In recent years, with the increasing demand for new energy vehicles, electric vehicles have attracted significant attention due to their advantages of zero emissions, low noise, and wide power sources. However, the noise of the gearbox in electric vehicles accounts for a large proportion of the overall vehicle noise, and the vibration and noise of the gears have a significant impact on the performance and comfort of the vehicle. Therefore, reducing the vibration and noise of the gears in the gearbox is crucial for improving the NVH (Noise, Vibration, Harshness) performance of electric vehicles. This article focuses on the helical gears in the gearbox of an electric vehicle and conducts in-depth research on gear modification and vibration noise reduction.
Introduction
The development of electric vehicles is driven by the need for energy conservation and environmental protection. However, the vibration and noise of the gearbox in electric vehicles have become a major concern. The gears in the gearbox are prone to vibration and noise due to various factors such as manufacturing errors, installation deviations, and dynamic loads. To address this issue, gear modification technology is widely used to improve the meshing performance, reduce vibration and noise, and increase the service life of the gears.
Background and Significance
The research on gear vibration noise has a history of over a hundred years. In the 1970s, British vibration noise expert Optiz H conducted the first systematic study on the dynamic characteristics of spur and helical gears. Since then, more and more experts and scholars have focused on this field. In the 1980s, Japanese scholars such as Saijo Takao, Aida Yoshio, and Umezaki Akihiko conducted comprehensive research on gearbox vibration noise using 3D modeling, computer simulation, and vibration noise testing. In the 1990s, Choy F K and others carried out numerical simulation and experimental studies on gearboxes, exploring the linear relationship between vibration and noise and the nonlinear relationship between fundamental noise frequency and harmonics. In the 21st century, the research on gear vibration noise has become more and more in-depth, and the methods and techniques for measuring and analyzing vibration noise have also been continuously improved.
The gear modification technology emerged in the 1930s and has gradually developed into an important means to reduce gear vibration and noise. Over the years, many scholars have conducted extensive research on gear modification, including the types, methods, and effects of modification. The research on the finite element simulation of helical gears has also made significant progress, providing important support for the design and optimization of gears.
The significance of this research lies in improving the performance and reliability of electric vehicles, enhancing the comfort of the vehicle, and promoting the development of the electric vehicle industry. By reducing the vibration and noise of the gears, the NVH performance of the electric vehicle can be improved, which is beneficial to the market competitiveness of the electric vehicle. At the same time, this research can also provide a reference for the design and manufacturing of gears, promoting the improvement of the quality and performance of gears.
Research Content and Methods
This article takes the helical gear pair of an electric vehicle gearbox as the research object and conducts the following research:
- Vibration Noise Mechanism Analysis: Analyze the vibration and noise mechanism of the electric vehicle gearbox and helical gears, establish a nonlinear vibration mathematical model, and study the internal dynamic excitation of the gears.
- Preliminary Optimization Modification and Meshing Contact Analysis: Use the KISSsoft software to explore the influence of gear modification technology and gear parameters on the meshing performance of the gears, and obtain the preliminary optimization modification scheme based on reducing the transmission error and Hertz contact stress.
- Secondary Optimization Modification and Multi-body Dynamics Analysis: Based on the preliminary optimization modification scheme, use the LMS Virtual Lab Motion module to further optimize the time-varying meshing force and time-varying meshing stiffness of the gears through multi-body dynamics simulation.
- Acoustic Analysis of the Secondary Optimization Modification Scheme: Use the LMS Virtual Lab Acoustic software to conduct acoustic analysis on the secondary optimization modification schemes to determine the best modification scheme with the lowest noise.
- Simulation and Experimental Study on the Influence of Traditional Empirical Modification on the Performance of Helical Gears: Based on the phenomenon that the vibration noise and service life of the helical gears decrease after empirical modification in an enterprise, conduct simulations and experiments to analyze the reasons behind this phenomenon.
