Wind power is a kind of important green energy. Thus, wind turbines have been widely utilized around the world. Wind turbines are composed of many important components. Among these components, the failure rate of the transmission system is relatively high in wind turbines. It is because the components are subjected to aerodynamic loads for a long time. In addition, its inertial load will result in fatigue fracture, wear and other problems. In this situation, wind turbines have to be repaired at a higher cost. Moreover, the traditional reliability methods are difficult to deal with the above challenges when performing the reliability analysis of the transmission system of wind turbines. To solve this problem, a stress-strength interference model based on performance degradation is introduced. Based on considering the strength degradation of each component, the improved Monte Carlo method simulation based on the Back Propagation neural network is used to obtain the curve of system reliability over time. Finally, the Miner linear cumulative damage theory and the Carten-Dolan cumulative damage theory method are used to calculate the cumulative damage and fatigue life of the gear transmission system.

With environmental pollution and energy shortages becoming more prominent, the development and utilization of new energy have become the focus of attention of all countries in the world. New energy will play a prominent role not only in improving the ecological environment and optimizing the energy structure, but also in promoting sustainable social and economic development. In addition to hydropower technology, wind power is the most mature, largest and most promising power generation method among new energy power generation technologies [

Among various new energy, wind energy has the advantages of huge reserves, no pollution, no damage, no need for transportation and wide distribution [

The failures of large-scale wind turbines are mainly concentrated in the gear transmission system [

Under the influence of external random loads, multiple parameters of the wind turbine gear transmission system tend to change over time [

The main research of this article is the dynamic reliability of planetary gear transmission systems. A stress-strength interference model based on performance degradation is introduced. Based on considering the strength degradation of each component, the improved Monte Carlo (MC) method simulation based on the Back Propagation (BP) neural network is used to obtain the curve of system reliability over time. Finally, using the Miner linear cumulative damage theory and the Carten-Dolan cumulative damage theory calculate the cumulative damage and fatigue life method of the gear transmission system.

Reliability reflects the changing law of product quality on the time scale. It is the ability to complete the corresponding functions within the specified time according to different purposes, requirements and occasions [

In the reliability calculation, interference analysis of random variables is required [

Stress refers to various physical coefficients that may cause components to fail. And strength is a performance index for components to resist corresponding stress.

For engineering equipment, it is usually not an independent system, but is composed of multiple systems. This article mainly analyzes the wind power gear transmission system, which is a critical component of the wind power unit. Due to the complicated working conditions and the difficulty of maintenance, its reliability problems have largely hindered its further development.

Regarding the wind turbine transmission system, planetary gear transmission is generally adopted. In terms of planetary gear transmission, planetary carrier input is generally selected. The planetary gear is mainly used to effectively share the load.

Combining relevant experience results, it can be found that in the process of analyzing the reliability of the system, it focuses on the analysis of the impact of key components [

The specific meaning of the unit number is:

1, 3, 5——contact fatigue unit of each component;

2, 4, 6——bending fatigue unit of each component;

7, 8——bending fatigue unit and contact fatigue unit of planetary gear;

9, 11, 13, 15——contact fatigue units of helical gears 1, 2, 3 and 4;

10, 12, 14, 16——bending fatigue units of helical gear 1, 2, 3 and 4.

Combined with the above diagram, the following equation can be derived:

The wind turbine transmission system includes the main shaft, speed-increasing gearbox, high-speed output shaft, braking equipment, coupling and other components. The wind turbine captures wind energy through the wind wheel. The transmission system transfers the kinetic energy to the generator and converts it into electrical energy. The transmission system is located on top of the wind turbine tower. The height above the ground is generally tens of meters or even higher. Under the action of the alternating load with unstable wind, the transmission chain will shake as a whole.

