A Study of the Nonlinear Attenuation Behavior of Preload in the Bolt Fastening Process for Offshore Wind Turbine Blades Using Ultrasonic Technology

Abstract

The attenuation of bolt preload is a critical factor leading to bolt fatigue failure, whereas the study of the nonlinear attenuation behavior of preload and its mechanism during installation is an inevitable challenge in engineering practice. The attenuation of the preload of a bolt is mainly related to the stiffness of the bolt body as well as the stiffness of the connected parts. This study aimed to develop an experimental system to analyze the nonlinear attenuation behavior of preload during bolt tightening. First, a simulation system replicating the bolt installation process was constructed in a laboratory setting, incorporating blade and pitch bearing specimens identical to those used in a 10 MW wind turbine, restoring the stiffness coupling characteristics of the “composite-metal bearing” heterogeneous interface at the blade root through a 1:1 full-scale simulation system for the first time. Second, ultrasonic preload measurement equipment was employed to monitor preload variations during the bolt tightening process. Finally, the instantaneous preload decay rate of the wind turbine blade-root bolts and the over-draw coefficient were quantified. Experiments have shown that the preload decay rate of commonly used M36 leaf root bolts is 11–16%. If a more precise value is required, each bolt needs to be calibrated. These findings provide valuable insights for optimizing bolt installation procedures, enabling precise preload control to mitigate fatigue failures caused by abnormal preload attenuation.

1. Introduction

With the growing emphasis on environmental awareness, clean energy has garnered increasing global attention. Among renewable energy sources, wind energy has emerged as a key focus for many nations. Wind turbine blades, essential for capturing wind energy, are connected to the turbine hub through blade-root bolts. During the operation of the turbine, the blade-root bolts are subjected to complex loads, including tension, compression, and torsion [1]. Their reliability directly affects the performance and safety of the wind turbine blades. Therefore, these high-strength bolts play a crucial role in the structural integrity and safety of offshore wind turbines.

Fatigue failure is a primary failure mode of bolts, often caused by insufficient preload or early preload attenuation. To mitigate such failures, appropriate preload must be applied to blade-root bolts before wind turbine operation. However, improper preload can lead to adverse consequences: excessive preload may result in bolt fracture, connector deformation, or thread damage, while insufficient preload can cause slippage, bolt breakage, or even catastrophic wind turbine failure. Preload is thus a critical performance indicator for assessing the reliability of bolted connections. Optimizing preload design can enhance the service life of blade-root bolts and reduce the risk of failure.

Existing studies have established a systematic framework for studying bolt preload attenuation mechanisms [2,3,4], monitoring methods [5,6,7], and tightening processes [8]. Regarding preload attenuation mechanisms, Pengwei Sun et al. [9] developed a static finite element simulation method to analyze initial preload relaxation, leveraging the similarity between creep and preload relaxation phenomena. Their model demonstrated strong agreement with experimental data, validating the accuracy of the approach. Similarly, Sun Yadong et al. [10] used ANSYS 2020 R2 to create a bolted connection model considering joint surface contact characteristics, explaining stress relaxation from a microstructural perspective. Ying Li et al. [11] proposed a time-varying model to predict residual bolt preload and conducted orthogonal tests involving tightening torque, amplitude, and frequency, identifying two distinct stages in the relaxation process of bolted joints under vibration.

Preload measurement methods include the strain gauge method, force ring method, and optical fiber method. However, these approaches face practical limitations in wind turbine applications. The ultrasonic pulse-echo reflection method, based on the relationship between ultrasonic wave propagation speed and stress, provides a real-time, accurate, and efficient alternative for measuring axial force. Pan Qinxue et al. [12] analyzed the relationship between nonlinear coefficients and wave amplitude using a nonlinear ultrasonic inspection system. Similarly, Sun Guofeng [5] investigated the application of ultrasonic technology for axial force measurement in high-strength bolts, exploring factors such as material properties, surface conditions, bolt size, and operator techniques.

