Fixed offshore wind turbine structure dynamic response obtaining method

Abstract

The invention discloses a structural dynamic response obtaining method for a fixed offshore wind turbine. The method comprises the following steps: establishing an initial finite element model according to related model data of a fixed offshore wind turbine to be tested, correcting the initial finite element model in combination with obtained actually measured modal parameters, and solving a vibration mode function based on the corrected finite element model; solving kinetic energy and potential energy of the to-be-tested wind driven generator structure; and according to the obtained structural kinetic energy and potential energy, a mass matrix, a stiffness matrix and a damping matrix are constructed based on an Euler-Lagrange equation and a basic kinetic equation, so that a dimensionality-reduced structural kinetic model of the offshore wind turbine is established, an inherent frequency value is obtained through solving, and the dynamic response is obtained. The method effectively overcomes the defects that a model is established depending on finite element software to solve the dynamic response in the prior art, and has the advantages that the modeling process is simple, the solving time is short, multi-field coupling load application can be met, and the control technology is easy to implement.

Description

Technical Field

[0001] The present invention belongs to the technical field of offshore wind turbines, and in particular relates to a method for obtaining a structural dynamic response of a fixed offshore wind turbine. Background Art

[0002] With the continuous acceleration of the global industrialization process, the environmental problems caused by the large-scale use of traditional fossil energy have been paid more and more attention, and offshore wind power has gradually been valued due to its advantages such as stable power generation efficiency and no site restrictions. At present, offshore wind turbines are developing towards larger impeller diameters and higher towers, and the environment in which fixed offshore wind turbines are located is complex, with wind loads, wave loads, seismic loads, etc. When these loads act at the same time, they will bring excessive dynamic response to the structure and even cause structural collapse. Therefore, it is necessary to study the dynamic response of fixed offshore wind turbines under multi-field coupling. The existing method of modeling and solving by relying on finite element software has the problems of cumbersome modeling process, long solution time, and possible nonlinear convergence in the solution process, and the existing finite element model is difficult to meet the model requirements of complex environmental load application and control technology. The so-called finite element model is a model established when using the finite element analysis method. It is a group of unit combinations that are connected only at nodes, transmit forces only at nodes, and are constrained only at nodes. Summary of the invention

[0003] The purpose of the present invention is to overcome the defects of the prior art and propose a method for obtaining the structural dynamic response of a fixed offshore wind turbine. The present invention also discloses a system and product for obtaining the structural dynamic response of a fixed offshore wind turbine.

[0004] In order to achieve the above object, the present invention proposes a method for obtaining the structural dynamic response of a fixed offshore wind turbine, comprising:

[0005] Step 1) establishing an initial finite element model according to the relevant model data of the fixed offshore wind turbine to be tested, correcting the initial finite element model in combination with the obtained measured modal parameters, and solving the vibration mode function based on the corrected finite element model;

[0006] Step 2) solving the kinetic energy and potential energy of the wind turbine structure to be tested;

[0007] Step 3) According to the obtained structural kinetic energy and potential energy, based on the Euler-Lagrange equation and the basic dynamic equation, the mass matrix, stiffness matrix and damping matrix are constructed to establish a reduced-dimensional offshore wind turbine structural dynamics model, solve the natural frequency value, and obtain the dynamic response.

[0008] Preferably, the model data of the fixed offshore wind turbine to be tested in step 1) includes:

[0009] Total length of blade R, mass of single blade m b , segment length, segment mass density Segmental bending stiffness EI fp (r), swing-wise segment bending stiffness EI eg (r) and the damping ratio ζ b 、The three azimuth angles of the blade ψ j (j=1,2,3), blade shape parameters, blade cross-section airfoil;

[0010] Including radial position R j , torsion angle θ, radial spacing L j Chord length L x and shape parameters of the tower;

[0011] The mass of the nacelle and wheel hub m nac 、m hub and damping ratio ζ jclg ;

[0012] The total length of the tower h, the segment length h i , segmented mass density Segmental bending stiffness EI t (z) and segmented tensile stiffness EA t (z), bottom wall thickness t d , bottom diameter d d , top wall thickness t u , top diameter d u ;

[0013] Base height h f , foundation wall thickness t f 、Base diameter D f , foundation translation stiffness k xyz and foundation rotation stiffness k xphi .

