Abstract
In recent years, urban rail transit has become a popular choice for commuting due to the rapid urbanization and expansion of cities worldwide. Subway systems, particularly with their 223 operational lines globally, have become a crucial component of urban transportation. Ensuring the safety of subway vehicles is paramount, and the transmission gearbox, with its helical gears, plays a vital role in the smooth and reliable operation of these vehicles. Accurate prediction and optimization of the bending fatigue life of these gears can significantly improve their reliability and reduce maintenance costs. This paper presents a comprehensive study on the prediction and optimization of the bending fatigue life of subway vehicle transmission helical gears under various operating conditions.
The study begins by establishing a finite element model of the helical gear pair based on actual subway vehicle gearbox parameters. Using ABAQUS, a transient dynamics simulation is conducted to obtain the tooth root stress distributions under different operating conditions. The results reveal significant stress variations during the meshing process, with the maximum stress occurring primarily during two-teeth meshing states.
To validate the simulation results, a bending fatigue test on equivalent spur gears is performed. The test results indicate that the fatigue life during the large crack propagation stage accounts for less than 10% of the total fatigue life, suggesting that the initiation life can be used as an accurate representation of the overall fatigue life. Based on these findings, a bending fatigue life prediction model is developed using the Miner’s linear cumulative damage theory and energy accumulation curves. The model’s prediction results are within a three-fold range of the experimental data, validating its effectiveness.
Furthermore, finite element models of helical gears with varying displacement coefficients are created to investigate their impact on the bending fatigue life. Through these models, the stress distributions and fatigue lives of gears with different displacement coefficients are analyzed. The results indicate that the displacement coefficients significantly affect the stress levels and fatigue lives of the gears.
Finally, an optimization method based on equal strength principles and the displacement coefficient-fatigue life relationship is proposed. The optimized gear pair achieves a 3.29-fold increase in the overall fatigue life compared to the prototype gear pair, while maintaining smooth meshing and low noise levels.
1. Introduction
With the rapid urbanization and expansion of cities, subway systems have emerged as a crucial component of urban transportation networks. The safety and reliability of subway vehicles are paramount, and the transmission gearbox, with its helical gears, plays a vital role in ensuring smooth and efficient operation. Accurate prediction and optimization of the bending fatigue life of these gears are essential to improve their reliability, reduce maintenance costs, and ultimately enhance the overall safety of subway systems.
This paper aims to predict and optimize the bending fatigue life of subway vehicle transmission helical gears by combining finite element analysis (FEA), experimental testing, and optimization techniques. The specific objectives are:
- Establish an accurate FEA model of the helical gear pair to simulate their transient dynamics under various operating conditions.
- Develop a bending fatigue life prediction model based on experimental data and theoretical frameworks.
- Investigate the impact of varying displacement coefficients on the bending fatigue life of the helical gears.
- Optimize the displacement coefficients of the helical gears to maximize their bending fatigue life while ensuring smooth meshing and low noise levels.
2. Literature Review
Numerous studies have been conducted on the bending fatigue of gears, particularly focusing on the prediction of their fatigue lives and optimization of their design parameters. Some of the key studies in this area are summarized below.
2.1 Bending Fatigue Life Prediction
Several models have been proposed for predicting the bending fatigue life of gears. Peng et al. studied the effect of laser shock peening on the bending fatigue performance of AISI 9310 steel spur gears. They observed a significant improvement in fatigue life after laser shock peening treatment. Li et al. proposed a probabilistic prediction model for gear life based on minimum order statistics, which could accurately predict the life of gears with varying tooth numbers.
2.2 Displacement Coefficient Optimization
The displacement coefficient plays a crucial role in the performance of helical gears. Ding et al. investigated the impact of varying displacement coefficients on the bending fatigue life of spiral bevel gears and proposed an optimization method based on data-driven approaches. Concli et al. studied the effect of gear design parameters on the stress histories induced by different tooth bending fatigue tests and proposed a numerical-statistical method for correlating single-tooth test results to meshing gears.