For hydraulic tensioning methods, Zuti Zhang et al. [13] studied tensile resilience in hydraulic bolts, accounting for friction coefficients and thread force distribution. They proposed a calculation method for the hydraulic bolt tension rebound rate, validated through simulations and empirical data. Tieneng Guo et al. [14] analyzed the relationship between initial tension and final preload in high-strength bolts used in heavy-duty gantry beams, presenting a calculation method to optimize bolt installation preload.

However, these studies exhibit three key limitations: (1) attenuation mechanism analysis: homogeneous material models are predominantly used, insufficiently accounting for the stiffness coupling characteristics at the “composite-metal bearing” heterogeneous interfaces in wind turbine blade roots, leading to significant deviations between theoretical predictions and actual conditions; (2) monitoring technology: approaches lack optimization for engineering the features of wind turbine bolts (e.g., high length-to-diameter ratios, compact installation spaces), and exhibit inadequate compensation mechanisms for environmental interference like temperature drift; and (3) tightening process modeling: reliance on Hooke’s law-based linear assumptions neglects the exponential variation in the preload attenuation rate caused by the stiffness nonlinearity of bolts and connected components.

Addressing these gaps, this study develops a 1:1-scale blade-root-bolt installation simulation system, integrating real-time ultrasonic monitoring with temperature compensation technology. It pioneers the quantitative analysis of nonlinear behaviors—the ”instantaneous preload attenuation rate” and “over-tightening coefficient”—for M36 blade-root bolts in offshore wind turbines. Compared to existing studies, this experiment accurately replicates the stiffness states of blade-root-bolt connection components via a full-scale simulation system. The resulting experimental data better reflect actual stiffness-matching relationships, offering a more engineering-applicable solution for optimizing bolt installation processes and achieving precise preload control.

This article contains the following five parts: 1. introduction of the ultrasonic measurement system and principle; 2. introduction of the experimental system of bolt preload attenuation; 3. discussion of the experimental results; 4. conclusion; and 5. suggestions for the direction of subsequent research.

2. Ultrasonic Axial Force Measurement Theory

Ultrasonic measurement of bolt axial force relies on the principle of acoustic elasticity. The propagation velocity of ultrasonic longitudinal waves varies with the material’s stress state; specifically, the longitudinal wave velocity decreases linearly with increasing stress. Under axial tensile stress, the relationship between the velocity of ultrasonic longitudinal waves and the applied stress can be expressed by Equation (1) [15]:

$$\begin{array}{c}{v}^2=v_0^2-\\ {\displaystyle \frac{\sigma }{\rho (3\lambda +2\mu )}}[{\displaystyle \frac{\lambda +\mu }{\mu }}(4\lambda +10\mu +4m)+\lambda +2l]\end{array}$$

(1)

where v is the ultrasonic longitudinal wave velocity with stress, v₀ is the ultrasonic longitudinal wave velocity without stress; σ is the axial tensile stress, λ and μ are the second-order elastic constants, m and l are the third-order elastic constants, and ρ is the material density.

Linearizing Equation (1), the relationship of ultrasonic longitudinal wave velocity before and after stress loading can be obtained:

$$v=v_0-k\sigma$$

(2)

where k is the elastic coefficient and can be calculated as follows:

$$k={\displaystyle \frac{(\mu +\lambda )(4\lambda +10\mu +4m)+\lambda \mu +2l\mu }{2\rho \mu (\lambda +2\mu )(3\lambda +2\mu )}}$$

(3)

In the elastic stage, the relationship between the bolt elongation and the preload force can be described:

$$F={\displaystyle \frac{E\cdot S\cdot \Delta L}{L}}$$

(4)

where F is the preload force of the bolt, E is the elastic modulus of the bolt material, S is the cross-sectional area of the bolt, ΔL is the deformation of the bolt, and L is the effective stress length of the bolt.