[0014] Preferably, the acquisition of measured modal parameters in step 1) includes:

[0015] A number of monitoring points are set on the blades and tower of the fixed offshore wind turbine to be tested, and the vibration mode, natural frequency and damping ratio are monitored respectively to obtain the main vibration mode, natural frequency and damping ratio of the blades and tower.

[0016] Preferably, the initial finite element model is corrected in step 1), comprising:

[0017] The blade is segmented and modeled based on the parameters in the aerodynamic characteristics of the blade section airfoil. For the tower part, the bottom wall thickness t d , top wall thickness t u , bottom diameter dd , top diameter d u The finite element model is established under the condition of uniform change of tower wall thickness and diameter;

[0018] The finite element model is subjected to modal analysis and then compared with the measured modal parameters, and the finite element model is corrected according to the modal parameter errors.

[0019] Preferably, the step 1) of solving the vibration mode function based on the corrected finite element model comprises:

[0020] Modal analysis is performed on the corrected finite element model to extract the displacement and position coordinates of the main vibration modes of the key nodes of the blade in the flapping and swinging directions, and the key nodes of the tower in the front-to-back and lateral directions.

[0021] The displacement and position of the top and root are normalized, that is, n key nodes are extracted, and their displacements are y1, y2…y n , where y1 is the root displacement, its value is 0, y n is the top displacement, and then the key node displacement is divided by y n ; Set the position coordinates to x1, x2…x n , where x1 is the root coordinate, its value is 0, x n is the top coordinate, that is, the length of the blade or tower, and the key node position is divided by x n , get the normalized position coordinates of the key nodes: (x 11 ,y 11 ), (x 12 ,y 12 )…(x 1n ,y 1n );

[0022] Select appropriate functions to fit the above coordinates and obtain the blade flapping and waving vibration mode function expressions: and Tower vibration function and

[0023] Preferably, the kinetic energy T in step 2) includes the kinetic energy of the blades, the kinetic energy of the nacelle and the hub, the kinetic energy of the tower and the kinetic energy of the foundation, and satisfies the following formula:

[0024]

[0025] in,

[0026]

[0027] In the formula, is the mass density of the blade along the r direction, R is the blade length; mnac , m hub are the masses of the nacelle and hub respectively; is the length mass density of the tower; m f , I f are the mass and moment of inertia of the foundation, h f ,t f and D f are the base height, base wall thickness and base diameter respectively; j represents the jth blade, v b (r,t) is the absolute velocity of the blade, v nac+hub (t) is the absolute speed of the nacelle and hub, v t (z,t) absolute velocity of the tower section, and are the time derivatives of the displacements in the flapping directions of the three blades respectively; and are the time derivatives of the displacements of the three blades in the flapping direction; and are the time derivatives of the tower side, front and vertical displacements respectively; and are the time derivatives of the lateral, frontal and vertical displacements of the foundation respectively; and are the time derivatives of the basic frontal and lateral angular displacements; It is the time derivative of the angular displacement of the side surface of the tower top. is the flapping vibration function of the fan blade based on the corrected finite element model; is the flapping vibration function of the fan blade based on the corrected finite element model; and are two types of vibration mode functions of the wind turbine tower obtained based on the corrected finite element model; ψ j is the azimuth angle of the blade, and its calculation formula is: Where Ω is the rotation speed of the fixed offshore wind turbine blades;

[0028] Potential energy V includes blade potential energy V b 、Tower potential energy V t and the basic potential energy V jc , satisfying the following formula:

[0029] V=V b +V t +V jc

[0030] in,

[0031]

[0032] Where, EI eg(r) is the blade's flapping bending stiffness along the r direction; EI fp (r) is the flapping bending stiffness of the blade along the r direction; F c (r, t) is the centrifugal force; F gj (r, t) is the gravity component acting on the jth blade at a distance r from the hub; k tx (z), k ty (z) and k tz (z) are the front and rear bending stiffness, lateral bending stiffness, angular stiffness at the top of the tower and vertical tensile stiffness, respectively, which is calculated by the tower segment bending stiffness EI t (z) and tensile stiffness EA t (z) is obtained; z represents the z direction, k xyz is the basic translation stiffness; k xyphi is the basic rotational stiffness.

