Analysis and Experimental Study of Contact Stress in Bolted Connections of Pitch Bearings

Abstract

In wind turbine systems, bolted connections in pitch bearings are subjected to working loads that reduce bolt preload. This reduction can lead to issues such as bolt loosening and eccentric loading, which in turn results in the nonuniform distribution of contact stress across joint surfaces. These issues can compromise structural integrity and reduce fatigue life. However, the study of contact stress mainly focuses on theoretical research, lacking relatively large, complex structures. Also, the stress testing methods for contact surfaces of bolted connections are limited in practical engineering. In this paper, a localized bolt connection model using the finite element method according to pitch bearings in wind turbine systems was established. The contact stress distribution patterns of bolt specimens under varying preloads were investigated. Comparative numerical simulation and experimental analysis using thin-film pressure sensors were conducted. Furthermore, the effect of bolt assembly in different tightening processes on the contours of contact stress was analyzed to identify the optimal tightening sequence. The experimental results demonstrate a positive correlation between preload and maximum contact stress, with stress distribution exhibiting symmetry around the bolt hole and decreasing radially outward. Thin-film pressure sensors can be used for contact stress detection. Furthermore, the diagonal tightening method can achieve a more uniform contact stress distribution compared to other methods, such as sequential and alternate tightening. The findings provide valuable insights for optimizing the contact stress distribution and tightening processes in bolted joint assemblies.

1. Introduction

In a typical wind turbine, power is generated through the rotation of the hub, which is driven by the blades, and subsequently transmitted to the generator via the main shaft and gearbox. Generally, three blades are connected to the hub using pitch bearings, which are fastened with preloaded bolts [1]. Contact stresses arise between the pitch bearing and the blade and hub connections during the installation and operation of the pitch-bearing system. Owing to harsh operating conditions, pitch bearings are subjected to alternating cyclic loads during power transmission. Bolt pretension and operational loads can lead to bolt loosening or uneven loading, resulting in nonuniform contact stress distributions on the connecting surfaces. This exacerbates the fatigue wear of the pitch bearing, ultimately affecting its lifespan. Over time, bolt connection failures can pose significant safety and reliability risks to the entire turbine system [2,3]. Consequently, contact stress distribution testing has received increasing attention from researchers. However, the measurement of contact stress distribution presents challenges, including inseparable contact surfaces and difficulty in sensor installation. Also, it is difficult to directly test the stress of the entire contact surface. Moreover, it is more difficult to test the contact stress distribution under dynamic loads.

To address these issues, both direct and indirect methods have been adopted to investigate contact load distribution law. Direct methods include needle sensors and integrated sensor measurement techniques [4,5,6]. Regarding indirect methods, Mills et al. [7,8,9] assumed that the test piece undergoes only elastic deformation under external loading. They proposed an indirect testing approach that uses the test results for inverse calculations to determine the normal and shear stresses on the contact surface. However, the limitation is that it is not applicable when the test piece undergoes elastic-plastic deformation. Wu et al. [10] employed a singularity detection technique to locate the positions of cracks on the outer race based on the stresses measured from the segments. The experimental results showed that the proposed method could effectively and accurately identify and locate cracks on the outer race of the bearing. However, this measurement method is only applicable to the outer ring of the bearing. For direct testing of contact stress distribution, Wang et al. [11] conducted a raceway contact experiment that utilized pressure-sensitive films and studied the effects of elliptical truncation rates on the raceway surface and subsurface stresses under various loads in a four-point contact pitch bearing. Xiao et al. [12] utilized pressure film sensors to measure the contact stress distribution at the ballast bed–soil subgrade interface of conventional railways during cyclic loading in model tests. Gutierrez-Rivera [13] developed a low-pressure extrinsic Fabry–Perot fiber optic sensor based on a thin polyester film using phase signal analysis. The cavity created was uniformly stressed by applying a pressure varying from 0 to 2 psi. Regarding the existing research on direct testing of contact stress, most of the geometric shapes of the research objects are relatively easy to measure directly, while measuring the contact stress at the bolt connection position is relatively difficult. Moreover, the contact theory analysis of bolted connections is also quite complex. To improve the prediction precision of the leakage rate, Bian et al. established a time-dependent leakage prediction model for bolted flange connections, considering the unevenness of contact stress and temperature distribution [14]. Reszka et al. [15] simplified bolt connections by replacing bolts with beam elements in the modeling method, equivalently studying the stress distribution law on the contact surface. Key parameters affecting the performance of bearing bolt connections include the preload, friction coefficient, and liner height. Among these, bolt preload under alternating loads is the most critical factor affecting connection performance [16,17]. In these studies, the equivalent calculation of contact stress or the simplification of beam models can only obtain approximate results, especially when applying preload on bolts, which makes the problem more complex and difficult. It is necessary to use numerical simulation and experimental techniques to study the contact stress of bolts. Fukuoka et al. proposed an effective mesh generation scheme that can provide helical thread models with accurate geometry to analyze specific characteristics of stress concentrations and contact pressure distributions caused by the helical thread geometry [18]. To quantitatively investigate the influence of flange gaps on bolt fatigue, Liu et al. proposed a nonlinear finite element model of a flange segment incorporating bolt pretension and contact elements. Three distinct types of flange gaps were defined. It was possible to determine the nonlinear relationship between the wall load and bolt internal force [19]. Chang et al. proposed a hybrid method (FT-FEM) combining fractal theory with the finite element method for bolted connection models that describes the interface contact evolution in the elastic, elastoplastic, and fully plastic stages [20]. When using three-dimensional finite element software to analyze stress concentration, contact pressure distribution, preload application, and contact elements in bolted connections, the meshing technique is particularly important. The quality of meshing directly affects the accuracy of the calculation results.