In the tightened state of the bolt, the deformation of the bolt is obtained according to the relationship between the time difference between the ultrasonic probe transmitting and receiving the echo signal, which is expressed as the following:

$$\Delta L={\displaystyle \frac{1}{2}}\cdot (t_1-t_2)\cdot V_{T,\sigma }$$

(5)

where V_T,σ represents the longitudinal wave velocity at temperature T under stress σ, t₁ is the time difference between the ultrasonic probe transmitting and receiving the echo signal when the bolt is not stressed, and t₂ is the time difference between the ultrasonic probe transmitting and receiving the echo signal when the bolt is stressed.

By combining Equations (4) and (5), the formula can be obtained:

$$F={\displaystyle \frac{E\cdot S\cdot V_{T,\sigma }}{2L}}(t_1-t_2)$$

(6)

In Equation (5), the elastic modulus of the bolt material, the effective force length of the bolt, the cross-sectional area of the bolt, and the temperature influence coefficient of the longitudinal wave velocity in the bolt are known parameters. Using these values, the preload can be determined based on the time difference in ultrasonic wave propagation through the bolt before and after the application of tensile stress.

As is illustrated in Figure 1, the static model of the bolt tightening process using the hydraulic tension method can be divided into three stages. In stage 1, the bolt is unstressed, and both the bolt and the connected part remain at their original lengths. In stage 2, the bolt is subjected to the tensile force exerted by the hydraulic tensioner, causing the bolt to elongate while the connected part is compressed. In stage 3, the hydraulic tensioner is released, allowing both the bolt and the connected part to rebound. At this stage, the bolt retains a specific preload, F₀, and the nut is tightened. During stage 2, it is assumed that the length of a section of the bolt is equal to the thickness of the connected part, denoted as D₁,while the total length of this section of the bolt is H.

In stage 2, ∆H₁ and ∆D₁ are given below:

$$\Delta H_1=H_1-H=D_1-H$$

(7)

$$\Delta D_1=D-D_1$$

(8)

where H is the H₁ is the stretched length of the bolt of length H in stage 1, ∆H₁ is the deformation of the bolt of length H after being stretched, D is the total thickness of the connected piece when it is not stressed, D₁ is the thickness of the connected part after compression in stage 2, and ∆D₁ is the deformation of the connected part being compressed in stage 2.

The hydraulic tensile force F is known. Then, ∆H₁ and ∆D₁ can be obtained by Hooke’s Law:

$$\Delta H_1={\displaystyle \frac{FH}{EA}}$$

(9)

$$\Delta D_1={\displaystyle \frac{F}{K}}$$

(10)

K is the stiffness of the connected part, E is the elastic modulus, and A is the cross-sectional area. K can be calculated by the following formula [16]:

$$K={\displaystyle \frac{\pi d_h{E}_0\tan \theta }{2\ln \left[\frac{(d_w+3d_h)}{(d_w-d_h)}\frac{(d_w+D\tan \theta -d_h)}{(d_w+D\tan \theta +3d_h)}\right]}}$$

(11)

where d_h is the diameter of the bolt hole, d_w is the diameter of the bearing surface of the gasket, θ is the half apex angle, and E₀ is the elastic modulus of the connected part.

By the above equations, the calculation formula of the H can be obtained.

$$H={\displaystyle \frac{(DK-F_h)EA}{(EA+K_H{F}_h)K}}$$

(12)

In stage 3, ∆D₂ and H₂ can be written as follows:

$$\Delta D_2=D-D_2$$

(13)

$$H_2=D_2-X$$

(14)

where ∆D₂ is the deformation of the connected part being compressed in stage 3, D₂ is the thickness of the connected part in stage 3, H₂ is the length of the bolt of length H in stage 3, and X is the difference between the length of the bolt of length H after rebound and the length of the rebound of the connected part in stage 3.

From stage 2 to stage 3, the deformation of the connected part ∆D₂ and the bolt deformation ∆H₂ can be obtained by Hooke’s Law:

$$\Delta D_2={\displaystyle \frac{F_0}{K}}$$

(15)

$$\Delta H_2={\displaystyle \frac{K_H{F}_{0}H}{EA}}$$

(16)

where F₀ is the preload force, K_H is the bolt tension coefficient, E is the bolt elastic modulus, and A is the bolt cross-sectional area.