The gearbox using the planetary gear transmission structure has many advantages such as smooth and precise meshing, power splitting and improvement of system load sharing. In addition, the safety coefficient of transmission system can be improved by reducing the size of the gearbox, reducing the weight, increasing the transmission efficiency, increasing the transmission ratio and increasing the load-bearing capacity. It is because the slight deformation of the planetary central axis makes the internal structure elastically adjusted. The load distribution of each planetary gear tends to be more consistent, so that the internal meshing is reasonably applied. Moreover, the planetary wheel and parallel wheel structure improve the ability of the system to resist impact loads and reduce the impact of components processing and assembly errors on the transmission.

This article mainly analyzes the main fault types of gearboxes and gears. Gearbox generally uses gear pairs to efficiently transmit power. The core function is variable speed. In addition, the types of gearboxes mainly involve cylindrical gearboxes, combined gearboxes, etc. Relevant statistics show that gearbox failures account for 40%–50% of the total failures, which is a relatively high proportion in wind turbines. The assembly space is not large for a gearbox, but it must bear the impact load of changing directions and changing loads. In addition, due to its complex failure causes, maintenance is more difficult. Therefore, it needs to be studied, which is significant to the avoidance of fault problems.

Under the influence of external random loads, many parameters of the wind turbine gear transmission system tend to change over time [

The strength and stress change over time. When the strength of the product degrades over time, the interference area of the strength and stress will become larger over time. It reflects that the reliability of the product is gradually decreasing. Therefore, the strength

Product reliability is

According to

When using the time-related stress intensity interference model to solve the reliability of the product after working

When

Tooth surface contact stress can be calculated as follows [

The limit of tooth surface contact fatigue stress can be analyzed by the following equation:

Based on the analysis of relevant specifications, the mean value and coefficient of variation can be deduced as follows [

The mean value and coefficient of variation of

The tooth root bending fatigue stress can be calculated as follows:

The limit of bending fatigue stress can be analyzed by the following equation:

In addition, the mean value and coefficient of variation of this parameter can be calculated as follows [

The mean value of

Because the strength is gradually degraded under the action of long-term load, the dynamic reliability model of the component of the stress-strength interference model is:

After the MC method is used to carry out the simulation analysis, the K-S test can be carried out according to the requirements. Then it can be concluded that its strength obeys the normal distribution law. At the same time, the parameters corresponding to all components conform to the Weibull distribution characteristics as a whole. At this time, they can be converted to a normal distribution. In this section, an MC improvement based on the BP neural network (BP-MC) is used [

First, determine the equivalent stress

Use the MC method to calculate, only when N is large enough, the obtained result is reliable. Therefore, the obtained result needs to be checked. This section uses the standard deviation to determine. Suppose

If

Take the 1.5 MW wind turbine transmission system as an example.

The radius of the impeller is 26.8 m. Input shaft speed is 14.6 r/min, rated impeller torque is 1.25 × 10^{6} Nm, rated wind speed is 12 m/s, wind energy coefficient is 0.55, gear material is 20CrMnTi, cut-in wind speed is 4 m/s, cut-out wind speed is 20 m/s, sun gear tooth number is 27, planetary gear tooth number is 44, internal gear tooth number is 115, gear 1 tooth number is 103, gear 2 teeth number is 24, gear 3 teeth number is 99, gear 7 teeth number is 24, low-speed shaft modulus is 16, meshing angle is 23°; medium-speed shaft normal surface modulus is 12, helix angle is 10.5°, meshing angle is 21°; high-speed shaft normal surface modulus is 24, helix angle is 12.5, meshing angle is 21°, random wind speed is

Under time-varying load conditions, during the analysis of gears’ reliability, the focus is on the problems caused by pitting on the tooth surface. Refer to

Combining

For all structures, if there is no difference in the stress concentration coefficient and the load spectrum, their life will be the same. This method generally uses load statistical analysis to clarify the nominal stresses corresponding to all stressed parts. Then estimates the fatigue life in combination with related theories [

Usually, due to the lack of components of the same shape, the P-S-N curve is modified under uniaxial loading of similar materials to calculate the fatigue life of the component [

Clarify the stress dangerous parts;

Define the nominal stress in conjunction with related manuals to determine the stress concentration coefficient KT;

Query the P-S-N curve of the material. If there is a lack, it can be replaced by the P-S-N curve of similar materials;

Combining the fatigue damage accumulation theory, calculate the fatigue life of components.

