A method for analyzing and evaluating the cost-reducing and efficiency-improving performance of additional damping measures for wind power support structures

Abstract

The application relates to a method for analyzing and evaluating the performance of wind power supporting structure additional damping measures in reducing cost and increasing efficiency, comprising the following steps: for different design schemes, respectively calculating the steel consumption cost per unit life; comparing the steel consumption cost per unit life corresponding to different design schemes, and screening out a design scheme with optimal performance in reducing cost and increasing efficiency; and using normalized cost and benefit to estimate the upper and lower limits of the cost and benefit of the screened design scheme. Compared with the prior art, the application quantifies the extension effect of the damping measures on the fatigue life, combines the steel consumption change brought by the damping measures, analyzes the cost of the steel material required per unit fatigue life to analyze the effect of reducing cost and increasing efficiency, uses the steel consumption per unit life as an evaluation index, can compare various constraint damping schemes in a unified scale, avoids the redesign of the original tower in the damping scheme comparison stage, and thus facilitates the rapid evaluation and optimization in the scheme design stage.

Description

Technical Field

[0001] This invention relates to the field of cost-benefit analysis technology for wind power structures, and in particular to a method for analyzing and evaluating the cost-reduction and efficiency-enhancing performance of additional damping measures for wind power support structures. Background Technology

[0002] In recent years, due to the profound transformation of the global energy structure, offshore wind power has become an important component of the clean energy sector and has shown rapid development momentum, with the trend towards larger wind turbine equipment becoming increasingly prominent. However, as wind turbine support structures evolve towards taller towers and longer blades, wind turbine towers, which rely on low-frequency excitation, also face multiple vibration challenges in extreme environments or long-term operation, under the requirements of cost reduction and efficiency improvement. Therefore, researching effective vibration control technologies is crucial.

[0003] Currently, among various passive control technologies, TMD (Tuned Mass Damper) and TLD (Tuned Liquid Damper) are two key inertial-based control methods. They effectively reduce the vibration of wind turbine structures by installing specific devices at the top of the tower and utilizing the principle of reaction force. While traditional TMD and TLD technologies can reduce the vibration of wind turbine structures to some extent, their limitations are becoming increasingly apparent when faced with the specific requirements of wind turbine support structures regarding installation space, multi-directional control, and high robustness. Therefore, improved TMDs such as RID-TMD (Rotating Inertial Dual-Tuned Mass Damper), PS-TMD (Prestressed Tuned Mass Damper), PTMD (Suspended Tuned Mass Damper), and TMDI (Inertial Mass Tuned Mass Damper), as well as various forms of TLDs, such as TLCD (tuned liquid column dampers), TTLCD (toroidal tuned liquid column dampers), and TLCGD (tuned liquid column gas damper), have been proposed and studied. However, inertial-based technologies have limitations, such as potentially unsatisfactory control effects for specific events like near-field earthquakes. Moreover, due to their inertial-based nature, computational analysis must comprehensively consider various complex working conditions to reflect the objective vibration reduction effect.

[0004] As an important complement to inertial-based technologies, material-based energy dissipation technologies have also received considerable attention in recent years, and their potential for cost reduction and efficiency improvement is beginning to emerge. These technologies are typically installed at the base of the structure, dissipating energy through material deformation such as friction, viscosity, and viscoelasticity, providing additional damping to reduce vibration. Related research includes scissor-jackbraced viscous dampers, friction energy dissipation devices installed at the base of the tower, ampulating damping transfer systems, high-damping viscoelastic dampers, and constrained damping. Material-based energy dissipation technologies are expected to effectively compensate for the shortcomings of inertial-based solutions in certain aspects, such as repairing and extending the lifespan of wind turbine towers or foundations. Machado points out that the construction and installation phases of wind turbine structures account for 32% and 31.5% of their lifecycle carbon emissions, respectively. This means that installing material-based solutions at the base of the structure will significantly reduce installation costs, especially when retrofitting existing wind turbines. Compared to other material-based energy dissipation solutions, the constrained damping solution, applied to the lower periphery of the wind turbine tower, is more convenient to implement and avoids complex local stress problems, thus offering significant advantages in practical application. The constrained damping layer consists of a viscoelastic material as the constrained layer, with an outer layer made of a material with a high modulus (such as steel) as the constraining layer. It can be applied to the surface of a cylindrical shell structure to provide damping performance. When the wind turbine tower bends and deforms, the constrained layer undergoes relative deformation between the base layer and the constraining layer, resulting in shear-dominated deformation that dissipates energy and provides additional damping to the structure.

