This article focuses on the optimization of single helical gear modification using the MASTA software. It begins with an introduction to the importance of gear modification in improving gear performance. The study involves analyzing a pair of single helical gears, considering different modification methods such as helix modification, crowning, and tip relief. Through loaded tooth contact analysis (LTCA), various parameters like transmission error, tooth surface contact stress, and load distribution are evaluated. The article presents a detailed account of the modification process, comparing different schemes and ultimately arriving at an optimized modification plan that significantly improves gear meshing performance.
1. Introduction
Gear systems are widely used in various mechanical applications. However, due to factors such as elastic deformation, gears often experience problems like meshing impact, uneven load distribution, and reduced transmission performance. Gear modification is an effective technique to address these issues without changing the macroscopic design parameters of the gears. It can reduce meshing impact, improve the distribution of tooth surface contact stress, enhance meshing stability, and increase the load-carrying capacity of gears.
Over the years, many studies have been conducted on gear modification. Researchers have explored different modification theories and methods, with a focus on parameters such as transmission error and tooth surface contact stress. However, from the perspective of ship power plants, in addition to controlling these parameters, the distribution of tooth surface contact stress is also crucial and should be optimized.
2. Gear Model and Initial Analysis
2.1 Single Helical Gear Parameters
The single helical gears in this study are made of 42CrMo with a machining accuracy of grade 4 (GB/T10095.1 – 2022). The lubrication method is oil injection lubrication, and the lubricant used is ISO – VG100. The gears operate under a specific condition where the pinion shaft rotates at 6000 r/min and transmits a power of 8000 kW. The detailed gear parameters are presented in Table 1.
| Parameter | Pinion | Gear |
|---|---|---|
| Number of teeth | 49 | 147 |
| Tooth width b/mm | 182 | 180 |
| Helix direction | Right-handed | Left-handed |
| Modification coefficient | 0.0588 | -0.4330 |
| Normal module m₀ | 5 | 5 |
| Helix angle/() | 12.5 | 12.5 |
| Pressure angle a/() | 20 | 20 |
| Center distance a/mm | 500 | 500 |
| Bearing span L/mm | 585 | 585 |
2.2 Initial Analysis Using MASTA
Using the MASTA software, a three-dimensional model of the single helical gear and gearbox was established. The finite element model of the box was created using Ansys Workbench, and the stiffness and damping matrices of the bearings were calculated using DyRoBeS software. LTCA analysis was then performed to obtain the transmission error, tooth surface contact stress nephogram, and gear parameters in the unmodified state.
The initial transmission error curve shows a certain degree of fluctuation, and the tooth surface contact stress nephogram indicates an uneven stress distribution, with the gear being in a state of eccentric load. The peak-to-peak value of the transmission error is 0.2391 m, and the maximum contact stress is 808.45 MPa, with a tooth surface load distribution coefficient KH of 1.1952. These results suggest that modification is necessary to improve gear performance.
3. Modification Strategies
3.1 Tooth Lead Modification
3.1.1 MASTA Micro-parameter Automatic Optimization Method
In the MASTA software, a model of the single helical gear pair was established, and micro-parameter automatic optimization was carried out with the goal of uniform tooth surface load. Helix modification and crowning optimization were performed, and different edge stress coefficient schemes were set for LTCA analysis. The results, including modification amounts, transmission errors, maximum tooth surface contact stresses, and stress distributions, are shown in Table 3 and Figure 4.
| Scheme | Edge Stress Coefficient | Helix Modification Amount/m | Crowning Amount/m | Transmission Error/m | Maximum Tooth Surface Contact Stress/MPa |
|---|---|---|---|---|---|
| 1 | 0.6 | 6.762 | 22.8000 | 0.3128 | 793.65 |
| 2 | 0.7 | 6.675 | 14.8940 | 0.1886 | 764.53 |
| 3 | 0.8 | 5.655 | 8.1000 | 0.0910 | 739.15 |
| 4 | 0.9 | 2.805 | 5.2237 | 0.1053 | 727.06 |
| 5 | 1.0 | 2.557 | 5.0718 | 0.1067 | 726.85 |
By comparing the tooth surface load distribution along the tooth width, transmission error, and maximum tooth surface contact stress, Scheme 3 was selected as the basis for further tip modification optimization. Compared to the unmodified gear, its transmission error was reduced by 61.9%, and the maximum tooth surface contact stress was reduced by 8.6%.
