A fast quantification method for critical wind speed of photovoltaic tracking bracket flutter based on damping ratio

Abstract

This invention relates to the technical field of photovoltaic (PV) bracket risk assessment, and particularly to a rapid quantification method for the critical flutter wind speed of PV tracking brackets based on damping ratio. The method includes the following steps: obtaining the self-excited aerodynamic forces or aerodynamic coefficients corresponding to different amplitudes of the PV tracking bracket under different wind attack angles, and establishing the vibration equation under single-degree-of-freedom torsional flutter; obtaining the equivalent wind speed of the PV tracking bracket at any wind attack angle and its flutter derivative at different amplitudes; establishing a three-dimensional mathematical model of the flutter derivative; substituting the three-dimensional mathematical model of the flutter derivative into the vibration equation under single-degree-of-freedom torsional flutter to obtain mathematical models of frequency and damping ratio relative to equivalent wind speed and amplitude, respectively; establishing the mapping relationship between the aerodynamic damping ratio, amplitude, and equivalent wind speed based on the vibration form of the PV tracking bracket, thereby obtaining the critical flutter wind speed of the PV tracking bracket, thus completing the rapid quantification of the critical flutter wind speed of the PV tracking bracket under different damping conditions.

Description

Technical Field

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

[0002] In recent years, with the global shortage of resources and the deterioration of the living environment, the gradual shift from traditional fossil fuels to clean energy has become a consensus, leading to the rapid development of photovoltaic energy. Among these, photovoltaic (PV) brackets are the supporting devices used to place, install, and fix PV modules in a solar photovoltaic power generation system.

[0003] Photovoltaic (PV) mounting systems include fixed mounting systems, PV tracking mounting systems, and flexible mounting systems. Fixed mounting systems are the simplest and most common type. The PV panels are installed at a fixed angle and do not adjust with the sun's movement; this type is typically used for rooftop and ground-mounted PV systems. Flexible mounting systems are a newer design, usually made of lightweight materials, capable of adapting to irregular surfaces or special terrains, and can even be bent or folded to suit different installation environments. Flexible mounting systems allow PV panels to be flexibly installed on irregular roofs, walls, or other surfaces. PV tracking mounting systems are those that can adjust the angle of the PV panels according to the sun's position. They are mainly divided into single-axis tracking and dual-axis tracking. PV tracking mounting systems can improve power generation efficiency; during tracking, the mounting system needs to rotate along its main axis.

[0004] In order to achieve efficient tracking of the sun, photovoltaic tracking brackets have low stiffness. In windy weather, they often experience wind-induced vibration and aerodynamic instability, and may even be damaged due to excessive amplitude, resulting in significant economic losses.

[0005] Common structural flutter phenomena mainly fall into two categories: bending-torsional flutter and separated-flow flutter. In wind-induced vibrations of structures, streamlined main beams generally experience bending-torsional flutter, while the vast majority of structural cross-sections are non-streamlined. When airflow passes over a vibrating non-streamlined cross-section, separation occurs at the corners on the windward side, simultaneously generating vortex shedding. Such structural cross-sections often exhibit single-degree-of-freedom torsional flutter, i.e., separated-flow flutter. The flutter instability of photovoltaic tracking brackets clearly belongs to the latter, a point that has been demonstrated by relevant scholars.

[0006] Currently, there are many theoretical solutions for flexural-torsional coupled flutter, most of which can provide a good quantitative assessment of its flutter critical wind speed. The flutter critical wind speed calculation methods based on flexural-torsional coupled flutter are basically derived from bridge structures. In bridge structures, flexural-torsional coupled flutter occurs first as vertical bending followed by torsion, and the frequency differences between the vertical bending and torsional motions are not significant.

[0007] Patent application CN118332719A discloses a method, system, and device for predicting the critical wind speed of flutter in a photovoltaic flexible support system. However, flexible supports are similar to bridge structures, and their modes involve vertical motion followed by torsional motion, so their flutter is generally a bending-torsional coupled flutter.

[0008] However, the photovoltaic tracking bracket exhibits torsion first, followed by vertical bending, with a significant difference in frequency between the torsional and vertical bending patterns. Furthermore, the flutter is primarily caused by torsion. Clearly, the traditional theory of torsional-bending coupled flutter is not applicable to calculating the critical wind speed for flutter in photovoltaic tracking brackets.

