Photovoltaic tracking support flutter critical wind speed rapid quantification method based on damping ratio

Abstract

The invention relates to the technical field of photovoltaic support risk assessment, in particular to a photovoltaic tracking support flutter critical wind speed rapid quantification method based on a damping ratio, and the method comprises the following steps: obtaining self-excitation aerodynamic force or aerodynamic force coefficients corresponding to different amplitudes of a photovoltaic tracking support under different wind attack angles; establishing a vibration equation under single-degree-of-freedom torsional flutter; the converted wind speed corresponding to any wind attack angle of the photovoltaic tracking support and flutter derivatives corresponding to different amplitudes are obtained; establishing a three-dimensional mathematical model of a flutter derivative; the three-dimensional mathematical model of the flutter derivative is substituted into a vibration equation under single-degree-of-freedom torsional flutter, and mathematical models of the frequency and the damping ratio and converted wind speed and amplitude are obtained; the mapping relation among the aerodynamic damping ratio, the amplitude and the converted wind speed is established based on the vibration form of the photovoltaic tracking support, so that the flutter critical wind speed of the photovoltaic tracking support is obtained, and rapid quantification of the flutter critical wind speed of the photovoltaic tracking support under different damping is completed.

Description

Technical Field

[0001] The present invention relates to the technical field of risk assessment of photovoltaic tracking brackets, and in particular to a fast quantification method for flutter critical wind speed of photovoltaic tracking brackets based on damping ratio. Background Art

[0002] In recent years, with global resource shortages and a deteriorating living environment, the shift from traditional fossil fuels to clean energy has become a consensus, leading to the rapid development of photovoltaic energy. Photovoltaic racks are the supporting devices used to place, install, and secure photovoltaic modules in solar photovoltaic power generation systems.

[0003] Photovoltaic brackets include fixed brackets, photovoltaic tracking brackets, and flexible brackets. Among them, fixed brackets are the simplest and most common form of photovoltaic brackets. Photovoltaic panels are installed at a fixed angle and do not adjust with the movement of the sun. They are usually suitable for rooftop and ground photovoltaic systems. Flexible brackets are a new type of bracket design, usually made of lightweight materials, which can adapt to irregular surfaces or special terrains, and can even bend or fold to adapt to different installation environments. Flexible brackets can flexibly install photovoltaic panels on irregular roofs, walls or other surfaces. Photovoltaic tracking brackets are a type of bracket that can adjust the angle of photovoltaic panels as the position of the sun changes. They are mainly divided into single-axis tracking and dual-axis tracking. Photovoltaic tracking brackets can improve power generation efficiency. Photovoltaic tracking brackets need to rotate along their main axis during the tracking process.

[0004] Among them, in order to achieve efficient tracking of the sun, the photovoltaic tracking bracket has low rigidity. In windy weather, wind-induced vibration and aerodynamic instability often occur, and it may even be damaged due to excessive amplitude, causing significant economic losses.

[0005] Common structural flutter phenomena primarily fall into two categories: bending-torsional coupled flutter and separated-flow flutter. In wind-induced structural vibrations, well-streamlined main beams typically experience bending-torsional coupled flutter. However, the vast majority of structural sections are non-streamlined. When air flows through these vibrating non-streamlined sections, separation occurs at the windward corners, leading to vortex shedding. Such sections often experience single-degree-of-freedom torsional flutter, also known as separated-flow flutter. Flutter instability in photovoltaic tracking mounts clearly falls into the latter category, and relevant scholars have demonstrated this.

[0006] Currently, there are numerous theoretical solutions for flexural-torsional coupled flutter, most of which can provide a good quantitative assessment of the critical flutter wind speed. These calculation methods for critical flutter wind speed based on flexural-torsional coupled flutter are generally derived from bridge structures. Flutter in flexural-torsional coupled bridge structures occurs primarily in vertical bending followed by torsion, and the formation frequencies of the vertical and torsion motions are not significantly different.

[0007] Patent application publication number CN118332719A discloses a method, system, and device for predicting the critical wind speed for flutter in a photovoltaic flexible support system. However, similar to bridge structures, flexible supports exhibit a modal pattern of vertical motion followed by torsional motion, and their flutter is typically coupled bending and torsional flutter.