[0005] Although there is a wealth of research on vibration control for wind turbine structures, previous studies have generally focused only on improving structural performance, neglecting the cost and constraints of the response. For example, Gao's research revealed potential limitations in existing literature when evaluating the effectiveness of inertial-based control measures such as TMD (Tower Damping Device). By comprehensively considering factors such as internal space constraints, cost-effectiveness, and the adverse effects of TMD and tower forces on fatigue, they found that relying solely on numerical and theoretical methods may overestimate the vibration reduction effect of TMD. In their study, by comprehensively considering these factors, they successfully achieved an additional damping ratio of approximately 1%, far lower than the values ​​reported in some other studies. The reason existing research often lacks cost-benefit analysis is due to the complexity of actual wind turbine structure design; reliable cost-benefit assessments require extensive operational condition analyses after considering the impact of vibration reduction devices, making simple, reliable, and rapid evaluation difficult, and hindering the accurate and efficient selection of the optimal solution from multiple vibration reduction design options. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a method for analyzing and evaluating the cost-saving and efficiency-enhancing performance of additional damping measures for wind power support structures. The method uses the amount of steel used per unit life as the evaluation index to evaluate the cost-effectiveness of different constraint damping schemes. This allows for comparison of various constraint damping schemes on a unified scale and avoids the need to redesign the original tower during the damping scheme selection stage, thereby facilitating rapid evaluation and optimization during the scheme design stage.

[0007] The objective of this invention can be achieved through the following technical solution: A method for analyzing and evaluating the cost reduction and efficiency improvement performance of additional damping measures for wind power support structures, comprising the following steps:

[0008] S1. Calculate the steel consumption cost per unit life for different design schemes.

[0009] S2. Compare the steel consumption cost per unit life corresponding to different design schemes, and select the design scheme with the best cost reduction and efficiency improvement performance.

[0010] S3. Using normalized cost-benefit analysis, estimate the upper and lower limits of cost-benefit for the design schemes selected in step S2.

[0011] Furthermore, the calculation of steel consumption cost per unit life in step S1 specifically includes the following steps:

[0012] S11. Damping Influence Analysis: The dynamic amplification factor (DAF) is obtained by calculating the additional damping.

[0013] S12. Wind load spectrum analysis: Analyze the bending moment spectrum at the control section of the tower caused by pulsating wind load, and evaluate the dynamic effect of wind load on the structure.

[0014] S13. Stress spectrum analysis: Calculate the stress spectrum of the critical point based on the bending moment spectrum, simplify the stress spectrum to a single-frequency stress spectrum about the fundamental frequency of the wind turbine tower, and calculate the stress amplitude of the constant amplitude stress time history.

[0015] S14. Fatigue life estimation: The fatigue life of the structure is estimated by combining the SN (stress amplitude-life) curve of the material.

[0016] S15. Calculation of unit life cost: Divide the cost of steel consumption by the estimated fatigue life to obtain the cost of steel consumption per unit life.

[0017] Furthermore, step S11 specifically involves using the modal strain energy method to calculate the additional damping, thereby obtaining the dynamic coefficient, in order to fully consider the impact of damping on structural performance.

[0018] Further, step S12 includes the following process:

[0019] Considering only the wind load acting on the nose, the wind load acting on the RNA (rotor-nacelle assembly) at a given wind speed is:

[0020]

[0021] Where, ρ a For air density, A R Where U is the swept area of ​​the impeller, and U is the total wind speed. Where u is the average wind speed, and C is the fluctuating wind speed. T For thrust coefficient,

[0022] The power spectral density of fluctuating wind speeds was calculated using the Kaimal spectrum:

[0023]

[0024] Where f is the frequency, σ U Let U be the standard deviation of wind speed U. I represents the turbulence intensity, L k This is the integration length parameter, where z is the distance from sea level;

[0025] Wind load is divided into average wind load (i.e., static load) and fluctuating wind load (i.e., dynamic load). After introducing the fluctuating wind speed spectrum, the fluctuating wind load spectrum is obtained as follows:

[0026]

[0027] Among them, F dyn For pulsating wind load, This is the spectrum of pulsating wind load.

