A calculation method for quickly extracting modal characteristic parameters of wind turbine blades

Abstract

The invention discloses a calculation method for rapidly extracting modal characteristic parameters of wind turbine blades, comprising: inputting geometric torsion angle, installation angle, bending stiffness data in flapping and swinging directions of each section of the blade, determining the blade pitch angle according to the incoming wind speed, calculating the bending stiffness inside and outside the wind rotor rotation plane at different spanwise positions of the blade; interpolating and calculating the rotation speed of the wind rotor under different incoming wind speeds, combining the spanwise position of each section, the section line density, the center of gravity position of the section blade section, the wind rotor radius and the wind rotor cone angle data, calculating the centrifugal force borne by each section of the blade; calculating the unit mass matrix and unit stiffness matrix of each blade section, assembling according to the unit number to obtain the blade system mass matrix and system stiffness matrix; performing vector inverse iteration loop calculation based on the generalized Lanczos algorithm to obtain the modal characteristic parameters of the wind turbine blade at different rotation speeds. The method has a fast operation speed and can realize the rapid extraction of the modal characteristic parameters of the wind turbine blade at different rotation speeds.

Description

Technical Field

[0001] The present invention relates to the technical field of wind turbine blades, and more particularly to a calculation method for rapidly extracting modal characteristic parameters of wind turbine blades. Background Art

[0002] As modern wind turbines develop towards larger and more flexible structures, the aeroelasticity of blades has attracted increasing attention. Blades are one of the most important components of wind turbines. Accurately identifying their modal characteristics at different speeds provides data support for blade vibration characteristic analysis, vibration fault diagnosis, and nonlinear large deformation prediction.

[0003] Modal analysis is divided into theoretical modal analysis and experimental modal analysis. For large megawatt-class flexible blades, the length of which is close to or even exceeds 100m, it is difficult to obtain excitation and response signals through experiments to identify the modal parameters of the system. Therefore, theoretical modal analysis methods based on the principle of linear vibration are becoming increasingly important.

[0004] The modal characteristics of wind turbine blades are obtained through theoretical modal analysis methods, mostly through commercial finite element software. However, for large wind turbine blades, most of them use steel plates as ribs, foam plastics as internal fillings, and fiberglass skins as external coverings. The complex structure makes it difficult to implement real solid modeling, and the simplified unit structure module in the software cannot truly reflect the structural characteristics of the blades. The complex internal structure of the blades brings new challenges to the accurate and rapid calculation of the blade modal characteristic parameters. Summary of the invention

[0005] Therefore, the technical problem to be solved by the present invention is to provide a calculation method for quickly and accurately extracting the modal characteristic parameters of wind turbine blades at different rotation speeds.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] A method for quickly extracting wind turbine blade modal characteristic parameters includes the following steps:

[0008] Step S1, inputting the geometric torsion angle, installation angle, bending stiffness in the flapping direction, and bending stiffness in the swinging direction of each section of the blade, determining the blade pitch angle according to the incoming wind speed, and calculating the bending stiffness in the rotor rotation plane and the bending stiffness outside the rotor rotation plane at different spanwise positions of the blade;

[0009] Step S2, interpolating and calculating the rotation speed of the wind rotor under different incoming wind speeds, and combining the spanwise position of each section, the cross-sectional line density, the position of the center of gravity of the cross-sectional blade segment, the wind rotor radius and the wind rotor cone angle data, to calculate the centrifugal force borne by each section of the blade;

[0010] Step S3, calculating the unit mass matrix and unit stiffness matrix of each blade segment, and assembling them according to the unit numbers to obtain the blade system mass matrix and system stiffness matrix;

[0011] Step S4, performing vector inverse iteration calculation based on the generalized Lanczos algorithm, eliminating singular eigenvectors, orthogonalizing the vectors to obtain tridiagonal matrix coefficients, performing module normalization, and cyclically performing inverse iteration calculation to obtain wind turbine blade modal characteristic parameters at different rotation speeds.

