In the field of mechanical engineering, the performance and reliability of gear transmission systems are crucial for the smooth operation of various machines and equipment. One of the key issues in gear design is to address the problem of uneven load distribution on the tooth surface, which can lead to excessive vibration, noise, and reduced service life of the gears. To solve this problem, gear modification techniques, such as tooth surface modification, have been widely studied and applied.
The background and significance of this research lie in the need to improve the performance and reliability of the reducer used in construction elevators. The output shaft gears of the reducer in construction elevators often experience uneven load distribution on the tooth surface, resulting in high vibration and noise. By optimizing the tooth surface modification of the output shaft helical gear pair, the load distribution can be made more uniform, the vibration and noise can be reduced, and the service life of the gears can be extended. This has important practical implications for the improvement of the performance and reliability of construction elevators.
Previous studies on gear modification have focused on various aspects, including the determination of the optimal modification amount, the selection of the modification method, and the evaluation of the modification effect. However, most of these studies either rely on theoretical calculations to determine the approximate modification amount or use simulation software to obtain the modification curve through multiple parameter inputs based on experience. This research aims to provide a more systematic and efficient approach to gear modification by combining theoretical calculations and optimization methods based on the ROMAX software.
The main content of this research includes the establishment of a parameterized model of the gear transmission system, the calculation of the maximum modification amount for the tooth alignment and profile, the design of the optimization scheme using the full factor method in ROMAX, and the comparison of the performance before and after the modification.
- Establishing the Parameterized Model
- Model Description: A parameterized model of the three-stage circular arc bevel gear transmission system of the SC200 construction elevator is established using ROMAXdesign. The power of the helical gear shaft at the output end is 18 kW, and the maximum speed is 382 r/min. The helical gears are made of 40CrMnMo, with surface hardening treatment, and the precision grade is 8. The lubricant is ISOVG680.
- Macro Parameters of the Output End Helical Gear Pair: The macro parameters of the output end helical gear pair, including the number of teeth, module, normal pressure angle, modification coefficient, helix angle, tooth width, center distance, pitch diameter, addendum coefficient, dedendum coefficient, and hand of rotation, are presented in Table 1.
| Parameter | Small Helical Gear | Output Shaft Helical Gear |
|---|---|---|
| Number of Teeth | 22 | 73 |
| Module (mm) | 2.5 | 2.5 |
| Normal Pressure Angle (°) | 20 | 20 |
| Modification Coefficient | 0.29 | 0.17 |
| Helix Angle (°) | 16.523 | 16.523 |
| Tooth Width (b) (mm) | 64 | 60 |
| Center Distance (mm) | 125 | 125 |
| Pitch Diameter (mm) | 57.3 | 190.2 |
| Addendum Coefficient | 1.0 | 1.0 |
| Dedendum Coefficient | 0.25 | 0.25 |
| Hand of Rotation | Right-Hand | Left-Hand |
- Maximum Modification Amount for Tooth Alignment and Profile
- Tooth Alignment Modification Amount
- Drum Shaping Amount Considering Comprehensive Factors: The bending and torsion deformation of the gear body and shaft, as well as manufacturing errors, box deformation, and bearing hole manufacturing errors, can cause uneven tooth alignment contact and stress concentration. To compensate for the influence of the comprehensive meshing tooth alignment error, drum shaping modification is applied. The run-in meshing tooth alignment error is calculated by Equation (1), and the maximum drum shaping amount is calculated by Equations (2) and (3). The maximum drum shaping amount is 20.75 μm, and the lower limit is 0 μm.
- Spiral Line Modification Amount: The spiral angle error of the helical gear can be divided into overall and local errors. To ensure that the gear teeth are in the theoretical position under load, spiral line modification is used to obtain the compensation amount for the spiral line error. Considering the bending and torsion deformation of the small gear shaft, the maximum bending deformation is calculated by Equations (4) and (5), and the mirror curve of the comprehensive deformation curve is the spiral line modification amount. The maximum deformation is 47 μm, and the minimum deformation is 20 μm.
- Involute Profile Modification: In the meshing process of the gear pair, due to the elastic deformation caused by the load, the non-integer coincidence degree, and the interference caused by the base pitch error and the processing error, the tooth profile modification is necessary to eliminate the meshing impact and improve the running stability. The tooth profile deformation amount is calculated by Equation (6), and the maximum modification amount is calculated by Equations (7) and (8). The maximum modification amount is 28.78 μm, and the lower limit is 0 μm.
- Tooth Alignment Modification Amount
- Design Optimization Scheme
- Optimization Process: Using the maximum modification amount calculated as the optimization parameter, the full factor method in ROMAX is used for parameter optimization to select the best modification amount. The optimization process includes microscopic geometric contact analysis, selection of the parameter study method (full factor method), setting the variable range based on the calculation results, setting the operating conditions, and setting the optimization target range.
