Wind-Induced Response and Fatigue Analysis of Corona Ring in Power Equipment

Abstract

With the increasingly significant impact of high-wind-load environments on power equipment, the wind stability of the corona ring has become a key issue to ensure the safe operation of power grids. The wind-induced vibration response and fatigue characteristics of the corona ring in power equipment under different wind speeds, wind direction angles and wind attack angles are systematically studied via wind tunnel tests and numerical simulation. The results show that the peak acceleration and displacement of the corona ring are positively correlated with the increase in wind speed, and the wind-induced response is the most significant under the condition of 0° wind direction angle and 5° wind attack angle. In the wind speed range of 5 m/s to 8 m/s, the corona ring is prone to vortex-induced vibration. Through fatigue analysis, it is determined that the vertical support rod and the welding position and the bolt connection of the support frame are the stress concentration areas. The research results reveal the key weak points of the corona ring and provide an important basis for optimization design and safety monitoring, and they are of great significance for improving the wind resistance of power equipment.

1. Introduction

With the increasing complexity of atmospheric environments, wind-induced vibration has become a critical factor affecting the mechanical safety of high-voltage (HV) power equipment. In particular, frequent moderate-to-strong winds, such as those prevalent in Western China, can induce severe structural issues—most notably the fatigue accumulation caused by vortex-induced vibration. The corona ring, which is designed primarily to control electric-field distribution around insulator terminals, is directly exposed to atmospheric wind and may experience vibration, deformation, and fatigue under long-term or extreme wind conditions. This issue is particularly pronounced for bushing corona rings used in substations. Unlike rings mounted on flexible transmission-line insulator strings, these components are typically rigidly fastened to the metal terminals of stiff porcelain or composite bushings via bolted connections, as shown in Figure 1. Consequently, they operate under a fixed boundary condition, making them distinct bluff bodies subject to specific aerodynamic excitation modes rather than the large-amplitude galloping often seen in flexible conductor systems. Such mechanically induced issues may compromise the stability of the ring itself and further affect the reliability of the entire HV insulation system. The existing studies on corona rings have mainly focused on electrical-field optimization, such as geometric refinement and stress mitigation, and this has significantly improved insulation performance [1,2,3].

Additional works have examined discharge-induced mechanical effects, showing that ionic wind and space-charge forces can contribute to vibration in HV conductors [4,5]. While these efforts provide an essential understanding of electrostatic behavior, research on the wind-induced dynamic performance of corona rings remains limited. Current optimization methods still emphasize electric-field control rather than aerodynamic or structural responses [6,7,8,9,10]. In contrast, extensive studies on transmission-line components have demonstrated that conductors, insulator strings, and accessories are highly sensitive to wind-induced excitation. Field monitoring and vibration analyses indicate that wind speed, turbulence, and damping strongly affect vibration amplitude and fatigue accumulation in overhead systems. Studies on structural dynamics have further shown that wind-induced responses of transmission components depend on natural frequencies, structural modes, and flow–structure interactions [11,12]. Numerical investigations on suspension insulator swing angles confirm significant aerodynamic coupling under high-wind conditions [13].

Wind-loading theories and aerodynamic models provide fundamental tools for analyzing exposed components and remain widely applied in evaluating mechanical safety under fluctuating wind fields [14]. Nonlinear vibration studies also demonstrate that vortex-induced vibration (VIV) can be notable in slender bluff-body structures, and its amplitude is sensitive to geometry and damping characteristics [15]. Research on bluff-body aerodynamics further reveals that geometric modifications can effectively influence vortex shedding and alter fluctuating forces [16,17,18]. Given the toroidal and axisymmetric nature of corona rings, these aerodynamic principles are directly relevant to understanding their potential wind-induced vibration behavior.

Although these studies have provided valuable insights into the wind performance of electrical equipment, few have focused specifically on corona rings. The current research tends to concentrate on local stress–strain distribution, with insufficient attention paid to the overall vibration characteristics, wind stability, and fatigue behavior of corona rings. However, despite the extensive research on the aerodynamic instability of transmission lines, a critical knowledge gap remains regarding the wind-induced dynamic behavior of corona rings used in substation equipment, such as bushings.

Unlike flexible conductors or insulator strings that are susceptible to galloping, bushing corona rings are rigidly attached to the bushing terminals. However, simulating the fully coupled vibration of the entire bushing-ring system in a wind tunnel is challenging due to scale limitations. Therefore, this study systematically investigates the wind-induced response and fatigue characteristics of a 330 kV corona ring body through full-scale wind tunnel experiments and numerical simulations. The primary contributions of this work include explicitly quantifying the acceleration and displacement responses under varying wind speeds and attack angles, identifying the critical wind speed range of 5–8 m/s that triggers resonant VIV.

