Vibration reduction and parameter optimization method of fan blades based on dynamic vibration absorber of inertia capacity

Abstract

The present invention discloses a method for reducing vibration of wind turbine blades and optimizing parameters based on an inertia capacity dynamic vibration absorber. First, the dynamic equation of a system consisting of a wind turbine blade and a dynamic vibration absorber based on an inertia capacity is established using the Euler-Lagrange equation, and then the transfer function from the external load on the wind turbine blade to the displacement in the blade swing direction is obtained; then the transfer function is dimensionless processed, and the analytical expression of the optimal structural parameters of the dynamic vibration absorber based on the inertia capacity is derived using the pole configuration method. The present invention applies the dynamic vibration absorber based on the inertia capacity to the swing control of wind turbine blades and gives the analytical expression of the optimal parameters. Compared with the traditional method of solving the optimal parameters using numerical optimization, the analytical form of the optimal parameter expression obviously has better simplicity and universality.

Description

Technical Field

[0001] The invention belongs to the field of wind turbine vibration reduction, and in particular is a method for reducing vibration of wind turbine blades and optimizing parameters of a dynamic vibration absorber based on an inertia capacity. Background Art

[0002] As one of the most important renewable energy sources, wind energy has experienced rapid growth worldwide in the past few decades. In the current design of wind turbines, wind turbines are designed with larger and larger capacities, longer blades, and taller towers to reduce the cost of wind power generation.

[0003] However, the increase in the size of wind turbine blades also makes them flexible and lightly damped, making them more susceptible to excitation by external loads. Unnecessary structural vibrations will reduce the fatigue life and power generation efficiency of wind turbines and increase power generation costs.

[0004] Structural control is an important method for controlling wind turbine blade vibration, which is mainly divided into active control, semi-active control and passive control. Active control and semi-active control require external energy input because they need brakes to provide control force. They are not only costly but also require appropriate control algorithms to achieve better vibration reduction effects. Passive control mainly relies on transmitting the vibration of the wind blade to the additional mass block and then dissipating the energy input by the external load through the damper. Therefore, it has the characteristics of simple structure, high reliability and low cost. However, due to the narrow effective frequency band, the traditional tuned mass damper has no obvious vibration reduction effect when facing complex wind input. Summary of the invention

[0005] The purpose of the present invention is to provide a method for reducing vibration and parameter optimization of wind turbine blades based on a dynamic vibration absorber of inertia capacity, which can reduce the fatigue load on the blades by effectively suppressing the swing of the blades, thereby achieving the purpose of reducing the cost of power generation and increasing the service life of the wind turbine.

[0006] The technical solution to achieve the purpose of the present invention is: a method for reducing vibration and optimizing parameters of fan blades based on a dynamic vibration absorber of an inertia volume, comprising the following steps:

[0007] Step 1, using the Euler-Lagrange equation to establish the dynamic equation of the system consisting of the wind turbine blades and the dynamic vibration absorber based on the inertia volume;

[0008] Step 2, solving the transfer function from the external load on the wind turbine blade to the displacement in the blade swing direction and performing dimensionless processing;

[0009] Step 3: Use the pole configuration method to obtain the analytical expression of the optimal structural parameters of the dynamic vibration absorber based on inertia capacity.

[0010] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the above-mentioned method for reducing vibration and optimizing parameters of fan blades based on an inertia-capacitance dynamic vibration absorber is implemented.

[0011] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned method for reducing vibration and optimizing parameters of fan blades based on an inertia-capacitance dynamic vibration absorber.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) The present invention does not require an actuator to provide active control force to control the vibration of the blade. Instead, a dynamic vibration absorber based on inertia capacitance is installed inside the blade to transfer the vibration of the blade to an additional mass block, and the energy is dissipated through damping to achieve the purpose of vibration reduction. This method is not only low in cost but also highly reliable and can cope with various complex external conditions. (2) Compared with the traditional tuned mass damper (TMD), the dynamic vibration absorber based on inertia capacitance has an additional inertia capacitance and a spring connected in series in terms of damping, and has better vibration reduction performance. (3) The present invention provides an analytical expression for the optimal structural parameters of the dynamic vibration absorber based on inertia capacitance. Compared with numerical optimization, this method has better universality and greatly simplifies the parameter tuning process of the dynamic vibration absorber based on inertia capacitance. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a system structure diagram of a dynamic vibration absorber based on inertia capacity and a wind turbine blade.