[0009] Furthermore, currently, the flutter critical wind speed of photovoltaic (PV) panel components is mainly determined through experiments. However, for different PV projects, the span, number of drive columns, column height, and wind attack angle of the PV tracking bracket will vary due to terrain limitations. This results in differences in the torsional frequency and structural damping ratio of the PV tracking bracket. Conducting experiments on each one would be a waste of significant manpower and resources. Therefore, it is of practical significance to rapidly quantify the flutter critical wind speed of PV tracking brackets based on damping ratio and frequency. Summary of the Invention

[0010] The purpose of this invention is to overcome the shortcomings of existing technologies, namely, firstly, the theory of bending-torsional flutter is basically derived from bridge structures, but the vibration modes of photovoltaic tracking brackets are quite different from those of bridge structures, making it unsuitable for the traditional theory of bending-torsional flutter; secondly, the critical flutter wind speed of photovoltaic panel components mainly relies on actual experiments, which is costly in terms of manpower and material resources. This invention provides a rapid quantification method for the critical flutter wind speed of photovoltaic tracking brackets based on damping ratio.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0012] This invention provides a rapid quantification method for the critical wind speed of flutter in photovoltaic tracking brackets based on 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. Based on the self-excited aerodynamic force or aerodynamic force coefficient obtained in step S1, obtain the equivalent wind speed of the photovoltaic tracking bracket at any wind angle of attack and the different flutter derivatives corresponding to different amplitudes.

[0015] S3. Based on the different amplitudes of the photovoltaic tracking bracket and the converted wind speed obtained in step S2, establish a three-dimensional mathematical model of the flutter derivative.

[0016] S4. Substitute 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 to obtain the first mathematical model of frequency and equivalent wind speed and amplitude, and the second mathematical model of damping ratio and equivalent wind speed and amplitude.

[0017] S5. Based on the first and second mathematical models, establish the mapping relationship between the aerodynamic damping ratio of the photovoltaic tracking bracket with respect to the corresponding flutter derivative and the amplitude and equivalent wind speed, thereby obtaining the critical flutter wind speed of the photovoltaic tracking bracket and completing the quantification of the critical flutter wind speed of the photovoltaic tracking bracket.

[0018] Steps S3 and S4 obtain three-dimensional models of flutter derivative, damping, and frequency relative to amplitude and wind speed, respectively. This enables rapid quantification of multiple flutter derivatives, damping, and frequencies, which helps save manpower and material costs and improves design efficiency.

[0019] Preferably, in step S5, the total damping ζ of the photovoltaic tracking bracket in the critical state is determined. total Total reduced frequency K total Based on the flutter derivative of the photovoltaic tracking bracket, a mapping relationship between the aerodynamic damping ratio of photovoltaic tracking and the amplitude and equivalent 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 equivalent wind speed, a three-dimensional aerodynamic damping surface diagram of the photovoltaic tracking bracket with respect to the corresponding vibration mode is established, and the corresponding aerodynamic damping cloud diagram is obtained according to the three-dimensional aerodynamic damping surface diagram.

[0021] Preferably, in the aerodynamic damping cloud map, 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.

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

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

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

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

[0026] Preferably, before step S4, an unsteady torsional flutter self-excited force model is established based on Scanlan's flutter analysis theory. The unsteady torsional flutter self-excited force model is represented by the flutter derivative.

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

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

[0029] Forced vibration testing in wind tunnels or CFD (Computational Fluid Dynamics) is used to identify flutter derivatives because it has good repeatability and a wide range of equivalent wind speeds.

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

[0031] This invention discloses a rapid quantification method for the critical flutter wind speed of photovoltaic tracking brackets based on damping ratio. First, it obtains the self-excited aerodynamic forces or aerodynamic coefficients at different amplitudes under various wind attack angles and establishes the corresponding vibration equations for single-degree-of-freedom torsional flutter. Then, it transforms these equations to obtain different equivalent wind speeds at the corresponding wind attack angles and their flutter derivatives at different amplitudes. Next, it establishes a three-dimensional mathematical model of the flutter derivatives based on different equivalent wind speeds and amplitudes, enabling accurate quantification of the flutter derivatives at different equivalent wind speeds and amplitudes under a given wind attack angle. Subsequently, it substitutes the corresponding flutter derivatives into the vibration equations for single-degree-of-freedom torsional flutter to obtain a mathematical model of frequency in relation to equivalent wind speed and amplitude. Furthermore, a mathematical model of damping ratio in relation to equivalent wind speed and amplitude can also be obtained. Finally, based on the three-dimensional mathematical model of frequency and damping ratio, it is possible to rapidly quantify the critical flutter wind speed of photovoltaic tracking brackets with different frequencies and damping ratios, allowing for accurate and effective evaluation of their wind resistance performance. This application primarily calculates the critical wind speed for flutter of a photovoltaic (PV) tracking bracket under torsional motion, adapting it to the vibration modes of the PV tracking bracket. Furthermore, it replaces the actual experimental measurement process by establishing a mathematical model of the flutter derivative, thus saving labor and material costs. This application overcomes the shortcomings of existing technologies: firstly, the theory of bending-torsional coupled flutter is mainly derived from bridge structures, but the vibration modes of PV tracking brackets differ significantly from those of bridge structures, making it unsuitable for traditional bending-torsional coupled flutter theory; secondly, the critical wind speed for flutter of PV panel components mainly relies on actual experimental measurements, resulting in high labor and material costs. Attached Figure Description