[0012] In the above-mentioned calculation method for quickly extracting modal characteristic parameters of wind turbine blades, in step S1:

[0013] The bending stiffness of each section of the wind wheel outside the rotating plane is EI X The bending stiffness in the rotor rotation plane is EI Y , the general expression is:

[0014] EI X =EI E cos 2 θ b +EI F sin 2 θ b

[0015] EI Y =EI F cos 2 θ b +EI E sin 2 θ b ;

[0016] Where, EI E is the bending stiffness of each section in the shimmy direction, EI F is the bending stiffness of each section in the swinging direction, θ b It is the sum of the geometric twist angle, installation angle and blade pitch angle of each section.

[0017] In the above-mentioned calculation method for quickly extracting modal characteristic parameters of wind turbine blades, in step S2, the general expression of the centrifugal force borne by each section of the blade is:

[0018]

[0019] In the formula, F zc is the centrifugal force on each section, r i is the spanwise position of the i-th section, m is the line density of the section, r c is the centroid position of the blade section in each section, Ω is the rotation speed of the wind wheel, β0 is the cone angle of the wind wheel, R is the radius of the wind wheel,

[0020] Center of gravity position of blade section in each section cfor:

[0021]

[0022] Where n is the total number of blade sections, is the line density of the ith section.

[0023] In the above-mentioned calculation method for quickly extracting modal characteristic parameters of wind turbine blades, in step S4: the shear deformation and centrifugal stiffening phenomenon are considered for the blade unit;

[0024] Element stiffness matrix K e for:

[0025]

[0026] Where, EI is the bending stiffness of each section of the blade inside and outside the rotor rotation plane, a is the shear deformation of each blade segment, and l is the length of each blade segment;

[0027] The shear deformation a of each blade segment is:

[0028]

[0029] In the formula, G is the shear elastic modulus of the blade, and A is the cross-sectional area;

[0030] Element mass matrix M e for

[0031]

[0032] Then, the blade system mass matrix M and system stiffness matrix K are obtained by assembling according to the unit numbers.

[0033] The above-mentioned calculation method for quickly extracting modal characteristic parameters of wind turbine blades includes the following sub-steps in step S4:

[0034] Step S4-1, randomly define a unit vector q0, eliminate the singular eigenvectors, and obtain the initial vector q1,

[0035] Step S4-2, perform vector inverse iteration calculation based on the initial vector q1 to obtain the intermediate vector

[0036] Step S4-3, perform vector orthogonalization to form vector, and obtain the orthogonalization coefficient, that is, the tridiagonal matrix coefficient α k and β k ,

[0037] Step S4-4, The vector is normalized modulo-normalized to obtain the k+1th Lanczos vector q k+1 ,

[0038] Step S4-5, looping the reverse iterative calculation until k is equal to the total number of cross sections n, and obtaining a tridiagonal matrix and an eigenvector matrix;

[0039] Step S4-6, using the fact that the eigenvalues ​​of the tridiagonal matrix and the generalized eigenvalues ​​are reciprocals of each other, the original generalized eigenvector is equal to the product of the tridiagonal matrix vector and the eigenvector matrix, to obtain the modal characteristic parameters of the wind turbine blade at different speeds.

[0040] In the above-mentioned calculation method for quickly extracting modal characteristic parameters of wind turbine blades, in step S4-1:

[0041] The initial vector q1 is:

[0042]

[0043]

[0044]

[0045] Where K is the blade system stiffness matrix, M is the blade system mass matrix, q0 is the unit vector, q1 is the initial Lanczos vector; is the initial intermediate vector; γ1 is the intermediate vector The M-norm of .

[0046] In the above-mentioned method for calculating the rapid extraction of wind turbine blade modal characteristic parameters, in step S4-2, the intermediate vector for:

[0047]

[0048] Where K is the blade system stiffness matrix, M is the blade system mass matrix, q k is the Lanczos vector when the cycle number is k; is the intermediate vector when the number of cycles is k.