[0008] However, PV trackers experience torsion first and then vertical bending, and the frequencies of the torsion and vertical bending formations differ significantly. Torsion is the primary cause of flutter. Clearly, the traditional torsion-bending coupled flutter theory is not suitable for calculating the critical wind speed for PV trackers.

[0009] Furthermore, the critical flutter wind speed of photovoltaic panel components is currently determined primarily through experimental measurements. However, due to terrain constraints, the span, number of drive columns, column height, and wind attack angle of the photovoltaic tracker can vary for different photovoltaic projects. This results in differences in the torsional frequency and structural damping ratio of the photovoltaic tracker. Conducting individual tests would waste significant manpower and material resources. Therefore, rapidly quantifying the critical flutter wind speed of photovoltaic trackers based on damping ratio and frequency is of practical significance. Summary of the Invention

[0010] The purpose of the present invention is to overcome the shortcomings existing in the prior art. First, the theory of bending-torsion coupling flutter is basically derived from the bridge structure, but the vibration mode of the photovoltaic tracking bracket is quite different from that of the bridge structure, which is not applicable to the traditional bending-torsion coupling flutter theory; second, the critical wind speed of flutter of the photovoltaic panel components is mainly measured by actual experiments, which has high manpower and material costs. A method for quickly quantifying the critical wind speed of flutter of the photovoltaic tracking bracket based on the damping ratio is provided.

[0011] In order to achieve the above object, the technical solution adopted by the present invention is:

[0012] The present invention provides a method for quickly quantifying the critical wind speed of flutter of a photovoltaic tracking bracket based on a damping ratio, comprising the following steps:

[0013] S1. Obtain the self-excited aerodynamic force or aerodynamic force coefficient corresponding to different amplitudes of the photovoltaic tracking bracket under different wind attack angles, and establish the corresponding vibration equation under single-degree-of-freedom torsional flutter;

[0014] S2. Obtain the converted wind speed corresponding to the photovoltaic tracking bracket at any wind attack angle and different flutter derivatives corresponding to different amplitudes according to the self-excited aerodynamic force or aerodynamic force coefficient obtained in step S1;

[0015] S3. Establishing a three-dimensional mathematical model of flutter derivatives based on the different amplitudes of the photovoltaic tracking bracket and the converted wind speed obtained in step S2;

[0016] S4. Substituting the three-dimensional mathematical model of the flutter derivative into the vibration equation under single-degree-of-freedom torsional flutter corresponding to the photovoltaic tracking bracket, obtain a first mathematical model of the frequency, the reduced wind speed, and the amplitude, and a second mathematical model of the damping ratio, the reduced wind speed, and the amplitude;

[0017] S5. A mapping relationship between the aerodynamic damping ratio of the photovoltaic tracking bracket corresponding to the flutter derivative and the amplitude and the converted wind speed is established based on the first mathematical model and the second mathematical model, thereby obtaining the flutter critical wind speed of the photovoltaic tracking bracket and completing the quantification of the flutter critical wind speed of the photovoltaic tracking bracket.

[0018] Steps S3 and S4 obtain three-dimensional models of flutter derivatives, damping, and frequency with amplitude and wind speed, respectively, which can achieve rapid quantification of multiple flutter derivatives, damping, and frequencies, helping to save labor and material costs and improve design efficiency.

[0019] Preferably, in step S5, according to the total damping ζ of the photovoltaic tracking bracket in the critical state total and the total conversion frequency K total ,Based on the flutter derivative of the photovoltaic tracking bracket, the mapping relationship between the aerodynamic damping ratio of photovoltaic tracking and the amplitude and converted wind speed is established.

[0020] Preferably, based on the mapping relationship between the aerodynamic damping ratio of the photovoltaic tracking bracket with respect to the corresponding flutter derivative and the amplitude and converted wind speed, a three-dimensional surface diagram of the aerodynamic damping of the photovoltaic tracking bracket with respect to the corresponding vibration form is established, and the corresponding aerodynamic damping cloud diagram is obtained according to the three-dimensional surface diagram of the aerodynamic damping.

[0021] Preferably, in the aerodynamic damping cloud diagram, when the difference between the amplitude and 0 is less than a threshold value, the corresponding wind speed is used as the flutter critical wind speed.

[0022] The threshold is determined based on the actual situation. When the amplitude approaches a non-zero value, the corresponding wind speed is used as the flutter critical wind speed.

[0023] Preferably, when the photovoltaic tracking bracket is in a critical state of vibration, the total damping ζ total =0.