Additionally, fatigue analysis is conducted under 10⁵ cycles of horizontal wind loading to identify key fatigue parameters and weak regions. The remainder of this paper is organized as follows: Section 2 details the experimental setup and sensor arrangement; Section 3 analyzes the experimental results and discussion regarding acceleration and displacement responses; Section 4 presents the numerical fatigue analysis and identifies potential failure modes; and Section 5 summarizes the key conclusions and engineering implications. The findings provide both experimental and theoretical support for the optimization design and safety monitoring of corona rings.

2. Wind Tunnel Experiments

2.1. Test Equipment and Models

The wind tunnel tests were carried out in the CSU-WT4 open-circuit wind tunnel at Central South University, as shown in Figure 2a. The wind tunnel test section is 15 m in length, 2.2 m in width, and 2.0 m in height. The flow velocity can be continuously adjusted in the range of 0–35 m/s, and the turbulence intensity is less than 1%. As shown in Figure 2b, the experimental data were recorded using a Donghua dynamic signal acquisition and analysis system equipped with independent 32-bit A/D converters for each channel. The system allows simultaneous acquisition of stress, strain, and acceleration signals. A Cobra probe (Turbulent Flow Instrumentation, Australia) was employed to measure the real-time wind velocity in the test section. Laser displacement sensors (Keyence, Osaka, Japan) were used to record the displacement of the corona ring, while piezoelectric accelerometers (model 1A803E, Donghua, Hangzhou, China) were used to measure vibration acceleration. The laser displacement sensors were mounted on rigid brackets to monitor horizontal and vertical displacements of the corona ring, and the accelerometers were firmly bonded to the surface of the corona ring at selected measurement positions to capture local acceleration responses.

The test model was a 1:1 full-scale 330 kV bushing corona ring provided by Xi’an XD High Voltage Switchgear Co., Ltd. (Xi’an, China). The ring was fabricated from a lightweight aluminum alloy. As shown in Figure 3a, the corona ring is a double-layer circular structure with an outer diameter of 600 mm, an inner diameter of 400 mm, and a wall thickness of 8 mm. The upper and lower rings are connected by four hollow vertical supporting rods, each 200 mm long and 8 mm thick. A longitudinal supporting plate is welded 35 mm above the lower end of each rod, allowing the ring to be bolted securely to the support frame. The support frame was specially designed for this experiment according to the geometric constraints of the wind tunnel.

Ideally, the experiment would utilize a full-scale bushing to support the corona ring. However, due to the geometric constraints of the wind tunnel test section (with a height limit of 2.0 m), employing a full-height bushing (typically exceeding several meters) was not feasible. Consequently, a simplified rigid support frame was designed, as shown in Figure 3b. This frame utilizes shorter, high-stiffness clamping brackets to simulate the fixed boundary condition found at the bolted interface between the ring and the bushing terminal. While this setup does not reproduce the flexibility of the bushing column, it accurately replicates the clamped constraint at the ring’s root. This design choice effectively decouples the ring’s vibration from the support structure, ensuring that the measured response reflects the aerodynamic instability of the corona ring geometry itself. As shown in Figure 3b, the frame consists of vertical rods with a total height of 1300 mm. This height was specifically selected based on the wind tunnel test-section dimensions (2.2 m × 2.0 m) to position the corona ring in the central core of the uniform airflow, thereby minimizing boundary-layer interference from the tunnel floor. A circular plate at the top connects to the corona ring via bolts and can rotate around its central axis, enabling the adjustment of the attack angle. The base of the support frame was bolted rigidly to the wind tunnel’s rotary turntable. To change the horizontal wind direction angle (e.g., from 0° to 90°), the entire assembly was rotated at the base by the turntable.

To ensure that the wind tunnel test accurately replicates the dynamic response characteristics of the corona ring support structure within the flow field, the design of the experimental model strictly adheres to the theory of aeroelastic similarity. Based on the Cauchy number similarity criterion, the ratio of fluid inertial forces to elastic restoring forces is maintained at a consistent level between the model and the prototype. In consideration of the discrepancies between the experimental and prototype support struts, as well as the non-linear stiffness variations induced by geometric scaling, a stiffness equivalence principle is adopted for the design of the support strut in this study. The governing similarity laws, the calculation of bending stiffness for both the prototype and the model, and the formulas for verifying design deviation are expressed as follows:

$${(EI)}_s={\displaystyle \frac{{(EI)}_r}{{\lambda }_L^4{\lambda }_V^2}}$$

(1)

$${(EI)}_r=E_r{\displaystyle \frac{\pi (D_r^4-d_r^4)}{64}}$$

(2)

$${(EI)}_t=E_t{\displaystyle \frac{\pi (D_t^4-d_t^4)}{64}}$$

(3)

$$\delta =\left|{\displaystyle \frac{{(EI)}_t-{(EI)}_s}{{(EI)}_s}}\right|\times 100\%$$