[0033] Preferably, the process of constructing the quality matrix in step 3) includes:

[0034] Substituting the kinetic energy T into the Euler-Lagrange equation, the mass matrix M is obtained after integration:

[0035]

[0036] The mass matrix M is a symmetric matrix, and the calculation expression of the elements in the upper right half is as follows:

[0037]

[0038] m 1414 =3m b +m nac +m hub +m f ,m 1314 =3m b +m nac +m hub ,

[0039]

[0040]

[0041] Preferably, the step 3) of constructing the stiffness matrix includes:

[0042] Substitute the potential energy V into the Euler-Lagrange equation and integrate to obtain the stiffness matrix K:

[0043]

[0044] The calculation expressions of each element in the stiffness matrix K are as follows:

[0045]

[0046]

[0047] Preferably, the construction process of the damping matrix in step 3) includes:

[0048] Through Rayleigh damping construction, the damping matrix C is obtained as:

[0049] C=a0M+b0K

[0050] Where M is the mass matrix; K is the stiffness matrix, a0 and b0 are two proportional coefficients, which are obtained according to the damping ratio of different structures in the system, and the damping ratio coefficient is obtained from the fan parameter manual.

[0051] Preferably, the dimensionally reduced offshore wind turbine structural dynamics model of step 3) satisfies the following formula:

[0052]

[0053] Where M is the mass matrix; K is the stiffness matrix; C is the damping matrix; Q i is the external load of the system, W i It is the virtual work of the external load borne by the system; the external load borne by the system includes the wind, wave current and earthquake load borne by the generator to be tested during operation.

[0054] Compared with the prior art, the advantages of the present invention are:

[0055] The present invention provides a method for quickly solving the dynamic response of key parts (such as blades, nacelles and towers) of fixed offshore wind turbines suitable for complex environmental loads, which effectively solves the many shortcomings of the existing reliance on finite element software to establish models for solving dynamic responses. It has the advantages of simple modeling process, short solution time, ability to meet multi-field coupling load application and easy control technology implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of a method for obtaining a structural dynamic response of a fixed offshore wind turbine according to the present invention;

[0057] FIG2 is a schematic diagram of the degrees of freedom of a 15-degree-of-freedom fixed offshore wind turbine, wherein FIG2(a) is a frontal degree of freedom display, and FIG2(b) is a side rear degree of freedom display;

[0058] Figure 3 It is a finite element model diagram of a fixed offshore wind turbine;

[0059] FIG. 4 is a partial schematic diagram of a blade, wherein FIG. 4( a ) is a front view of the blade portion, and FIG. 4( b ) is a side view of the blade portion. DETAILED DESCRIPTION

[0060] The purpose of the present invention is to provide a fast solution method for the dynamic response of key parts (such as blades, nacelles and towers, etc.) of fixed offshore wind turbines under complex environmental loads, which can solve many shortcomings of existing methods that rely on finite element software to build models to solve dynamic response, such as cumbersome modeling process, long solution time, and difficulty in meeting the model requirements of multi-field coupling load application and control technology. It is a new method for solving the dynamic response of key parts of fixed offshore wind turbines based on the Euler-Lagrange equations and basic kinematic equations.

[0061] Example 1

[0062] Embodiment 1 of the present invention proposes a method for obtaining the structural dynamic response of a fixed offshore wind turbine. The specific method steps are as follows: Figure 1 As shown, including:

[0063] Step 1: Finite element model establishment

[0064] Step 101: Measured vibration mode, frequency and damping ratio

[0065] Multiple monitoring points are set on the blades and towers of fixed offshore wind turbines to monitor their vibration modes, natural frequencies and damping ratios, and obtain the main vibration modes, natural frequencies and damping ratios of the blade flapping and beating directions, and the front-to-back and lateral directions of the tower.