[0028] Furthermore, step S13 includes the following process:

[0029] Under pulsating wind load, the tower and pile foundation will generate a dynamic response. The tower-pile bending moment response spectrum considering the dynamic coefficient is as follows:

[0030]

[0031] Where H is the height of the rotor above sea level, h is the height of the cross section above sea level, and DAF is the dynamic coefficient;

[0032] The structural dynamic response under pulsating wind load only considers the contribution of the first-order mode. The wind turbine tower is equivalent to a single-degree-of-freedom system with inertia concentrated at the top of the tower. Its dynamic coefficient is:

[0033]

[0034] Where β is the frequency ratio, β=f / f0, f0 is the first-order mode frequency of the wind turbine tower, and ξ is the first-order mode damping ratio of the wind turbine tower;

[0035] The maximum normal stress spectrum at the section at a distance h from sea level, calculated from the bending moment response spectrum, is:

[0036]

[0037] Where W is the section bending modulus;

[0038] According to linear (Airy) wave theory, the stress time history under pulsating wind load is obtained from the stress spectrum through harmonic superposition. Since the structural dynamic response under pulsating wind load is mainly concentrated near the first-order mode frequency of the wind turbine tower, to facilitate fatigue life assessment, only the main components of the harmonics are retained, simplifying the variable amplitude fatigue problem into a constant amplitude fatigue problem. That is, only the harmonic components corresponding to the first-order mode frequency of the stress spectrum are retained, resulting in the following stress time history:

[0039] S max,dyn (t)=S0cos(2πf0t)

[0040] Where S is the stress amplitude. Stress power spectrum function The area in the frequency range of 0.75f0 to 1.25f0.

[0041] Furthermore, the fatigue life estimation formula in step S14 is as follows:

[0042]

[0043] logN = -m log S + C

[0044] Where T is the fatigue life in years, N is the number of failure cycles, m is the fatigue strength index of the material, and C is the fatigue limit of the material.

[0045] Furthermore, the cost of steel consumption per unit lifespan in step S15 is:

[0046]

[0047] in, M is the steel consumption per unit lifespan index. total,steel This represents the total amount of steel used in the wind turbine tower.

[0048] Furthermore, in step S2, the design scheme with the lowest steel consumption cost per unit life is selected as the design scheme with the best cost reduction and efficiency improvement performance.

[0049] Furthermore, step S3 specifically uses the fatigue life and steel consumption of the uncontrolled structure as a benchmark, performs normalization processing to obtain the normalized fatigue life and steel consumption per unit year. Within the preset range of the damping ratio of the uncontrolled structure, the upper limit and lower limit of the cost-effectiveness of the design scheme are determined by optimizing the parameters of the constraint damping in the design scheme.

[0050] Furthermore, in step S3, the preset range of the damping ratio of the uncontrolled structure is 1% to 5%. When the damping ratio of the uncontrolled structure is at the upper limit of 5%, the lower limit of the benefit of the design scheme's constraint damping is obtained; when the damping ratio of the uncontrolled structure is at the lower limit of 1%, the upper limit of the benefit of the design scheme's constraint damping is obtained.

[0051] Compared with the prior art, the present invention has the following advantages:

[0052] This invention calculates the steel consumption cost per unit life for different design schemes. By comparing the steel consumption costs per unit life for different design schemes, the design scheme with the best cost reduction and efficiency improvement performance is selected. Therefore, a cost reduction and efficiency improvement analysis scheme based on the steel consumption cost per unit fatigue life is proposed. This scheme quantifies the effect of vibration reduction measures on extending fatigue life and combines it with the steel consumption changes brought about by vibration reduction measures. The cost reduction and efficiency improvement effect is directly evaluated by calculating the steel cost required per unit fatigue life. If the vibration reduction scheme can significantly reduce the steel consumption cost per unit fatigue life, its significant advantages in economy and long-term operational reliability are verified. This invention not only facilitates rapid evaluation in the scheme design stage but also provides a solid theoretical foundation for subsequent optimization design. It allows different vibration reduction schemes to be compared under a unified scale benchmark and avoids redesigning the original tower during the damping scheme selection stage, thus facilitating rapid evaluation and optimization in the scheme design stage.

[0053] This invention comprehensively considers multiple aspects such as damping effect, wind load, stress analysis, fatigue life and economic performance when calculating the steel consumption cost per unit life. It provides a comprehensive analytical framework for performance optimization and cost reduction of constrained damping structures. This includes obtaining the stress spectrum at the tower section using the pulsating wind load spectrum and estimating the fatigue life based on the stress spectrum and fatigue life curve, which can fully ensure the reliability of the steel consumption cost per unit life.