3.1.2 Mechanical Design Manual Calculation Method
According to the “Mechanical Design Manual”, the formulas for the tooth lead elastic deformation of a single helical gear were used to calculate the bending deformation amount δb = 1.6358 μm and the torsional deformation amount δt = 5.3829 μm. Considering the thermal deformation due to the high line speed of the gear (105.01 m/s), the thermal deformation modification amount Δδ = 2 μm was added. The total helix modification amount was 7.3829 μm (bending + torsional + thermal), and the crowning amount was also 7.3829 μm. The transmission error in this case was 0.1228, and the maximum tooth surface contact stress was 788.20 MPa.
Although the empirical formulas in the mechanical design manual can reduce the transmission error and maximum tooth surface contact stress, there are still some differences compared to the optimization results provided by the software. The MASTA optimization scheme shows better performance in terms of reducing the transmission error and maximum tooth surface contact stress when compared to the mechanical design manual optimization scheme and the unmodified gear.
3.2 Gear Tip Modification
3.2.1 Modification Curve
The modification curve can be divided into two types: linear and parabolic. Different modification curves can affect the distribution of stress and load on the tooth surface.
3.2.2 Modification Length
The modification length refers to the distance from the modification starting point to the tooth tip and can be classified as long modification and short modification. The long modification starts from the critical point of single-double tooth alternation and extends to the tooth tip, while the short modification length is half of the long modification length. The calculation formula for the modification length is given, and the modification parameters for different schemes are presented in Table 5.
| Scheme | Pinion Tip Modification Circle Radius/mm | Gear Tip Modification Circle Radius/mm | Modification Length/ mm |
|---|---|---|---|
| Long modification | 252.1789 | 750.2299 | 11.63 |
| Short modification | 256.6105 | 754.2683 | 5.815 |
3.2.3 Modification Amount
Using the empirical formulas provided by MAAG, the ranges of the tip modification amounts for the pinion and gear were calculated. Based on these results, a tip modification scheme was designed using an enumeration method with an interval of 4 μm. The details of the modification amounts for different schemes are shown in Table 6.
3.2.4 Tip Modification Optimization
There are two methods for tip modification of heavy-duty and high-speed gear pairs. In this study, the method of modifying both the pinion and gear was adopted. Different combinations of modification curves and lengths were analyzed using LTCA in MASTA. The results of the transmission error and maximum contact stress for each scheme are presented in Table 7.
From the data in Table 7, it can be seen that long modification (linear and parabolic) generally shows better performance in terms of reducing the transmission error compared to short modification. The parabolic long modification also has a more uniform tooth surface load distribution and a relatively smaller maximum contact stress.
Based on the results of the MAAG empirical formulas, the parabolic long modification method was selected for tip modification. Using the modification design space search function of MASTA with a step size of 1 μm and a modification amount range of 10 – 30 μm, 441 modification schemes were obtained. After considering the tooth surface load distribution, transmission error, and maximum tooth surface contact stress, the final tip modification amounts for the pinion and gear were determined to be 19 μm and 20 μm, respectively. The transmission error curve, stress nephogram, and gear performance parameters in the final scheme are shown in Figure 6, Figure 7, and Table 8.
4. Results and Discussion
4.1 Comparison of Tooth Lead Modification Results
Using the MASTA software for tooth lead modification optimization, the transmission error was reduced by 61.9% compared to the mechanical design manual optimization method and 25.9% compared to the unmodified gear when the tooth surface contact stress was uniformly distributed along the tooth width. The maximum tooth surface contact stress was reduced by 8.6% compared to the unmodified gear and 6.2% compared to the mechanical design manual optimization method.