By the above equations, the calculation formula of the F₀ can be obtained:

$$F_0=F_h-{\displaystyle \frac{(EA+K_H{F}_h)KX}{EA+K_{H}CK}}$$

(17)

It can be seen from Equation (17) that the final preload force is nonlinear with the hydraulic tension force.

3. Experimental Test System for MW Offshore Wind Power Blade-Root Bolt

3.1. Simulation Test System for MW Offshore Wind Power Blade-Root Bolt

In this study, a test system was utilized to investigate the bolt tensile force attenuation rate and the bolt over-draw coefficient. As is depicted in Figure 2, the test system comprised the iFast ultrasonic bolt-condition real-time monitor, a wind-turbine-scale composite blade-root prosthesis, a pitch bearing prosthesis, a cast-iron blade-root prosthesis, a blade-root flange prosthesis, an HTE36E bolt hydraulic tensioner (Hangzhou WREN Hydraulic Equipment Manufacturing Co., Ltd., Hangzhou, China), and other components. The iFast ultrasonic monitor (Beijing iFast Technology Development Co., Ltd., Beijing, China) was connected to a computer via an RJ45 network interface, enabling communication between the devices. It converts acoustic signals received from the ultrasonic probe and temperature signals from the sensor into electrical signals, which are then transmitted to the computer. The computer calculated the bolt force using a calibration file embedded in the specialized software. This calibration file was derived from pre-experiment results obtained with the iFast Bolt Preload Monitoring System. As the calibration process is not the primary focus of this paper, the calibration data are provided directly in

Table 1. Calibration results of bolts.

Temperature/°C	Echo Time/ns	Transit Time Difference/ns	Measured Value/kN
12.91	168,323.8	1264.1	500
12.94	168,118.8	1058.6	420
12.93	167,938.8	878.8	350
12.96	167,757.8	697.2	280
12.95	167,581.6	521.2	210
12.98	167,406.2	345.3	140
12.91	167,233.1	173.4	70

. The ceramic patch and test bolt are shown in Figure 3.

Figure 4 illustrates the linear relationship between the ultrasonic transit time difference and the pulling force generated by the hydraulic pump. The R² value is approximately 1, indicating excellent linearity. The performance parameters of the wind turbine blade-root-bolt test system are summarized in

Table 2. Performance index of wind turbine blade-root-bolt test system.

Index Type	Performance Index
Bolt performance levels	10.9
Yield limit/MPa	940
Measurement accuracy of preload	±3%
Maximum output tension of stretcher/kN	678
Maximum output pressure of hydraulic pump/Mpa	200
Operating temperature/°C	10~26

Bolt performance classes comply with ISO 898-1 standard [17]; grade 10.9 indicates tensile strength ≥ 1000 MPa and yield-to-tensile strength ratio of 0.9.

.

3.2. Test Method

The hydraulic stretching method operates as follows:

• A high-pressure oil pump generates a specific oil pressure.
• The oil pressure is transmitted to the piston surface of the hydraulic stretching device through a transmission pipe.
• The bolt is stretched by the interaction between the tension head and the internal thread of the tensioner, applying axial force to the bolt.
• Once the bolt is stretched to the desired length, a tightening wrench is used to secure the nut, ensuring proper contact with the connected part’s surface.
• The oil pressure in the hydraulic cylinder is then released, achieving the desired preload.

Because this method applies only axial tension during tightening, avoiding torsional motion and minimizing frictional effects, the tension is easier to control. Consequently, the hydraulic stretching method is widely employed in connecting critical components of wind turbines. However, the hydraulic tensioner may sustain impacts during transportation, potentially impairing its performance. As such, calibration is necessary before use to ensure accuracy and reliability.