[0024] Preferably, in step S3, a three-dimensional mathematical model of flutter derivatives is established based on the displacement expression of the photovoltaic panel section of the photovoltaic tracking bracket and the linear self-excited aerodynamic force expression.

[0025] Preferably, the expression of the three-dimensional mathematical model of the flutter derivative is obtained by a least square method.

[0026] Preferably, before step S4, an unsteady torsional flutter self-excited force model is established according to Scanlan's flutter analysis theory, and the unsteady torsional flutter self-excited force model is represented by flutter derivatives.

[0027] Preferably, the self-excited aerodynamic force obtained in step S1 includes the lift moment M of the photovoltaic tracking bracket; the aerodynamic force coefficient includes the first-order torsional frequency w a .

[0028] Preferably, in step S1, the self-excited aerodynamic force or aerodynamic force coefficient corresponding to different amplitudes of the photovoltaic tracking bracket at different wind attack angles is obtained through a wind tunnel forced vibration test or CFD forced vibration.

[0029] Wind tunnel forced vibration tests or CFD (Computational Fluid Dynamics) forced vibration identification have good repeatability and a wide range of converted wind speeds, so forced vibration is used.

[0030] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0031] The present invention provides a method for rapidly quantifying the critical wind speed of photovoltaic tracking bracket flutter based on damping ratio. The method first obtains the self-excited aerodynamic forces or aerodynamic force coefficients of different amplitudes at various wind attack angles and establishes the corresponding vibration equations for single-degree-of-freedom torsional flutter. This method then converts the flutter derivatives to obtain the different reduced wind speeds and amplitudes at the corresponding wind attack angles. A three-dimensional mathematical model of the flutter derivatives is then established based on the different reduced wind speeds and amplitudes, enabling accurate quantification of the flutter derivatives at different reduced wind speeds and amplitudes at a given wind attack angle. The corresponding flutter derivatives are then substituted into the vibration equations for single-degree-of-freedom torsional flutter to obtain a mathematical model of frequency, reduced wind speed, and amplitude. Furthermore, a mathematical model of damping ratio, reduced wind speed, and amplitude is also obtained. Finally, based on the three-dimensional mathematical model of frequency and damping ratio, the critical wind speed of photovoltaic tracking bracket flutter at different frequencies and damping ratios can be rapidly quantified, accurately and effectively evaluating its wind resistance. This application primarily calculates the critical wind speed of flutter in torsional motion of a photovoltaic tracking bracket, adapting to the vibration modes of the photovoltaic tracking bracket. By establishing a mathematical model of flutter derivatives instead of actual experimental measurements, this approach helps save labor and material costs. This application overcomes the shortcomings of the prior art: first, the theory of bending-torsion coupled flutter is fundamentally derived from bridge structures, but the vibration modes of photovoltaic tracking brackets differ significantly from those of bridge structures, making it unsuitable for traditional bending-torsion coupled flutter theory; and second, the critical wind speed of flutter of photovoltaic panel components is primarily determined through actual experimental measurements, resulting in high labor and material costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of a method for rapidly quantifying the critical wind speed of flutter of a photovoltaic tracking bracket based on damping ratio of the present invention;

[0033] Figure 2This is a schematic diagram of the calculation domain and boundary conditions of the photovoltaic panel;

[0034] Figure 3 This is the amplitude-dependent aerodynamic derivative fitting result of the photovoltaic tracking bracket

[0035] Figure 4 This is the amplitude-dependent aerodynamic derivative fitting result of the photovoltaic tracking bracket

[0036] Figure 5 is a three-dimensional surface plot of the frequency fitting result;

[0037] Figure 6 is the three-dimensional surface diagram of aerodynamic damping;

[0038] Figure 7 It is the aerodynamic damping cloud map;

[0039] Figure 8 is the angular displacement time history graph; DETAILED DESCRIPTION

[0040] The present invention will be further described in detail below with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments, as all technologies implemented based on the present invention fall within the scope of the present invention.

[0041] Unless otherwise specified, in the description of the specific embodiments of the present invention, the terms indicating the orientation or positional relationship, such as "upper", "lower", "left", "right", "center", "inside", and "outside", are based on the expressions of the orientation or positional relationship shown in the accompanying drawings, or are the orientation or positional relationship in which the invented product / device / apparatus is placed when it is conventionally used. These terms of orientation or positional relationship are merely for the purpose of facilitating the description of the scheme of the present invention or simplifying the description of the specific embodiments to facilitate the rapid understanding of the scheme by technicians, and do not indicate or imply that a specific device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship, and therefore should not be understood as limiting the present invention.