(4)

where (EI)_s denotes the theoretical bending stiffness required for the model to satisfy similarity laws; (EI)_r represents the bending stiffness of the actual support strut; (EI)_t is the bending stiffness of the test model support strut; λ_L is the geometric scale factor with a value of 4; λ_V is the wind speed scale factor set to 1; E_r and E_t denote the Young’s moduli of the high-strength porcelain prototype and the Q235 steel model, taking values of 80 GPa and 206 GPa, respectively; D_r and d_r represent the outer and inner diameters of the actual support strut, taking standard values of 400 mm and 340 mm; D_t and d_t correspond to the outer and inner diameters of the test support strut, set as 100 mm and 95 mm, respectively; and δ signifies the relative deviation of the equivalent stiffness design for the test support strut. By substituting the aforementioned parameters into Equation (1) through to Equation (4), the relative deviation δ of the designed model’s stiffness is below the engineering allowable limit of 5%, thereby fully satisfying the requirements for the aeroelastic wind tunnel test.

Furthermore, the lock-type counterweights applied at the base provided a strictly fixed boundary condition (clamped support), effectively eliminating base rocking or sliding. Consequently, the acceleration and displacement responses observed in this study are primarily attributed to the intrinsic aeroelastic behavior of the corona ring structure itself, rather than the global vibration of the supporting frame. This setup ensures that the identified stress concentration points and fatigue characteristics are representative of the ring’s actual design performance under wind loads.

Regarding the support element, it is essential to note that a real bushing insulator comprises a load-bearing core wrapped in non-structural insulation material. The structural stiffness is governed by the core, not the external insulation [19]. Therefore, the experimental support rod was designed to represent this internal load-bearing structure. The external insulation layer was omitted in the physical model. This simplification is mechanically valid because the insulation material contributes negligible stiffness to the boundary condition. Additionally, the use of a rigid support rod minimizes the potential for the support structure’s own vibration to interfere with the corona ring, thereby isolating the wind-induced response of the ring body. Furthermore, removing the insulation layer eliminates potential aerodynamic damping effects from the sheds, yielding a conservative assessment of the vibration amplitude.

2.2. Test Methods

The layout of the corona ring model in the wind tunnel is illustrated in Figure 4. The model was bolted to the support frame, and the frame was fixed to the wind tunnel platform using bolts. To ensure stability and to simulate real operational conditions, the base of the support was weighted using lock-type counterweights. Accelerometers were installed on both the upper and lower rings to monitor the acceleration response at different wind speeds. Laser displacement sensors were arranged above, behind, and on the side of the corona ring to measure vertical and horizontal displacements. All sensors were connected to the data acquisition system for real-time monitoring and storage of the measured signals. The base of the support frame was rigidly bolted to the rotary turntable of the wind tunnel. To vary the horizontal wind direction angle (e.g., from 0° to 90°), the entire assembly was rotated at the base by the turntable. The tilting element positioned along the height of the corona ring was specifically designed to adjust the vertical wind attack angle (β), while ensuring that the ring center remained within the uniform flow region of the test section. In addition, these auxiliary brackets used solely for sensor mounting were structurally independent and were anchored directly to the wind tunnel floor. They were physically separated from the corona ring and the support frame, ensuring that they introduced no additional mass, stiffness, or mechanical damping to the vibrating system.

To ensure the fidelity of the aerodynamic data, the potential interference from the support structure and auxiliary equipment was assessed. The blockage ratio was calculated based on the maximum projected frontal area of the model and the support frame relative to the wind tunnel cross-sectional area. Considering the toroidal geometry of the corona ring and the slender profile of the support rods, the maximum projected area was estimated to be approximately 0.19 m². Consequently, the calculated blockage ratio is below 5%, which meets the standard requirements.

Regarding the auxiliary structure, the vertical support rods were designed with a circular cross-section to minimize wake turbulence. Furthermore, all signal transmission cables from the accelerometers were routed along the leeward side of the vertical rods. These cables were secured with aerodynamic tape to prevent flow separation or cable-induced vibration. Therefore, the aerodynamic field surrounding the corona ring was maintained undisturbed, and the measured response is considered free from significant auxiliary interference.

