wherein, denotes the rotation matrix of the i segmented blade around the z axis in the global coordinate system; denotes the rotation matrix of the i segmented blade around the y axis in the global coordinate system; denotes the rotation matrix of the i segmented blade around the x axis in the global coordinate system.

[0078] Step 32: Based on the local rotation matrix, the compound rotation matrix of the i segmented blade in the global coordinate system is obtained, and the expression is:

[0079]

[0080] In the formula, is the compound rotation matrix of the i segmented blade in the global coordinate system; denotes the compound rotation matrix of the i -1stsegmented blade in the global coordinate system.

[0081] Step 33: Obtain the geometric shape vector of the first segment of the blade when not deformed i Segmented blade geometric shape vector when not deformed , the expression is:

[0082]

[0083] wherein, is the position vector of the first segment of the blade when not deformed, i is the position vector of the first segment of the blade when not deformed, is the position vector of the first segment of the blade when not deformed. i Further,

[0084] is the position vector of the first segment of the blade when not deformed, the expression is: i

[0085] wherein, represents the axial coordinate of the first segment of the blade when not deformed in the global coordinate system;

[0086] represents the axial coordinate of the first segment of the blade when not deformed in the global coordinate system; represents the axial coordinate of the first segment of the blade when not deformed in the global coordinate system. i x Pre-bending is a typical geometric feature of a fan blade. In view of the problem that pre-bending / pre-twist is often ignored or simplified in a traditional super-long blade, the present application breaks through the limitation of the traditional super-long blade assumption, adopts accurately characterizes the geometric shape of the first segment of the blade when not deformed. i y Step 34: Based on the composite rotation matrix of each segment of the blade in the global coordinate system and the geometric shape when not deformed, and from the root of the super-long blade (the end next to the middle hub of the fan) to the outside, the position vector of each segment of the blade after deformation is obtained, the expression is: i z

[0087] wherein, is the position vector of the first segment of the blade after deformation; i is the position vector of the first segment of the blade after deformation.

[0088] Further,

[0089]

[0090] wherein, is the position vector of the first segment of the blade after deformation; i is the position vector of the first segment of the blade after deformation. i Further,

[0091] ​​​​​​​

[0092] wherein, denotes the axial coordinate of the i-th segment of the deformed blade in the global coordinate system; i denotes the axial coordinate of the i-th segment of the deformed blade in the global coordinate system; x denotes the axial coordinate of the i-th segment of the deformed blade in the global coordinate system; denotes the axial coordinate of the i-th segment of the deformed blade in the global coordinate system; i denotes the axial coordinate of the i-th segment of the deformed blade in the global coordinate system; y denotes the axial coordinate of the i-th segment of the deformed blade in the global coordinate system; denotes the axial coordinate of the i-th segment of the deformed blade in the global coordinate system; i denotes the axial coordinate of the i-th segment of the deformed blade in the global coordinate system; z denotes the axial coordinate of the i-th segment of the deformed blade in the global coordinate system.

[0093] Step 4: obtaining the blade deformation vector according to the position vector of the deformed blade and the position vector of the undeformed blade, and the expression is:

[0094]

[0095] wherein, denotes the blade deformation vector; denotes the position vector of the deformed blade; denotes the position vector of the undeformed blade.

[0096] It can be understood that the position vector of the deformed blade is composed of the position vectors of the deformed segments of the blade; the position vector of the undeformed blade is composed of the position vectors of the undeformed segments of the blade.

[0097] Step 5: performing blade quality assessment based on the real-time reconstructed blade deformation vector.

[0098] Specifically, according to the real-time reconstructed blade deformation vector, the blade displacement amount is obtained, and it is judged whether the maximum displacement amount exceeds the maximum displacement amount design value. If the maximum displacement amount exceeds the maximum displacement amount design value, the overlong blade is unstable, and the aerodynamic instability risk alarm is triggered.