[0042] In addition, if the terms "horizontal", "vertical", "overhanging", "parallel" and the like appear, it does not mean that the corresponding devices / components / elements are required to be absolutely horizontal or vertical or overhanging or parallel, but may be slightly tilted or have deviations. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but may be slightly tilted. Alternatively, it can be simply understood that the corresponding devices / components / elements are set in directions such as "horizontal", "vertical", "overhanging", and "parallel", and can have an error / deviation of ±10% relative to the corresponding direction setting, more preferably an error / deviation within ±8%, more preferably an error / deviation within ±6%, more preferably an error / deviation within ±5%, and more preferably an error / deviation within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its role in the solution of the present invention.

[0043] In addition, the expressions “first”, “second”, “third”, etc. in the terms are merely used to distinguish the description of the same or similar components, and should not be understood as emphasizing or implying the relative importance of specific components.

[0044] In addition, in the description of the embodiments of the present invention, "several," "plurality," and "a number" represent at least two. It can also be any number such as two, three, four, five, six, seven, eight, nine, or even more than nine.

[0045] Furthermore, in the description of the technical solution of the present invention, unless otherwise expressly specified, defined, or limited, the terms "disposed," "installed," "connected," "connected," "provided with," "laid," and "arranged" should be understood broadly. For example, they may refer to fixed connections, detachable connections, or integral connections. They may be welded, riveted, bolted, threaded, or other commonly used connection methods in the art. Such connections may be mechanical, electrical, or communicative; they may be direct, indirect via an intermediate medium, or internally connected between two components.

[0046] Example 1

[0047] like Figure 1 As shown, the present embodiment adopts a method for rapidly quantifying the critical wind speed of flutter of a photovoltaic tracking bracket based on the damping ratio, which includes the following steps:

[0048] S1. Obtain the self-excited aerodynamic force or aerodynamic force coefficient corresponding to different amplitudes of the photovoltaic tracking bracket under different wind attack angles, and establish the corresponding vibration equation under single-degree-of-freedom torsional flutter;

[0049] S2. Obtain the converted wind speed corresponding to the photovoltaic tracking bracket at any wind attack angle and different flutter derivatives corresponding to different amplitudes according to the self-excited aerodynamic force or aerodynamic force coefficient obtained in step S1;

[0050] S3. Establishing a three-dimensional mathematical model of flutter derivatives based on the different amplitudes of the photovoltaic tracking bracket and the converted wind speed obtained in step S2;

[0051] S4. Substituting the three-dimensional mathematical model of the flutter derivative into the vibration equation under single-degree-of-freedom torsional flutter corresponding to the photovoltaic tracking bracket, obtain a first mathematical model of the frequency, the reduced wind speed, and the amplitude, and a second mathematical model of the damping ratio, the reduced wind speed, and the amplitude;

[0052] S5. A mapping relationship between the aerodynamic damping ratio of the photovoltaic tracking bracket corresponding to the flutter derivative and the amplitude and the converted wind speed is established based on the first mathematical model and the second mathematical model, thereby obtaining the flutter critical wind speed of the photovoltaic tracking bracket and completing the quantification of the flutter critical wind speed of the photovoltaic tracking bracket.

[0053] The present invention provides a method for rapidly quantifying the critical wind speed of photovoltaic tracking bracket flutter based on damping ratio. The method first obtains the self-excited aerodynamic forces or aerodynamic force coefficients of different amplitudes at various wind attack angles and establishes the corresponding vibration equations for single-degree-of-freedom torsional flutter. This method then converts the flutter derivatives to obtain the different reduced wind speeds and amplitudes at the corresponding wind attack angles. A three-dimensional mathematical model of the flutter derivatives is then established based on the different reduced wind speeds and amplitudes, enabling accurate quantification of the flutter derivatives at different reduced wind speeds and amplitudes at a given wind attack angle. The corresponding flutter derivatives are then substituted into the vibration equations for single-degree-of-freedom torsional flutter to obtain a mathematical model of frequency, reduced wind speed, and amplitude. Furthermore, a mathematical model of damping ratio, reduced wind speed, and amplitude is also obtained. Finally, based on the three-dimensional mathematical model of frequency and damping ratio, the critical wind speed of photovoltaic tracking bracket flutter at different frequencies and damping ratios can be rapidly quantified, accurately and effectively evaluating its wind resistance.