[0014] Figure 2(a) to Figure 2(c) The frequency response curves of the blade swing direction displacement obtained by the present invention, wherein FIG2(a) is the frequency response curve when the blade speed is 0, FIG2(b) is the frequency response curve when the blade speed is the rated speed, and FIG2(c) is the frequency response curve when the blade speed is three times the rated speed.

[0015] Figure 3 This is the curve of wind load on the blade in the swing direction.

[0016] Figure 4(a) to Figure 4(b) 4( a ) represents the time domain curve of the blade displacement in the swing direction, and FIG. 4( b ) represents the Fourier spectrum diagram corresponding to FIG. 4( a ). DETAILED DESCRIPTION

[0017] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0018] In conjunction with the accompanying drawings, a method for reducing vibration and optimizing parameters of a fan blade based on an inertia capacity dynamic vibration absorber of the present invention comprises the following steps:

[0019] Step 1: Use the Euler-Lagrange equation to establish the dynamic equation of the system consisting of the wind turbine blade and the dynamic vibration absorber based on the inertia capacity; the dynamic vibration absorber based on the inertia capacity is composed of a spring k1, an inertia capacity b and a damping c in series and a spring k in parallel. d and with the additional mass m d The specific process is as follows:

[0020] 1) Define the blade azimuth angle Ψ as

[0021] Ψ=Ωt (1)

[0022] Where Ω represents the angular velocity of the blade rotation; the displacement u(x2, t) of the blade in the swing direction at a distance x2 from the rotation center can be expressed as

[0023] u(x2, t) = Φ(x2)q(t) (2)

[0024] where Φ(x2) is the fundamental mode shape function of the blade in the swing direction and is normalized relative to the value of the shape at the blade tip; q(t) is the generalized displacement corresponding to the fundamental mode; in particular, the displacement of the blade at the installation position x0 of the dynamic vibration absorber based on the inertia volume can be expressed as

[0025] u(x2, t) = aq(t) (3)

[0026] Where a = Φ(x0), which depends on the modal vibration shape value at the installation location of the dynamic vibration absorber;

[0027] 2) The kinetic energy T of the entire system can be expressed as

[0028]

[0029] Where L represents the length of the fan blade; μ(x2) represents the mass per unit length of the blade; m d Represents the mass of the additional mass block; v b and v mThey represent the velocity of the blade element at x2 and the velocity of the additional mass block at x0, respectively, and can be expressed as

[0030]

[0031]

[0032] u d represents the relative displacement of the additional mass block;

[0033] The potential energy U of the entire system can be expressed as

[0034]

[0035] Where k0 represents the modal stiffness of the blade, which can be expressed as

[0036]

[0037] Where EI(x2) represents the bending stiffness of the blade in the swing direction, Φ′ and Φ″ represent the first-order derivative and second-order derivative of the basic mode shape with respect to x2, respectively; F c (x2, Ω) represents the centrifugal force caused by the rotation of the blades;

[0038] Let Q represent the generalized load vector, which mainly includes the wind load f w , gravity load f g and the control force f generated by the dynamic vibration absorber based on the inertia d ; Virtual work done by wind load δW w , virtual work done by gravity load δW g The virtual work done by the control force can be expressed as

[0039] δW w =f w δq,δW g =f g δq,δW d =f d δu d (9)

[0040] in

[0041]

[0042] p(x2, t) represents the wind load density in the blade swing direction;

[0043]

[0044]

[0045] in stands for inverse Laplace transform; s stands for Laplace operator, F d Represents f d In the Pull domain, Represents the relative displacement u of the mass block d Symbolic representation in pull domain.

[0046] Let u(t) = [q(t), u d (t)] T represents the generalized coordinate vector of the system; then according to the principle of virtual work, we can get

[0047]

[0048] Substituting (4), (7) and (13) into the Euler Lagrange equation

[0049]

[0050] in represents the differential of the generalized coordinate vector u with respect to time; the kinematic equation of the entire system can be written in the Las Vegas domain as

[0051]

[0052] in represents the symbolic representation of the generalized displacement q of the blade in the Latten domain, and

[0053]

[0054]

[0055] in represents the modal mass of the blade, stands for Laplace transform.