[0099] The above merely describes the preferred embodiments of the present application, but the protection scope of the present application is not limited thereto, and any changes or replacements within the technical range disclosed by the present application can be easily thought by those skilled in the art, which shall be covered within the protection scope of the present application.​​​

Claims

1. A method for analyzing deformation of an ultra-long blade based on finite element simulation, characterized by, The specific steps are as follows: Step 1. Establishing a finite element model of the fan over-long blade in the undeformed state; determining the reference line of the fan over-long blade in the undeformed state; and discretizing the fan over-long blade in the undeformed state on the reference line into a plurality of segmented blades; Step 2. Based on the modal analysis of the finite element model of the fan over-long blade in the undeformed state and the local strain information of the fan over-long blade, the reference line curvature of the deformed fan over-long blade is obtained, and the specific steps are as follows: extracting the strain mode and the rotation angle mode of each finite element grid element of the finite element model of the fan over-long blade in the undeformed state through modal analysis; obtaining a strain mode matrix based on the strain mode of each finite element grid element; obtaining a rotation angle mode matrix based on the rotation angle mode; obtaining the local strain information of the fan over-long blade, and obtaining a modal coordinate vector based on the strain mode matrix; based on the modal coordinate vector, the rotation angle vector on the reference line of the fan over-long blade is obtained by using the rotation angle mode matrix; interpolating the rotation angle vector on the reference line of the fan over-long blade into a continuous function vector of the rotation angle vector; based on the continuous function vector of the rotation angle vector and the reference line arc length coordinate of the fan over-long blade in the undeformed state, the reference line curvature of the deformed fan over-long blade is obtained; Step 3. Based on the reference line curvature of the deformed fan over-long blade, the position vector of each segmented blade after deformation is obtained, and the specific steps are as follows: based on the reference line curvature of the deformed fan over-long blade, the local rotation matrix of each segmented blade relative to the previous segmented blade in the global coordinate system is obtained; based on the local rotation matrix, the composite rotation matrix of each segmented blade in the global coordinate system is obtained; obtaining the geometric shape vector of each segmented blade in the undeformed state; based on the composite rotation matrix of each segmented blade in the global coordinate system and the geometric shape vector in the undeformed state, the deformed position vector of each segmented blade is obtained by deformation summation from the root of the fan over-long blade to the outside; Step 4. According to the position vector of each segmented blade after deformation and the position vector in the undeformed state, the blade deformation vector is obtained; wherein, based on the reference line curvature of the deformed fan over-long blade, the specific steps of obtaining the local rotation matrix of each segmented blade relative to the previous segmented blade in the global coordinate system are as follows: the reference line arc length coordinate of the fan over-long blade in the undeformed state and the reference line curvature of the deformed fan over-long blade are segmented according to the discretization manner of the plurality of segmented blades obtained in step 1, to obtain segmented arc length coordinates and segmented reference line curvatures; based on the segmented arc length coordinates and the segmented reference line curvatures, the rotation angle change amount on each segmented blade is obtained; based on the rotation angle change amount on each segmented blade, the local rotation matrix of each segmented blade relative to the previous segmented blade in the global coordinate system is obtained.

2. The super-long blade deformation analysis method according to claim 1, characterized by, Step 5, based on the blade deformation vector, the blade quality is evaluated.

3. The super-long blade deformation analysis method according to claim 1, characterized by, The specific steps of establishing the finite element model of the fan over-long blade in the undeformed state are as follows: meshing the fan over-long blade in the undeformed state to obtain a plurality of finite element grid elements; determining the element properties and material characteristics of each finite element grid element; and setting boundary conditions; Based on the finite element grid unit, the unit attribute, the material characteristics and the boundary condition, a finite element model of the fan super-long blade in non-deformation is obtained.

4. The super-long blade deformation analysis method according to claim 1, characterized by, Based on the local rotation matrix, a composite rotation matrix of each segmented blade in the global coordinate system is obtained, and the expression is as follows: wherein: is the i is the is the i is the is the i is the i is the 5. The ultralong blade deformation analysis method according to claim 4, characterized by, The position vector of each segmented blade after deformation, and the expression is as follows: wherein is the position vector of the first i segment blade after deformation; is the position vector of the first i -1 segment blade after deformation; denotes the geometric shape vector of the first i segment blade before deformation.

6. The super-long blade deformation analysis method according to claim 2, wherein The local strain information of the fan super-long blade is obtained through the strain sensor, and based on the strain modal matrix, the modal coordinate vector is obtained by using the least square method.

7. The super-long blade deformation analysis method according to claim 2, wherein The expression of the modal coordinate vector is as follows: wherein, is the modal coordinate vector; denotes the strain modal matrix; denotes the local strain information within the finite element mesh element of the finite element model of the fan overhang blade.

8. The ultralong blade deformation analysis method according to claim 7, wherein The expression of the rotation angle vector on the reference line of the fan super-long blade is as follows: wherein, denotes a rotation angle vector on a reference line of the fan overlength blade; denotes a rotation angle modal matrix.

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