[0054] This invention utilizes normalized cost-effectiveness to further evaluate the upper and lower limits of the cost-effectiveness of a solution, enabling rapid assessment of these limits and facilitating quick decision-making at the solution stage. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0056] Figure 2 This is a schematic diagram illustrating the process of calculating the steel consumption cost per unit life for different design schemes in the embodiments.

[0057] Figure 3 This is a schematic diagram of the stress spectral density;

[0058] Figure 4a This is a schematic diagram comparing the fatigue life and total steel consumption of each scheme under the condition of uncontrolled modal damping ratio (FA1%, SS1%) in the examples;

[0059] Figure 4b This is a schematic diagram comparing the normalized fatigue life and annual steel consumption of each scheme under the uncontrolled modal damping ratio (FA1%, SS1%) in the embodiments.

[0060] Figures 5a-5c This is a schematic diagram illustrating how the added damping and cost-effectiveness vary with the damping layer thickness t1 and the constraint layer thickness t2 in the embodiment.

[0061] Figure 6a This is a schematic diagram comparing the normalized fatigue life under the conditions of 5% and 1% uncontrolled damping ratio in the example.

[0062] Figure 6b This is a schematic diagram comparing the normalized annual steel consumption under the conditions of 5% and 1% uncontrolled damping ratio in the examples. Detailed Implementation

[0063] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0064] Example

[0065] like Figure 1 As shown, a method for analyzing and evaluating the cost reduction and efficiency improvement performance of additional damping measures for wind power support structures includes the following steps:

[0066] S1. Calculate the steel consumption cost per unit life for different design schemes.

[0067] S2. Compare the steel consumption cost per unit life corresponding to different design schemes, and select the design scheme with the best cost reduction and efficiency improvement performance.

[0068] S3. Using normalized cost-benefit analysis, estimate the upper and lower limits of cost-benefit for the design schemes selected in step S2.

[0069] This embodiment applies the above-described solution, such as Figure 2 As shown, it includes:

[0070] 1) Damping effect analysis: First, the additional damping is calculated by modal strain energy method, and then the dynamic coefficient (DAF) is obtained to fully consider the impact of damping on structural performance.

[0071] 2) Wind load spectrum analysis: Analyze the bending moment spectrum at the control section of the tower caused by pulsating wind load to evaluate the dynamic effect of wind load on the structure.

[0072] 3) Stress spectrum analysis: Based on the bending moment spectrum, the stress spectrum of the critical point is calculated, and the stress spectrum is simplified to a single-frequency stress spectrum about the fundamental frequency of the wind turbine tower. The stress amplitude of the constant amplitude stress time history is calculated to provide basic data for subsequent fatigue life estimation.

[0073] 4) Fatigue life estimation: Based on the SN curve of the material, the fatigue life of the structure is estimated in a simplified manner.

[0074] 5) Calculation of unit life cost: Divide the cost of steel consumption by the estimated fatigue life to obtain the cost of steel consumption per unit life, which provides a basis for economic performance evaluation.

[0075] 6) Design Scheme Comparison: Compare the unit life cost of different design schemes to select the design scheme that performs best in terms of cost reduction and efficiency improvement.

[0076] 7) Cost reduction and efficiency improvement effect evaluation: Finally, the entire analysis process is summarized to evaluate the actual effect of high-strength steel constrained damping structure in reducing unit life cost, and to provide guidance for engineering practice.

[0077] The above analytical framework comprehensively considers multiple aspects such as damping effects, wind loads, stress analysis, fatigue life, and economic performance, providing a comprehensive analytical framework for performance optimization and cost reduction of high-strength steel constrained damping structures.

[0078] Specifically, when calculating the fluctuating wind load spectrum, under normal operating conditions at rated wind speed, the wind load acting on the nose cone (RNA) in the FA direction is much greater than the wind load acting on the tower. Therefore, this scheme only considers the wind load acting on the nose cone. The wind load acting on the RNA at a given wind speed can be approximately calculated by the following formula:

[0079]

[0080] Where: ρ a For air density, take 1.225 kg / m³. 3 A R U is the swept area of ​​the impeller; U is the total wind speed. C represents the average wind speed, u represents the fluctuating wind speed; T For thrust coefficient,

[0081] The power spectral density of fluctuating wind speeds can be calculated using the Kaimal spectrum:

[0082]

[0083] Where: f is the frequency, σ U Let U be the standard deviation of wind speed U. I is the turbulence intensity, L k It is the integration length parameter. z is the distance from sea level.