3.2.1. Hydraulic Pump Calibration

The performance requirements for the tensioner are typically based on the technical specifications outlined in JB/T 6390-2007 “Hydraulic Bolt Pretensioner” [18]. This standard specifies that the technical requirements for hydraulic cylinders must adhere to the relevant provisions of JB/T 10205 “Hydraulic Cylinder” [19]. According to these standards, the tension deviation of the hydraulic tensioner must not exceed ±10%. Repeated experiments were conducted using the HTE36E bolt hydraulic tensioner, with the experimental results presented in

Table 3. Experimental data of hydraulic pump calibration.

Calibration Point/MPa	Indicator Indication/kN
	1	2	3	4	5	Average Value
10	47.2	53.2	48.5	49.5	50.1	49.7
20	100.5	100.8	103.2	100.8	103.5	101.8
30	155.2	155.4	154.8	154.3	155.7	155.1
40	207.2	207.4	207.2	206.5	209.8	207.6
50	258.9	261.2	262.3	258.8	258.8	260.0
60	317.7	314.5	312.3	313.9	311.2	313.9
70	366.1	365.3	363.2	363.8	362.6	364.2
80	415.7	418.2	416.5	414.6	414.2	415.8
90	469.1	470.2	467.5	467.4	465.3	467.9
100	523.1	521.8	519.7	518.1	517.1	520.0

.

Table 3 demonstrates the selected measurement point based on the OMEGA pressure sensor with an accuracy of 0.5%. The data in Table 3 are fitted to draw the calibration curve of the hydraulic pump, as shown in Figure 5.

The calibration equation of the hydraulic pump is as follows:

$$P=0.19135F+0.35014$$

(18)

The hydraulic tensioner has good linearity. The R² of the linear fitting is 0.99997.

3.2.2. iFast Ultrasonic Bolt-Condition Real-Time Monitoring System

The iFast ultrasonic bolt-condition real-time monitoring system consists of the iFast ultrasonic real-time bolt condition monitor, an ultrasonic probe, a temperature sensor, and iFast software. The operation procedure of the system is as follows:

• Set the parameters on the iFast software panel, configuring the probe frequency to 2 MHz and the gain to 27 dB. Then, import the calibration file and enable temperature compensation.
• Attach the ultrasonic probe to the piezoelectric ceramic pasted on the bolt’s end face and save the initial ultrasonic echo when no tensile force is applied. The initial echo is shown in Figure 6.
• Apply axial tensile force to the bolt by pressurizing the hydraulic pump. Then, click “Measure” in the software. Using the acoustic time difference between the ultrasonic echo and the initial echo, along with the imported calibration curve, the software calculates the stress value and bolt elongation in real time.

To generalize the findings, M36×460 bolts used in the blade-root connection of a 5 MW offshore wind turbine were selected for this study. Each bolt was tested three times, with the average value calculated from the repeated tests. The technological conditions for the bolt tests are presented in

Table 4. Technological conditions of bolt test.

Experimental Parameters	Process Condition
Test object	M36 stud bolt, length 460 mm
Tightening process	Hydraulic stretch method
Frequency of ultrasonic probe	2 MHz
Probe gain	27 dB
Ambient temperature/°C	22

.

4. Results and Discussion

In the assembly of MW offshore wind turbine blade-root bolts, the bolt pre-tightening force is crucial for the stability of the blade-to-turbine connection. To better study and analyze the relationship between hydraulic tension and the final bolt preload in the hydraulic tensioning method, the tensile force attenuation rate, denoted as D_F, is defined as follows:

$$D_F={\displaystyle \frac{F_h-F_0}{F_h}}\times 100\%$$

(19)

where F_h is the set hydraulic stretcher tension, and F₀ is the final bolt pre-tightening force.

In this section, the nonlinear law in the hydraulic tension tightening process is studied from the two aspects of the tensile force attenuation rate and the over-draw coefficient by analyzing the test data.