[0066] Step 102: Data acquisition for fixed offshore wind turbines

[0067] Obtain the total length R of the blades and the mass m of a single blade of the corresponding model of wind turbine from the user manual of the fixed offshore wind turbine b , segment length h i , segmented mass density Segmental bending stiffness EI fp (r), swing-wise segment bending stiffness EI eg (r) and the damping ratio ζ b ; The three azimuth angles of the blade ψ j (j=1,2,3); blade shape parameters; nacelle and hub mass m nac 、m hub and damping ratio ζ jclg ; The total length h of the tower, the length of each segment, and the mass density of each segment Segmental bending stiffness EI t (z) and segmented tensile stiffness EA t (z), bottom wall thickness t d , bottom diameter d d , top wall thickness t u, top diameter d u ; Foundation height h f , foundation wall thickness t f 、Base diameter D f ; Foundation translation stiffness k xyz ; Foundation rotation stiffness k xphi ; Blade cross-section airfoil (radial position R j , torsion angle θ, radial spacing L j Chord length L x ) and tower shape parameters.

[0068] Step 103: Initial finite element model creation and calibration

[0069] The data of the fixed offshore wind turbine obtained in step 102 is finely modeled based on finite element software. In the modeling process, the blade is segmented based on the parameters in the aerodynamic characteristics of the blade section airfoil. The tower part is modeled based on the bottom wall thickness t d , top wall thickness t u , bottom diameter d d , top diameter d u The finite element model is established based on the conditions of uniform change of tower wall thickness and diameter.

[0070] The finite element model is subjected to modal analysis and then compared with the measured modal parameters obtained in step 101 , and the finite element model is corrected according to the modal parameter errors.

[0071] Step 104: Solve the vibration mode function based on the finite element model:

[0072] The steps to solve the vibration mode function are as follows:

[0073] 1) Performing modal analysis on the finite element model corrected in step 103, respectively extracting the displacement and position coordinates of the main vibration modes of the key nodes of the blade in the flapping direction and the swinging direction, and the key nodes of the tower in the front-back direction and the lateral direction;

[0074] 2) Normalize the displacement (including top and root displacement) and position of the above key nodes, that is, assume that n key nodes are extracted, and their displacements are y1, y2…y n , where y1 is the root displacement, its value is 0, y n is the top displacement, and then the key node displacement is divided by y n ; Assume the position coordinates are x1, x2…x n , where x1 is the root coordinate, its value is 0, x n is the top coordinate, that is, the length of the blade or tower, and then the key node position is divided by x nThrough the above steps, we can get the normalized displacement and position of the key node, that is: (x 11 ,y 11 ), (x 12 ,y 12 )…(x 1n ,y 1n ).

[0075] 3) Select a suitable function to fit the above coordinates, and obtain the blade flapping and waving vibration mode function expression: Tower vibration function

[0076] 4) Extract the displacement and position coordinates of the vibration mode when the translation of the top of the tower is 0 and the rotation angle is 1°;

[0077] 5) Fit the above position coordinates to obtain the tower vibration function

[0078] Step 2: Calculation of kinetic and potential energy of fixed offshore wind turbine structures

[0079] Step 201: Kinetic Energy Expression

[0080] The total kinetic energy of a fixed offshore wind turbine includes the total kinetic energy of the blades, the kinetic energy of the nacelle and hub, the kinetic energy of the tower and the kinetic energy of the foundation:

[0081] Blade part:

[0082] Nacelle and hub parts:

[0083] Tower section:

[0084] Basics:

[0085] In the formula, is the mass density of the blade along the r direction; R is the blade length; m nac , m hub is the mass of the nacelle and hub; j represents the jth blade; is the length mass density of the tower; m f , I f The mass and moment of inertia of the basis are obtained by the following formula:

[0086]

[0087]

[0088] In the formula, h f ,t f and Df They are foundation height, foundation wall thickness and foundation diameter respectively.

[0089] The absolute speed of the blade in the forward, backward, lateral and vertical directions is:

[0090]

[0091] The absolute speed of the blade part is:

[0092]

[0093] The absolute speed of the nacelle and hub is:

[0094]

[0095] The absolute speed of the tower section is:

[0096]

[0097] In the formula, and are the time derivatives of the displacements in the flapping directions of the three blades respectively; and are the time derivatives of the displacements of the three blades in the flapping direction; and are the derivatives of the tower's fore-aft, lateral and vertical displacements with respect to time, respectively; and are the derivatives of the foundation's fore-aft, lateral and vertical displacements with respect to time, respectively; and is the time derivative of the basic anteroposterior and lateral rotational displacements; is the derivative of the rotational displacement of the tower top and the nacelle in the front and rear directions with respect to time. The above degrees of freedom are shown in Figure 2, where Figure 2(a) is the front degree of freedom display and Figure 2(b) is the side and rear degree of freedom display. is the flapping vibration function of the fan blade along the r direction obtained based on the corrected finite element model; is the flapping vibration function of the fan blade along the r direction obtained based on the corrected finite element model; is the vibration mode function of the wind turbine tower along the vertical z direction based on the corrected finite element model; ψ j (t) is the azimuth angle of the blade, and its calculation formula is: Where Ω is the rotational speed of the fixed offshore wind turbine blades.