The research methods mainly include theoretical analysis, numerical simulation, and experimental verification. The theoretical analysis is used to establish the mathematical model and analyze the mechanism of gear vibration and noise. The numerical simulation is carried out using professional software such as KISSsoft and LMS Virtual Lab to simulate the meshing process, dynamics, and acoustics of the gears. The experimental verification is conducted through contact spot tests and noise bench tests to validate the simulation results.
Results and Discussion
- Vibration Noise Mechanism Analysis
- Noise Sources in the Gearbox: The noise in the electric vehicle gearbox is mainly composed of gear whine and gear rattle, and the vibration noise of the gears accounts for about 80% of the total noise.
- Factors Affecting Gear Vibration Noise: The internal dynamic excitation and tooth shape of the gears are the main factors affecting the vibration noise, especially the gear whine noise. The stiffness excitation, error excitation, and meshing impact excitation are the main sources of internal dynamic excitation.
- Influence of Stiffness Excitation and Error Excitation: The time-varying meshing stiffness and time-varying meshing force caused by stiffness excitation, and the transmission error caused by error excitation all have a significant impact on the vibration and noise of the gears. By reducing the transmission error, time-varying meshing stiffness, and time-varying meshing force, the meshing impact excitation can be suppressed.
- Preliminary Optimization Modification and Meshing Contact Analysis
- Influence of Gear Parameters on Meshing Performance: Increasing the tooth width and pressure angle of the helical gear can improve the transmission efficiency and Hertz contact stress, but it will increase the transmission error. The appropriate helix angle can reduce the transmission error, Hertz contact stress, and time-varying meshing force, but a larger helix angle will result in lower transmission efficiency.
- Effect of Tooth Profile Modification and Tooth Direction Modification: Tooth profile modification mainly reduces the Hertz contact stress on the tooth surface to improve the strength and life of the gear, but it can also reduce the transmission error. Tooth direction modification mainly reduces the transmission error to reduce the internal dynamic excitation of the gear, but it can also reduce the Hertz contact stress.
- Preliminary Optimization Modification Scheme: Based on the analysis of tooth profile modification and tooth direction modification, several preliminary optimization modification schemes are proposed, such as long tooth profile addendum linear modification, long tooth profile addendum arc-like modification, long tooth profile addendum progressive modification, and tooth profile drum modification. These schemes can effectively reduce the transmission error and Hertz contact stress of the gears.
- Meshing Performance Improvement after Modification: After the preliminary optimization modification, the meshing performance of the gears is significantly improved, including the increase in transmission efficiency, the reduction in transmission error, the improvement in oil film thickness, the decrease in flash temperature and contact temperature, the optimization of the tooth surface load distribution, the reduction in tooth surface contact stress, and the stability of the sliding coefficient.
- Secondary Optimization Modification and Multi-body Dynamics Analysis
- Influence of Gear Parameters on Time-varying Meshing Stiffness and Time-varying Meshing Force: The appropriate helix angle can significantly reduce the time-varying meshing force and make the meshing smoother, but it will increase the time-varying meshing stiffness. The tooth side clearance has no effect on the time-varying meshing stiffness, but a smaller tooth side clearance will reduce the time-varying meshing force at low speeds. The large pressure angle is beneficial to reducing the time-varying meshing stiffness. The tooth width only affects the time-varying meshing force at low speeds, and a larger tooth width can reduce the time-varying meshing force, but it will increase the time-varying meshing stiffness.
- Effect of Helical Gear Optimization Modification on Time-varying Meshing Stiffness and Time-varying Meshing Force: Among the long tooth profile addendum modification schemes, the linear modification can reduce the time-varying meshing force and time-varying meshing stiffness to a certain extent. The arc-like and progressive modifications can significantly reduce the time-varying meshing force and time-varying meshing stiffness, and eliminate the meshing impact phenomenon. The tooth profile drum modification can effectively reduce the time-varying meshing force and meshing impact, and the choice of the modified gear is crucial. The composite modification schemes generally do not have a significant effect on reducing the time-varying meshing force and improving the meshing impact, and they also increase the cost. Therefore, in the case where the single modification scheme can meet the requirements, the composite modification is not recommended.