[0049] In the above-mentioned method for quickly extracting the modal characteristic parameters of wind turbine blades, in step S4-3, the tridiagonal matrix coefficients α k and β k for:

[0050]

[0051] In the formula, q k-1 is the Lanczos vector when the cycle number is k-1, is the intermediate vector when the cycle number is k+1; is the orthogonalized vector when the cycle number is k+1.

[0052] In the above-mentioned calculation method for quickly extracting modal characteristic parameters of wind turbine blades, in step S4-4:

[0053] The k+1th Lanczos vector q k+1 for:

[0054]

[0055] γ k+1 is the orthogonalized vector The M-norm of .

[0056] The technical solution of the present invention achieves the following beneficial technical effects:

[0057] According to the present invention, a calculation method for quickly extracting the modal characteristic parameters of wind turbine blades is used. The blade structure is discretized using the finite element concept, and the blade system mass matrix and the system stiffness matrix are obtained after assembly according to the unit number. The modal characteristic parameters of wind turbine blades at different speeds are obtained by performing vector cyclic inverse iteration calculation based on the generalized Lanczos algorithm. The method has a fast operation speed, and only needs to input a small amount of blade geometry and stiffness parameters to obtain high-precision modal eigenvalues ​​and eigenvectors. It can realize the rapid extraction of modal characteristic parameters of wind turbine blades at different speeds, and provide data support for blade vibration characteristic analysis, vibration fault diagnosis and nonlinear large deformation prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a flow chart of a calculation method for quickly extracting modal characteristic parameters of a wind turbine blade in an embodiment of the present invention;

[0059] Figure 2 is a graph showing the relationship between the incoming wind speed of the wind turbine and the blade pitch angle and the rotor speed in an embodiment of the present invention;

[0060] Figure 3 is a diagram showing the variation of the bending stiffness and geometric twist angle of a wind turbine blade with the spanwise position of the blade in an embodiment of the present invention;

[0061] Figure 4 This is a flow chart of vector de-iteration loop calculation based on the generalized Lanczos algorithm in an embodiment of the present invention;

[0062] Figure 5 is the natural frequency of the blades in the first-order rotor rotation plane and out of the rotation plane under speed variation;

[0063] Figure 6 is the natural frequency of the first three orders of the blades in and out of the rotation plane of the wind wheel under speed changes;

[0064] Figure 7It is the vibration mode of the first three orders of the blades in and out of the rotation plane of the rotor at rated speed. DETAILED DESCRIPTION

[0065] In this embodiment, a 5MW offshore wind turbine blade of the National Renewable Energy Laboratory (NREL) of the United States is taken as an example to specifically illustrate a calculation method for rapidly extracting modal characteristic parameters of the wind turbine blade.

[0066] Figure 1 It is a flow chart of a calculation method for rapidly extracting modal characteristic parameters of wind turbine blades in an embodiment of the present invention.

[0067] Figure 2 : is a graph showing the relationship between the incoming wind speed of the wind turbine, the blade pitch angle and the rotor speed in an embodiment of the present invention; Figure 1 As shown, the calculation method for quickly extracting the modal characteristic parameters of wind turbine blades specifically includes the following steps:

[0068] Step S1, inputting the geometric torsion angle, installation angle, bending stiffness in the flapping direction, and bending stiffness in the swing direction of each section of the blade, and Figure 2 The figure shows the relationship between the incoming wind speed and the blade pitch angle of the wind turbine given by NREL. The pitch angle of each section of the blade is determined according to the incoming wind speed, and the bending stiffness inside and outside the rotor rotation plane at different spanwise positions of the blade is calculated.

[0069] Bending stiffness EI of each section of the wind rotor outside the rotating plane X and the bending stiffness in the rotation plane EI Y The general expression is:

[0070] EI X =EI E cos 2 θ b +EI F sin 2 θ b

[0071] EI Y =EI F cos 2 θ b +EI E sin 2 θ b

[0072] Where, EI E is the bending stiffness of each section in the shimmy direction, EI F is the bending stiffness of each section in the swinging direction, θ b It is the sum of the geometric twist angle, installation angle and pitch angle of each section.

