1. Introduction
Based on statistical data from the
People’s Daily, in 2022 [
1], China’s wind-power generation capacity surpassed 10 trillion kilowatts for the first time, demonstrating an unstoppable trend in development. The issue of the oil temperature exceeding its limits in gearboxes has become one of the high-frequency faults in wind power generators. Xiang, et al. [
2]. conducted a fault analysis investigation on three wind farms, revealing that oil-temperature exceedance faults ranked in the top three among various failures. The monitoring and reliability assessment of wind-turbine gearboxes are currently becoming focal points of research [
3].
Due to the frequent occurrence of high-temperature faults, an increasing number of researchers are dedicating their efforts to studying the temperature field of wind-turbine gearboxes. Extensive research and analyses have been conducted by domestic and international scholars, such as Xu and Zhao, detailing the causes of and solutions to the high-temperature issues in wind-turbine gearboxes [
4,
5,
6]; however, these investigations focus on external factors affecting the gearbox temperature field. To enhance preventive measures and mitigate downtime failures caused by high temperatures, researchers have initiated an analysis of internal high-temperature faults in gearbox systems.
Huang, et al. proposed a fault-prediction method based on PCA and SPC-dynamic neural networks for online learning, allowing for the long-term online prediction of wind-turbine-gearbox oil temperature. However, relying solely on lubricating oil temperature for gearbox fault prediction poses the issue of potential failure omission [
7]. Gu, et al. introduced a novel approach for fault prediction in wind-turbine gearboxes by segmenting intervals, thereby overcoming the limitations of using a constant lubricating oil temperature as the warning threshold. However, the exclusive consideration of gearbox oil-temperature data during fault prediction [
8]. Jing, et al. proposed a method based on KECA-GRNN capable of conducting gearbox condition monitoring, fault prediction, and health assessment, enabling the early prediction of gearbox faults. However, this method only predicts gearbox oil temperature and bearing temperature [
9]. He. proposed a method based on the conditional convolutional autoencoder Gaussian mixture model (CCAE-GMM), which addresses the inaccuracies or missed alarms in fault information due to the limited number of sensor variables. This method achieves health assessment and fault prediction for gearbox temperature, power, and wind speed, and provides other information [
10].
Although the aforementioned methods enable fault prediction for wind-turbine-gearbox temperature fields, they overly rely on SCADA data, making them susceptible to errors from sensors and other devices themselves. Moreover, they encounter challenges related to high model instability and lack of interpretability.
Utilizing finite element analysis methods for analyzing gearbox temperature fields can help address the aforementioned shortcomings. Song Hai. employed this approach to individually analyze the temperature field of wind-turbine gearbox bearings [
11]. Liu [
12] conducted an investigation on the steady-state thermal performance of the gearbox. Deshpande [
13] utilized this method to predict the temperature of gears in oil-jet lubricated transmissions. In conclusion, the finite element method can accurately predict the temperature distribution of the gearbox. However, finite element modeling entails complexity, necessitates precise boundary conditions, requires significant computational resources, and is less suited for the comprehensive calculation of entire wind-turbine gearboxes.
The method that can simultaneously avoid the drawbacks of the two aforementioned approaches and accomplish the analysis of the temperature distribution in wind-turbine gearboxes is the thermal network approach. Based on internal heating and heat-transfer principles, this method enables the prediction of temperatures for all internal gearbox components while mitigating the risk of prediction errors due to data collection and component inaccuracies. Moreover, it demonstrates a low computational burden, swift processing speed, and robust applicability in forecasting temperatures for large structures such as wind-turbine gearboxes. Therefore, this study opted to employ the thermal network approach for research purposes. The thermal network approach has mature applications in areas such as helicopters [
14] and electric cars [
15]. X. Dong et al. [
2] first introduced this method to the structure of wind-turbine gearboxes, enabling the prediction of internal temperatures for 1.5 MW wind-turbine gearboxes. However, 1.5 MW wind-turbine gearboxes utilize a relatively simplistic spur-gear transmission method, and the thermal network model in their paper does not account for the impact of oil-spray lubrication on the gearbox temperature.
The aforementioned research on the temperature field of wind-turbine gearboxes primarily focuses on 1.5 MW wind power systems. However, with technological advancements, the application of 2 MW and larger, gigawatt-scale wind turbines is becoming more widespread. Moreover, the structures and stress factors of gigawatt-scale wind-turbine gearboxes are more intricate. Gigawatt-scale wind turbines utilize a combination of oil-spray lubrication and splash lubrication in their cooling and lubrication systems, which significantly impacts the gearbox temperature field. Nevertheless, research on temperature fields in gigawatt-scale wind power systems remains relatively scarce at present.