[0098] The total kinetic energy expression of a fixed offshore wind turbine is:

[0099]

[0100] Step 202: Potential Energy Expression

[0101] The total potential energy of a fixed offshore wind turbine includes the total potential energy of the blades, the tower potential energy and the potential energy of the foundation:

[0102] Blade part:

[0103]

[0104] Tower section:

[0105]

[0106] Basics:

[0107] Where, EI eg (r) is the blade's flapping bending stiffness along the r direction; EI fp (r) is the flapping bending stiffness of the blade along the r direction; is the centrifugal force; is the gravity component acting on the jth blade at a distance r from the hub; k tx (z), k ty (z) and k tz (z) are the front and rear bending stiffness, lateral bending stiffness, angular stiffness at the top of the tower and vertical tensile stiffness, which can be calculated from the tower segment bending stiffness EI t (z) and vertical tensile stiffness k z (z) obtain; k xyz is the basic translation stiffness; k xyphi is the basic rotational stiffness.

[0108] The total potential energy expression of a fixed offshore wind turbine is:

[0109] V=V b +V t +V jc (17)

[0110] Step 3: Establishment of the equation of motion for fixed offshore wind turbines

[0111] Step 301: Integrate potential energy and kinetic energy into the equation

[0112] Based on the Euler-Lagrange equations and basic dynamic equations, a multi-field coupled dynamic model of a 15-degree-of-freedom fixed offshore wind turbine is established. The loads such as wind, wave current and earthquake that the fixed offshore wind turbine is subjected to during operation are taken as external loads, and the dynamic response equation of the fixed offshore wind turbine is constructed.

[0113] The Euler-Lagrange equation is shown below:

[0114]

[0115] Where i = 1, 2, ..., n; n is the number of dynamic degrees of freedom of the complete constrained particle system; q i is the i-th generalized displacement of the particle system; is the i-th generalized velocity of the particle system; T is the kinetic energy of the wind turbine system; V is the potential energy of the wind turbine system; Q i is the external load of the system.

[0116] The structural dynamics equation of a wind turbine is as follows:

[0117]

[0118] Where M is the mass matrix of the system; K is the stiffness matrix of the system; C is the damping matrix of the system; W i It is the virtual work of the external load on the system.

[0119] Step 302: Mass Matrix Construction

[0120] Substituting the kinetic energy expression (13) into equation (18) and integrating it into the form of equation (19), the mass matrix can be obtained as shown below:

[0121]

[0122] The mass matrix is ​​a symmetric matrix, and the calculation expression of the elements in the upper right half is as follows:

[0123] m 1414 =3m b +m nac +m hub +m f , m 1314 =3m b +m nac +m hub

[0124]

[0125]

[0126] Step 303: Stiffness matrix construction

[0127] Substituting the potential energy expression (17) into equation (18) and integrating it into the form of equation (19), the stiffness matrix can be obtained as shown below:

[0128]

[0129] The calculation expressions of each element in the stiffness matrix are as follows:

[0130]

[0131]

[0132] Step 304: Damping matrix construction

[0133] The damping matrix is ​​constructed by Rayleigh damping, which assumes that the damping of the system is a linear combination of stiffness and mass, as shown in the following formula:

[0134] C=a0M+b0K(23)

[0135] In the formula, a0 and b0 are two proportional coefficients, which can be obtained according to the damping ratio of different structures in the system. The damping ratio coefficient can be obtained from the fan parameter manual.

[0136] Step 305: Solve the mode

[0137] According to the determined mass matrix (19), stiffness matrix (20) and damping matrix (21), the dimension-reduced offshore wind turbine structural dynamics model (17) is established. At the same time, according to the mass matrix (19) and stiffness matrix (20), the structural natural frequency is solved to obtain the natural frequency value of the dimension-reduced offshore wind turbine model.