[0073] In step S1 of this embodiment, the NREL 5MW wind turbine blade is divided into 37 sections along the span direction, and the blade installation angle is 0°.

[0074] Figure 3 The figure is the variation of blade bending stiffness and geometric twist angle with blade spanwise position. Based on the given spanwise position, geometric twist angle, bending stiffness in the flapping direction, and bending stiffness in the swing direction parameters of each section, the bending stiffness outside the rotating plane of the wind rotor and the bending stiffness inside the rotating plane are calculated, and then S2 is entered.

[0075] Step S2, according to Figure 2 The corresponding relationship diagram between the wind speed of the wind turbine and the rotor speed given by NREL is shown in the figure. The rotor speed under different wind speeds is determined by interpolation. Combined with the spanwise position of each section, the line density of the section, the center of gravity position of the blade section, the rotor radius and the rotor cone angle data, the centrifugal force calculation formula of each section is:

[0076]

[0077] In the present embodiment, step S2, F zc The centrifugal force on each section of the blade, r i is the spanwise position of the ith section, is the linear density of each section, r c is the center of gravity of each blade segment, Ω is the rotation speed of the wind wheel, the value range is 0≤Ω≤12.1rpm, the wind wheel cone angle β0=2.5°, the wind wheel radius R=63m, n is the total number of blade sections, in this embodiment n=37, and then enter S3.

[0078] Step S3, calculate the unit mass matrix and unit stiffness matrix of each blade segment, consider the shear deformation and centrifugal stiffening phenomenon, and combine the centrifugal force load of each section obtained in step S2 to obtain the unit stiffness matrix K e and the element mass matrix M e for:

[0079]

[0080]

[0081] Where EI is the bending stiffness of each section in the rotor rotation plane or the bending stiffness outside the rotor rotation plane obtained in step S1, and the shear deformation of each blade segment is l is the length of each blade segment, G is the shear elastic modulus of the blade, and A is the cross-sectional area.

[0082] After assembling according to the unit number, two 74×74-order blade system mass matrices M and system stiffness matrices K are obtained, and then enter S4.

[0083] Step S4, performing vector inverse iterative loop calculation based on the generalized Lanczos algorithm to obtain modal characteristic parameters of the wind turbine blades at different rotation speeds.

[0084] Figure 4 This is a flow chart for vector inverse iteration calculation based on the generalized Lanczos algorithm:

[0085] like Figure 4 As shown, step S4 specifically includes the following steps:

[0086] Step S4-1, randomly define a 74×1 unit vector q0, and make the initial vector q1 eliminate the singular eigenvector in the following way:

[0087]

[0088]

[0089]

[0090] Where, K and M are the blade system stiffness matrix and system mass matrix obtained in step S3, respectively; q1 is the initial Lanczos vector; is the initial intermediate vector; γ1 is the intermediate vector The M-norm of .

[0091] Step S4-2, perform vector inverse iteration calculation based on the initial vector q1 to obtain the intermediate vector Middle vector for:

[0092]

[0093] q k is the Lanczos vector when the cycle number is k; is the intermediate vector when the number of cycles is k.

[0094] Step S4-3, perform vector orthogonalization to form vector, and obtain the orthogonalization coefficient, that is, the tridiagonal matrix coefficient α k and β k , the method is as follows:

[0095]

[0096]

[0097] Where β1 = 0;

[0098] q k-1 is the Lanczos vector when the cycle number is k-1, is the intermediate vector when the cycle number is k+1; is the orthogonalized vector when the cycle number is k+1.

[0099] Step S4-4, The vector is normalized modulo-normalized to obtain the k+1th Lanczos vector q k+1 , the method is as follows:

[0100]

[0101]

[0102] γ k+1 is the orthogonalized vector The M-norm of .