[0084] The wind load in the above formula can be divided into average wind load (static load) and fluctuating wind load (dynamic load), where the fluctuating wind load can be approximately calculated by the following formula:

[0085]

[0086] By introducing the fluctuating wind speed spectrum, the fluctuating wind load spectrum can be obtained:

[0087]

[0088] Next, the structural dynamic response is calculated. Under pulsating wind load, the tower and pile foundation will generate a dynamic response. The tower-pile bending moment response spectrum considering the dynamic coefficient can be calculated by the following formula:

[0089]

[0090] Where: H is the rotor height above sea level, h is the cross-section height above sea level, and DAF is the Dynamic Amplification coefficient.

[0091] The structural dynamic response under pulsating wind load can be considered only by the contribution of the first-order mode. After the wind tower is equivalent to a single-degree-of-freedom system with inertia concentrated at the top of the tower, its dynamic coefficient can be calculated by the following formula:

[0092]

[0093] Where: β is the frequency ratio, β=f / f0, f0 is the first-order mode frequency of the wind turbine tower; ξ is the first-order mode damping ratio of the wind turbine tower.

[0094] The maximum normal stress spectrum at a distance h from sea level can be further calculated from the bending moment response spectrum.

[0095]

[0096] Wherein: W is the flexural modulus of the section.

[0097] According to linear (Airy) wave theory, the stress time history under pulsating wind load can be obtained from the stress spectrum using the harmonic superposition method. Since the structural dynamic response under pulsating wind load is mainly concentrated near the first-order modal frequency of the wind turbine tower, to facilitate fatigue life assessment, only the main components of the harmonics are retained, simplifying the variable-amplitude fatigue problem into a constant-amplitude fatigue problem. That is, after retaining only the harmonic components corresponding to the first-order modal frequency of the stress spectrum, the stress time history can be calculated using the following formula:

[0098] S max,dyn (t)=S0cos(2πf0t)

[0099] Where: S is the stress amplitude. Stress power spectrum function The area in the frequency range of 0.75f0 to 1.25f0 (e.g.) Figure 3 (As shown).

[0100] Next, fatigue life prediction and economic evaluation are conducted. Predicting fatigue life is crucial for assessing the reliability and economy of wind turbine towers under long-term wind loads. Generally, the pile wall is thick and the design redundancy is high, making fatigue failure less likely. For ease of discussion, this embodiment only studies the fatigue life of the portion of the wind turbine tower above the mean sea level, thus only considering pulsating wind loads.

[0101] Based on the constant amplitude stress of the control section, the fatigue life of the wind turbine tower can be quickly calculated according to the SN (stress amplitude-life) relationship of the steel.

[0102] The relationship between fatigue period N and stress range S is shown in the following formula:

[0103] logN = -m log S + C

[0104] Where m and C are the fatigue parameters of the material, and the fatigue parameters of steels with different strengths are shown in Table 1. N is the number of failure cycles.

[0105] Table 1 Fatigue parameters of steel

[0106] Q355 Q460 Q550 Q690 Q960 m 3 3 3 4 4 C 12.449 12.994 13.360 15.564 15.834

[0107] Fatigue life T (years) is calculated using the following formula:

[0108]

[0109] To facilitate the evaluation of the economic efficiency of wind turbine towers throughout their entire life cycle, a steel consumption per unit life cycle index is introduced. (kg per year); This indicator comprehensively considers the total construction cost and service life of wind turbine towers and can be used as an evaluation indicator to measure the economic efficiency of wind turbine towers.

[0110]

[0111] Where: M total,steel This refers to the total steel consumption (kg) of the wind turbine tower, including the tower casing, pile casing, etc.

[0112] Using the updated modal dynamic amplification factor and stress spectrum, the simplified evaluation of the section fatigue life was obtained, as shown in Table 2. The high-strength steel constrained damping scheme improved the fatigue life of the control section to varying degrees. This is because an approximate equal-strength replacement principle was adopted when determining the analysis scheme. Therefore, although the tower wall thickness of the constrained damping section was reduced, the NS curve of high-strength steel indicates that it has a better fatigue life, meaning the control section for the final fatigue life is not on the high-strength steel section. However, at the same time, the high-strength steel constrained damping, due to the additional damping, reduces the dynamic amplification factor under the same wind load, ultimately leading to a decrease in the cyclic stress amplitude.