[0056] Step 2: Solve the transfer function from the external load on the wind turbine blade to the displacement in the blade swing direction and perform dimensionless processing; the specific process is as follows:

[0057] The transfer function from the external load on the wind turbine blade to the displacement in the blade swing direction is:

[0058]

[0059] Among them, H i (s) represents the transfer function from the external load on the blade to its displacement in the swing direction; H di (s) represents the transfer function from the external load to the relative displacement of the mass block. The following dimensionless parameters are defined:

[0060]

[0061] in represents the fundamental modal frequency of the blade; let s = jω in equation (18), and substitute equation (19) into equation (18) to obtain the dimensionless frequency response function of the blade swing direction displacement:

[0062]

[0063] in

[0064]

[0065] in

[0066] c1=1-ρ 2 -a 2 ρ 2 μ,c2=ρ 2 (1-ρ 2 ) (twenty two)

[0067] Step 3: Use the pole placement method to obtain the analytical expression of the optimal structural parameters of the dynamic vibration absorber based on inertia capacity; the specific process is as follows:

[0068] Let the denominator of equation (20) equal to 0, and the characteristic equation of the whole system is:

[0069]

[0070] The three complex roots λ1, λ2 and λ3 of the characteristic equation are distributed in the first quadrant of the complex λ plane, and the other three roots and (The horizontal bar represents conjugation) is symmetrically distributed in the second quadrant of the complex λ plane about the imaginary axis. According to the requirements of the pole placement method, the optimal parameters are obtained by making the modal damping ratios of the two free vibrations equal, that is, the two complex roots of the first quadrant of the characteristic equation are about a radius of λ r , the center of the circle is at the inverse point of the circle at the origin, and the third root is on the circle, that is, it satisfies the following relationship:

[0071]

[0072] When ζ→0, the characteristic equation (24) can be viewed as a 2 The quadratic polynomial equation of

[0073]

[0074] The characteristic equation can now be rewritten as

[0075]

[0076] Comparing (23) and (26), we can see that the ratio of the constant term to the quartic term coefficient is therefore

[0077]

[0078] When ζ→∞, the characteristic equation (23) can be regarded as a 2 The cubic polynomial equation of

[0079]

[0080] The characteristic equation can now be rewritten as

[0081]

[0082] Comparing (23) and (29), we can see that the ratio of the constant term to the quartic term coefficient is The ratio of the coefficients of the quadratic term to the quartic term is therefore

[0083]

[0084]

[0085] Solving equations (27), (30) and (31) together yields

[0086]

[0087]

[0088]

[0089] In order to obtain the optimal expressions for the inertia-mass ratio β and the damping ratio ζ, it is assumed that the root locus of the characteristic equation (23) (obtained by varying ζ from 0 to ∞) intersects at a triple bifurcation point λ * , that is, at the triple bifurcation point, the three complex roots λ1, λ2, and λ3 of the characteristic equation are equal. At this time, the characteristic equation can be rewritten as

[0090]

[0091] Similarly, by comparing equation (23) and equation (35), we can see

[0092]

[0093]

[0094]

[0095] The parameters at the triple bifurcation point mean that the maximum isomodal damping ratio is obtained. However, since the three identical vibration mode frequencies will produce coherent interference, the parameters at the triple bifurcation point are not optimal. A lower modal damping ratio will provide better damping performance. Therefore, we introduce two proportional coefficients for β * and * To adjust,

[0096] β=nβ * , ζ=ζ * / m (39)

[0097] Finally, the optimal parameter expression of the dynamic vibration absorber based on inertia is summarized as follows:

[0098]

[0099] Where m and n are two adjustment parameters. According to formula (40), when the rated speed of the wind turbine blade is known, the optimal parameters of the mechanical components inside the inertia-based dynamic vibration absorber can be calculated by designing the installation position of the inertia-based dynamic vibration absorber inside the blade and the mass ratio of the additional mass block in advance.