[0054] Example 2

[0055] This embodiment is a specific implementation of the method for rapidly quantifying the critical wind speed of flutter of a photovoltaic tracking bracket based on the damping ratio described in Example 1, and includes the following steps:

[0056] 1. Rapid quantification of critical wind speed for photovoltaic tracking system flutter based on damping ratio and frequency

[0057] During the design phase of a photovoltaic tracker, wind tunnel forced vibration tests or CFD forced vibration tests are typically conducted to investigate the self-excited aerodynamic characteristics of the tracker, taking into account safety, cost-effectiveness, and design rationality. This provides relatively detailed performance support for the tracker's design. This method, utilizing limited data, can calculate the flutter derivatives of the tracker at different frequencies and damping ratios, enabling accurate assessment and rapid quantification of the critical wind speed for flutter. This method is efficient and rapid, minimizing waste of manpower and material resources. Beyond trackers, this method is also applicable to other types of trackers with torsional flutter in other degrees of freedom, as well as similar thin-plate structures.

[0058] 1.1 Rapid quantification of critical wind speed for photovoltaic tracking bracket flutter

[0059] In the field of wind engineering and structural wind-resistant design, the displacement response of a structure's forced vibration can be obtained by solving the structural vibration equation. The motion equation of the structure under lift and lift moment, that is, the vibration equation under single-degree-of-freedom torsional flutter, is expressed as follows:

[0060]

[0061] Where L and M are lift and lift moment respectively; m and I are mass per unit length and moment of inertia per unit length respectively; ζ h ,ζ a are the damping ratios for vertical and torsional motions, respectively; ω h 、ω a are the frequencies of vertical and torsional motion, respectively; are the displacement, velocity and acceleration of the vertical motion of the model respectively; are the displacement, velocity and acceleration of the torsional motion of the model, respectively.

[0062] Flutter derivatives are important aerodynamic parameters that characterize the self-excited aerodynamic forces of a structural section. Their linear combination with the structural section's motion state represents the linear portion of the aerodynamic force. Given the advantages of forced vibration methods for identifying flutter derivatives, including good repeatability and a wide range of converted wind speeds, this application uses forced vibration as an example to identify flutter derivatives using a state-separated single-degree-of-freedom forced vibration method.

[0063] For streamlined and blunt sections, the self-excited aerodynamic forces can be expressed by linear combinations of section motion parameters, as shown in formulas (3) and (4). In order to describe in detail the relationship between the unsteady self-excited aerodynamic forces and section motion, an unsteady torsional flutter self-excited force model is established, which can express the aerodynamic self-excited lift L and torque M through 8 flutter derivatives:

[0064]

[0065] Where L(t) and M(t) are the expressions of the aerodynamic self-excited lift and torque with respect to the flutter time t, respectively; ρ is the air density; U is the incoming wind speed; K is the conversion frequency, which is a dimensionless number and K = Bω / U; B is the width of the photovoltaic panel; ω is the circular frequency of vibration; h and are vertical displacement and vertical velocity respectively; a and are torsional displacement and torsional velocity, respectively; is the flutter derivative, i is 1 to 4, that is, and and and are flutter derivatives.

[0066] When the photovoltaic panel section is subjected to torsional forced vibration and vertical forced vibration, the corresponding torsional and vertical displacements are:

[0067] a(t)=a0 sinωt (5)

[0068] h(t)=h0sinωt (6)

[0069] Where a0 and h0 are the amplitudes of torsional motion and vertical motion, respectively.

[0070] By determining the amplitude and different converted wind speed ranges, a three-dimensional mathematical model of the photovoltaic panel cross-section flutter derivative can be established using the least squares method based on the self-excited aerodynamic time history of the photovoltaic panel cross-section under different amplitudes and different converted wind speeds.

[0071] The linear self-excited aerodynamic force of the photovoltaic panel section is expressed as a sinusoidal function, as shown in formulas (7) and (8).