Most of the existing studies are mainly about plate contact, and the number of bolts studied is relatively low. Contact stress focuses more on theoretical research, and the stress testing methods in practical engineering are limited. In this study, a bolt specimen model between the blade and the pitch bearing was established. The contact stress distributions of bolted connections were analyzed using numerical simulations. The experiments of contact stress for the bolt specimen connection were accomplished using thin-film pressure sensors. Furthermore, the effects of the bolt assembly for different tightening processes in the pitch bearing were investigated.

2. Simulation of Contact Stress of Pitch Bearing Bolted Connection

2.1. Finite Element Modeling

The 3.4 MW pitch bearing system, as shown in Figure 1, was used as the basis for finite element numerical simulation. However, this full-scale model introduced challenges, such as high computational volume and difficulty in result convergence. To facilitate the processing and testing, the “blade-bearing inner ring” specimen model was scaled down, with chamfers, positioning holes, and other non-critical features removed to minimize computational complexity without affecting the accuracy of the results. The geometric dimensions of the simplified model after scaling are shown in Figure 2.

To investigate the stress distribution pattern on the contact surface under the effect of preloading force, a localized “blade-bearing inner race” connection specimen model was developed. This scaled-down model features symmetry in its bolted connections. To maintain the contact state while reducing computational demand, a 30° segment of the model was extracted, as shown in Figure 3a. This segment included a double-headed bolt, a blade, and the pitch-bearing inner race. The model dimensions of the experimental specimens for these components are detailed in Figure 3b.

2.2. Mesh Element Size Analysis

In the 3.4 MW wind turbine pitch bearing bolted connection model, the pitch-bearing material was 42CrMo4. Double-headed bolts were used to connect the blades to the pitch bearing. The material parameters are listed in

Table 1. Material properties.

Material	Modulus of Elasticity (GPa)	Poisson’s Ratio	Yield Strength (MPa)	Ultimate Strength (MPa)
Bearing inner ring	210	0.3	930	1080
Blade	72	0.26	—	1173
Bolt	206	0.3	720	1080

. In ANSYS 2022^® Workbench, mesh quality significantly affected the computational load and the accuracy of numerical simulations. In this study, mesh independence was validated to minimize errors caused by mesh quality. Quadratic hexahedral elements were used in the model to achieve higher precision. The mesh size of the inner ring of the bearing, double-headed bolts, and nuts was 1 mm. The blades’ mesh size was set to 2 mm, as shown in Figure 4. The total number of mesh elements was 65,731, with 256,331 nodes. The average mesh quality parameter exceeded 0.8.

2.3. Bolted Connection Contact Settings

The bolt specimens connection model includes four contact pairs, as shown in Figure 5. The A-A contact pair between the blade specimen and the inner ring specimen of the bearing is the focus, where the contact surface stress distribution is extracted. Therefore, the frictional contact was set according to the working conditions, and the friction coefficient was set to 0.2. The B-B contact pair is the contact between the nut and the surface of the inner ring specimen of the bearing. The C-C and D-D contact pairs were thread contacts. The real contact models used for B-B, C-C, and D-D contact pairs were calculated and analyzed using the augmented Lagrange method.

