In the field of mechanical engineering, the reliability and performance of gears in transmission systems are crucial for the safe and efficient operation of various machinery, especially in subway vehicles. This article focuses on the bending fatigue life prediction and optimization of variable displacement helical gears used in subway vehicle transmissions.
The background and significance of this research are highlighted by the increasing importance of urban rail transit, such as subway systems, in modern cities. Subway vehicles play a vital role in providing reliable and efficient transportation, and the gears in their transmission systems directly affect the safety and stability of the vehicles. Ensuring the durability and reliability of these gears is essential to prevent failures and reduce maintenance costs.
Previous studies on gear bending fatigue have made significant contributions to the understanding of gear behavior under different operating conditions. Domestic researchers have conducted extensive research in this area, including finite element analysis, fatigue life prediction models, and experimental studies. For example, some studies have used finite element methods to analyze the stress distribution in gears and predict their fatigue life. Others have focused on developing fatigue damage models based on linear or nonlinear cumulative damage theories. Additionally, experimental studies have been carried out to validate these models and investigate the factors influencing gear fatigue life.
Internationally, researchers have also made notable progress in gear bending fatigue research. They have proposed various models and methods for predicting fatigue life, considering factors such as material properties, loading conditions, and gear geometry. Some studies have focused on improving the accuracy of fatigue life predictions by considering the interaction between different fatigue damage mechanisms. Others have investigated the effects of different manufacturing processes and surface treatments on gear fatigue performance.
The main content of this research includes the following aspects:
- Finite Element Analysis of Transmission Gears Based on Subway Vehicle Operating Characteristics:
- Introduction: To ensure the accuracy of the bending fatigue life prediction model for subway vehicle transmission gears, it is necessary to consider the driving characteristics of the subway, the load characteristics of the gear pair, and the stress situation of the transmission gears under various actual operating conditions.
- Finite Element Method and Transient Dynamics: The finite element method is a powerful numerical analysis technique that combines elastic theory, computational mathematics, and computer software. It is widely used in engineering for its strong solving ability and good stability. Transient dynamics analysis is used to study the dynamic response of structures under time-varying loads, which is applicable to the meshing process simulation of subway vehicle transmission gear pairs.
- Gear Pair Finite Element Analysis: A finite element model of the subway vehicle transmission gear pair is established, and the model is meshed and simplified in the preprocessing software. The model is then imported into the finite element analysis software for transient dynamics analysis. The boundary conditions data for the gear pair under different operating conditions are obtained based on the motor traction characteristic curve and the wheel circumferential traction force variation curve.
- Results and Analysis: The analysis results show that the gear pair is always in the alternating state of two-tooth and three-tooth meshing, and the maximum bending stress of the gear root varies greatly under different operating conditions. Only in the speed range of 0 – 50 km/h, the maximum root bending stress of the helical gear is greater than the fatigue limit of the material, which plays a major role in the accumulation of bending fatigue damage to the helical gear.
| Analysis Aspect | Details |
|---|---|
| Objective | Analyze the stress distribution and variation of the root of the helical gear during the meshing process and determine the working conditions that have a major impact on the bending fatigue damage of the gear. |
| Methodology | Establish a finite element model of the helical gear pair, perform transient dynamics analysis, and obtain the boundary condition data for the gear pair under different operating conditions. |
| Results | The gear pair is always in the alternating state of two-tooth and three-tooth meshing, and the maximum bending stress of the gear root varies greatly under different operating conditions. Only in the speed range of 0 – 50 km/h, the maximum root bending stress of the helical gear is greater than the fatigue limit of the material, which plays a major role in the accumulation of bending fatigue damage to the helical gear. |
- Gear Bending Fatigue Life Prediction:
- Introduction: A suitable and convenient bending fatigue life prediction model for cylindrical gears is important due to the large variation in root bending stress during the traction of subway vehicles.
- Linear Cumulative Damage Theory and Nonlinear Fatigue Cumulative Damage Models: The Palmgren – Miner cumulative damage theory is widely used in engineering for fatigue life prediction, but it has some limitations. Nonlinear fatigue cumulative damage models have been proposed to address these limitations, considering factors such as the interaction between loads, the degradation of material physical properties, and energy criteria.
- Gear Single Tooth Bending Fatigue Test: Bending fatigue tests are conducted on gears to study their fatigue life. The test results show that the fatigue life corresponding to the large crack expansion stage is often less than 10%, and the initiation life of the gear can be predicted and taken as the fatigue life.
- Energy-Based Gear Bending Fatigue Life Prediction Model: Based on the linear cumulative damage theory and the energy accumulation curve obtained from the test results, a gear bending fatigue life prediction model is established. The model is validated by comparing the predicted life with the test data, and the results show that the model can be used for predicting the bending fatigue life of cylindrical gears.
| Analysis Aspect | Details |
|---|---|
| Objective | Establish a bending fatigue life prediction model for cylindrical gears and validate its effectiveness and applicability. |
| Methodology | Conduct bending fatigue tests on gears, calculate the energy accumulation curve and the fracture cumulative energy curve under different stress amplitudes, and establish a nonlinear energy cumulative damage model based on the Palmgren – Miner linear cumulative damage theory. |
| Results | The test results show that the fatigue life corresponding to the large crack expansion stage is often less than 10%, and the initiation life of the gear can be predicted and taken as the fatigue life. The predicted life is within the 3 – times life interval of the test life, which validates the model. |
- Influence of Displacement Coefficient on the Bending Fatigue Life of Helical Gears:
- Introduction: Selecting the appropriate displacement coefficient for the transmission gear pair can effectively improve the transmission quality. This chapter aims to analyze the influence of different displacement coefficients on the root stress and bending fatigue life of the helical gear pair.
