This article focuses on the fatigue life analysis of the output gear pair of the reducer used in shared bicycle locks. With the popularization of shared bicycles, the development and application of relevant reducers have become crucial. The fatigue life of the output gear pair significantly affects the effective life of the reducer. Traditional methods for testing gear fatigue life have limitations. Therefore, a finite element simulation-based method for predicting the life of the output gear pair is proposed. The finite element model of the gear pair is established in ANSYS software, and its structural parameters are improved. Dynamics simulation is carried out in ADAMS software to obtain the dynamic contact force, which is used as a load spectrum in nCode DesignLife software for fatigue life prediction. Finally, experiments are conducted to verify the correctness of the finite element simulation method.
1. Introduction
The emergence and widespread use of shared bicycles have led to an increased demand for shared bicycle lock reducers. The reducer typically consists of multiple gear pairs, and the output gear pair is crucial as it experiences the maximum torque and is more prone to damage during operation. Thus, the fatigue life of the output gear pair determines the overall effective life of the reducer.
Previous research on gear life mainly focused on metallographic structure analysis and experimental analysis methods. However, these methods have several drawbacks. For example, the samples used in experiments may have significant variations in life due to external factors during manufacturing and testing. The test cycle is long, and if problems occur during testing, redesign and retesting are required, consuming substantial manpower and resources. Additionally, experimental methods are limited by testing means and sample preparation, imposing certain requirements on enterprises or design units.
In contrast, the finite element fatigue life prediction method can effectively reduce the development cycle and testing costs. This article takes the output gear pair of the shared bicycle lock reducer as the research object and conducts a series of analyses and experiments.
2. Finite Element Analysis
2.1 Elastic Contact Problem Finite Element Theory
Contact problems are indefinite boundary problems, and even elastic contact problems exhibit surface nonlinearity. The solution to contact problems involves an iterative process. For a system composed of two contact bodies and , the finite element stiffness equation can be derived from the virtual work principle. Different contact states have different equality constraint equations, such as continuous state, sliding state, and separation state, each with its specific conditions and equations.
2.2 Finite Element Model Establishment
The geometric parameters of the output gear pair are first determined, including parameters such as the number of teeth, material, modulus, and pressure angle for both the driving and driven wheels. To establish an accurate finite element model, a force analysis of the output gear pair is necessary. The driving shaft gear is subjected to forces such as support forces from bearings at both ends, torque transmitted from the upper gear pair, and reaction torque from the driven wheel. Based on experimental data and calculations, the values of these forces can be obtained.
The process of establishing the finite element model includes grid division and the application of boundary conditions and loads. The three-dimensional geometric model of the gear pair is imported into Workbench for grid division, with the meshing part of the gear pair being refined. After grid division, the number of solid elements and nodes of the gear pair finite element model is determined. Boundary conditions are applied according to the force analysis results, including constraints on the driving and driven wheels, the application of torque and reaction torque, and the setting of friction contact properties.
2.3 Finite Element Calculation and Results Analysis
The Von Mises stress of the output gear pair is solved in ANSYS. The results show that the maximum Von Mises stress of the driving wheel and the driven wheel appears near the gear meshing pitch circle. The maximum Von Mises stress of the driven wheel exceeds the yield strength of the gear material, indicating that the driven wheel is prone to damage under cyclic stress. To improve the performance and lifespan of the output gear pair, the pressure angle of the driven wheel is modified. After the modification, the Von Mises stress of both the driving and driven wheels is significantly reduced, improving the stress situation of the gear pair and increasing its service life.
| Gear Wheel | Before Modification | After Modification |
|---|---|---|
| Driving Wheel Stress (MPa) | 500.21 | 349.25 |
| Driven Wheel Stress (MPa) | 640.19 | 392.38 |
3. Fatigue Life Prediction
3.1 Load Spectrum Acquisition
Dynamics simulation of the output gear pair is carried out in ADAMS. The material properties of the gears are set, and constraints and drives are added. The contact between the gears is defined using the impact function method, and the contact stiffness coefficient is calculated. Through simulation, the change in the contact force of the output gear pair in the time domain is obtained. The contact force is periodic, and its period is consistent with the theoretical value. The data obtained is exported as a load spectrum for fatigue life analysis.
3.2 Material S – N Curve
The S – N curve is fundamental to stress fatigue analysis and represents the relationship between the stress fatigue life of a part material. The commonly used expression for the S – N curve is . By referring to relevant literature, the values of and for the gear material are determined, and the material S – N curve is obtained.