2.4. Boundary Load Condition

To simulate the experimental constraints, fixed boundary conditions were applied at both ends of the inner ring, and the preload F₀ and radial force F_r are shown in Figure 6. Torque ranging from 30 to 60 N·m was applied to the bolt center in four steps. The relationship between the torque and preload is described by Equation (1) [21], and it is shown in

Table 2. The relationship between preload and torque.

T (N·m)	F0 (N)
5	2272.7
10	4545.5
20	9090.9
30	13,636.4
40	18,181.8
50	22,727.3
60	27,272.7

.

$$T=K{F}_{0}d$$

(1)

where T represents torque; F₀ represents the bolt preload; K represents the tightening torque coefficient; and d represents the nominal diameter.

2.5. Contact Stress Analysis

Finite element analysis provides critical insights into stress distribution, deformation, and strain, offering solutions to engineering problems that theoretical calculations alone cannot address. For example, equivalent stress distribution contour maps can assess the location of the maximum stress (dangerous point) of the model under external loads. By comparing these stresses with the material’s yield strength and tensile strength, the structural safety under operating loads can be assessed. Additionally, structural design can be optimized by analyzing stress concentration areas and deformation results. However, the accuracy of these calculations should not solely rely on software analysis. Instead, it must be validated using foundational knowledge, fundamental concepts, and engineering experience within the relevant industry.

In this study, the contact stress distribution was analyzed under preload. According to Equation (1), the assembly torque values were 30, 40, 50, and 60 N·m, corresponding to preload values of 13,636.4, 18,181.8, 22,727.3, and 27,272.7 N [21]. The maximum contact stress values were 118.84 MPa, 175.86 MPa, 250.05 MPa, and 296.75 MPa, as shown in Figure 7. The maximum contact stress occurred at the bolt hole location. The stress distribution about the bolt hole was symmetrical, decreasing outward in a circular pattern.

A path was established from the bolt center to the bearing inner ring edge, as shown in Figure 8, to extract the contact stress distribution along this path and investigate the effect of preload on the contact area (Figure 9). The results showed that the area of influence with a higher contact stress was approximately 1.5 d (where d represents the diameter of the bolt hole), and the contact stress rapidly decreased within this range. Beyond 1.5 d, the contact stress was less affected by the preload and was considered negligible at 2.5 d. The curves further demonstrate that the preload magnitude affects only the magnitude of the contact stress and not the area of influence of the contact stress. These findings provide a reference for designing the number of bolts in sealing devices.

As shown in Figure 6, the radial forces of 500 N, 1000 N, 1500 N, and 2000 N were respectively applied to the blade to analyze the variation in contact stress. The contours of contact stress are shown in Figure 10. As the radial load increased, the contact stress also increased, while the affected area gradually decreased in the direction of the applied radial force. The radial force tends to cause separation on one side of the contact surface. When the external load was excessive, the position of the maximum contact stress moved from the center to the edge. Increasing the preload caused the bolt’s affected area to shift outward slowly. Therefore, effective bolt preload is essential for maintaining the overall integrity of the assembly.

The contact stress distribution was extracted under a preload of 60 N·m using a bolt and by changing the diameter of the connected member’s through-hole to 11 mm and 12 mm, as shown in Figure 11. It was observed that the maximum contact stress decreased as the bolt-hole diameter increased. To ensure proper bolt installation, reducing the diameter of the connected member’s through-hole increased the affected area of the bolted connection, thereby improving its resistance to external loads.

3. Experimental Study of Contact Stress Distribution for Bolt Specimens Based on Thin-Film Pressure Sensors

Numerical simulation provides an ideal distribution of the contact surface stress. However, practical engineering often necessitates direct measurement to address the real-world stress distribution on joint surfaces. This is particularly relevant for bolt connections, where complex working conditions demand uniform stress distribution during installation to prevent uneven load sharing. Uneven stress exacerbates load deviation and contributes to the fatigue failure of pitch bearings over time. To address this, this study employed thin-film pressure sensors to directly test contact stress distribution.

3.1. Experimental Principle

The thin-film pressure sensor used in this study is shown in Figure 12. It consists of two thin-film polyester fiber substrates with a conductive layer inserted between the substrates. The conductive layers intersect to form a sensing point. Typically, each thin-film pressure sensor has more than 2000 sensing points.