[0072] L(t)=L0sin(ωt+φ L ) (7)

[0073] M(t)=M0 sin(ωt+φ M ) (8)

[0074] Where: L0, M0 are the aerodynamic amplitudes; φ L 、φ M is the hysteresis phase of the aerodynamic force relative to the displacement. From the expressions of the eight flutter derivatives, it can be seen that the change of the flutter derivative can be determined by L0 / a0, M0 / a0, L0 / h0, M0 / h0 and φ L 、φ M represents, and the flutter derivative Associated with torsional motion.

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] As mentioned above, the flutter of the flat single-axis photovoltaic tracking bracket belongs to the separated flow flutter. Only its torsional flutter needs to be considered. The torsional flutter equation of its first-order torsional vibration mode can be transformed by formula (2) (4) as shown below:

[0084]

[0085] By moving the right side of the above equation to the left side, we can get:

[0086]

[0087] Where, is the mass moment of inertia; α is the damping ratio of torsional motion; ω α is the frequency of torsional motion (rad / s); are the displacement, velocity and acceleration of the torsional motion of the model, respectively.

[0088] That is, the total damping and total stiffness of the structure under the action of self-excited aerodynamic force are:

[0089]

[0090]

[0091] When total When ζ is greater than zero, the total damping of the system is positive, the vibration is stably attenuated, and torsional flutter does not occur; when ζ total When it is equal to zero, the structure enters an unstable flutter critical state. That is, the flutter critical wind speed can be calculated according to the following formula:

[0092]

[0093] When the photovoltaic tracking bracket undergoes wind-induced torsional motion, due to the fluid-structure coupling effect, the structure has aerodynamic stiffness in addition to its own torsional stiffness. At this time, the vibration frequency of the structure will change compared to the fixed torsional frequency. Its true torsional frequency ω can be obtained by combining Ktotal= and formula (20), as shown in formula (22), where is the aerodynamic derivative.

[0094]

[0095] Since ω>0, the true torsional circular frequency ω can be obtained from the following formula:

[0096]

[0097] When the structure experiences torsional flutter, the aerodynamic force will change with the frequency and amplitude of the vibration. In addition to the change in aerodynamic stiffness, the aerodynamic damping will also dissipate or accumulate with the vibration. In addition, when the structure reaches the critical state of flutter, the total damping of the structure tends to 0, and at this time, ζtotal=ζaero+

[0098] ζstruc=0, that is, ζstruc=-ζaero, where ζstruc is the inherent damping of the photovoltaic tracking bracket. The aerodynamic damping ratio ζaero based on the structure of formula (21) can be expressed as:

[0099]

[0100] At this time, based on formulas (23) and (24), the photovoltaic tracking bracket can be obtained and The three-dimensional frequency surface plot and aerodynamic damping contour plot are displayed. The aerodynamic damping contour plot can be used to intuitively calculate and analyze the effects of reduced wind speed and nonlinear structural damping on flutter amplitude. Furthermore, when the flutter critical state is reached, the amplitude approaches a non-zero value, and the intersection of the damping ratio contour and the reduced wind speed coordinate axis can be considered the critical flutter wind speed.

[0101] Example 3

[0102] Example 3 is the practical application of Example 2. Based on an actual photovoltaic project, CFD is used to perform forced vibration. Since the critical flutter wind speed of the flat single-axis photovoltaic tracking bracket near the 0° inclination angle is high, when a small inclination angle is used for protection, the high wind protection angle is usually set to 0°. Therefore, the photovoltaic section at 0 degrees is selected for the self-excited aerodynamic amplitude effect analysis. The photovoltaic panel cross-sectional shape, calculation domain and boundary conditions are as follows: Figure 2 As shown in the figure, the PV panel's cross-sectional width (B) is 2.278m, and its height (H) is 0.030m. The computational domain is set to 40B × 20B (B is the PV panel's cross-sectional width). The computational domain and boundary conditions are as follows: the left side of the computational domain is the velocity inlet boundary, the right side is the pressure outlet boundary, the upper and lower sides of the computational domain are symmetry boundaries, and the PV panel cross-sectional area is a fixed wall boundary.

[0103] Flutter derivatives are important aerodynamic parameters that characterize the self-excited aerodynamic forces of a structural section. Their linear combination with the structural section's motion state represents the linear portion of the aerodynamic force. Given the advantages of forced vibration methods for identifying flutter derivatives, including good repeatability and a wide range of converted wind speeds, this application uses forced vibration as an example to identify flutter derivatives using a state-separated single-degree-of-freedom forced vibration method.