[0138] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0139] Example 2

[0140] In Example 2 of the present invention, a NERL 5MW wind turbine is used as an example to verify the effectiveness of the proposed method. The freedom degree of a 15-degree-of-freedom fixed offshore wind turbine is shown in FIG2 , where FIG2(a) is a front-to-back freedom degree display, and FIG2(b) is a side-to-back freedom degree display. Specifically, the following steps are included:

[0141] Step 1: Obtain the finite element model of the fixed offshore wind turbine; the specific implementation steps are:

[0142] (1) Multiple monitoring points are set on the blades and tower of the structure to monitor the vibration mode, natural frequency and damping ratio, and obtain the main vibration mode, natural frequency and damping ratio of the blade flapping and flapping directions and the front-to-back and side directions of the tower.

[0143] (2) Obtain the segment length, segment mass density, and segment bending stiffness of the blade and tower from the NERL 5MW generator manual. Also obtain the blade section airfoil parameters and the nacelle mass m nac =240000kg; wheel mass mhub =56780kg; basic mass m f =190342kg; basic moment of inertia I f =1679166kg·m 2 ; Tower top angular stiffness k ro =440.333N·m / rad; foundation translation stiffness k x =3.89·10 9 N / m; foundation rotation stiffness k xphi =1.14·10 11 N·m / rad; single blade mass m b =17740kg; tower height h = 87.6m; single blade length R = 61.5m; blade structure damping ratio ζ b =0.00477465; tower structure damping ratio ζ t =0.01; foundation structure damping ratio ζ jc =0.006; Nacelle hub structureζ jclg =0.02; bottom wall thickness t d =0.027m, bottom diameter d d =6m, top wall thickness t u =0.019m, top diameter d u =3.87m.

[0144] (3) Establishing finite element model

[0145] Figure 3 Finite element model of a fixed offshore wind turbine was established.

[0146] (4) Solution of vibration mode function based on finite element model

[0147] The obtained vibration mode function is shown as follows:

[0148]

[0149] Step 2: Calculation of kinetic and potential energy of fixed offshore wind turbine structures

[0150] (1) The three blade azimuth angles are 0°, 120° and 240° respectively. Based on equations (1)-(13), the various parts and total kinetic energy of the wind turbine generator under shutdown conditions are calculated;

[0151] (2) Similarly, based on equations (14)-(17), the various parts and total potential energy of the wind turbine generator under shutdown conditions are calculated. A partial schematic diagram of the blade part is shown in FIG4 , where FIG4 (a) is a front view of the blade part, and FIG4 (b) is a side view of the blade part;

[0152] Step 3: Construction of structural dynamics model of fixed offshore wind turbine

[0153] (1) Substituting the kinetic energy expression (13) into equation (18), and then integrating it into the form of equation (19), we can obtain the mass matrix:

[0154]

[0155] (2) Substituting the potential energy expression (17) into equation (18) and integrating it into the form of equation (19), the stiffness matrix can be obtained as follows:

[0156]

[0157] (3) Construction of damping matrix C

[0158] The damping matrix is ​​constructed through Rayleigh damping. Based on the mass matrix M and stiffness matrix K obtained, the damping matrix can be obtained:

[0159]

[0160] Step 4: Solve for its natural frequency and make comparison

[0161] The natural frequency is solved and compared with the natural frequency obtained based on FAST finite element software as shown in Table 1. It can be seen from Table 1 that the 15-DOF model proposed in the present invention is basically consistent with the natural frequency obtained based on FAST finite element software, and the maximum relative error is 7.253%.

[0162] Table 1 Natural frequency comparison table

[0163]

[0164] Example 3

[0165] Embodiment 3 of the present invention provides a system for acquiring the structural dynamic response of a fixed offshore wind turbine, which is implemented based on the method of embodiment 1. The system includes:

[0166] The finite element model building module is used to build an initial finite element model according to the relevant model data of the fixed offshore wind turbine to be tested, calibrate the initial finite element model in combination with the measured modal parameters, and solve the vibration mode function based on the corrected finite element model;

[0167] A calculation module is used to solve the kinetic energy and potential energy of the wind turbine structure to be tested;

[0168] The structural dynamics model building module is used to construct the mass matrix, stiffness matrix and damping matrix based on the obtained structural kinetic energy and potential energy, based on the Euler-Lagrange equation and the basic dynamics equation, so as to establish a reduced-dimensional offshore wind turbine structural dynamics model, solve the natural frequency value, and obtain the dynamic response.