3. Methodology
The overall methodology adopted in this study involves several key steps, including the establishment of FEA models, experimental testing, prediction model development, and optimization of displacement coefficients.
3.1 Finite Element Analysis
An FEA model of the helical gear pair is established using Solidworks and GearTrax plugins, followed by preprocessing in Hypermesh and simulation in ABAQUS. The model considers the transient dynamics of the gears under various operating conditions, including different speeds and loads.
3.2 Experimental Testing
Bending fatigue tests are conducted on equivalent spur gears using a PLG-200 high-frequency fatigue testing machine. The tests provide valuable data on the fatigue behavior of the gears under various stress levels, which are used to validate the FEA results and develop the prediction model.
3.3 Prediction Model Development
Based on the experimental data and theoretical frameworks, a bending fatigue life prediction model is developed using the Miner’s linear cumulative damage theory and energy accumulation curves. The model predicts the fatigue life of helical gears under various operating conditions and stress levels.
3.4 Optimization of Displacement Coefficients
The displacement coefficients of the helical gears are optimized using the prediction model and equal strength principles. The optimized gear pair aims to maximize the bending fatigue life while ensuring smooth meshing and low noise levels.
4. Finite Element Analysis
4.1 Model Establishment
The helical gear pair model is established based on the actual parameters of a subway vehicle gearbox. The gears have a module of 6, a pressure angle of 20°, and a spiral angle of 19°. The material used is 18CrNiMo7-6, with properties such as a density of 7.85 g/cm³, an elastic modulus of 235 GPa, a Poisson’s ratio of 0.3, and a fatigue limit of 385.5 MPa.
4.2 Transient Dynamics Simulation
The transient dynamics simulation is conducted using ABAQUS to obtain the tooth root stress distributions under different operating conditions. The simulation results show that the maximum stress occurs primarily during two-teeth meshing states, which account for approximately 15% of the meshing process. The stress levels vary significantly under different speeds and loads, with the highest stress occurring at speeds between 0 and 40 km/h (Table 1).
Table 1: Maximum Tooth Root Stress under Different Operating Conditions
| Operating Condition | Speed (km/h) | Maximum Stress (MPa) |
|---|---|---|
| I | 0-40 | 603.375 |
| II | 40-50 | 472.877 |
| III | 50-60 | 245.208 |
| IV | 60-80 | 185.659 |
5. Experimental Testing
Bending fatigue tests are conducted on equivalent spur gears using a PLG-200 high-frequency fatigue testing machine. The tests are performed at various stress levels, and the fatigue lives are recorded. The results indicate that the fatigue life during the large crack propagation stage accounts for less than 10% of the total fatigue life, suggesting that the initiation life can be used as a reliable representation of the overall fatigue life.
6. Prediction Model Development
Based on the experimental data and theoretical frameworks, a bending fatigue life prediction model is developed using the Miner’s linear cumulative damage theory and energy accumulation curves. The model considers the effects of varying stress levels and loading histories on the fatigue life of the gears.
6.1 Energy Accumulation Curve
The energy accumulation curve represents the cumulative energy dissipated during the fatigue process. It is calculated based on the strain-energy density during each loading cycle. The curve is used to estimate the fatigue damage accumulated during the fatigue test.
6.2 Fatigue Life Prediction
The fatigue life prediction model is formulated as follows:
N = \frac{E^*}{\sum_{i=1}^{n} \frac{E_i}{N_i}} \] where \( N \) is the predicted fatigue life, \( E^* \) is the fracture energy, \( E_i \) is the energy dissipated during the \( i \)-th cycle, and \( N_i \) is the number of cycles to failure at the corresponding stress level.
8. Conclusion
This study presents a comprehensive approach for predicting and optimizing the bending fatigue life of subway vehicle transmission helical gears. Through a combination of FEA, experimental testing, and optimization techniques, an accurate prediction model is developed and applied to optimize the displacement coefficients of the gears. The optimized gear pair achieves a significant increase in fatigue life while maintaining smooth meshing and low noise levels. The results demonstrate the effectiveness of the proposed method and provide valuable insights into the design and optimization of helical gears for subway vehicle transmissions.