- Factor Selection and Range Setting: The design factors are the drum shaping amount, spiral line modification amount, and tooth top modification amount of the left tooth surface of the small helical gear. The modification range of these three factors is determined based on the theoretical calculation, as shown in Table 2.
- Optimization Objectives and Results: The optimization objectives are the tooth alignment contact load distribution coefficient (KHβ) and the tooth root bending strength load distribution coefficient (KFβ). The target range is set as KHβ ∈ (1.10, 1.20) and KFβ ∈ (1.10, 1.20). After calculating 3375 schemes, the top 10 best schemes are selected based on the weight value, as shown in Table 3. By comparing these 10 schemes and following the principle of making the modification amounts integers and close to the nearest, the best modification parameters are obtained, as shown in Table 4.
| Table 2 | Theoretical Modification Scope (Unit: μm) | |
|---|---|---|
| Spiral Line Modification Amount | Tooth Alignment Drum Shaping Amount | Tooth Top Modification Amount |
| (20, 47) | (0, 20) | (0, 28) |
| Table 3 | 10 Candidate Modification Schemes | ||||
|---|---|---|---|---|---|
| Candidate Scheme | Tooth Alignment Slope (m) | Tooth Alignment Drum Shaping Amount (m) | Tooth Top Modification Amount (m) | Kup | Ky |
| 1371 | 36.43 | 6.07 | 5.36 | 1.1 | 1.089 |
| 549 | 32.14 | 11.43 | 3.57 | 1.1 | 1.089 |
| 2562 | 41.79 | 10.36 | 11.79 | 1.1 | 1.089 |
| 285 | 31.07 | 8.21 | 22 | 1.1 | 1.089 |
| 292 | 31.07 | 9.29 | 6.43 | 1.1 | 1.089 |
| 328 | 31.07 | 11.43 | 3.26 | 1.1 | 1.089 |
| 1672 | 37.5 | 11.43 | 6.43 | 1.101 | 1.089 |
| 1898 | 38.57 | 11.43 | 7.5 | 1.101 | 1.089 |
| 2352 | 40.71 | 11.43 | 11.79 | 1.101 | 1.089 |
| 2561 | 41.79 | 10.36 | 10.71 | 1.101 | 1.09 |
| Table 4 | Best Shape Modification Scheme (Unit: μm) | |
|---|---|---|
| Tooth Alignment Drum Shaping Amount | Spiral Line Modification Amount | Tooth Top Modification Amount |
| 12 | 37 | 3 |
- Comparison Before and After Modification
- Root Stress Distribution: Before modification, the root stress of the gear is concentrated in the tooth width range of 0 – 20 mm. After modification, the root stress is dispersed over the entire tooth width, and the maximum principal stress is reduced from 362.1 MPa to 204.3 MPa, indicating that the tooth top modification also improves the root stress of the meshing gear.
- Tooth Surface Load Distribution: Before modification, the tooth surface load is mainly distributed in the tooth width range of 0 – 30 mm, with the maximum unit length load reaching 522 N/mm at the beginning of meshing, showing a severe uneven load distribution. After modification, the tooth surface load is evenly distributed over the entire tooth surface, with the maximum unit length load of 218 N/mm at the midpoint of the tooth width, and the loads at the meshing and disengaging points are relatively small.
- Transmission Error: The transmission error before modification is 1.43 μm, and after modification, it is reduced to 0.35 μm. The reduction in transmission error indicates that the mechanical excitation of the gear will decrease, thereby improving the vibration performance of the reducer.
- Acceleration Response of the Box: By virtual sensors on the surface of the box and applying the extracted transmission error excitation, the acceleration response of the box surface is obtained. At the maximum speed of 382 r/min, the acceleration of the box surface before modification is 0.045 m/s², and after modification, it is reduced to 0.024 m/s².
The main conclusions of this research are as follows:
- By combining theoretical calculations to determine the modification amount range and using the full factor method for optimization design, the combination of the best modification amounts can be quickly determined.
- After the comprehensive modification, the transmission error of the gear is reduced to 0.35 μm, a decrease of 75.5% compared to before modification.
- The maximum acceleration response of the box surface after optimization is 0.024 m/s², a decrease of 47.8% compared to before optimization.
- The maximum unit length load on the tooth surface after optimization is 218 N/mm, a decrease of 58.2% compared to before, indicating that the tooth surface load distribution of the gear after comprehensive modification is more uniform, and the mechanical excitation generated by gear meshing is smaller, which can effectively improve the dynamic characteristics of the gear and has a certain reference role in reducing the uneven load distribution on the tooth surface and improving the transmission stability.
However, this research also has some limitations. For example, the influence of factors such as temperature, lubrication conditions, and manufacturing tolerances on the modification effect is not fully considered. Future research could focus on addressing these limitations and further improving the accuracy and reliability of the gear modification design.
In conclusion, this research provides a valuable approach for optimizing the tooth surface modification of helical gears, which can contribute to the improvement of the performance and reliability of gear transmission systems. Further research in this area can lead to more advanced and effective gear modification techniques.