- Selection of Displacement Coefficient for Subway Vehicle Transmission Helical Gears: The displacement coefficient selection range for the subway transmission helical gear is determined based on the commonly recognized line graph method.
- Finite Element Analysis of Helical Gears with Different Displacement Coefficients: A finite element model of the single – tooth meshing of the helical gear with different displacement coefficients is established, and the accuracy of the model is verified by comparing the finite element analysis results with the calculated values based on the national standard GB/T 3480.
- Finite Element Bending Fatigue Life Analysis of Helical Gears with Different Displacement Coefficients: The finite element model is imported into the fatigue analysis software FE – Safe for fatigue analysis, and the bending fatigue life of the helical gear with different displacement coefficients is obtained.
| Analysis Aspect | Details |
|---|---|
| Objective | Analyze the influence of different displacement coefficients on the root stress and bending fatigue life of the helical gear pair. |
| Methodology | Establish a finite element model of the single – tooth meshing of the helical gear with different displacement coefficients, apply a torque to the pinion to simulate the meshing process, and compare the root stress calculated by the finite element model with the value calculated based on GB/T 3480 to verify the accuracy of the model. Import the finite element model into the fatigue analysis software FE – Safe for fatigue analysis. |
| Results | The root stress and bending fatigue life of the pinion and the ring gear change with the displacement coefficient. The error of the root stress of the pinion calculated by the finite element model is – 1.127% compared with the value calculated based on GB/T 3480, and the error of the root stress of the ring gear is 5.387%. The bending fatigue life of the gear pair also changes with the displacement coefficient. |
- Optimization of Subway Vehicle Transmission Gears Based on Fatigue Performance:
- Introduction: Based on the analysis results of the single – tooth meshing finite element model of the subway vehicle transmission gear, this chapter aims to optimize the transmission gear to ensure smooth meshing, low noise, and high fatigue performance.
- Fatigue Analysis of Subway Vehicle Transmission Gears: The tooth root stress and bending fatigue life of the transmission gear are analyzed, and the accuracy of the line graph method is verified by comparing the predicted values with the finite element analysis results.
- Bending Fatigue Life Optimization Design of Transmission Gears: The optimal displacement coefficient combination of the subway vehicle transmission helical gear is selected based on the equal strength principle and the equal life principle using the line graph method. The transmission quality of the optimized gear pair is analyzed.
| Analysis Aspect | Details |
|---|---|
| Objective | Optimize the transmission gear based on fatigue performance to ensure smooth meshing, low noise, and high reliability. |
| Methodology | Analyze the tooth root stress and bending fatigue life of the transmission gear, verify the accuracy of the line graph method by comparing the predicted values with the finite element analysis results, and optimize the gear by selecting the optimal displacement coefficient combination based on the equal strength principle and the equal life principle. |
| Results | The line graph method can accurately predict the tooth root stress and fatigue life of the subway transmission gear pair. The optimized gear pair based on the equal strength principle has a comprehensive fatigue life that is 3.29 times that of the original gear pair, and the optimized gear pair has a good transmission quality with smooth meshing and low noise. |
The main conclusions of this research are as follows:
- The gear pair in the subway vehicle transmission is always in the alternating state of two – tooth and three – tooth meshing, and the maximum bending stress in the two – tooth meshing state is greater than that in the three – tooth meshing state. Only in the speed range of 0 – 50 km/h, the maximum root bending stress of the helical gear is greater than the fatigue limit of the material, which plays a major role in the accumulation of bending fatigue damage to the helical gear.
- The fatigue life corresponding to the large crack expansion stage of the gear is often less than 10%, and the initiation life of the gear can be predicted and taken as the fatigue life.
- The finite element model can accurately calculate the root stress of the gear, and the error of the root stress of the pinion is – 1.127% compared with the value calculated based on GB/T 3480, and the error of the root stress of the ring gear is 5.387%.
- When the displacement coefficient changes within the allowable range, the root stress of the pinion first decreases to a certain value and then increases, and the root stress of the ring gear first decreases to a certain value, then increases slightly to a certain value, and then decreases.
- The line graph method can accurately predict the tooth root stress and fatigue life of the subway transmission gear pair, with the minimum error of the tooth root stress being 0.02% and the maximum being 1.51%; the minimum error of the gear fatigue life being 0.59% and the maximum being 18.76%.
- The optimized gear pair based on the equal strength principle has a comprehensive fatigue life that is 3.29 times that of the original gear pair, which is better than the equal life principle. When optimizing the displacement coefficient of the helical gear using the line graph method, the equal strength principle should be given priority.
However, this research also has some limitations. For example, only the bending stress and fatigue life of the helical gears with two specific tooth numbers have been studied, and the research on other tooth numbers is needed. Additionally, the gear bending fatigue test in this study is conducted on the equivalent spur gears, and further studies should be carried out on the bending fatigue test of the helical gears.
Future research directions could include further improving the accuracy and applicability of the gear bending fatigue life prediction model, considering more factors such as the surface quality, temperature, and lubrication conditions of the gear. Additionally, the optimization of the gear transmission system could be explored to further improve the performance and reliability of the subway vehicle transmission.
In conclusion, this research provides valuable insights into the bending fatigue life prediction and optimization of variable displacement helical gears for subway vehicles, which can contribute to the safe and reliable operation of subway systems.