2.3. Operating Conditions

To rigorously define the experimental scope and ensure the validity of the results, the test conditions were established based on a statistical meteorological analysis of typical installation sites. Specifically, a field investigation of 330 kV substations in representative cities in western China (e.g., Xining and Yushu) analyzed the annual maximum sustained wind speeds over the past 20 years.

As illustrated in Figure 5, the historical data indicates that the maximum sustained wind speeds in these regions generally remained below 15 m/s. Notably, for approximately half of the recorded years (10 years), the annual maximum wind speeds were concentrated below 8 m/s. This meteorological pattern provided critical guidance for the experimental design: the selected test range of 5 to 18 m/s was chosen to not only encompass the realistic maximum extreme wind conditions (providing a conservative margin above the 15 m/s historical peak), but also to fully cover the frequent low-to-moderate wind speed regime where critical VIV phenomena are most likely to occur.

Consequently, a structured experimental design was implemented where the independent variables included the wind speed, the horizontal wind direction angle (α), and the vertical wind attack angle (β), while the dependent variables were defined as the vibration acceleration and displacement responses of the corona ring. To facilitate reproducibility, the schematic diagrams for different operating conditions were designed as illustrated in Figure 6. Specifically, α refers to the azimuth of the incoming flow in the horizontal plane relative to the support frame, where 0° parallels the side plates of the U-shaped bracket and 90° corresponds to the flow perpendicular to the bracket plane. The wind attack angle β represents the vertical inclination of the wind vector relative to the horizontal plane, with positive values denoting updrafts and negative values denoting downdrafts.

Based on this framework, a series of representative test cases were executed covering wind speeds from 5 to 18 m/s, three wind directions (0°, 45°, 90°), and three attack angles (−5°, 0°, +5°), as detailed in

Table 1. Experimental conditions.

Wind Direction Angle/α	Wind Attack Angle/β	Test Wind Speed
0°	−5°	5 m/s–18 m/s
45°	0°
90°	5°

. For each test condition, a stabilization period of 30 s was applied to ensure steady flow, followed by a 60 s data acquisition period at a sampling frequency of 1000 Hz. The measured acceleration and displacement responses presented stable periodic characteristics under the same wind conditions. Furthermore, the high consistency between the experimental modal parameters and the subsequent numerical results further validates the reliability of the measurements.

3. Results and Discussion

3.1. Acceleration Response

Figure 7 presents the time history of the acceleration response of the corona ring under the conditions of a wind direction angle of 0°, an attack angle of 0°, and a wind speed of 18 m/s. The acceleration variation exhibits a clear periodic pattern. During the 120 s sampling period, the acceleration amplitude of the upper ring was significantly larger than that of the lower ring, with peak accelerations of 5.1825 m/s² and 3.8926 m/s².

The variation in peak acceleration with wind speed under an attack angle of 0° is shown in Figure 8. Both the upper and lower rings exhibited a positive correlation between peak acceleration and wind speed, indicating that higher wind speeds result in stronger wind-induced vibration responses. When comparing different wind direction angles, the maximum acceleration occurred at 0°, followed by 90° and 45°. This phenomenon can be attributed to the structural geometry of the corona ring. At a 0° wind direction angle, the four vertical supporting rods overlap along the flow direction, and the wind acts perpendicular to the smallest projected area of the supporting frame, resulting in the lowest aerodynamic resistance, and consequently, the weakest wind stability. As the wind direction angle increased to 45° and 90°, the effective windward area of the structure was enlarged, leading to enhanced aerodynamic stability.

In addition, the peak acceleration was found to be positively correlated with the wind attack angle. As the attack angle increased from −5° to +5°, the peak acceleration of the corona ring increased gradually. As shown in

Table 2. Peak acceleration of the corona ring at a wind speed of 18 m/s.

Structural Component	Attack Angle (°)	0° Wind Dir. (m/s2)	45° Wind Dir. (m/s2)	90° Wind Dir. (m/s2)
Upper ring	−5	4.3019	3.8035	4.1615
	0	5.1825	4.4083	4.8472
	+5	6.2178	5.2973	5.6474
Lower ring	−5	3.1398	2.4892	2.8351
	0	3.8926	3.2172	3.6945
	+5	4.5184	3.6875	4.0301

, under a wind direction angle of 0° and a wind speed of 18 m/s, the peak accelerations of the upper ring were 4.3019, 5.1825, and 6.2178 m/s², corresponding to attack angles of −5°, 0°, and +5°, respectively. The corresponding peak accelerations of the lower ring were 3.1398, 3.8926, and 4.5184 m/s². The results indicate that the upper ring is more sensitive to variations in attack angle, while the lower ring, due to its proximity to the support frame, exhibits relatively smaller fluctuations.