[0032] Figure 1 This is a flowchart of a method for rapid quantification of the critical wind speed of flutter in a photovoltaic tracking bracket based on damping ratio, according to the present invention.

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

[0034] Figure 3 This is a graph showing the fitting results of the aerodynamic derivative of the amplitude dependence of the photovoltaic tracking bracket.

[0035] Figure 4 This is a graph showing the fitting results of the aerodynamic derivative of the amplitude dependence of the photovoltaic tracking bracket.

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

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

[0038] Figure 7 It is an aerodynamic damping cloud diagram;

[0039] Figure 8 It is a time history curve of angular displacement; Detailed Implementation

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

[0041] Unless otherwise specified, the use of terms such as "upper," "lower," "left," "right," "center," "inner," and "outer" to indicate orientation or positional relationships in the description of specific embodiments of the present invention is based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is typically placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0042] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," and "parallel" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, or parallel, but rather that it can be slightly tilted or have a deviation. For example, "horizontal" merely means that its direction is more horizontal relative to "vertical," not that the structure must be completely horizontal, but that it can be slightly tilted. Alternatively, it can be simplified to mean that the corresponding device / component / element, when set in a "horizontal," "vertical," "suspended," or "parallel" direction, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the present invention.

[0043] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0044] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as 2, 3, 4, 5, 6, 7, 8, or 9, and can even exceed nine.

[0045] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to common connection methods in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0046] Example 1

[0047] like Figure 1 As shown, the rapid quantification method for the critical wind speed of flutter of a photovoltaic tracking bracket based on damping ratio used in this embodiment 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. Based on the self-excited aerodynamic force or aerodynamic force coefficient obtained in step S1, obtain the equivalent wind speed of the photovoltaic tracking bracket at any wind angle of attack and the different flutter derivatives corresponding to different amplitudes.

[0050] S3. Based on the different amplitudes of the photovoltaic tracking bracket and the converted wind speed obtained in step S2, establish a three-dimensional mathematical model of the flutter derivative.

[0051] S4. Substitute 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 to obtain the first mathematical model of frequency and equivalent wind speed and amplitude, and the second mathematical model of damping ratio and equivalent wind speed and amplitude.

[0052] S5. Based on the first and second mathematical models, establish the mapping relationship between the aerodynamic damping ratio of the photovoltaic tracking bracket with respect to the corresponding flutter derivative and the amplitude and equivalent wind speed, thereby obtaining the critical flutter wind speed of the photovoltaic tracking bracket and completing the quantification of the critical flutter wind speed of the photovoltaic tracking bracket.

[0053] This invention discloses a rapid quantification method for the critical flutter wind speed of photovoltaic tracking brackets based on damping ratio. First, it obtains the self-excited aerodynamic forces or aerodynamic coefficients at different amplitudes under various wind attack angles and establishes the corresponding vibration equations for single-degree-of-freedom torsional flutter. Then, it transforms these equations to obtain different equivalent wind speeds at the corresponding wind attack angles and their flutter derivatives at different amplitudes. Next, it establishes a three-dimensional mathematical model of the flutter derivatives based on different equivalent wind speeds and amplitudes, enabling accurate quantification of the flutter derivatives at different equivalent wind speeds and amplitudes under a given wind attack angle. Subsequently, it substitutes the corresponding flutter derivatives into the vibration equations for single-degree-of-freedom torsional flutter to obtain a mathematical model of frequency in relation to equivalent wind speed and amplitude. Furthermore, a mathematical model of damping ratio in relation to equivalent wind speed and amplitude can also be obtained. Finally, based on the three-dimensional mathematical model of frequency and damping ratio, it is possible to rapidly quantify the critical flutter wind speed of photovoltaic tracking brackets with different frequencies and damping ratios, allowing for accurate and effective evaluation of their wind resistance performance.