[0113] Table 2 Fatigue life of cross section and control section

[0114]

[0115]

[0116] To further analyze the benefits of high-strength steel constrained damping compared to the uncontrolled scheme, this embodiment focuses on the cost of steel consumption per unit life. Calculations are performed when the high-strength steel scheme... When the value is greater than that of the original tower, it indicates that the high-strength steel constrained damping has a positive effect of cost reduction and efficiency improvement. It is worth noting that the positive effect of high-strength steel constrained damping is obvious. This is because by replacing the corresponding parts of the original tower structure with high-strength steel constrained damping sections, damping can be increased without increasing the amount of steel used.

[0117] Plot the annual steel consumption for each scheme under uncontrolled modal damping ratios (FA1%, SS1%). Total steel consumption (e.g.) Figure 4a As shown), further normalization is performed based on the fatigue life and steel consumption of the controlled structure to obtain the normalized fatigue life and steel consumption per unit year (e.g., ...). Figure 4b (As shown). By Figure 4a It can be seen that the Q460-T30(30)30 scheme can increase additional damping without changing the amount of steel used. Other high-strength steel schemes with higher strength can even achieve additional damping on the basis of the original structure while reducing the amount of steel used. This is because the reduction in the cross section of high-strength steel in high-strength steel constraint damping is greater than the increase in the amount of steel in the constraint layer in constraint damping. Figure 4bThe results show that, under the design strategy of equal thickness of the constraint layer, constraint damping layer, and high-strength steel cylinder wall, the normalized annual steel consumption cost decreases significantly with the increase of high-strength steel strength. This means that as the strength of high-strength steel increases, the cost reduction and efficiency improvement benefits brought by the high-strength steel constraint damping scheme become more and more significant.

[0118] Finally, the upper and lower limits of cost-benefit analysis are estimated. Figure 4a and Figure 4b While the trends and patterns of high-strength steel constrained damping have been described, this is insufficient to fully capture its potential. Firstly, the various schemes were not optimized, thus failing to fully realize the cost-reduction and efficiency-enhancing effects of high-strength steel constrained damping. Secondly, since high-strength steel constrained damping directly affects fatigue life and annual steel consumption costs by indirectly influencing additional damping, the relative relationship between additional damping and the original structural damping directly impacts cost-effectiveness assessment. Given the complexity of the damping cost and its value for the original uncontrolled structure, it is generally considered to be within the range of 1% to 5%. Therefore, the parameters for optimizing high-strength steel constrained damping are calculated for uncontrolled structures with damping ratios ranging from 1% to 5%, and the impact of high-strength steel constrained damping on fatigue performance is evaluated. When the damping ratio of the uncontrolled structure reaches an upper limit of 5%, the lower limit of the benefit of high-strength steel constrained damping can be obtained; while when the damping ratio of the uncontrolled structure reaches an upper limit of 1%, the upper limit of the benefit of high-strength steel constrained damping can be obtained. It is worth noting that although Q690 and 960 exhibit better damping enhancement effects, the lower strength grades Q550 and Q460 have relatively more mature application conditions. Therefore, we will analyze the upper and lower limits of the performance influence of high-strength steel constrained damping, using Q550 as a representative grade.

[0119] Based on the Q550-T20(20)20 scheme, assuming the damping ratio of the uncontrolled structure is 5%, and taking the damping layer t1 and the constraint layer thickness t2 as variables, the modal damping, normalized fatigue life, and normalized annual steel consumption of the Q550 scheme are calculated as follows: Figures 5a-5c As shown. Figure 5a and 5b The results show that the modal damping ratio and normalized fatigue life decrease with increasing damping layer thickness t1 and increase with increasing constraint layer thickness t2. For example, in scheme Q550-T20(6)26 with a damping layer thickness of 5mm and a constraint layer thickness of 5mm, an additional damping ratio of 0.97% was obtained based on an uncontrolled 5% damping ratio. This means that compared to the additional damping ratio of 0.54% of Q550-T20(20)20, a further damping increment of 0.43% can be obtained by adjusting the dimensions of t1 and t2. Figure 5cThe pattern shows that although increasing t2 will lead to a certain increase in steel consumption, the annual steel consumption cost will actually decrease due to the contribution of additional damping. The damping improvement effect of the constrained damping scheme is affected by the shear stiffness of the damping layer and the axial stiffness of the constrained layer. Within a certain range, the constrained damping scheme can achieve a better damping improvement effect by increasing the shear stiffness of the damping layer and the axial stiffness of the constrained layer.