- Acoustic Analysis of the Secondary Optimization Modification Scheme
- Modal Analysis of the Gearbox Housing: The modal analysis is conducted to study the natural modes and frequencies of the gearbox housing, which is helpful to understand the vibration characteristics of the housing and avoid resonance. The results show that the low-frequency vibration characteristics of the housing are good, and the natural frequencies of the first 10 modes are relatively high, so the influence of the housing structure on the vibration and noise of the gears can be ignored.
- Acoustic Simulation and Results Analysis: The acoustic simulation is carried out using the LMS Virtual Lab Acoustic software to analyze the noise characteristics of the gears after different modification schemes. The results show that the tooth profile drum modification (with both large and small gears modified) has the best vibration and noise reduction effect, followed by the long tooth profile addendum arc-like and progressive modifications. The long tooth profile addendum linear and tooth profile drum modifications (only the small gear modified) have relatively poor effects. The composite modification schemes do not have a significant effect on noise reduction.
- Determination of the Best Modification Scheme: Based on the analysis of the optimization degree, the tooth profile drum modification (with both large and small gears modified) is determined as the best modification scheme. This scheme can reduce the internal dynamic excitation of the gears, and the tooth shape is also suitable, so the vibration and noise of the gears can be effectively reduced.
- Simulation and Experimental Study on the Influence of Traditional Empirical Modification on the Performance of Helical Gears
- Parameters and Experimental Setup: The study takes two pairs of helical gears before and after empirical modification provided by an enterprise as the research object. The specific empirical modification scheme is the combined tooth profile and tooth direction drum modification of both large and small gears with a modification amount of 25 μm. The gearbox is simplified and designed as a rectangular shape for the noise bench test.
- Results and Analysis: The results show that after the empirical modification, the transmission error, Hertz contact stress, time-varying meshing force, and time-varying meshing stiffness of the helical gears increase, which leads to the aggravation of vibration and noise, the serious wear of the tooth surface, and the shortening of the service life. This is because the empirical modification scheme does not effectively reduce the internal dynamic excitation of the gears and the tooth shape is not suitable, resulting in the increase of the vibration and noise of the gears.
Conclusions
- The appropriate increase in the pressure angle of the helical gear can improve the transmission efficiency, Hertz contact stress, and time-varying meshing stiffness, but it will increase the transmission error. The appropriate helix angle can reduce the transmission error, Hertz contact stress, and time-varying meshing force, but a larger helix angle will result in lower transmission efficiency. Increasing the tooth width can reduce the time-varying meshing force at low speeds, but a larger tooth width will increase the time-varying meshing stiffness. The tooth side clearance has no effect on the time-varying meshing stiffness, but a smaller tooth side clearance will reduce the time-varying meshing force at low speeds.
- Tooth profile modification mainly reduces the Hertz contact stress on the tooth surface to improve the strength and life of the gear, but it can also reduce the transmission error. Tooth direction modification mainly reduces the transmission error to reduce the internal dynamic excitation of the gear, but it can also reduce the Hertz contact stress.
- Comparing the multi-body dynamics and acoustic numerical simulation results of the long tooth profile addendum linear modification, long tooth profile addendum zigzag arc modification, and only the tooth profile drum modification of the small gear, it is found that although the time-varying meshing force of the gears does not decrease and even increases at high speeds, the noise power level decreases relatively before the modification. Therefore, it is considered that the vibration noise of the helical gear at high speeds (10000 r/min) may mainly depend on the stiffness excitation (time-varying meshing stiffness) and error excitation (transmission error).
- Taking this gear pair as an example, from the perspective of vibration and noise reduction, it is recommended to modify both the large and small gears simultaneously. If only reducing the transmission error and improving the gear strength are desired, only the large gear can be modified, but it is recommended to modify both the large and small gears simultaneously, and the possibility of composite modification should be considered (such as only the long tooth profile addendum arc-like modification of the large gear by 3 μm + tooth direction drum modification by 3 μm, the transmission error decreases by about 8.2%, and the Hertz contact stress decreases by about 3.6%). In addition, except for the tooth profile drum modification, only modifying the small gear has a poor effect on vibration and noise reduction and life extension.