[0054] Example 2

[0055] This embodiment is a specific implementation of the rapid quantification method for the critical wind speed of flutter of a photovoltaic tracking bracket based on damping ratio described in Embodiment 1, including the following steps:

[0056] 1. A rapid quantification method for the critical wind speed of flutter in photovoltaic tracking brackets based on damping ratio and frequency.

[0057] During the design phase of photovoltaic (PV) tracking brackets, considering safety, economy, and design rationality, wind tunnel forced vibration tests or CFD forced vibration tests are typically conducted to investigate the self-excited aerodynamic characteristics of the PV tracking brackets. This provides relatively detailed performance support for the design of the PV tracking brackets. This method can calculate the flutter derivatives of the PV tracking brackets at different frequencies and damping ratios using limited data, achieving accurate assessment and rapid quantification of the critical flutter wind speed of the PV tracking brackets. It is efficient and fast, reducing the waste of manpower and resources to a certain extent. In addition to PV tracking brackets, this method is also applicable to other types of PV tracking brackets with torsional flutter of other degrees of freedom, as well as similar thin-plate structures.

[0058] 1.1 Rapid Quantification of Critical Wind Speed ​​for Flutter of Photovoltaic Tracking Mounts

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

[0060]

[0061] In the formula, L and M represent lift force and lift torque, respectively; m and I represent mass per unit length and moment of inertia per unit length, respectively; ζ h ζ a These are the damping ratios for vertical and torsional motions, respectively; ω h ω a These are the frequencies of vertical and torsional motion, respectively. These represent the displacement, velocity, and acceleration of the model's vertical motion, respectively. These represent the displacement, velocity, and acceleration of the model's torsional motion, respectively.

[0062] Flutter derivative is an important aerodynamic parameter characterizing the self-excited aerodynamic forces of a structural cross section. Its linear combination with the motion state of the structural cross section represents the linear part of the aerodynamic forces. Considering that the forced vibration method has the advantages of good repeatability and a wide range of equivalent wind speeds, this application takes forced vibration as an example and adopts the sectional single-degree-of-freedom forced vibration method to identify the flutter derivative.

[0063] For streamlined and blunt cross sections, the self-excited aerodynamic forces can be expressed by a linear combination of cross section motion parameters, as shown in equations (3) and (4). To describe in detail the relationship between unsteady self-excited aerodynamic forces and cross 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 eight flutter derivatives:

[0064]

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

[0066] When the cross-section of the photovoltaic panel undergoes torsional forced vibration and vertical forced vibration respectively, the corresponding torsional and vertical displacements are as follows:

[0067] a(t)=a0 sinωt (5)

[0068] h(t)=h0sinωt (6)

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

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

[0071] The linear self-excited aerodynamic force of the photovoltaic panel cross section is expressed as a sine 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] In the formula: L0 and M0 are the aerodynamic amplitudes; φ L φ M This represents the hysteresis phase of the aerodynamic force relative to the displacement. From the expressions for the eight flutter derivatives, it can be seen that the change in the flutter derivative can be determined by L0 / a0, M0 / a0, L0 / h0, M0 / h0, and φ. L φ M This indicates that the flutter derivative is... Related to torsional motion.

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] As mentioned above, the flutter of the 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 mode can be obtained by transforming formulas (2) and (4), as shown below:

[0084]

[0085] Moving the right side of the above equation to the left side, we get:

[0086]

[0087] In the formula, Let ζ be the moment of inertia due to mass. α ω is the damping ratio for torsional motion; α The frequency of the torsional motion (rad / s); These represent the displacement, velocity, and acceleration of the model's torsional motion, respectively.

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

[0089]

[0090]

[0091] When ζ total When ζ is greater than zero, the total damping of the system is positive, the vibration is steadily decaying, and torsional flutter will not occur; when ζ... total When the wind speed equals zero, the structure enters an unstable flutter critical state. That is, the flutter critical wind speed can be calculated using the following formula:

[0092]

[0093] When the photovoltaic tracking bracket undergoes wind-induced torsional motion, due to fluid-structure interaction, the structure possesses both torsional stiffness and aerodynamic stiffness. Consequently, the vibration frequency of the structure changes compared to the fixed torsional frequency. The actual torsional frequency ω can be obtained by simultaneously solving Ktotal = and formula (20), as shown in formula (22), where... This is the aerodynamic derivative.