4.1. Nonlinear Law of Tensile Force Attenuation Rate

Based on the static analysis of the bolt, the tensile force attenuation rate was tested for the bolt under different tensile forces output by the hydraulic tensioner. Due to the large volume of test data, only the data for bolt 1 is presented in this paper. The tensile force attenuation rate was measured under various pressures from the hydraulic pump. The resulting data for the change in tensile force attenuation rate is shown in

Table 5. Bolt 1 experimental data.

Hydraulic Pump Pressure/Mpa	Calibrated Hydraulic Pump Pressure/Mpa	Bolt Tension Before Pressure Relief/kN	Tensile Force of Bolt After Pressure Relief/kN	The Attenuation Rate of Bolt Tensile Force
10	10.85	54.9	35.7	34.97%
20	20.30	104.3	73.9	29.15%
30	30.634	158.3	119.6	24.45%
40	40.33	209	160.2	23.35%
50	51.12	265.4	217.8	17.94%
60	61.30	318.6	264.8	16.89%
70	70.90	368.8	310.7	15.75%
80	81.37	423.5	363.9	14.07%
90	90.76	472.6	411.2	12.99%
100	100.78	525	466.3	11.18%

.

The data in Table 5 were plotted into a scatterplot and fitted, as shown in Figure 7.

As is shown in Figure 7, with the increase in the output pressure of the hydraulic pump, the tensile force attenuation rate of the bolt during tightening by the hydraulic tensioning method gradually decreases. By fitting the relationship between the hydraulic pump output pressure and the tension attenuation rate using an exponential decay function, the R² value is 0.9984, indicating a strong fit. Based on the fitting results, the following conclusions can be drawn: When bolts are tightened using the hydraulic tensioning method, the tensile force attenuation rate at the root of the wind turbine blade decreases as the hydraulic pump pressure increases, following an exponential decay trend.

From the curve in Figure 8, it can be observed that the tension attenuation differs even among bolts of the same specification. As the output pressure of the hydraulic pump increases, the tension attenuation becomes more stable. The fitting formula for the tensile force attenuation rate of all tested bolts is presented in

Table 6. Bolt test data fitting results.

Bolt Number	Fitting Formula	R2
01	$y=60.53\cdot e^{{\displaystyle \frac{-x}{31.21}}}+5.28$	0.9984
02	$y=38.54\cdot e^{{\displaystyle \frac{-x}{27.78}}}+8.29$	0.9925
03	$y=28.59\cdot e^{{\displaystyle \frac{-x}{39.47}}}+10.72$	0.9795
04	$y=33.47\cdot e^{{\displaystyle \frac{-x}{44.92}}}+8.30$	0.9984
05	$y=25.30\cdot e^{{\displaystyle \frac{-x}{66.13}}}+11.73$	0.9890

.

As is shown in Table 6, the tensile force attenuation rate of MW offshore wind turbine blade-root bolts decreases exponentially with increasing hydraulic pump pressure; this in line with the results of prior studies reporting 8–10% attenuation rates [20]. This study’s results (11–16%) show minor discrepancies, attributed to 1:1 full-scale simulation of composite-metal interfaces, which validates the conclusions.

4.2. Nonlinear Law of Over-Draw Coefficient

Due to various factors such as bolt diameter, effective length, thread form, and concentricity, the axial force obtained through the hydraulic stretching method does not exactly match the force exerted on the bolt by the hydraulic cylinder.

In engineering, the ratio between the hydraulic setting tension F_h and the preload force F₀ is defined as the over-draw coefficient. The empirical formula [21,22] of the bolt over-draw coefficient is as follows:

$${\displaystyle \frac{F_{\mathrm{h}}}{F_0}}=1.15+{\displaystyle \frac{2}{{\left(\frac{L_k}{d}\right)}^2}}$$

(20)

where L_k is the length of the clamping part of the bolt, and d is the nominal diameter of the bolt.

This empirical formula only considers the influence of the clamping length of the bolt and the nominal diameter of the bolt. However, several other factors, such as the pre-tension force and the number of stretching cycles, also affect the over-draw coefficient. In this test, the values of L_k and d are 365 mm and 36 mm, respectively. The calculated over-draw coefficient is 1.17.