The testing circuit can control the scanning sequence, frequency, and sensitivity adjustment and optimize the matrix film pressure sensor. Each sensing point in the film pressure sensor can be considered a variable resistor. When the resistance reached its maximum, no external force was applied, and the resistance was inversely proportional to the external force.

3.2. Experimental System

The I-Scan system was used to directly test the distribution of contact surface stress. It utilized a thin and flexible film pressure sensor to accurately measure and analyze the static and dynamic stress distributions of the contact surface, as shown in Figure 13. The system comprises three parts: a thin-film pressure sensor, a data acquisition device, and software. The thin-film pressure sensor converted the obtained resistance signal into data, which were then transmitted to the data acquisition device through a data cable and finally analyzed by software to obtain the stress distribution contour. The stress magnitudes and distribution patterns were observed using a stress distribution contour.

Thin-film pressure sensors have over 200 different specifications according to their size, shape, resolution, and measurement range. For this study, the 6220-type thin-film pressure sensor was chosen to suit the blade bolt connection and bearing inner ring structure, as shown in Figure 14. The basic parameters are listed in

Table 3. Basic parameters of the thin-film pressure sensor.

L (mm)	W (mm)	l (mm)	d (mm)	D (mm)	SW (mm)	RW (mm)	RS (mm)	SA (deg)	Sensing Point	Pressure Range (kPa)
254	76.6	189.8	10	50.8	0.5	0.3	0.6	6.9	1235	0~226,850

. A sector range of 55° in the figure was used to lay the signal transmission circuit, and there were no sensing points in this part.

3.3. Experimental Procedure

The experimental specimens were manufactured according to the geometric dimensions in Figure 3. The thin-film pressure sensors were calibrated using a tensile testing machine, as shown in Figure 15. The sensors were placed between two fixtures, with a square test piece positioned on top. Load F was input into the calibration software to establish the correspondence between the load and the test results of the thin-film pressure sensor.

The thin-film pressure sensor was embedded between the blade and the inner ring of the bearing by inserting an M10 bolt through the sensor, connecting the blade and inner ring of the bearing, as shown in Figure 16. A torque wrench was used to apply 30 N·m, 40 N·m, 50 N·m, and 60 N·m of torque to the nuts, respectively, and the data were collected using a data acquisition instrument under different preloads.

3.4. Analysis of Experimental Results

The extracted test results under different preloads were compared with the simulation stress results, as shown in Figure 17. The left and right contours show the simulation and test results, respectively. When the preload was 13,636.4 N, the maximum value of the simulation result was 118.84 MPa, and the maximum value of the test result was 107.5 MPa, with a difference of 9.54%. When the preload was 18,181.8 N, the difference was 18.12%. When the preload was 22,727.3 N, the difference was 24.42%. When the preload was 27,272.7 N, the difference was 27.89%. With an increase in the preload, the difference increased. However, the distribution and trend of contact stress in experiments and simulations are almost consistent. This value discrepancy is attributed to factors such as the nonlinear relationship between the force and stress of the thin-film pressure sensor, contact surface machining differences, and human operation differences during tightening. Additionally, the idealization of simulation results should also be considered, and it should be recognized that the test results truly reflect the contact stress distribution under preload. Both experimental and simulation results indicated that the maximum stress occurred at the bolt hole’s inner ring. Stress values in the affected area decreased by more than 60% within a range of 1.5 d (where d represents the bolt-hole diameter). Beyond 2.5 d, the contact stress was negligible. From the experimental results, it can be concluded that the stress results changed with increased preload. Still, the stress distribution range remained unchanged, which is consistent with the conclusion drawn in the previous paragraph.

4. Experimental Study of Stress Distribution in Bolt Assembly

Currently, the stress distribution of bolted joints primarily relies on numerical simulations and theoretical calculations. However, in practical engineering, manufacturing processes can alter the surface contact of the joint, leading to changes in the contact stress distribution. During the tightening process of the pitch-bearing bolted joint, the contact stress distribution was more complex owing to the mutual influence of the bolts. Furthermore, the I-Scan system with multiple thin-film pressure sensors was used to study the contact stress distribution under different tightening processes for bolt assembly, and an effective bolt-tightening process that can be applied in practical engineering was obtained.