Thus, this paper innovatively establishes a thermal network model suitable for a 3 MW wind-turbine gearbox. In contrast to the 1.5 MW wind turbine, the gearbox of a 3 MW wind turbine employs a triple-stage transmission system, entirely characterized by helical gear transmissions capable of withstanding significant alternating loads, rendering them more structurally complex. Furthermore, the oil-spray system is incorporated into the thermal network model for the first time, resulting in steady-state nodal temperatures and enabling the prediction of gearbox temperatures under various high-temperature conditions. This thermal network model can be applied to gigawatt-scale (exceeding 2 MW) wind-turbine gearboxes with similar transmission structures and lubrication methods. However, it is essential to note that when critical components’ structures differ, corresponding calculation methods need adjustment (such as bearing selection and heat generation methods in the transmission system under different input load conditions). Additionally, this paper investigates the impact of the oil spray parameters on the gearbox steady-state temperatures, providing robust model support for the temperature prediction and design optimization of the cooling and lubrication systems.
5. Steady-State Temperature Calculation and Result Validation in the Gearbox
5.1. Programming Calculation and Results
Utilizing the SCADA data from a high-altitude wind farm of a certain enterprise, the steady-state oil temperature, air temperature inside the nacelle, and air temperature inside the gearbox, as well as the high-speed bearing temperature data, can be obtained. Taking the steady-state oil temperature and gearbox temperature during the high-temperature months of June to August as input values for six actual operating conditions, the conditions are detailed in
Table 6. Based on this, employing a first-order steady-state iterative method for solving the balance equation system (Equations (2)–(4)), the computed results are depicted in
Figure 6.
Analyzing the results from
Figure 6 reveals that high-temperature nodes are predominantly concentrated at the third-stage high-speed position. The temperature at nodes 35 to 48, corresponding to the third high-speed position, is on average 3.4 to 3.6 °C higher than the nodes of the other two stages of transmission. This is because the third-stage transmission is primarily responsible for acceleration, resulting in higher gear and bearing speeds, intensified friction, and, consequently, higher heat generation compared to other locations within the gearbox. The downwind bearing position in the high-speed stage (node 41) attains the highest rotational speeds, and its proximity to other heat-generating points in the third stage makes heat dissipation challenging. Consequently, this node experiences the highest temperature and is the most susceptible location to the occurrence of high-temperature faults. The high-temperature position in the first stage occurs at the meshing point of the planetary and sun gears (node 15), which endure significant input loads. Failure at this location incurs substantial replacement and maintenance costs.
Analyzing the overall temperature distribution, except for the external air node temperatures, other node temperatures stabilize between 50 and 70 °C. Furthermore, under various operating conditions, the temperature distribution trends remain consistent. High-temperature nodes act as heat sources, resulting in a trend where temperatures decrease to varying degrees from the heat source, following the heat propagation pattern. The temperatures predicted by the thermal network model in this paper conform to the flow patterns of heat propagation within the gearbox.
5.2. Comparative Validation of the Thermal Network Model’s Efficacy
To validate the efficacy of the thermal network model in predicting the temperature of the 3 MW wind-turbine gearbox, a comparison was made between the model’s output parameters and the actual steady-state operating parameters from the wind farm’s SCADA data. For validation, SCADA data from the high-temperature months of June, July, and August 2021 were selected. Each month, a stable operating day with continuous data points collected at 10 min intervals was chosen, resulting in a total of 312 data sets for comparison.
Due to the challenges in installing internal sensors in the gearbox, actual data included only output parameters such as the input-side bearing temperature, output-side bearing temperature, gearbox oil temperature, and ambient air temperature inside the nacelle. The gearbox oil temperature and nacelle air temperature were used as input values for the model, and the output-side bearing temperature served as the data for the validation and comparison.
Figure 7,
Figure 8 and
Figure 9 below illustrate the comparison results between the model’s predicted bearing temperature and the actual SCADA data for the output-side bearing temperature.