4.2 Overall Modification Results
When both tooth lead modification and tip modification were carried out using the MASTA software, compared to the unmodified scheme, the transmission error was reduced by 8.0% and the transmission error curve was closer to a sine curve when the tooth surface contact stress was more uniformly distributed. The maximum tooth surface contact stress was reduced by 6.2%, and the tooth surface load distribution coefficient KHB was reduced from 1.1952 to 1.1445. These results indicate that the modification optimization scheme effectively improves the meshing performance of the gear.
4.3 Significance of Modification Optimization
The optimized modification scheme not only reduces the transmission error and maximum tooth surface contact stress but also improves the distribution of tooth surface load. This leads to a more stable meshing process, reduces wear and tear on the gears, and prolongs the service life of the gear system. It is of great significance for improving the performance and reliability of gear-driven equipment in various fields such as ship power plants.
5. Conclusion
In this study, a pair of single helical gears was analyzed and modified using the MASTA software. Different modification strategies were explored, and an optimized modification scheme was obtained. The main conclusions are as…
6. Future Research Directions
Although significant progress has been made in the optimization of single helical gear modification in this study, there are still several areas that can be further explored in future research.
6.1 Consideration of More Complex Working Conditions
In real applications, gears often operate under more complex working conditions, such as variable loads, different speeds, and varying temperatures. Future research could focus on studying the performance of modified gears under these more complex conditions. This may involve conducting experiments or simulations that incorporate these factors to better understand how the modification affects gear performance and to develop more robust modification strategies.
For example, variable load conditions can cause different stress distributions on the tooth surface compared to constant load situations. Understanding how the gear modification adapts to these changing loads and maintaining good performance under such conditions is crucial for practical applications. Similarly, different operating speeds can affect the dynamic behavior of the gears, and temperature variations can lead to changes in material properties and gear dimensions, all of which need to be considered in the design and optimization of gear modification.
6.2 Optimization of Modification Parameters for Different Gear Materials
The current study focused on gears made of 42CrMo. However, different gear materials have different mechanical properties, such as elastic modulus, Poisson’s ratio, and hardness. These material properties can influence the effectiveness of gear modification. Future research could investigate how to optimize the modification parameters for different gear materials to achieve the best performance.
For instance, a gear material with a higher elastic modulus may require different modification amounts or curves compared to a material with a lower elastic modulus. By studying the relationship between material properties and modification parameters, more precise and effective modification strategies can be developed for a wide range of gear materials, expanding the applicability of the research findings.
6.3 Incorporation of Advanced Manufacturing Technologies
With the development of advanced manufacturing technologies, such as 3D printing and precision machining techniques, there is an opportunity to explore how these technologies can be integrated with gear modification. For example, 3D printing allows for the production of gears with complex geometries and customized modification features. Research could focus on how to design and optimize gear modification for 3D printed gears to take full advantage of this manufacturing method.
Precision machining techniques can also provide higher accuracy in achieving the desired modification parameters. Future studies could investigate how to combine these machining techniques with the optimization of gear modification to ensure that the modification is accurately implemented and to further improve gear performance.
6.4 Investigation of the Long-Term Performance of Modified Gears
The current study mainly focused on the immediate effects of gear modification on performance parameters such as transmission error and contact stress. However, the long-term performance of modified gears is also of great importance. Future research could involve long-term tests or simulations to monitor the wear, fatigue, and degradation of modified gears over time.
This would help in understanding how the modification affects the service life of the gears and whether any adjustments or improvements to the modification strategy are needed to ensure long-term reliability. For example, studying how the modified tooth surface wears over a long period and whether the initial optimization of load distribution and stress reduction is maintained throughout the gear’s life cycle can provide valuable insights for improving the design and maintenance of gear systems.
In conclusion, while the current research on single helical gear modification based on MASTA has yielded valuable results, there are still many opportunities for further exploration and improvement in future research. By addressing these potential research directions, more comprehensive and effective gear modification strategies can be developed, contributing to the advancement of gear technology and the improvement of mechanical systems that rely on gears.