[0120] Figure 6a and Figure 6b The cost-effectiveness of uncontrolled structures with damping ratios of 1% and 5% was compared. Figure 6a Normalized fatigue life based on uncontrolled structural fatigue life; Figure 6b This is the normalized annual steel consumption based on the steel consumption per unit life of uncontrolled structures. Figure 6a and Figure 6b The upper and lower limits of the influence of the high-strength steel scheme relative to the uncontrolled structure are depicted under two uncontrolled structural damping conditions. Furthermore, optimizing the design by adjusting t1 and t2 can further increase the lower limit of the normalized fatigue life and reduce the upper limit of the normalized annual steel consumption.

[0121] The damping ratio is improved by 0.4% to 1.0%, the normalized fatigue life is improved by 14% to 35%, and the normalized annual steel consumption is reduced by 17% to 27%. Therefore, by optimizing the cross-sectional parameters of the high-strength steel section, the Q550 scheme can achieve at least a 35% improvement in fatigue life and a 27% reduction in cost.

[0122] In summary, this scheme quantifies the effect of vibration reduction measures on fatigue life extension and combines it with the change in steel consumption caused by these measures. The cost reduction and efficiency improvement effect is directly evaluated by calculating the steel cost per unit fatigue life. If the vibration reduction scheme can significantly reduce the steel cost per unit fatigue life, its significant advantages in economy and long-term operational reliability are verified. This method not only facilitates rapid evaluation during the scheme design phase but also provides a solid theoretical foundation for subsequent optimization design.

[0123] This scheme allows for comparison of various constrained damping schemes on a unified scale and avoids the need to redesign the original tower during the damping scheme selection stage. This facilitates rapid evaluation and optimization during the scheme design stage. The scheme adopts normalized cost-benefit analysis, which can quickly assess the upper and lower limits of the scheme's cost-benefit, facilitating rapid decision-making during the scheme design stage.

[0124] This scheme uses steel consumption per unit life as the evaluation index to simplify the cost-effectiveness assessment of different constraint damping schemes. Experimental comparisons in the examples show that the high-strength steel constraint damping scheme has lower steel consumption per unit life compared to uncontrolled structures and ordinary constraint damping schemes, significantly reducing costs and increasing efficiency for wind power support structures. Furthermore, as the strength of high-strength steel increases, the synergistic effect of the high-strength steel constraint damping scheme becomes more pronounced, leading to even greater cost reduction and efficiency improvement.

Claims

1. A method for analyzing the cost-reducing and benefit-increasing performance of additional damping measures for a wind power supporting structure, characterized in that, The method comprises the following steps: S1, for different design schemes, the corresponding unit life steel consumption cost is calculated respectively; S2, the unit life steel consumption cost corresponding to different design schemes is compared, and the design scheme with the optimal cost reduction and benefit increase performance is screened out; S3, the cost benefit of the design scheme screened out in step S2 is estimated by using the normalized cost benefit; The unit life steel consumption cost in step S1 specifically comprises the following steps: S11, damping effect analysis: the dynamic coefficient DAF is obtained by calculating the additional damping; S12, wind load spectrum analysis: the bending moment spectrum of the tower drum control section caused by the fluctuating wind load is analyzed to evaluate the dynamic effect of the wind load on the structure; S13, stress spectrum analysis: the stress spectrum of the dangerous point is calculated based on the bending moment spectrum, the stress spectrum is simplified to a single frequency stress spectrum about the wind turbine tower fundamental frequency, and the stress amplitude of the constant amplitude stress time history is calculated; S14, fatigue life estimation: the fatigue life of the structure is estimated in combination with the S-N curve of the material; S15, unit life cost calculation: the unit life steel consumption cost is obtained by dividing the steel consumption cost by the estimated fatigue life; Step S3 is specifically to take the fatigue life of the uncontrolled structure and the steel consumption as the benchmark for normalization to obtain the normalized fatigue life and unit annual steel consumption. Within the preset range of the damping ratio of the uncontrolled structure, the parameters of the constraint damping in the design scheme are optimized to determine the upper limit and lower limit of the cost benefit of the design scheme.