Comparing the aforementioned 312 sets of data, it is observed that the average error falls within the range of 1 to 4 °C. Furthermore, during periods of stable input temperatures, the average error narrows to 1 to 2 °C. However, when the input temperature undergoes significant changes, the error tends to increase, yet it remains below 4 °C at its maximum. At 11:39, as depicted in
Figure 8, the effective power of the turbine drops to 0. At this moment, the temperature deviation reaches its peak for the day, reaching 4 °C. Subsequently, the turbine begins to slowly decelerate, and the deviation stabilizes within the range of 0 to 2.2 °C.
Analysis of the potential error sources reveals two main aspects:
- (1)
Errors stemming from the node simplification: The thermal network model simplifies components like gear bearings into ideal nodes for computation. In practical scenarios, heat generation points in bearing positions may be at the contact points of rollers and other components, whereas the thermal network model treats the entire bearing node as a heat source.
- (2)
Errors arising from the lubrication system simplification: In actual lubrication processes, the lubricating oil flows out of the gearbox for secondary cooling. Moreover, the lubricating oil temperatures at different positions in the gearbox should be varied, and the oil-spray quantities should be adjusted in real time based on the gearbox temperature conditions. However, for computational efficiency, the thermal network model simplifies the lubricating oil temperature and spray parameters as ideal conditions.
Considering the above, the overall error is within a reasonable range, Furthermore, the refinement of the thermal network model at critical research positions can help reduce the aforementioned errors. The thermal network model proves effective in predicting the steady-state temperature of a large-megawatt wind-turbine gearbox in practical operations.
5.3. Finite Element Simulation Validation of the Thermal Network Model’s Efficacy
However, comparison with SCADA data can only validate the temperature predictions for the output shaft bearing at this particular node position. Thus, the study of the internal temperature distribution within the gearbox cannot be verified through comparison with SCADA data alone. Therefore, this paper employs finite element analysis to analyze the temperatures of the internal gearbox nodes, allowing for a comparative analysis with the results obtained from the thermal network model. This approach validates the effectiveness of temperature predictions for other internal nodes. Due to the extensive computational requirements and high-performance demands on computing resources, this study focuses solely on the simulation of the steady-state temperature field in the high-speed gear transmission area where temperatures are elevated.
The purpose of the simulation is to verify the consistency between the steady-state temperature field within the gearbox and the thermal network model. This encompasses the temperature distribution and magnitude during steady-state conditions. Given the omission of dynamic considerations for the rotational motion of gear engagement, the simulation uniformly distributes the heat generated by gear engagement as a heat flux on the gear surfaces. Additionally, it applies the theoretically calculated heat flux at the points of gear engagement. In the thermal network method, bearings are treated as nodes, simplifying the bearing model to a circular ring, with heat flux applied to the geometric body. Considering the heat exchange processes between the lubricating oil, gears, and bearings, convective heat transfer is applied to the outer surface of the bearing, gear engagement surfaces, and side surfaces, with numerical values based on theoretical calculations. Material definitions and parameters for the shaft, gears, and bearings were established, with the initial temperature set at the ambient temperature of 22 °C. The simulation was conducted for the steady-state temperature field under the operating conditions specified in
Table 6.
As depicted in
Figure 10, under various operating conditions, the highest internal temperatures occur at the gear meshing positions and the downwind bearing position of the high-speed stage (Point 2). Conversely, the lowest temperature manifests at the upwind bearing position of the low-speed stage (node 43).
Upon analyzing the results depicted in
Figure 10, it is observed that the average temperature at Point 2 exceeds that of the lower temperature positions by 10 °C. This temperature disparity suggests the following potential causes for the elevated temperatures: The high heat generation at the downwind bearing of the high-speed stage stems from the fact that the highest speed in the third-stage transmission resides at the output end. Additionally, the downwind bearing bears significant inclined gear meshing forces, resulting in heightened heat generation. Similarly, the temperature of the low-speed downwind bearing (Point 1) averages 4 to 5 °C higher than that of the upwind bearing. Furthermore, the heat generation points in the high-speed section are denser than those in the low-speed section, and heat transfers occur between these points, thereby elevating the temperature of the high-speed section above that of the low-speed section.
The observed temperature variation trend and distribution align with the results obtained from the thermal network model, validating its effectiveness in predicting the overall gearbox temperature. However, the simulated temperatures at each bearing location notably fall below the predicted values of the thermal network model, while the temperatures at the high-speed section nodes exceed the predicted values.
Table 7 below records the simulated temperatures of the downwind bearing of the high-speed stage (Point 1), the downwind bearing of the low-speed stage (Point 2), and the maximum and minimum temperatures of the third-stage transmission.