[0103] Step S4-5, looping the inverse iterative calculation until k=74, obtaining a tridiagonal matrix and an eigenvector matrix;

[0104] Step S4-6, using the tridiagonal matrix eigenvalues ​​and generalized eigenvalues ​​as reciprocals, the original generalized eigenvector is equal to the product of the tridiagonal matrix vector and the eigenvector matrix, to obtain the modal characteristic parameters of the wind turbine blade at different speeds.

[0105] Figure 5 It is the natural frequency of the first-order wind wheel of the blade in and out of the rotation plane under speed changes.

[0106] exist Figure 5 The variation trend of the blade's first-order natural frequency in the flapping direction is given in the figure when the blade speed increases from static to the rated speed of 12.1 rpm. The natural frequency of the blade at rest is consistent with the experimental data published by NREL, indicating that the algorithm in this paper is accurate and reliable. The centrifugal stiffening effect caused by the blade rotation causes the first-order natural frequency in the out-of-plane direction to increase by 6.4%, and the first-order natural frequency in the in-plane direction to increase by 2.6%.

[0107] Figure 6 It is the natural frequency of the first three orders of the blades in and out of the rotation plane of the wind wheel under speed changes.

[0108] exist Figure 6 The figure shows the change trend of the natural frequencies of the first three orders of the blade in and out of the rotation plane of the wind wheel when the blade speed increases from static to the rated speed of 12.1rpm. The figure shows that the centrifugal stiffening effect has a greater impact on the natural frequency in the out-of-plane direction and a relatively smaller impact on the in-plane direction. The degree of influence gradually decreases with the increase of the modal order.

[0109] Figure 7 It is the vibration mode of the first three orders of the blades in and out of the rotation plane of the rotor at rated speed.

[0110] Example Function and Effect

[0111] According to the present invention, a method for calculating the modal characteristics of a wind turbine blade at different rotation speeds is used to discretize the blade structure using the finite element method, and the system mass matrix and system stiffness matrix of the blade are obtained after assembly according to the unit number, and the eigenvalue and eigenvector matrix of the tridiagonal matrix are obtained by vector cyclic inverse iteration calculation based on the generalized Lanczos algorithm. The method has a fast operation speed, and only needs to input a small amount of blade geometric shape and stiffness parameters to obtain high-precision modal eigenvalues ​​and eigenvectors, which can realize the rapid extraction of wind turbine modal characteristic parameters at different rotation speeds, and provide data support for blade vibration characteristic analysis, vibration fault diagnosis, avoiding wind turbine resonance, and accurately predicting large nonlinear deformation of flexible blades.

[0112] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the claims of this patent application.

Claims

1. A method for quickly extracting modal characteristic parameters of wind turbine blades, characterized in that: The steps include: Step S1, inputting the geometric torsion angle, installation angle, bending stiffness in the flapping direction, and bending stiffness in the swinging direction of each section of the blade, determining the blade pitch angle according to the incoming wind speed, and calculating the bending stiffness in the rotor rotation plane and the bending stiffness outside the rotor rotation plane at different spanwise positions of the blade; Step S2, interpolating and calculating the rotation speed of the wind rotor under different incoming wind speeds, and combining the spanwise position of each section, the cross-sectional line density, the position of the center of gravity of the cross-sectional blade segment, the wind rotor radius and the wind rotor cone angle data, to calculate the centrifugal force borne by each section of the blade; Step S3, calculating the unit mass matrix and unit stiffness matrix of each blade segment, and assembling them according to the unit numbers to obtain the blade system mass matrix and system stiffness matrix; Step S4, performing vector inverse iteration calculation based on the generalized Lanczos algorithm, eliminating singular eigenvectors, orthogonalizing the vectors to obtain tridiagonal matrix coefficients, performing module normalization processing, and cyclic inverse iteration calculation to obtain modal characteristic parameters of wind turbine blades at different speeds; In step S4, the following sub-steps are included: Step S4-1, randomly define a unit vector q0, eliminate the singular eigenvectors, and obtain the initial vector q1, Step S4-2, perform vector inverse iteration calculation based on the initial vector q1 to obtain the intermediate vector q k , Step S4-3, perform vector orthogonalization to form vector, and obtain the orthogonalization coefficient, that is, the tridiagonal matrix coefficient α k and β k , Step S4-4, The vector is normalized modulo-normalized to obtain the k+1th Lanczos vector q k+1 , Step S4-5, looping the reverse iterative calculation until k is equal to the total number of cross sections n, and obtaining a tridiagonal matrix and an eigenvector matrix; Step S4-6, using the fact that the eigenvalues ​​of the tridiagonal matrix and the generalized eigenvalues ​​are reciprocals of each other, the original generalized eigenvector is equal to the product of the tridiagonal matrix vector and the eigenvector matrix, to obtain the modal characteristic parameters of the wind turbine blade at different speeds.