3.3 Fatigue Life Prediction Results
The finite element results file is imported into nCode DesignLife software, and the dynamic contact force obtained in ADAMS is used as a load spectrum file. The gear material S – N curve is loaded, and the Gerber method is selected for average stress correction. The fatigue simulation results show that the lowest fatigue life region is at the tooth root of the driven wheel on the tensile side, indicating that the driven wheel of the output gear pair is prone to fatigue fracture. Initially, the minimum fatigue cycle life of the gear pair does not meet the enterprise design requirements. However, after changing the pressure angle of the driven wheel, the fatigue life of the gear pair increases significantly, meeting the design requirements.
| Pressure Angle | Minimum Fatigue Cycle Life (times) |
|---|---|
| 20° | 36750 |
| 25° | 82890 |
4. Fatigue Test
4.1 Fatigue Test Device
The fatigue test equipment used is a micro motor dedicated fatigue testing machine. The motor is installed on the product test stand, and the controller is set to determine the operation sequence and rated voltage of the motor. The power supply and counter are connected, and the experiment is started.
4.2 Test Results
Two types of micro motors with different pressure angles of the output gear pair (20° and 25°) are assembled and tested for fatigue life on the fatigue testing machine. The test results show that the first failure occurs at the driven wheel of the output gear pair, with tooth breakage observed.
| Pressure Angle | 1# | 2# | 3# | 4# | Average Life |
|---|---|---|---|---|---|
| 20° | 14876 | 14798 | 26402 | 77090 | 33292 |
| 25° | 27542 | 73426 | 82020 | 115608 | 74650 |
4.3 Simulation Prediction Results and Test Results Comparison Analysis
The finite element simulation prediction results are compared with the test results. The error between the two is less than 10%, which verifies the effectiveness of the finite element analysis method for the output gear pair of the shared bicycle lock reducer.
| Name | Simulation Result | Test Result | Error (%) |
|---|---|---|---|
| 20° | 36750 | 33292 | 9.42 |
| 25° | 82890 | 74650 | 9.94 |
5. Conclusions
(1) Using ANSYS software, finite element models of the output gear pair with different pressure angles are established. When the pressure angle is changed from 20° to 25°, the stress of the driving wheel of the output gear pair is reduced by 30.18%, and the stress of the driven wheel is reduced by 38.71%.
(2) In this research range, the error between the dynamics simulation results and the theoretical value is less than 5%, providing accurate load spectrum data for fatigue life analysis. The change in the pressure angle has a positive correlation with the fatigue life of the output gear pair, increasing the fatigue life by 124.23% when the pressure angle is changed from 20° to 25°.
(3) The test results show that the error between the life of the output gear pair of the shared bicycle lock reducer and the simulation prediction life is less than 10%, within an acceptable range. The finite element simulation analysis method can significantly shorten the development cycle, reduce development costs, and overcome the problems caused by difficult-to-satisfy test conditions.
In conclusion, the proposed method for analyzing the fatigue life of the output gear pair of the shared bicycle lock reducer is effective and has practical application value.
6. Methodology Details
6.1 Finite Element Model Refinement
The refinement of the finite element model is a crucial step in accurately predicting the fatigue life of the gear pair. In the initial model, certain assumptions and simplifications might have been made. To improve the accuracy, a more detailed analysis of the gear geometry and material properties was conducted.
For example, the tooth profile was modeled with a higher level of precision, taking into account the actual shape and curvature of the teeth. This was achieved by using more advanced geometric modeling techniques. The material properties were also updated based on more accurate experimental data. The elastic modulus and Poisson’s ratio were re-evaluated to ensure that they reflected the real characteristics of the gear material.
Moreover, the mesh refinement was further optimized. A finer mesh was applied to the areas of high stress concentration, such as the tooth root and the contact area between the gears. This allowed for a more accurate calculation of the stress distribution within the gear pair. The number of elements and nodes in these critical areas was increased to capture the complex stress patterns more precisely.
6.2 Dynamics Simulation Settings
In the ADAMS software, the dynamics simulation settings play a vital role in obtaining accurate dynamic contact forces. The rotational inertia of the gears was carefully calculated and set based on their geometric and material properties. This ensured that the simulation accurately represented the real-world behavior of the gear pair during rotation.
The contact stiffness and damping coefficients were also fine-tuned. These parameters affect the way the gears interact during contact and have a significant impact on the calculated contact forces. By adjusting these coefficients based on experimental data and theoretical analysis, a more realistic simulation of the gear contact behavior was achieved.
Furthermore, the simulation time step was selected carefully. A smaller time step was used to capture the rapid changes in the contact forces during gear meshing. This allowed for a more detailed analysis of the dynamic behavior of the gear pair and provided more accurate data for the subsequent fatigue life analysis.
6.3 Fatigue Life Analysis in nCode DesignLife
In the nCode DesignLife software, several key aspects were considered for an accurate fatigue life analysis. The selection of the appropriate fatigue analysis method was based on the characteristics of the gear fatigue problem. As mentioned earlier, the nominal stress method was chosen due to its suitability for high – cycle fatigue problems.