[0169] Example 4

[0170] Embodiment 4 of the present invention may also provide a computer program product, including a computer program / instruction. When the computer program / instruction is executed by a processor, each step in the above method embodiment can be implemented.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A method for obtaining a structural dynamic response of a fixed offshore wind turbine, comprising: Step 1) establishing an initial finite element model according to the relevant model data of the fixed offshore wind turbine to be tested, correcting the initial finite element model in combination with the obtained measured modal parameters, and solving the vibration mode function based on the corrected finite element model; Step 2) solving the kinetic energy and potential energy of the wind turbine structure to be tested; Step 3) According to the obtained structural kinetic energy and potential energy, based on the Euler-Lagrange equation and the basic dynamic equation, the mass matrix, stiffness matrix and damping matrix are constructed to establish a reduced-dimensional offshore wind turbine structural dynamics model, solve the natural frequency value, and obtain the dynamic response.

2. The method for obtaining the structural dynamic response of a fixed offshore wind turbine according to claim 1, characterized in that: The model data of the fixed offshore wind turbine to be tested in step 1) includes: Total length of blade R, mass of single blade m b , segment length, segment mass density Segmental bending stiffness EI fp (r), swing-wise segment bending stiffness EI eg (r) and damping ratio ζ b 、The three azimuth angles of the blade j (j=1,2,3), blade shape parameters, blade cross-section airfoil; Including radial position R j , torsion angle θ, radial spacing L j Chord length L x and shape parameters of the tower; The mass of the nacelle and wheel hub m nac 、m hub and damping ratio ζ jclg ; The total length of the tower h, the segment length h i , segmented mass density Segmental bending stiffness EI t (z) and segmented tensile stiffness EA t (z), bottom wall thickness t d , bottom diameter d d , top wall thickness t u , top diameter d u ; Base height h f , foundation wall thickness t f 、Base diameter D f , foundation translation stiffness k xyz and foundation rotation stiffness k xphi .

3. The method for obtaining the structural dynamic response of a fixed offshore wind turbine according to claim 1, characterized in that: The acquisition of measured modal parameters in step 1) includes: A number of monitoring points are set on the blades and tower of the fixed offshore wind turbine to be tested, and the vibration mode, natural frequency and damping ratio are monitored respectively to obtain the main vibration mode, natural frequency and damping ratio of the blades and tower.

4. The method for obtaining the structural dynamic response of a fixed offshore wind turbine according to claim 3, characterized in that: The step 1) of correcting the initial finite element model includes: The blade is segmented and modeled based on the parameters in the aerodynamic characteristics of the blade section airfoil. For the tower part, the bottom wall thickness t d , top wall thickness t u , bottom diameter d d , top diameter d u The finite element model is established under the condition of uniform change of tower wall thickness and diameter; The finite element model is subjected to modal analysis and then compared with the measured modal parameters, and the finite element model is corrected according to the modal parameter errors.