[0100] The present invention is a method for reducing vibration and optimizing parameters of fan blades based on a dynamic vibration absorber of inertia capacity. Figure 1 As shown in FIG. 1 , the entire system consists of a hollow blade and a dynamic vibration absorber based on an inertia capacity installed inside the blade, wherein the dynamic vibration absorber based on an inertia capacity is composed of a spring k1, an inertia capacity b and a damper c connected in series and a spring k1 connected in parallel. d And add the mass m d When the blade vibrates due to the excitation of the external load, the additional mass block will also be displaced relative to the blade and this part of the energy will be dissipated through the damper, thereby achieving the purpose of vibration reduction. In order to obtain the optimal expression of the structural parameters of the dynamic vibration absorber based on inertia, the entire system needs to be modeled first, and then the transfer function from the external load to the displacement in the swing direction of the fan blade is obtained and dimensionless, and finally the pole configuration method is used to derive the analytical expression of the optimal structural parameters of the dynamic vibration absorber based on inertia.

[0101] The dynamic vibration absorber based on inertia capacity in the present invention has an additional inertia capacity and spring element, so that the effective frequency band is widened and can better cope with complex wind input, and thus has a better vibration reduction effect. In addition, according to the pole configuration method, an analytical expression of the optimal structural parameters of the dynamic vibration absorber based on inertia capacity is given, which not only has stronger universality, but also greatly simplifies the parameter tuning process.

[0102] The following is a more detailed description in conjunction with the embodiments:

[0103] Example

[0104] Taking the structural parameters of a NREL-5Mw wind turbine blade as an example, its rated speed is Ω = 1.27 rad / s, the basic modal mass is m0 = 1354 kg, the blade length is L = 61.5 m, and the basic modal vibration function of the blade swing direction is

[0105]

[0106] Assume that the dynamic vibration absorber based on inertia is installed at a distance of 45 m from the blade root, that is, a = Φ(x0) = 0.516, and the mass ratio μ = 0.03 is selected. At this time, the proportional coefficient can be set to n = 0.3, m = 1.255n + 0.035.

[0107] Firstly, the frequency domain performance of the inertia-based dynamic vibration absorber is verified. Figure 2(a) to Figure 2(c) The frequency response curve of the displacement of the fan blade in the swing direction is shown in Figure 2. The dynamic vibration absorber based on inertia capacity is compared with the traditional TMD under three different operating conditions (i.e., Ω = 0 corresponds to the shutdown state, Ω = Ω0 corresponds to the fan operating at the rated speed, and Ω = 3Ω0 represents an extreme case). It can be seen that no matter which state the fan is operating in, the dynamic vibration absorber based on inertia capacity has a smaller and flatter frequency response, and the effective frequency band is also wider, which means that the dynamic vibration absorber based on inertia capacity has better vibration reduction performance than the traditional TMD.

[0108] The time domain performance of the dynamic vibration absorber based on inertia can be further verified. First, the external load on the blade needs to be calculated. The external load on the blade is mainly composed of wind load and the blade's own gravity. The wind load on the blade can be calculated by the blade element momentum (BEM) theorem, and the result is as follows: Figure 3 Substituting the external load into the kinematic equation of the entire system, the displacement of the blade in the swing direction can be obtained. Figure 4(a) to Figure 4(b) The figure shows the time domain curve of the displacement in the swing direction of the blade and its corresponding Fourier spectrum, and compares the uncontrolled state, TMD and the dynamic vibration absorber based on inertia. It can also be seen from the figure that the dynamic vibration absorber based on inertia does effectively reduce the vibration of the wind blade, and has better vibration reduction performance than the traditional TMD, which is more obvious in the Fourier spectrum.