3.2. Displacement Response

The displacement response of the corona ring under different wind conditions was analyzed to further investigate its deformation characteristics. Figure 9 shows the time–history curves of displacement at a wind speed of 18 m/s, a wind direction angle of 0°, and an attack angle of 0°. Figure 9a represents the vertical displacement of the upper ring, while Figure 9b,c correspond to the along-wind displacements of the upper and lower rings, respectively. The displacement response exhibits a distinct periodic variation, consistent with the acceleration response. During the 120 s measurement period, the maximum along-wind displacement of the upper ring reached 0.5673 mm, while that of the lower ring was 0.4636 mm. The maximum vertical displacement of the upper ring was 0.2944 mm.

The variation in the peak displacement of the corona ring with wind speed under different wind direction angles is shown in Figure 10, Figure 11 and Figure 12.

At a wind direction angle of 0° (Figure 10), the displacement first increases, then decreases, and rises again with increasing wind speed, showing a non-monotonic trend. This phenomenon indicates that vortex-induced vibration occurs when the wind speed ranges between 5 and 8 m/s. Within this range, the vertical displacement of the upper ring reaches approximately 0.1544 mm [20,21]. The along-wind displacement of both the upper and lower rings also exhibits periodic fluctuations, which correspond well with the acceleration response characteristics observed in the experiment.

At a wind direction angle of 45° (Figure 11), the overall displacement amplitude of the corona ring decreases significantly compared with that at 0°. The peak displacement curve becomes smoother, and the influence of vortex shedding is weakened. This is mainly because multiple vertical supporting rods are simultaneously subjected to the airflow at 45°, which enhances aerodynamic damping and suppresses large-amplitude oscillations. Consequently, the structure exhibits better aerodynamic stability under this condition.

When the wind direction angle increases to 90° (Figure 12), the displacement of the corona ring rises slightly compared with 45°, but it remains smaller than that at 0°. The overall deformation pattern is more stable, and no obvious resonance is observed. The results indicate that as the wind direction angle increases, the aerodynamic load acting on the corona ring becomes more uniformly distributed, thereby improving its vibration stability.

Under varying wind attack angles, the peak displacement of the corona ring exhibits a positive correlation with the attack angle, consistent with the variation pattern observed in the acceleration response. As the wind attack angle increases from −5° to +5°, both the along-wind and vertical peak displacements of the corona ring increase gradually. Among the tested conditions, the largest peak displacement occurs at a wind attack angle of −5°, followed by that at 0°, while the smallest displacement is observed at +5°. As summarized in

Table 3. Peak displacement of the corona ring under different attack angles at a wind speed of 18 m/s.

Structural Component	Displacement Direction	Attack Angle (°)	0° Wind Dir. (mm)	45° Wind Dir. (mm)	90° Wind Dir. (mm)
Upper ring	Along-wind	−5	0.4935	0.4328	0.4652
		0	0.5673	0.4453	0.4837
		+5	0.6481	0.5214	0.5944
Upper ring	Vertical	−5	0.2277	0.1862	0.2053
		0	0.2944	0.2371	0.2718
		+5	0.3843	0.3318	0.3572
Lower ring	Along-wind	−5	0.3941	0.2372	0.3195
		0	0.4636	0.3049	0.3626
		+5	0.5832	0.4591	0.5102

, when the wind direction angle is 0° and the incoming flow velocity is 18 m/s, the along-wind peak displacements of the lower ring are 0.3941 mm, 0.4636 mm, and 0.5832 mm for attack angles of −5°, 0°, and +5°, respectively. The corresponding along-wind peak displacements of the upper ring are 0.4935 mm, 0.5673 mm, and 0.6481 mm, while the vertical peak displacements of the upper ring are 0.2277 mm, 0.2944 mm, and 0.3843 mm. A comparison of these values reveals that the vertical displacement of the upper ring shows a noticeably larger amplitude variation, indicating that it is more sensitive to changes in the attack angle. This behavior aligns well with the acceleration response trend, suggesting that the upper ring experiences greater aerodynamic influence under varying inflow angles due to its more exposed position within the flow field.

3.3. Discussion on Wind-Induced Response of Corona Ring

From an engineering perspective, the practical implications of these experimental results are significant. Although the maximum measured displacement of 0.648 mm (at 18 m/s) accounts for less than 0.2% of the ring diameter and remains well within the allowable static deformation limits for maintaining insulation clearance, the associated acceleration and frequency characteristics may pose a potential fatigue risk.