5. The method for obtaining the structural dynamic response of a fixed offshore wind turbine according to claim 4, characterized in that: The step 1) solves the vibration mode function based on the corrected finite element model; comprising: Modal analysis is performed on the corrected finite element model to extract the displacement and position coordinates of the main vibration modes of the key nodes of the blade in the flapping and swinging directions, and the key nodes of the tower in the front-to-back and lateral directions. The displacement and position of the top and root are normalized, that is, n key nodes are extracted, and their displacements are y1, y2…y n , where y1 is the root displacement, its value is 0, y n is the top displacement, and then the key node displacement is divided by y n ; Set the position coordinates to x1, x2…x n , where x1 is the root coordinate, its value is 0, x n is the top coordinate, that is, the length of the blade or tower, and the key node position is divided by x n , get the normalized position coordinates of the key nodes: (x 11 ,y 11 ), (x 12 ,y 12 )…(x 1n ,y 1n ); Select appropriate functions to fit the above coordinates and obtain the blade flapping and waving vibration mode function expressions: and Tower vibration function and 6. The method for obtaining the structural dynamic response of a fixed offshore wind turbine according to claim 2, characterized in that: The kinetic energy T in step 2) includes the kinetic energy of the blades, the kinetic energy of the nacelle and the hub, the kinetic energy of the tower and the kinetic energy of the foundation, and satisfies the following formula: in, In the formula, is the mass density of the blade along the r direction, R is the blade length; m nac , m hub are the masses of the nacelle and hub respectively; is the length mass density of the tower; m f , I f are the mass and moment of inertia of the foundation, h f ,t f and D f are the base height, base wall thickness and base diameter respectively; j represents the jth blade, v b (r,t) is the absolute velocity of the blade, v nac+hub (t) is the absolute speed of the nacelle and hub, v t (z,t) absolute velocity of the tower section, and are the time derivatives of the displacements in the flapping directions of the three blades respectively; and are the time derivatives of the displacements of the three blades in the flapping direction; and are the time derivatives of the tower side, front and vertical displacements respectively; and are the time derivatives of the lateral, frontal and vertical displacements of the foundation respectively; and are the time derivatives of the basic frontal and lateral angular displacements; is the time derivative of the angular displacement of the side surface at the top of the tower; is the flapping vibration function of the fan blade based on the corrected finite element model; is the flapping vibration function of the fan blade based on the corrected finite element model; and are two types of vibration mode functions of the wind turbine tower obtained based on the corrected finite element model; ψ j is the azimuth angle of the blade, and its calculation formula is: Where Ω is the rotation speed of the fixed offshore wind turbine blades; Potential energy V includes blade potential energy V b 、Tower potential energy V t and the basic potential energy V jc , satisfying the following formula: V=V b +V t +V jc in, Where, EI eg (r) is the blade's flapping bending stiffness along the r direction; EI fp (r) is the flapping bending stiffness of the blade along the r direction; F c (r, t) is the centrifugal force; F gj (r, t) is the gravity component acting on the jth blade at a distance r from the hub; k tx (z), k ty (z) and k tz (z) are the front and rear bending stiffness, lateral bending stiffness, angular stiffness at the top of the tower and vertical tensile stiffness, respectively, which is calculated by the tower segment bending stiffness EI t (z) and tensile stiffness EA t (z) is obtained; z represents the z direction, k xyz is the basic translation stiffness; k xyphi is the basic rotational stiffness.

7. The method for obtaining the structural dynamic response of a fixed offshore wind turbine according to claim 6, characterized in that: The construction process of the quality matrix in step 3) includes: Substituting the kinetic energy T into the Euler-Lagrange equation, the mass matrix M is obtained after integration: The mass matrix M is a symmetric matrix, and the calculation expression of the elements in the upper right half is as follows: m 1414 =3m b +m nac +m hub +m f ,m 1314 =3m b +m nac +m hub , 8. The method for obtaining the structural dynamic response of a fixed offshore wind turbine according to claim 6, characterized in that: The step 3) of constructing the stiffness matrix includes: Substitute the potential energy V into the Euler-Lagrange equation and integrate to obtain the stiffness matrix K: The calculation expressions of each element in the stiffness matrix K are as follows: k 99 =k 1111 =k 1414 =k xyz ,k 1010 =k 1212 =k xyphi , 9. The method for obtaining the structural dynamic response of a fixed offshore wind turbine according to claim 6, characterized in that: The construction process of the damping matrix in step 3) includes: Through Rayleigh damping construction, the damping matrix C is obtained as: C=a0M+b0K Where M is the mass matrix; K is the stiffness matrix, a0 and b0 are two proportional coefficients, which are obtained according to the damping ratio of different structures in the system, and the damping ratio coefficient is obtained from the fan parameter manual.

10. The method for obtaining the structural dynamic response of a fixed offshore wind turbine according to claim 6, characterized in that: The dimension-reduced offshore wind turbine structural dynamics model of step 3) satisfies the following formula: Where M is the mass matrix; K is the stiffness matrix; C is the damping matrix; Q i is the external load of the system, W i It is the virtual work of the external load borne by the system; the external load borne by the system includes the wind, wave current and earthquake load borne by the generator to be tested during operation.

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