2. The method for analyzing and evaluating the performance of cost reduction and benefit increase of additional damping measures for wind power supporting structures according to claim 1, characterized in that, The step S11 specifically calculates the additional damping by using the modal strain energy method, and then obtains the dynamic coefficient to comprehensively consider the influence of damping on the structural performance.

3. The method for analyzing and evaluating the performance of cost reduction and benefit increase of additional damping measures for wind power supporting structures according to claim 1, characterized in that, The step S12 comprises the following processes: Only the wind load acting on the machine head is considered, and the wind load acting on the RNA wind wheel-nacelle assembly under a given wind speed is: wherein, is the air density, is the swept area of the impeller, is the total wind speed, is the average wind speed, is the fluctuating wind speed, is the thrust coefficient, ; The power spectral density of the fluctuating wind speed is obtained by Kaimal spectrum calculation: wherein f is the frequency, is the wind speed is the standard deviation, , is the turbulence intensity, is the integral length parameter, z is the distance from sea level; The wind load is divided into average wind load and fluctuating wind load, and the fluctuating wind load spectrum obtained after introducing the fluctuating wind speed spectrum is: wherein, is the fluctuating wind load, is the fluctuating wind load spectrum.

4. A method for analyzing and assessing the performance of cost reduction and benefit increase of additional damping measures for wind power supporting structures according to claim 3, characterized in that, The step S13 comprises the following processes: Under the action of fluctuating wind load, the tower drum and pile foundation will produce dynamic response, and the tower pile bending moment response spectrum considering the dynamic coefficient is: wherein, D is the distance of the rotor from sea level, h D is the distance of the rotor from sea level, The structural dynamic response under the action of fluctuating wind load only considers the contribution of the first-order modal, and the wind turbine tower is equivalent to a single degree of freedom system with inertia concentrated at the tower top, and its dynamic coefficient is: wherein, is the frequency ratio, , is the first modal frequency of the wind turbine tower, is the first modal damping ratio of the wind turbine tower; Calculation of distance from sea level using bending moment response spectrum h The maximum normal stress spectrum at the section is: wherein E is the cross-sectional flexural modulus; According to the linear Airy wave theory, the stress time history under the action of fluctuating wind load is obtained by the harmonic superposition method from the stress spectrum. Since the structural dynamic response under the action of fluctuating wind load is mainly concentrated near the first-order modal frequency of the wind turbine tower, in order to facilitate fatigue life evaluation, only the main component in the harmonic is retained, and the variable amplitude fatigue problem is simplified to a constant amplitude fatigue problem, that is, only the harmonic component corresponding to the first-order modal frequency of the stress spectrum is retained, and the stress time history is: wherein is the stress amplitude, , is the stress power spectral function In the area of the frequency interval.

5. A method for analyzing the performance of cost reduction and benefit increase of additional damping measures for wind power supporting structures according to claim 4, characterized in that, The fatigue life estimation formula in step S14 is: where T is the fatigue life in years, N is the number of cycles to failure, m is the fatigue strength exponent of the material, C is the fatigue limit of the material.

6. A method for analyzing the performance of cost reduction and benefit increase of additional damping measures for wind power supporting structures according to claim 5, characterized in that, The unit life steel consumption cost in step S15 is: Wherein, is the total steel consumption of the wind turbine tower, is the total steel consumption of the wind turbine tower.

7. The method for analyzing and assessing the performance of cost reduction and benefit increase of additional damping measures for wind power supporting structures according to claim 1, characterized in that, In step S2, the design scheme corresponding to the lowest unit life steel consumption cost value is taken as the design scheme with the optimal cost reduction and benefit increase performance.

8. The method for analyzing and evaluating the performance of cost reduction and benefit increase of additional damping measures of wind power supporting structure according to claim 1, characterized in that, In step S3, the preset range of the damping ratio of the uncontrolled structure is 1% to 5%. When the damping ratio of the uncontrolled structure is taken as the upper limit of 5%, the lower limit of the benefit of the design scheme's constraint damping is obtained. When the damping ratio of the uncontrolled structure is taken as the lower limit of 1%, the upper limit of the benefit of the design scheme's constrained damping is obtained.

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