- Among all the long tooth profile addendum secondary optimization modification schemes (linear, progressive, arc-like, zigzag arc) of the helical gear, in terms of reducing the gear error excitation and improving the gear strength, the linear effect is the best (the transmission error decreases by about 17.6%, and the Hertz contact stress decreases by about 6.6%). In terms of reducing the time-varying meshing force and time-varying meshing stiffness of the gear, the arc-like and progressive effects are better (the time-varying meshing force decreases by 123.41 N, 1606.187 N, 2492.734 N, and 122.687 N, 1540.64 N, 2348.992 N at low, medium, and high speeds, respectively, and the time-varying meshing stiffness decreases by about 14.3% and 14.1%, respectively). In terms of the overall noise reduction effect, the arc-like and progressive effects are better (the average sound power in the full frequency range decreases by 5.2 dBA, 1.6 dBA, 2.8 dBA, and 4 dBA, 2.1 dBA, 2.9 dBA at low, medium, and high speeds, respectively).
- Among all the modification schemes of the helical gear in the electric vehicle gearbox optimized by the transmission error, Hertz contact stress, time-varying meshing force, and time-varying meshing stiffness, the tooth profile drum (with both large and small gears modified) has the best vibration and noise reduction effect (the average sound power in the full frequency range at low, medium, and high speeds decreases by 8.4 dBA, 1.7 dBA, 3 dBA, respectively). Since the overall noise reduction effect of the tooth profile drum (only the large gear modified) optimization scheme is close to that of most secondary optimization modification schemes, considering the production cost, only the tooth profile drum optimization modification of the large gear can be used more in engineering practice. For the tooth profile drum modification, the choice of the modified gear is extremely important. If the main purpose is to reduce the stiffness excitation of the helical gear, it is recommended to modify both the large and small gears simultaneously (the time-varying meshing stiffness decreases by about 16.3%). If the goal is to reduce the time-varying meshing force of the helical gear, it is recommended to only modify the large gear (the time-varying meshing force decreases by 425.59 N, 5174.793 N, 5925.515 N at low, medium, and high speeds, respectively). If only reducing the gear error excitation and improving the gear strength are desired, only the small gear can be modified (the transmission error decreases by about 16.3%, and the Hertz contact stress decreases by about 13.8%), but this is not recommended (the high-frequency noise (4978.5 Hz – 8525 Hz) power level significantly increases at low speeds).
- Many studies simply evaluate whether the gear meshing noise is improved based on the level of the transmission error before and after gear modification, which is not rigorous. From the simulation results, only by reducing the time-varying meshing stiffness, time-varying meshing force, and transmission error simultaneously through gear modification, and having a suitable tooth shape, can the vibration noise of the helical gear be reduced.
- Blind empirical modification of gears should be avoided, as it will only increase the production cost, aggravate the vibration noise of the gear pair, and shorten its service life, as shown by the case of the helical gears in an enterprise (the combined tooth profile and tooth direction drum modification of both large and small gears by 25 μm).
- A novel idea for gear optimization modification is summarized: 1. Determine the modification goal. 2. Develop the modification scheme. 3. Based on the modification scheme, use KISSsoft to preliminarily optimize the meshing performance of the gear pair, such as transmission error and Hertz contact stress. 4. Based on the preliminary optimization modification scheme, use LMS Virtual Lab Motion to secondarily optimize the dynamic performance of the helical gear, such as time-varying meshing force and time-varying meshing stiffness. 5. Use LMS Virtual Lab Acoustic to compare the acoustic performance of all the secondary optimization modification schemes of the helical gear. 6. Further verify the optimal modification scheme of the helical gear through contact spot tests, noise bench tests, transmission error tests, etc. 7. Put into production by the enterprise.