[0104] In this case analysis, the converted wind speed U cr The torsional motion amplitude α0 is 1°, 2°, 3°, 4°, 5°, 6°, and 7°, respectively. The relevant working conditions are shown in Table 1. The Reynolds number Re is 1.2×10 5 ~5.5×10 5 The forced vibration frequency f is 1.0 Hz. In Table 1, h is the vertical bending amplitude of the photovoltaic tracking bracket.

[0105] Table 1 Different converted wind speeds (U cr ) and amplitude (α0, h)

[0106]

[0107]

[0108] Common structural flutter phenomena mainly include two types: bending-torsion coupled flutter and separated flow flutter. In the wind-induced vibration of the structure, the main beam with good streamline generally undergoes bending-torsion coupled flutter, while the vast majority of structural sections are non-streamlined. When the airflow flows through the vibrating non-streamlined section, separation will occur at the corners of the windward side, and vortex shedding will occur at the same time. This type of structural section often undergoes single-degree-of-freedom torsional flutter, that is, separated flow flutter. The flutter instability of the photovoltaic tracking bracket obviously belongs to the latter, and relevant scholars have also demonstrated this. Since the flutter instability of the photovoltaic tracking bracket belongs to single-degree-of-freedom torsional flutter, and the flutter derivative It has nothing to do with the torsional motion, which is only related to the flutter derivative and Refer to formula (23) (24), the subsequent calculation of the critical wind speed of photovoltaic tracking bracket flutter only involves and Here we only plot the wind speed and amplitude based on the reduced wind speed. and A three-dimensional surface plot of Figure 3-Figure 4 shown.

[0109] By formula (23) and Figure 4 , we can get the three-dimensional surface of frequency, such as Figure 5As shown. As the converted wind speed increases, the vibration frequency gradually decreases, indicating that the greater the wind speed, the greater the amplitude, the stronger the aerodynamic stiffness effect, and the stronger the fluid-solid coupling effect. In addition, Figure 4 The medium amplitude is the torsional amplitude under forced vibration, so its frequency is less affected by the torsional amplitude.

[0110] Combine formula (23) and Figure 5 Substituting the result into formula (24), we can get the three-dimensional surface diagram of the aerodynamic damping of the photovoltaic tracking bracket, as shown in Figure 6 shown. Figure 7 for Figure 6 The mapping diagram is the aerodynamic damping contour map. The aerodynamic damping contour map can be used to intuitively calculate and analyze the effects of reduced wind speed and nonlinear structural damping on flutter amplitude. Furthermore, when the flutter critical state is reached, the amplitude approaches a non-zero value. The intersection of the damping ratio contour and the reduced wind speed coordinate axis at this point can be considered the critical flutter wind speed. That is, the critical flutter wind speed for a photovoltaic tracking bracket is U = U / fB*fB = 14.2*1*2.78≈32.3m / s.

[0111] To verify the accuracy of the calculation results, in addition to forced vibration, free vibration was also calculated using CFD. Both forced and free vibrations were calculated by embedding the Newmark-Bate numerical algorithm into Fluent using a user-defined function (UDF) to solve equations (1) and (2), respectively, to calculate the forced and free vibration responses of the photovoltaic panel section. The relevant parameters for the free vibration calculation characteristics of the photovoltaic panel section are shown in Table 2.

[0112] Table 2 Characteristic parameters for free vibration calculation of thin plate section

[0113]

[0114] The displacement time history curve of the critical state of single-degree-of-freedom torsional flutter is as follows: Figure 8 The calculation results of the critical wind speed and frequency for PV panel cross-section flutter, as well as their comparison with the frequency domain theoretical solution, are shown in Table 1. As can be seen from the table, the error between the frequency domain theoretical solution and the CFD calculation is small, and this method for rapidly quantifying the critical wind speed for PV tracking bracket flutter based on damping ratio and frequency has good accuracy.

[0115] Table 1 Critical flutter wind velocity and frequency of the PV plate section

[0116]

[0117]

[0118] Note: The error of flutter critical wind speed is 1.55%, and the error of flutter critical frequency is 8.5%.