The gear transmission system operates in a diverse environment. Because the gear transmission system is affected by random loads, the components tend to form alternating stresses, which leads to the accumulation of internal damage and fatigue failure of the components. In the fatigue reliability analysis of components, the statistical analysis of stress-time history uses the rain flow counting method [

The stress spectrum of each component is shown in

Because the random wind speed is constantly changing, the stress applied to each component also changes non-directionally. To clarify the fatigue life, not only can the P-S-N curve be used, but also the fatigue cumulative damage criterion can be used to carry out the analysis. The dynamic random stress of each gear pair of the transmission system is counted cyclically. Then the P-S-N curve of the transmission system component is obtained according to the fatigue performance of the material. Finally, use the Miner linear cumulative damage theory and Corten-Dolan cumulative damage theory to calculate the cumulative damage and fatigue life of the gears of the wind turbine gear transmission system under random wind loads. It is a reliable and effective fatigue life prediction method.

The gear material is 20GrMnTi, while the bearing material is high-strength bearing steel GCr15SiMnA. Assume that the wind turbine gear transmission system works 20 h a day. Combined with the rain flow calculation program, the number of cycles corresponding to the stress amplitude at each level should be clarified. At this time, the contact stress spectrum should be equivalent to the contact stress through the Goodman equation. Then the fatigue life equation will be used as the core. The total working time when the gear in the transmission system is damaged can be calculated as shown in

Working hours at the time of destruction _{c} |
||
---|---|---|

Miner | Corten-dolan | |

Sun gear and planetary gear | 26.5901 | 16.2199 |

Ring gear and planetary gear | 24.0324 | 14.1791 |

Gear 1 and gear 2 | 20.1963 | 11.9158 |

Gear 3 and gear 4 | 20.9978 | 12.5987 |

It can be found that with the continuous increase of input torque, the gear stress has further increased. The limit value of the contact stress is about 1000 MPa. However, it can be found in combination with the fatigue damage theory that because the speed of the planetary gear is relatively low, the corresponding contact damage of the high-speed gear is relatively large, and its useful life is relatively short. In addition, the fatigue life calculated by Carten-Dolan theory of each component is smaller than that of Miner theory, indicating that Carten-Dolan damage theory is more reliable than Miner theory.

This article mainly analyzes and evaluates the dynamic reliability of the planetary gear transmission system. Based on the strength degradation of each component, a stress-strength interference model based on performance degradation is introduced. Through the BP-MC, the system reliability curve with time is obtained. Finally, Miner linear cumulative damage theory and Carten-Dolan cumulative damage theory are used to calculate the cumulative damage and fatigue life of gears in the transmission system. The results show that Carten-Dolan damage theory is more reliable than Miner theory.

Probability density function of stress

Probability density function of strength

Input torque

Output torque

Strength of the product

External stress

Diffusion coefficient

Drift coefficient

Elastic coefficient

Node area coefficient

Coincidence degree function

Helix angle coefficient

Use coefficient

Tooth load distribution coefficient

Tooth load distribution coefficient

Circumferential force

Contact fatigue limit of the experimental gear

Roughness coefficient

Speed coefficient

Lubricant coefficient

Work hardening coefficient

Denotes the size coefficient

Tooth profile coefficient

Stress correction coefficient

Coincidence coefficient

Helix angle coefficient

Tooth root bending fatigue limit stress

Stress correction coefficient

Life coefficient

Sensitivity coefficient

Condition system

The supports from the National Natural Science Foundation of China (Grant Nos. 52075081 and 52175130), the Innovation Training Programme for Chengdu university Students (CDUCX2022047), and The Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, China (MSSB-2022-08) are gratefully acknowledged.