Specifically, resonance is observed within the common wind speed range of 5–8 m/s, which corresponds to frequent daily meteorological conditions rather than extreme storm events. Such high-cycle accumulation suggests that the dominant failure mechanism is more likely to be fatigue cracking at stress concentration regions, particularly at the welded joints identified in the corona ring, rather than instantaneous structural failure or insulation breakdown caused by excessive deformation.

In real-world engineering applications, the wind direction acting on bushing corona rings is inherently random and time-varying. Furthermore, substations represent complex aerodynamic environments where corona rings are frequently subjected to wake effects from adjacent transmission towers, busbars, or other insulators. Consequently, the experimental finding that structural interference at a 0° wind angle induces the maximum vibration response provides a critical guideline for actual engineering design. This suggests that the anti-wind design of corona rings should prioritize these worst-case interference conditions rather than assuming an idealized laminar flow, ensuring structural safety even under complex upstream flow disturbances.

Therefore, from a practical engineering standpoint, strict quality control in the welding process and regular non-destructive inspection of the support roots are considered more effective mitigation measures than merely increasing the static stiffness of the structure.

4. Fatigue Numerical Simulation Analysis

4.1. Finite Element Model and Validation

To further evaluate the fatigue performance and wind resistance stability of the corona ring, a numerical fatigue analysis was conducted using the Static Structural module in ANSYS Workbench 2024 R1. A 3D finite element model (FEM) of the corona ring was established based on engineering drawings, as shown in Figure 13a. The corona ring was modeled as an aluminum alloy component using solid elements, while the support rods and connecting plates were fully represented to reflect the structural stiffness and load-transfer characteristics. To ensure calculation accuracy, the entire model was discretized using tetrahedral elements, and mesh refinement was applied at welded and bolted connection zones where stress concentrations were expected. The final model consisted of approximately 630,000 elements and 1.15 million nodes, as illustrated in Figure 13b. The mesh density and element quality met the convergence requirements of the static and fatigue analyses. To strictly ensure consistency with the wind tunnel experimental setup, the boundary conditions in the numerical model were defined as a fixed support at the bottom of the support frame, constraining all degrees of freedom to simulate the clamped counterweight installation.

The analysis simulated the working conditions corresponding to a horizontal incoming flow with a wind direction angle of 0°, an attack angle of 0°, and a wind speed of 18 m/s, which represent the most critical wind load observed in the wind tunnel tests. The wind pressure corresponding to the critical wind speed of 18 m/s was calculated using the Bernoulli equation, and was mapped as a uniform normal pressure onto the windward surfaces of the corona ring and the support rods. This pressure load was then applied cyclically to the static structural model to simulate the alternating stress state induced by the airflow. The fatigue evaluation was carried out under 10⁵ horizontal wind-load cycles to determine the maximum stress, fatigue safety factor, and potential failure regions. The results from the analysis provide a theoretical reference for the structural optimization and durability improvement of the corona ring.

Before conducting the fatigue assessment, the reliability of the numerical model was rigorously verified through quantitative cross-validation against the experimental results. Specifically, the natural frequencies extracted from the finite element modal analysis were directly compared with the peak frequencies identified from the wind tunnel acceleration spectra. The acceleration time history data of the upper and lower rings of the grading structure obtained from wind tunnel tests were utilized to verify the accuracy and reliability of the numerical simulation. The time-domain signals were transformed into the frequency domain using Fourier transform, and the corresponding frequency spectra were plotted, as shown in Figure 14. The peak-picking method was applied to analyze the spectra and identify the first three natural frequencies of the corona ring. By detecting prominent peaks in the spectra, the resonant frequencies corresponding to each mode of the corona ring were determined, thus revealing the primary dynamic characteristics of the structure.

Modal analysis of the numerical model was conducted to extract the modal parameters of the corona ring, as illustrated in Figure 15. It should be noted that the deformations in the figure are displayed with a magnified scale factor to visualize the vibration tendencies. Quantitatively, taking the first mode as an example, the maximum displacement occurs at the upper ring (lateral deformation) at a magnitude of approximately 0.3 mm. The first three mode shapes of the corona ring correspond to longitudinal vibration, lateral vibration, and torsion in the ring center, respectively. The agreement between the natural frequencies obtained from the simulation and those measured in the wind tunnel tests was evaluated using relative error. The frequencies measured from the upper and lower rings in the wind tunnel tests and the simulated frequencies are denoted as RE1 and RE2, respectively. The comparison results are summarized in

Table 4. Comparative verification of modes.