4.1. Experimental System Construction

The testing principle and system used for the bolt group stress distribution test were consistent with those described in the previous section. However, owing to the large size of the real model of the pitch bearing, a scaled-down bolt group test model was established to x as shown in Figure 18. Eight M10 bolts were used to connect the two disk components with an outer diameter of 300 mm and an inner diameter of 240 mm, which can be regarded as a connection structure between the inner and outer rings of the bearing.

At positions 1, 3, 5, and 7 (Figure 19), thin-film pressure sensors were embedded to study the stress distribution status of the bolt group by tightening the bolts using a torque wrench. Prior to the experiment, each of the four thin-film pressure sensors was calibrated. Then, the No.1 thin-film pressure sensor was connected to a data acquisition system, which was connected to a computer. The eight bolts were tightened according to the bolt pre-tightening sequence, and the real-time data for bolt No. 1 were recorded. Finally, the data acquisition system was connected to bolts 3, 5, and 7 to record the static data of the three bolts.

4.2. Influence of Tightening Process on Contact Stress Distribution

During the tightening process of the bolt group [22], the bolts interacted with each other, and the preloading sequence changed the stress distribution pattern. Three tightening processes were studied, as shown in Figure 19: sequential tightening (bolts 1-2-3-4-5-6-7-8 tightened in order), alternate tightening (bolts 1-3-5-7-2-4-6-8 tightened in order), and diagonal tightening (bolts 1-5-2-6-3-7-4-8 tightened in order). The torque wrench was adjusted to 60 N·m, and the bolts were tightened sequentially. After each experiment, a new set of bolts was used to avoid changes in the preloading effect owing to the repeated use of bolts.

Figure 20 shows the resultant force measured by the No. 1 thin-film pressure sensor for the three tightening processes. The tested range of the thin-film pressure sensor reflects the connection area of the bolt, and the pretension status can be determined by the resultant force within the area. From the curve, it can be observed that when the tightening torque of the No. 1 bolt reached 60 N·m, the resultant forces of the bolt connection area under the three tightening processes were all around 20,000 N. The interactions among the other bolts affected the resultant force of bolt No. 1, which eventually stabilized, measuring 23,108.8 N for sequential tightening, 23,694.5 N for alternate tightening, and 23,785.3 N for diagonal tightening. Diagonal tightening generated the maximum resultant force in the bolt connection area after the completion of the tightening process.

Figure 21 shows the load values of bolts 1, 3, 5, and 7 tested under different tightening processes. Sequential tightening exhibited the greatest difference between maximum and minimum load values, while diagonal tightening produced the smallest difference. During sequential tightening, greater deformation occurred owing to uneven contact on one side of the joint. Diagonal tightening methods showed more uniform load distributions, which can achieve the best pre-tensioning effect.

The bolt assembly experimental results for the three tightening sequences are shown in

Table 4. Contour of stress for different tightening sequences.

Bolt Number	Sequential Tightening	Alternate Tightening	Diagonal Tightening
1
3
5
7

. The stress distribution of sequential tightening was affected by the axial deformation of the bearing’s outer ring, resulting in a bias load phenomenon in which the position of the maximum contact stress was shifted to one side. This could increase stress on the biased side under load, potentially reducing the bearing’s service life. While alternate tightening improved stress distribution, some unevenness remained. Diagonal tightening produced a more uniform stress distribution, verifying its advantages and providing data support for practical engineering applications.

5. Conclusions

(1)

This study utilized numerical simulation to calculate the contact stress distribution of bolted connections according to the pitch bearing and blade of wind turbines. Additionally, the experiments of contact stress for the bolt specimen and bolt assembly were respectively designed based on a thin-film pressure sensor that could obtain the stress distribution pattern on the contact surface.

(2)

The results were compared and analyzed for numerical simulations and experiments. The preload was positively correlated with the maximum contact stress. The contact stress was symmetrically distributed around the bolt hole and decreased radially in a circular pattern. The contact stress decreased rapidly within 1.5 d and became negligible beyond 2.5 d. The magnitude of the preload force affected the contact stress magnitude but not its distribution range, whereas radial load affected the contact stress area.

(3)

The effects of different tightening methods on the test model of the bolt assembly were studied according to the experimental results. The contact stress distribution of bolted assemblies was obtained. These findings validate the advantages of diagonal tightening and provide a reliable tightening process for bolted assemblies in engineering applications.