[0094]

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

[0096]

[0097] When a structure experiences torsional flutter, the aerodynamic forces change with the frequency and amplitude of the vibration. At this point, in addition to changes in aerodynamic stiffness, aerodynamic damping also dissipates or accumulates with the vibration. Furthermore, when the structure reaches the flutter critical state, the total structural damping tends to zero, at which point ζtotal=ζaero+

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

[0099]

[0100] At this point, the photovoltaic tracking bracket can be obtained based on formulas (23) and (24). and The frequency 3D surface plot and aerodynamic damping contour plot are used. The aerodynamic damping contour plot can be used to intuitively calculate and analyze the equivalent wind speed and the influence of nonlinear structural damping on flutter amplitude. In addition, when the flutter critical state is reached, the amplitude tends to a non-zero value, and the intersection of the damping ratio contour line and the equivalent wind speed coordinate axis at this time can be regarded as its flutter critical wind speed.

[0101] Example 3

[0102] Example 3 is a practical application of Example 2, based on a real photovoltaic project, using CFD for forced vibration. Since the flutter critical wind speed of the single-axis photovoltaic tracking bracket is high near a 0° tilt angle, when using a small tilt angle for protection, the high-wind protection angle is usually set to 0°. Therefore, this case study selects the photovoltaic cross-section at 0° for self-excited aerodynamic amplitude effect analysis. The photovoltaic panel cross-sectional shape, computational domain, and boundary conditions are as follows... Figure 2 As shown in the figure, the photovoltaic panel has a cross-sectional width B of 2.278m and a height H of 0.030m. The computational domain is set to 40B×20B (B is the cross-sectional width of the photovoltaic panel). 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 top and bottom sides of the computational domain are symmetry boundaries, and the photovoltaic panel cross-section is a fixed wall boundary.

[0103] Flutter derivative is an important aerodynamic parameter characterizing the self-excited aerodynamic forces of a structural cross section. Its linear combination with the motion state of the structural cross section represents the linear part of the aerodynamic forces. Considering that the forced vibration method has the advantages of good repeatability and a wide range of equivalent wind speeds, this application takes forced vibration as an example and adopts the sectional single-degree-of-freedom forced vibration method to identify the flutter derivative.

[0104] In this case study, the converted wind speed U cr The speeds are 2 m / s, 4 m / s, 6 m / s, 8 m / s, 10 m / s, 12 m / s, 16 m / s, and 18 m / s, respectively, and the torsional motion amplitude α0 is taken as 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 × 10⁻⁶. 5 ~5.5×10 5 The forced vibration frequency f is 1.0 Hz. In Table 1, h represents the vertical bending amplitude of the photovoltaic tracking bracket.

[0105] Table 1 Different converted wind speeds (U cr Examples of working conditions for amplitude (α0, h)

[0106]

[0107]

[0108] Common structural flutter phenomena mainly include two types: bending-torsional flutter and separated-flow flutter. In wind-induced vibrations of structures, streamlined main beams generally experience bending-torsional flutter, while the vast majority of structural cross-sections are non-streamlined. When airflow passes over a vibrating non-streamlined cross-section, separation occurs at the corners on the windward side, simultaneously generating vortex shedding. Such structural cross-sections often experience single-degree-of-freedom torsional flutter, i.e., separated-flow flutter. The flutter instability of photovoltaic tracking brackets clearly belongs to the latter, and relevant scholars have also demonstrated this. Since the flutter instability of photovoltaic tracking brackets is single-degree-of-freedom torsional flutter, and the flutter derivative... It is unrelated to torsional motion; torsional motion is only related to the flutter derivative. and Related. Referring to formulas (23) and (24), the subsequent calculation of the critical wind speed for flutter of the photovoltaic tracking bracket only involves... and This only shows the data based on converted wind speed and amplitude. and Three-dimensional surface plot, such as Figures 3-4 As shown.

[0109] By formula (23) and Figure 4 This allows us to obtain a three-dimensional surface with frequency, such as... Figure 5As shown, the vibration frequency gradually decreases with increasing equivalent wind speed, indicating that the higher the wind speed, the larger the amplitude, the stronger the aerodynamic stiffness effect, and the stronger the fluid-structure interaction. Furthermore, Figure 4 The intermediate amplitude is the torsional amplitude under forced vibration, so its frequency is less affected by the torsional amplitude.