In this section, the over-draw coefficients corresponding to reaching different target preload are studied. The test data of bolt 1 are shown in

Table 7. Bolt 1 over-draw coefficient.

Hydraulic Setting Tension/kN	Preload/kN	Over-Draw Factor
54.9	35.7	1.54
104.3	73.9	1.41
158.3	119.6	1.32
209.0	160.2	1.30
265.4	217.8	1.22
318.6	264.8	1.20
368.8	310.7	1.19
423.5	363.9	1.16
472.6	411.2	1.15
525.0	466.3	1.13

.

The data in Table 7 were fitted, and the results are shown in Figure 9. Fitting of the data of the over-draw coefficient corresponding to all of the test bolts is shown in Figure 10.

From Figure 9, it can be concluded that as the target preload increases, the over-draw coefficient gradually decreases, following an exponential decay trend. This behavior is inconsistent with the results predicted by the empirical formula. Additionally, within the yield limit, the over-draw coefficient stabilizes as the target preload increases. Therefore, in actual assembly, the corresponding over-draw coefficient should be determined based on the target preload to ensure that the residual preload meets the connection requirements.

As is shown in Figure 10, the over-draw coefficients of different bolts vary, but all follow a nonlinear trend that adheres to the law of exponential decay. This pattern aligns with the results of Wang et al. [23], who observed a negative exponential relationship between the coefficient and load for M36 bolts via hydraulic tension tests, with a fitting error of <4.2%. Gong et al. [24] further confirmed through nonlinear FEM that stress redistribution at thread interfaces causes double exponential decay, consistent with this study’s experimental trends.

5. Conclusions

This paper presents a systematic study of the nonlinear preload attenuation and over-draw coefficient of MW offshore wind turbine blade-root bolts during hydraulic tensioning, utilizing the iFast ultrasonic real-time monitoring system. A novel 1:1 full-scale simulation system was developed to replicate the stiffness coupling at the composite-metal interface, enabling accurate capture of multidimensional stresses that are ignored in conventional simplified models. Through combined theoretical modeling and experimental validation, the following key conclusions are drawn:

• Within the yield limit of the material, as the hydraulic pump pressure increases, the tensile force attenuation rate of the MW offshore wind turbine blade-root bolt decays exponentially. Selecting an appropriate target preload helps to reduce the attenuation of tensile force during actual assembly.
• Within the yield limit of the material, as the target preload increases, the over-draw coefficient gradually decreases, following an exponential decay trend. This behavior is inconsistent with the empirical formula results. Furthermore, the over-draw coefficient begins to stabilize as the target preload increases. Therefore, the over-draw coefficient should be determined based on the target preload during the actual assembly process to ensure the residual preload meets the connection requirements.
• A preload decay rate of 11–16% exists for commonly used M36 leaf root bolts. Under the same test conditions, bolts of the same specification exhibit different tensile force attenuation rates after stabilization and different over-draw coefficients. This variability may be attributed to differences in the bolt processing technology. As a result, for some wind turbine blade-root connecting pairs with small design margins, the preload decay value of each bolt can be measured before use.

With the iterative development of wind power technology, the future wind turbine will show two major trends: first, the blades and pitch bearings and other key components are gradually adopting new composite structures; second, the fastening system will be upgraded to use 12.9-grade, 14.9-grade, and other ultra-high strength bolts. Our research on 10.9-grade bolts indicates that with the widespread application of ultra-high-strength bolts such as 12.9-grade and 14.9-grade bolts in the future, there is an urgent need to conduct more systematic research on the preload attenuation law and over-tension coefficient threshold, and establish a preload attenuation testing system for the assembly stage under the synergy of “material–structure–process”. In future research, our achievements can be aligned with standards such as IEC 61400 and directly applied to the design of bolted connection systems for new-generation wind power equipment, providing theoretical support for improving the reliability and safety of offshore wind power equipment.