[0119] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A fast quantification method for critical wind speed of photovoltaic tracking bracket flutter based on damping ratio, characterized in that: The following steps are included: S1. Obtain the self-excited aerodynamic force or aerodynamic force coefficient corresponding to different amplitudes of the photovoltaic tracking bracket under different wind attack angles, and establish the corresponding vibration equation under single-degree-of-freedom torsional flutter; S2. According to the self-excited aerodynamic force or aerodynamic force coefficient obtained in step S1, obtain the converted wind speed corresponding to the photovoltaic tracking bracket at any wind attack angle and different flutter derivatives corresponding to different amplitudes; S3, establishing a three-dimensional mathematical model of flutter derivatives based on different amplitudes of the photovoltaic tracking bracket and the converted wind speed obtained in step S2; S4, bringing the three-dimensional mathematical model of the flutter derivative into the vibration equation under the single-degree-of-freedom torsional flutter corresponding to the photovoltaic tracking bracket, and obtaining a first mathematical model of the frequency, the converted wind speed, and the amplitude, and a second mathematical model of the damping ratio, the converted wind speed, and the amplitude; S5. A mapping relationship between the aerodynamic damping ratio of the photovoltaic tracking bracket corresponding to the flutter derivative and the amplitude and the converted wind speed is established according to the first mathematical model and the second mathematical model, so as to obtain the flutter critical wind speed of the photovoltaic tracking bracket and complete the quantification of the flutter critical wind speed of the photovoltaic tracking bracket.

2. According to the damping ratio-based rapid quantification method for flutter critical wind speed of photovoltaic tracking brackets in claim 1, it is characterized in that: In step S5, according to the total damping ζ of the photovoltaic tracking bracket in the critical state total And the total conversion frequency K total , Based on the flutter derivative of the photovoltaic tracking bracket, the mapping relationship between the aerodynamic damping ratio of photovoltaic tracking and the amplitude and converted wind speed is established.

3. According to claim 2, a method for rapid quantification of critical wind speed of photovoltaic tracking bracket flutter based on damping ratio is characterized in that: Based on the mapping relationship between the aerodynamic damping ratio of the photovoltaic tracking bracket with respect to the corresponding flutter derivative and the amplitude and converted wind speed, a three-dimensional surface diagram of the aerodynamic damping of the photovoltaic tracking bracket with respect to the corresponding vibration form is established, and the corresponding aerodynamic damping cloud diagram is obtained according to the three-dimensional surface diagram of the aerodynamic damping.

4. According to claim 3, a method for rapid quantification of critical wind speed of photovoltaic tracking bracket flutter based on damping ratio is characterized in that: In the aerodynamic damping cloud diagram, when the difference between the amplitude and 0 is less than the threshold, the corresponding wind speed is taken as the flutter critical wind speed.

5. According to claim 2, a method for rapid quantification of critical wind speed of photovoltaic tracking bracket flutter based on damping ratio is characterized in that: When the photovoltaic tracking bracket is in the critical state of flutter, the total damping ζ total =0.

6. A method for rapidly quantifying the critical wind speed of flutter of a photovoltaic tracking bracket based on damping ratio according to any one of claims 1 to 5, characterized in that: In step S3, a three-dimensional mathematical model of flutter derivatives is established according to the displacement expression of the photovoltaic panel section of the photovoltaic tracking bracket and the linear self-excited aerodynamic force expression.

7. The method for rapid quantification of critical wind speed of photovoltaic tracking bracket flutter based on damping ratio according to claim 6 is characterized in that: The expression of the three-dimensional mathematical model of flutter derivatives is obtained by the least squares method.

8. A method for rapid quantification of critical wind speed of photovoltaic tracking bracket flutter based on damping ratio according to any one of claims 1-5, characterized in that: Before step S4, an unsteady torsional flutter self-excited force model is established according to Scanlan's flutter analysis theory, and the unsteady torsional flutter self-excited force model is represented by flutter derivatives.

9. A method for rapid quantification of critical wind speed of flutter of photovoltaic tracking bracket based on damping ratio according to any one of claims 1-5, characterized in that: The self-excited aerodynamic force obtained in step S1 includes the lift moment M of the photovoltaic tracking bracket; the aerodynamic force coefficient includes the first-order torsional frequency w a .

10. A method for rapid quantification of critical wind speed of flutter of photovoltaic tracking bracket based on damping ratio according to any one of claims 1-5, characterized in that: In step S1, the self-excited aerodynamic force or aerodynamic force coefficient corresponding to different amplitudes of the photovoltaic tracking bracket at different wind attack angles is obtained through a wind tunnel forced vibration test or a CFD forced vibration test.

Images