2. A calculation method for rapidly extracting modal characteristic parameters of wind turbine blades according to claim 1, characterized in that: In step S1: The bending stiffness of each section of the wind wheel outside the rotating plane is EI X The bending stiffness in the rotor rotation plane is EI Y , the general expression is: In the formula, EI E is the bending stiffness of each section in the shimmy direction, EI F is the bending stiffness of each section in the swinging direction, θ b It is the sum of the geometric twist angle, installation angle and blade pitch angle of each section.

3. A calculation method for rapidly extracting modal characteristic parameters of wind turbine blades according to claim 2, characterized in that: In step S2, the general expression of the centrifugal force borne by each section of the blade is: In the formula, F zc is the centrifugal force on each section, r i is the spanwise position of the ith section, is the linear density of the cross section, r c is the centroid position of the blade section in each section, Ω is the rotation speed of the wind wheel, β0 is the cone angle of the wind wheel, R is the radius of the wind wheel, Center of gravity position of blade section in each section c for: Where n is the total number of blade sections, is the line density of the ith section.

4. A calculation method for rapidly extracting modal characteristic parameters of wind turbine blades according to claim 3, characterized in that: In step S4: the blade unit considers shear deformation and centrifugal stiffening phenomena; Element stiffness matrix K e for: Where, EI is the bending stiffness of each section of the blade inside and outside the rotor rotation plane, a is the shear deformation of each blade segment, and l is the length of each blade segment; The shear deformation a of each blade segment is: In the formula, G is the shear elastic modulus of the blade, and A is the cross-sectional area; Element mass matrix M e for Then, the blade system mass matrix M and system stiffness matrix K are obtained by assembling according to the unit numbers.

5. The method for rapidly extracting wind turbine blade modal characteristic parameters according to claim 1, characterized in that: In step S4-1: The initial vector q1 is: Where K is the blade system stiffness matrix, M is the blade system mass matrix, q0 is the unit vector; q1 is the initial Lanczos vector; is the initial intermediate vector; γ1 is the intermediate vector The M-norm of .

6. A calculation method for rapidly extracting modal characteristic parameters of wind turbine blades according to claim 5, characterized in that: In step S4-2, the intermediate vector q k for: Where K is the blade system stiffness matrix, M is the blade system mass matrix, q k is the Lanczos vector when the cycle number is k; is the intermediate vector when the number of cycles is k.

7. A calculation method for rapidly extracting modal characteristic parameters of wind turbine blades according to claim 6, characterized in that: In step S4-3, the tridiagonal matrix coefficients α k and β k for: In the formula, q k-1 is the Lanczos vector when the cycle number is k-1, is the intermediate vector when the cycle number is k+1; is the orthogonalized vector when the cycle number is k+1.

8. A calculation method for rapidly extracting modal characteristic parameters of wind turbine blades according to claim 7, characterized in that: In step S4-4: The k+1th Lanczos vector q k+1 for: γ k+1 is the orthogonalized vector The M-norm of .

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