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

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

[0112] Table 2 Characteristic parameters for calculating free vibration of thin plate cross sections

[0113]

[0114] The displacement-time history curve of the critical state of single-degree-of-freedom torsional flutter is as follows: Figure 8 As shown in Table 1, the calculation results of the critical wind speed and frequency for flutter of the photovoltaic panel cross-section and their comparison with the frequency domain theoretical solution are presented. The table shows that the calculation results of the frequency domain theoretical solution have a small error compared with the CFD calculation. Therefore, the rapid quantification method for the critical wind speed of flutter of the photovoltaic tracking bracket 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 for the critical flutter wind speed is 1.55%, and the error for the critical flutter frequency is 8.5%.

[0119] The above are merely 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 within the protection scope of the present invention.

Claims

1. A rapid quantification method for the critical wind speed of flutter in photovoltaic tracking brackets based on damping ratio, characterized in that, It includes the following steps: 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. Based on the self-excited aerodynamic force or aerodynamic force coefficient obtained in step S1, obtain the equivalent wind speed of the photovoltaic tracking bracket at any wind angle of attack and the different flutter derivatives corresponding to different amplitudes. S3. Based on the different amplitudes of the photovoltaic tracking bracket and the converted wind speed obtained in step S2, establish a three-dimensional mathematical model of the flutter derivative. S4. Substitute 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 to obtain the first mathematical model of frequency and equivalent wind speed and amplitude, and the second mathematical model of damping ratio and equivalent wind speed and amplitude. S5. Based on the first and second mathematical models, establish the mapping relationship between the aerodynamic damping ratio of the photovoltaic tracking bracket with respect to the corresponding flutter derivative and the amplitude and equivalent wind speed, thereby obtaining the critical flutter wind speed of the photovoltaic tracking bracket and completing the quantification of the critical flutter wind speed of the photovoltaic tracking bracket. In step S5, based on the total damping of the photovoltaic tracking bracket in the critical state... Total frequency conversion Based on the flutter derivative of the photovoltaic tracking bracket, a mapping relationship between the aerodynamic damping ratio of photovoltaic tracking and the amplitude and equivalent wind speed is established.

2. The method for rapid quantification of critical wind speed for flutter of photovoltaic tracking brackets based on damping ratio as described in claim 1, 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 equivalent wind speed, a three-dimensional aerodynamic damping surface diagram of the photovoltaic tracking bracket with respect to the corresponding vibration mode is established, and the corresponding aerodynamic damping cloud diagram is obtained from the three-dimensional aerodynamic damping surface diagram.

3. The method for rapid quantification of critical wind speed for flutter of photovoltaic tracking brackets based on damping ratio according to claim 2, characterized in that, In aerodynamic damping cloud diagrams, 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.

4. The method for rapid quantification of critical wind speed for flutter of photovoltaic tracking brackets based on damping ratio according to claim 1, characterized in that, When the photovoltaic tracking bracket is in a critical state of flutter, the total damping .

5. A rapid quantification method for the critical wind speed of flutter of a photovoltaic tracking bracket based on damping ratio, as described in any one of claims 1-4, characterized in that, In step S3, a three-dimensional mathematical model of the flutter derivative is established based on the displacement expression of the photovoltaic panel cross-section and the linear self-excited aerodynamic expression of the photovoltaic tracking bracket.

6. The method for rapid quantification of critical wind speed for flutter of photovoltaic tracking brackets based on damping ratio according to claim 5, characterized in that, The expression for the three-dimensional mathematical model of flutter derivative is obtained by using the least squares method.

7. A rapid quantification method for the critical wind speed of flutter of a photovoltaic tracking bracket based on damping ratio, as described in any one of claims 1-4, characterized in that, Before step S4, an unsteady torsional flutter self-excited force model is established based on Scanlan's flutter analysis theory. The unsteady torsional flutter self-excited force model is expressed by the flutter derivative.

8. A rapid quantification method for the critical wind speed of flutter of a photovoltaic tracking bracket based on damping ratio, as described in any one of claims 1-4, characterized in that, The self-excited aerodynamic force obtained in step S1 includes the lift torque of the photovoltaic tracking bracket. Aerodynamic coefficients include the first-order torsional frequency. .

9. A rapid quantification method for the critical wind speed of flutter of a photovoltaic tracking bracket based on damping ratio, as described in any one of claims 1-4, characterized in that, In step S1, the self-excited aerodynamic force or aerodynamic coefficient corresponding to different amplitudes of the photovoltaic tracking bracket under different wind attack angles is obtained by wind tunnel forced vibration test or CFD forced vibration.

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