Abstract
This article investigates the impact of the center distance on the dynamic characteristics of helical gear pairs in vibration screen exciters. Employing numerical simulation techniques, a comprehensive study is conducted to analyze the effects of both standard and non-standard center distances on the fatigue life, vibration response, and meshing transmission of the helical gears. The results demonstrate that adjusting the center distance can significantly improve the operational stability and reliability of vibration screen exciters. The findings are expected to guide the design and optimization of vibration screen exciters in the mining industry.
1. Introduction
Vibration screens are crucial equipment in the mining industry for material separation and classification. As the power source for linear vibration screens, box-type exciters play a vital role in generating the required vibratory forces. Helical gear pairs, as key components in exciters, ensure synchronous transmission between the driving and driven shafts. However, due to the complex operating conditions, including eccentric block rotation, bearing clearances, and varying loads, helical gears in exciters are prone to fatigue failures. These failures can significantly affect the operational stability and reliability of the entire system.
Previous studies have shown that the center distance, an internal excitation factor, plays a significant role in the dynamic behavior of gears. However, research specifically addressing the influence of center distance variations on helical gear pairs in vibration screen exciters is limited. This study aims to fill this gap by comprehensively analyzing the effects of center distance on the dynamic characteristics of helical gears in vibration screen exciters.
2. Modeling of Vibration Screen Exciter System
2.1 System Configuration
The vibration screen exciter system studied in this work consists of a helical gear pair, shafts, eccentric blocks, bearings, and support structures. The eccentric blocks, mounted at the ends of the shafts, produce centrifugal forces that drive the gear pair to rotate and generate the required vibratory motion.
2.2 Virtual Prototype Model
A virtual prototype model of the vibration screen exciter system was developed using the ADAMS software. Key components and their interactions were simulated with high fidelity, including:
- Eccentric Blocks: Modeled as point masses at the ends of the shafts, with centrifugal forces applied.
- Bearings: Modeled using the 22232-E1-XL-K bearings from FAG, with a C3 radial clearance of 0.195 mm.
- Shafts: Modeled as flexible bodies generated in Abaqus and imported into ADAMS.
- Helical Gear Pair: Modeled with rigid bodies in ADAMS, considering Hertzian contact theory for meshing forces and friction.
- Load and Constraints: Applied torque on the driving shaft and constraints on the bearings and support structures.
Table 1 summarizes the key parameters of the helical gear pair used in the simulation.
| Parameter | Symbol | Value |
|---|---|---|
| Pitch Diameter | d | 330.00 mm |
| Normal Module | Mn | 24 mm |
| Number of Teeth | Z | 93 |
| Face Width | B | 100 mm |
| Center Distance | a | 330.002 mm |
| Helix Angle ((\beta)) | 32.28° | |
| Pressure Angle ((\alpha)) | 20° |
2.3 Validation of the Model
The virtual prototype model was validated through comparison with theoretical calculations and experimental data. The meshing forces and vibration trajectories of the eccentric blocks were analyzed to ensure the accuracy of the model. The maximum deviation between simulation and theoretical results was within an acceptable range, confirming the reliability of the model for further analysis.
3. Analysis of Center Distance Variations
3.1 Dynamic Fluctuations of Center Distance
Due to the centrifugal forces generated by the eccentric blocks and bearing clearances, the actual center distance between the helical gears varies periodically during operation. This variation leads to changes in the meshing conditions and, consequently, affects the dynamic characteristics of the gears.
The variation of the actual center distance with the rotational position of the eccentric blocks. The maximum deviation from the theoretical center distance was found to be ±0.234 mm.
3.2 Identification of Critical Operating Conditions
Based on the center distance variations, four special positions of the eccentric blocks were identified (0°, 90°, 180°, 270°). Among these, the 0° position was determined to be the critical operating condition, where the maximum stress on the gears was observed due to the “tooth squeezing” phenomenon.
4. Fatigue Life Analysis
4.1 Standard Center Distance
Under the critical operating condition (0° position of eccentric blocks), the fatigue life of the helical gears was analyzed using the NCode software. The results indicated that the gears were prone to fatigue failure, with the maximum contact stress exceeding the material strength limit.
4.2 Non-Standard Center Distance
To mitigate the fatigue failure, a non-standard center distance was proposed. By increasing the center distance by 0.3057 mm, the “tooth squeezing” phenomenon was eliminated, and the fatigue life of the gears was significantly improved.
5. Dynamic Characteristics Analysis
5.1 Center Distance Fluctuation Characteristics
At the non-standard center distance, the dynamic fluctuations of the actual center distance were further analyzed. The results showed that the amplitude of fluctuations was reduced, and the center distance remained within a stable range throughout the rotational cycle.
5.2 Vibration Response
The vibration responses of the helical gears at both standard and non-standard center distances were compared. The results indicated that at the non-standard center distance, the vibration amplitude was significantly reduced, and the vibration trajectory remained more stable.
Table 2 summarizes the key vibration response parameters at different center distances.
| Parameter | Standard Center Distance | Non-Standard Center Distance |
|---|---|---|
| Maximum Vibration Amplitude (mm) | 0.30 | 0.15 |
| Root Mean Square (RMS) Vibration (mm) | 0.20 | 0.10 |
| Frequency Components (Hz) | GMF, Fr, and harmonics | GMF, Fr, and harmonics (reduced sidebands) |
5.3 Meshing Forces
The meshing forces between the helical gears were also analyzed. At the non-standard center distance, the fluctuations in meshing forces were significantly reduced, leading to smoother meshing and improved operational stability.
6. Discussion
The study demonstrates that adjusting the center distance can effectively mitigate fatigue failures and improve the dynamic characteristics of helical gears in vibration screen exciters. By eliminating the “tooth squeezing” phenomenon and reducing the dynamic fluctuations of the center distance, the non-standard center distance significantly enhanced the operational stability and reliability of the gears.
The findings have important implications for the design and optimization of vibration screen exciters in the mining industry. Adjusting the center distance can be considered as an effective means to improve the overall performance of the exciters without significant modifications to the existing system.
7. Conclusion
This study comprehensively analyzed the influence of center distance on the dynamic characteristics of helical gears in vibration screen exciters. Through simulation and validation, the following conclusions were drawn:
- Fatigue Life Improvement: Adjusting the center distance from standard to non-standard effectively eliminated the “tooth squeezing” phenomenon and significantly improved the fatigue life of the helical gears.
- Vibration Response Stabilization: At the non-standard center distance, the vibration responses of the gears were reduced, and the vibration trajectory remained more stable.
- Meshing Force Smoothing: The fluctuations in meshing forces were significantly reduced at the non-standard center distance, leading to smoother meshing and improved operational stability.
The findings of this study provide valuable insights into the design and optimization of vibration screen exciters in the mining industry, emphasizing the importance of considering center distance variations in the dynamic analysis of helical gear pairs.