Analyzing the discrepancies between the simulation and the thermal network model reveals that in the thermal network model, the bearing is considered a singular node endowed with a heat source. However, the thermal resistance is computed based on the actual heat-transfer area of the bearing. In the finite element simulation, the heat source is uniformly applied to the entire bearing geometry through heat flux, and the convective heat transfer coefficient is assigned to all bearing outer surfaces based on theoretical calculations. This results in an average temperature at the bearing position that is lower than that of the thermal network model. Furthermore, the simulation does not account for the heat conduction between the housing and various components, leading to an increase in temperature at some nodes.
Setting the same boundary conditions as the thermal network model in the finite element simulation is challenging, making it difficult to precisely reflect the temperature at various nodes in the gearbox. However, the overall temperature distribution trend aligns with thermal equilibrium principles and corresponds with the results of the thermal network model. This effectively validates the efficacy of the thermal network model in predicting the temperature of the 3 MW wind-turbine gearbox.
5.4. Conclusion of Thermal Network Model Verification
Based on the temperature predictions for different operating conditions obtained from
Section 5.1, the analysis reveals that high-temperature nodes within the gearbox are concentrated in the third stage of the high-speed transmission section. Node 41 and node 15 are identified as the most susceptible locations to high-temperature faults within the gearbox. Therefore, in the actual process of optimizing gearbox structure and designing internal lubrication cooling systems, targeted improvements should be made based on the predictive results. Additionally, health monitoring devices should be installed at these node positions.
In
Section 5.2, by juxtaposing the numerical values of the output shaft bearing temperature extracted from the SCADA data of the 3 MW wind-turbine gearbox, the thermal network model’s accuracy in predicting node temperatures can be corroborated. Furthermore, the data analysis in
Section 5.2 indicates that to minimize predictive errors in this model, it is imperative to analyze the wind turbine when it has reached a stable operational state or is undergoing gradual changes.
In
Section 5.3, by conducting a thorough comparison with the steady-state temperature field simulation of the high-speed gear transmission using finite element analysis, the model’s effectiveness in predicting the overall temperature distribution is confirmed. Additionally, an analysis of the root causes of high temperatures in the nodes of the high-speed gear transmission section was performed.
In conclusion, the thermal network model presented in this study effectively predicts the temperature of the gearbox and accurately identifies the precise location of high-temperature faults within the gearbox. It serves to prevent high-temperature faults and contributes to reducing the associated cost losses.
6. Exploring the Influence of Oil Injection Parameters on the Steady-State Temperature Field
The 3 MW wind-turbine gearbox employs both oil-injection lubrication and splash lubrication methods, with the design of the oil-injection lubrication system playing a pivotal role in the overall temperature regulation of the gearbox. M. Shuai et al. [
23] conducted a study on the convective heat transfer effects of oil-injection lubrication on gears. L. Ruirui [
24] analyzed oil-injection lubrication in planetary gear transmissions through finite element simulation. L. Jiadong and F. Jin [
25] explored the impact of different oil-injection aperture sizes and lengths on lubrication effectiveness. These studies collectively underscore the significance of the oil-injection lubrication system in the gearbox. Therefore, in establishing the thermal network model, this paper considered the parameters of the oil-injection lubrication system. After validating the model’s effectiveness, this study investigated the influence of the oil injection aperture, injection velocity, and injection angle on the overall gearbox temperature field. The relevant results are presented in
Figure 11,
Figure 12 and
Figure 13.
To illustrate the impact of the oil injection system on the steady-state temperature field of the gearbox, we selected ten nodes significantly influenced by the oil injection parameters for observation. These ten nodes represent the positions directly subjected to oil-spray lubrication, or in close proximity to the oil spray. They exhibit the most significant temperature variations with changes in oil spray parameters, thereby reflecting the profound impact of oil spray parameters on node temperatures. Based on the results in
Figure 11,
Figure 12 and
Figure 13, the nozzle diameter and injection velocity in the oil injection system have a substantial impact on the gearbox temperature, especially at the gear meshing positions, where an increased nozzle diameter and injection velocity result in more pronounced cooling effects, while the injection angle has a relatively minor effect. When designing the overall oil-injection lubrication and cooling system, it is crucial to comprehensively consider these three factors. Introducing the designed boundary conditions into the thermal network model presented in this paper allows for the prediction of relevant results. This thermal network model provides theoretical support for the optimization and validation of the cooling and lubrication systems in 3 MW wind-turbine gearboxes, offering a convenient and efficient computational approach.