Mode	Upper-Ring Test (Hz)	Lower-Ring Test (Hz)	Numerical Simulation (Hz)	Relative Error RE1 (%)	Relative Error RE2 (%)
1st	9.06	9.02	8.81	2.83	2.38
2nd	10.28	10.25	9.87	4.15	3.85
3rd	27.59	27.52	26.92	2.48	2.23

. The relative errors between the first three frequencies of the upper ring in the wind tunnel tests and the simulation (RE1) are 2.83%, 4.15%, and 2.48%, respectively, while those of the lower ring (RE2) are 2.38%, 3.85%, and 2.23%. These results indicate that the relative errors for the first three frequencies between the simulation model and the wind tunnel tests are all within 5%, confirming the accuracy and reliability of the numerical model established in this study.

This high degree of consistency serves as a robust validation of the model’s mass and stiffness matrices, ensuring that the subsequent static and fatigue stress calculations are based on a physically accurate structural representation. In addition to this frequency agreement, the vibration mode shapes were also consistent, with both showing a dominant first-order bending motion. This high degree of consistency confirms that the boundary conditions and material properties defined in the simulation accurately reflect the physical reality. Since the numerical model represents a clean structure without sensors or cables, this close match confirms that the additional elements introduced in the experiment (such as accelerometers and signal cables) had a negligible effect on the corona ring’s mass and stiffness matrices. This validates that the experimental data accurately reflects the intrinsic behavior of the corona ring.

4.2. Fatigue Analysis Results

Based on the numerical fatigue analysis under a steady horizontal wind flow with a speed of 18 m/s and 10⁵ loading cycles, the total deformation, maximum principal stress, fatigue life, fatigue damage, and fatigue safety factor of the corona ring were obtained, as shown in Figure 16. The simulation results indicate that the maximum total deformation reached 6.732 mm, with a maximum vertical deformation of 3.275 mm, suggesting that the overall vibration in the corona ring is relatively small and mainly occurs along the wind direction. The deformation distribution reveals that the upper and lower rings exhibit consistent movement trends, and the structure experiences elastic vibration within a limited range under cyclic aerodynamic excitation. It can be observed that stress concentration mainly occurs at the joints between the vertical support rods and the upper and lower rings, as well as at the connection regions between the supporting frame and the ring body. The maximum principal stress reached 15.34 MPa, which is close to the allowable stress of the aluminum alloy material used in the structure. This implies that these connection zones are potential sites for the initiation of tensile cracking or local fatigue damage. This localization phenomenon is physically attributed to the inertial bending moment generated by the flapping motion of the ring, which acts effectively as a cantilever beam rooted at the support points. Furthermore, the welded joints at these locations introduce geometric discontinuities that create a significant stress concentration factor. Consequently, the dynamic loads that are distributed across the large surface area of the ring tube are effectively funneled into these small connection interfaces, resulting in local stress peaks that significantly exceed the nominal stress levels observed in the main tube body.

From the perspective of fatigue life, fatigue damage, and fatigue safety factor, it can be concluded that the welded joints between the vertical support rods and the rings, as well as the flattened regions of the support rods, are the most fatigue-sensitive locations. The supporting rods located on the windward side, which are directly exposed to cyclic aerodynamic loading, exhibit a smaller fatigue safety factor and a shorter fatigue life, suggesting a higher risk of fatigue failure in these components. This structural vulnerability is intrinsically governed by the mechanical interaction between the global vibration mode and the local geometric constraints. Specifically, as the corona ring undergoes the vertical flapping motion excited by the incoming flow, the support rods act as rigid anchor points that must counteract the intense inertial forces generated by the oscillating ring body. This dynamic load transfer mechanism compels the bending moments to accumulate precisely at the welded interfaces, leading to significant stress concentration. The fatigue risk in these regions is further compounded by the metallurgical characteristics of the welded structure, as the heat-affected zone typically possesses lower fatigue resistance and higher residual stress compared to the base aluminum material, making it the preferred initiation site for micro-cracks under cyclic loading. Furthermore, the analysis reveals a distinct aerodynamic asymmetry where the supporting rods located on the windward side exhibit a notably smaller fatigue safety factor and a shorter predicted life than their leeward counterparts. This heightened risk of failure is physically attributed to the superposition of aerodynamic loads; the windward components are directly exposed to the undisturbed incoming flow and must withstand the combined impact of the steady mean drag force and the fluctuating lift force. In contrast, the leeward rods benefit from an aerodynamic shielding effect known as wake shelter, which significantly attenuates the local wind velocity and reduces the amplitude of the cyclic stress they experience.