The loading conditions were defined accurately using the load spectrum obtained from the ADAMS simulation. The stress – life curve (S – N curve) of the gear material was properly inputted into the software. This curve was determined based on extensive experimental data and literature review.
The mean stress correction method, Gerber method in this case, was applied to account for the effect of mean stress on the fatigue life. This method is widely used and has been proven to provide more accurate fatigue life predictions in many engineering applications.
7. Results and Discussions
7.1 Stress Distribution and Its Impact on Fatigue Life
The stress distribution within the gear pair, as obtained from the finite element analysis, has a direct impact on its fatigue life. The areas of high stress concentration, such as the tooth root and the contact area between the gears, are more prone to fatigue damage.
The reduction in stress levels after modifying the pressure angle of the driven wheel is significant. This reduction not only improves the immediate strength of the gear pair but also has a long – term impact on its fatigue life. The lower stress levels mean that the gears are less likely to experience fatigue cracks and failures over time.
The stress distribution also affects the way the fatigue damage accumulates within the gear pair. In areas of high stress, the damage accumulates more rapidly, leading to a shorter fatigue life. By optimizing the stress distribution through parameter modifications, the fatigue life can be extended.
7.2 Comparison of Different Pressure Angles
The comparison of the gear pair’s performance at different pressure angles provides valuable insights into the design optimization. When the pressure angle is increased from 20° to 25°, not only does the stress decrease, but the fatigue life also increases significantly.
This indicates that the pressure angle is a critical parameter in determining the fatigue life of the gear pair. A larger pressure angle can improve the load – carrying capacity of the gears and reduce the stress levels, thereby increasing the fatigue life. However, it should be noted that increasing the pressure angle too much may have other implications, such as a decrease in the transmission efficiency.
Therefore, a balance needs to be struck between the fatigue life and other performance aspects when choosing the appropriate pressure angle for the gear pair.
7.3 Validation of the Simulation Method
The comparison between the simulation results and the experimental results validates the effectiveness of the proposed simulation method. The close agreement between the two, with an error less than 10%, indicates that the simulation can accurately predict the fatigue life of the gear pair.
This validation is important as it gives confidence in using the simulation method for future design optimizations and analyses. It also shows that the assumptions and models used in the simulation are reasonable and can be relied upon for engineering decisions.
8. Practical Implications and Applications
8.1 Design Optimization for Shared Bicycle Lock Reducers
The findings of this study have direct implications for the design optimization of shared bicycle lock reducers. By understanding the relationship between the gear pair’s parameters and its fatigue life, designers can make more informed decisions during the design process.
For example, they can optimize the pressure angle of the gears to achieve a better balance between fatigue life and transmission efficiency. They can also use the simulation method to evaluate different design alternatives and select the one that best meets the requirements of the application.
This can lead to the development of more reliable and efficient shared bicycle lock reducers, which can improve the overall performance and user experience of shared bicycles.
8.2 Generalization to Other Gear Applications
The methodology and findings of this study can also be generalized to other gear applications. The principles of finite element analysis, dynamics simulation, and fatigue life prediction are applicable to a wide range of gear systems.
Whether it is in automotive transmissions, industrial machinery, or other fields, the understanding of gear fatigue life is crucial for ensuring the reliability and durability of the equipment. By applying the similar techniques and methods described in this study, engineers can better predict and optimize the fatigue life of gears in different applications.
9. Future Research Directions
9.1 Consideration of More Complex Loading Conditions
In future research, it would be beneficial to consider more complex loading conditions. In real – world applications, gears may be subjected to a variety of loading scenarios, such as variable torque, impact loads, and combined loads.
By incorporating these more complex loading conditions into the analysis, a more accurate prediction of the fatigue life can be achieved. This may require the development of more advanced simulation models and techniques to handle the complexity of the loading situations.
9.2 Investigation of the Influence of Surface Roughness on Fatigue Life
The surface roughness of gears can have an impact on their fatigue life. A rougher surface may lead to higher stress concentrations and increased wear, which can in turn affect the fatigue life.
Future research could focus on investigating the relationship between surface roughness and fatigue life. This could involve experimental studies to measure the effect of different surface roughness levels on the fatigue life of gears and the development of models to predict this relationship.
9.3 Integration of Multi – Physics Simulation
Another potential area of future research is the integration of multi – physics simulation. In addition to mechanical aspects, gears may be affected by other physical phenomena, such as thermal effects and lubrication.
By integrating thermal, lubrication, and mechanical simulations, a more comprehensive understanding of the gear behavior and its fatigue life can be obtained. This would require the development of coupled simulation models that can handle multiple physical domains simultaneously.
In conclusion, the fatigue life analysis of the output gear pair of the shared bicycle lock reducer is a complex but important topic. The proposed method based on finite element simulation has been shown to be effective in predicting the fatigue life and can be used for design optimization. Future research directions offer opportunities to further improve the accuracy and applicability of the method in more complex situations.