[0109] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for reducing vibration and optimizing parameters of fan blades based on a dynamic vibration absorber of inertia capacity, characterized in that: The following steps are involved: Step 1, using the Euler-Lagrange equation to establish the dynamic equation of a system consisting of a wind turbine blade and a dynamic vibration absorber based on an inertia capacity; the dynamic vibration absorber based on an inertia capacity is composed of a first spring, an inertia capacity and a damping connected in series, a second spring in parallel and connected to an additional mass, wherein k1 represents the elastic coefficient of the first spring, b represents the value of the inertia capacity, c represents the value of the damping, k d represents the elastic constant of the second spring, m d represents the value of the added mass; The Euler-Lagrange equation is used to establish the dynamic equation of the system consisting of the wind turbine blade and the dynamic vibration absorber based on the inertia volume. The specific process is as follows: 1) Define the blade azimuth angle Ψ as Ψ = Ωt (1) Where Ω represents the angular velocity of the blade rotation; the displacement u(x2, t) of the blade in the swing direction at a distance x2 from the rotation center can be expressed as u(x2, t) = Φ(x2)q(t) (2) Where Φ(x2) is the fundamental mode vibration function of the blade in the swing direction, and is normalized relative to the vibration value at the blade tip; q(t) is the generalized displacement corresponding to the fundamental mode; the displacement of the blade at the installation position x0 of the dynamic vibration absorber based on inertia can be expressed as u(x2, t) = aq(t) (3) Where a = Φ(x0), which depends on the modal vibration shape value at the installation location of the dynamic vibration absorber; 2) The kinetic energy T of the entire system can be expressed as Where L represents the length of the fan blade; μ(x2) represents the mass per unit length of the blade; m d Represents the mass of the additional mass block; v b and v m They represent the velocity of the blade element at x2 and the velocity of the additional mass block at x0, respectively, and can be expressed as u d represents the relative displacement of the additional mass block; The potential energy U of the entire system can be expressed as Where k0 represents the modal stiffness of the blade, which can be expressed as Where EI(x2) represents the bending stiffness of the blade in the swing direction, Φ' and Φ" represent the first-order derivative and second-order derivative of the basic mode shape with respect to x2, respectively; F c (x2,Ω) represents the centrifugal force caused by the rotation of the blades; Let Q represent the generalized load vector, including the wind load f w , gravity load f g and the control force f generated by the dynamic vibration absorber based on the inertia d ; Virtual work done by wind load δW w , virtual work done by gravity load δW g and the virtual work δW done by the control force d Can be expressed as δW w =f w δq,δW g =f g δq,δW d =f d δu d (9) in p(x2,t) represents the wind load density in the blade swing direction; in stands for inverse Laplace transform; s stands for Laplace operator, F d Represents f d In the Pull domain, Represents the relative displacement u of the mass block d Symbolic representation in the pull domain; Let u(t)=[q(t),u d (t)] T represents the generalized coordinate vector of the system; then according to the principle of virtual work, we can get Substituting (4), (7) and (13) into the Euler Lagrange equation in represents the differential of the generalized coordinate vector u with respect to time; the kinematic equation of the entire system can be written in the Las Vegas domain as in represents the symbolic representation of the generalized displacement q of the blade in the Latten domain, and in represents the modal mass of the blade, stands for Laplace transform; Step 2, solving the transfer function from the external load on the wind turbine blade to the displacement in the blade swing direction and performing dimensionless processing; Step 3: Use the pole configuration method to obtain the analytical expression of the optimal structural parameters of the dynamic vibration absorber based on inertia capacity.

2. The method for reducing vibration and optimizing parameters of fan blades based on a dynamic vibration absorber of inertia capacity according to claim 1 is characterized in that The transfer function from the external load on the wind turbine blade to the displacement in the blade swing direction is solved in step 2 as follows: Among them, H i (s) represents the transfer function from the external load on the blade to its displacement in the swing direction; H di (s) represents the transfer function from the external load to the relative displacement of the mass block, and the following dimensionless parameters are defined: in represents the fundamental modal frequency of the blade; let s = jω in equation (18), and substitute equation (19) into equation (18) to obtain the dimensionless frequency response function of the blade swing direction displacement: in in c1=1-ρ 2 -a 2 r 2 μ,c2=ρ 2 (1-p 2 ) (22).

3. The method for reducing vibration and optimizing parameters of fan blades based on a dynamic vibration absorber of inertia capacity according to claim 2 is characterized in that In step 3, the pole placement method is used to obtain the analytical expression of the optimal structural parameters of the dynamic vibration absorber based on inertia capacity: Where m and n are two adjustment parameters. According to formula (23), when the rated speed of the wind turbine blade is known, the optimal parameters of the mechanical components inside the inertia-based dynamic vibration absorber can be calculated by designing the installation position of the inertia-based dynamic vibration absorber inside the blade and the mass ratio of the additional mass block in advance.

4. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the fan blade vibration reduction and parameter optimization method based on the inertia capacity dynamic vibration absorber as described in any one of claims 1-3 is implemented.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method for reducing vibration and optimizing parameters of fan blades based on an inertia capacity dynamic vibration absorber as described in any one of claims 1 to 3 is implemented.

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