Consequently, it is concluded that the long-term structural integrity of the corona ring is defined not by the global strength of the tube body, but critically, by the local manufacturing quality of these connection nodes. Therefore, to enhance the operational reliability under complex wind environments, it is recommended to structurally reinforce the supporting elements on the windward side, and more importantly, to optimize the transition filet radius at welded joints while strictly enforcing post-weld heat treatment processes to mitigate residual stresses and improve the fatigue resistance of the heat-affected zones.

4.3. Fatigue Analysis Discussion

It is important to acknowledge the limitations of the fatigue analysis method employed in this study. The current simulation method is based on a static structural framework, where the wind load is applied as a constant pressure derived from the peak wind speed (18 m/s), rather than a fully coupled dynamic wind–structure interaction (FSI) model. Consequently, this approach simplifies certain dynamic characteristics, such as aerodynamic damping and the time-varying amplification effects caused by vortex shedding frequencies. This simplification implies that the predicted fatigue life represents a quasi-static estimation. In reality, resonance effects could lead to higher instantaneous stresses, potentially reducing the actual fatigue life compared to the simulation results. Furthermore, the primary focus of this study is the fatigue characteristics of the corona ring under a stiffness-equivalent fixed boundary condition. However, we acknowledge that in full-scale engineering applications, the height and flexibility of the support insulator may introduce coupled vibration effects. In our future research, we plan to employ FSI methodologies to specifically investigate the coupled aeroelastic characteristics of corona rings under varying support heights and wind speeds.

However, despite these limitations, the method remains highly valuable for engineering applications. By applying the worst-case aerodynamic load, the analysis successfully captures the maximum stress distribution patterns determined by the structure’s geometry. Therefore, the identification of critical failure zones—specifically the welded joints and support rod connections—is accurate and reliable. This provides a valid basis for structural optimization, even if the dynamic coupling effects are not explicitly modeled.

Regarding the variability of operating conditions, the numerical simulation focused on the standard reference condition (0° wind direction and 0° attack angle at 18 m/s), which corresponds to the nominal horizontal airflow acting on the installed equipment. The experimental results presented in Section 3 indicate that the structural response is sensitive to the attack angle. Specifically, under the extreme condition of a +5° attack angle, the peak acceleration increases by approximately 20.5% compared to the 0° case simulated in this study. Consequently, the stress results obtained from this simulation serve as a critical baseline. It is important to note that while the magnitude of stress may vary with wind conditions, the locations of stress concentration (i.e., the welded joints identified by the FEM) remain consistent, ensuring the validity of the failure analysis.

5. Conclusions

In this study, a combination of wind tunnel tests and numerical simulations was used to investigate the wind-induced response and fatigue performance of the corona ring in power equipment. The main conclusions are summarized as follows:

(1)

Wind tunnel tests indicate that the peak acceleration of the corona ring is positively correlated with wind speed, with the magnitude ranking as 0° > 90° > 45° across wind angles. Peak displacement follows an increase–decrease–increase trend, and vortex-induced vibration is prone to occur within the 5–8 m/s range.

(2)

Peak acceleration and displacement of the corona ring are positively correlated with the wind attack angle. Both values increase gradually as the attack angle rises from −5° to +5°. Specifically, at a 0° yaw angle and 18 m/s wind speed, compared to the −5° case, the peak acceleration at 0° and +5° attack angles increased by 20.5% and 44.5%, respectively, while the peak displacement increased by 15.0% and 31.3%, respectively.

(3)

Numerical verification using modal analysis demonstrates good agreement between the experimental and simulated natural frequencies, with relative errors below 5%. This confirms that the finite element model accurately captures the dynamic characteristics of the corona ring and can be reliably used for fatigue simulation.

(4)

Fatigue analysis and life evaluation reveal that stress is primarily concentrated at the bolted joints and the connections of vertical support rods, particularly at the welded joints and flattened regions. The maximum principal stress reaches 15.34 MPa, approaching the allowable limit of the aluminum alloy. Consequently, the windward-side rods, which are directly subjected to cyclic aerodynamic loading, exhibit lower safety factors and shorter fatigue lives, identifying them as the most critical regions prone to local fatigue failure.

Distinct from the existing literature, which predominantly focuses on electric-field optimization and geometric refinement, the primary novelty of this study lies in the explicit identification of the VIV wind speed range and the discovery of critical fatigue weak points at welded support connections. These findings provide a theoretical basis for the wind-resistant design and engineering maintenance of corona rings, offering actionable standards for structural reinforcement and non-destructive testing cycles.