In recent years, the rapid growth of the electric car industry, particularly in the China EV market, has heightened the importance of Noise, Vibration, and Harshness (NVH) performance. As an engineer specializing in powertrain systems, I have encountered numerous challenges related to gear whine noise in electric car reducers. Unlike traditional internal combustion engine vehicles, electric cars lack the masking effect of engine noise, making high-frequency gear whine more perceptible and irritating to occupants. This paper details my investigation into a specific case of gear whine noise in a China EV model, focusing on the analysis, optimization, and validation processes. The study involves comprehensive NVH testing, dynamic simulations, and structural modifications to address the issue, with an emphasis on the role of gear modal properties in whine generation.
The electric car under study exhibited a pronounced whine noise during acceleration, specifically at a speed of 110 km/h, which corresponds to a reducer input speed of 8,280 rpm. Initial subjective evaluations indicated that the noise was most noticeable under full-throttle acceleration conditions. To objectively characterize this issue, I conducted NVH tests in accordance with standard protocols, measuring sound pressure levels at the rear passenger seat and vibration accelerations on the reducer housing. The data acquisition included signals from the vehicle’s CAN bus, such as motor speed and torque, to facilitate order analysis. The test setup involved accelerometers mounted on the reducer output shaft and a microphone positioned inside the cabin, ensuring accurate capture of the noise and vibration responses.
Order analysis of the acquired data revealed a significant peak at the 26th order of the reducer input speed, with a sound pressure level exceeding 42.5 dB(A) at 8,280 rpm, well above the target of 35 dB(A). This order corresponds to the meshing frequency of the first-stage gears in the reducer. The reducer in this electric car employs a two-stage gear train, and the gear parameters are summarized in Table 1. The first-stage gears have 26 and 81 teeth for the pinion and wheel, respectively, resulting in a meshing order of 26. At 8,280 rpm, the meshing frequency is calculated as 3,588 Hz using the formula:
$$f_m = \frac{n \times Z}{60}$$
where \( f_m \) is the meshing frequency, \( n \) is the input speed in rpm, and \( Z \) is the number of teeth on the pinion. This frequency became the focal point of the investigation, as it coincided with the observed whine noise.
| Parameter | First-Stage Pinion | First-Stage Wheel | Second-Stage Pinion | Second-Stage Wheel |
|---|---|---|---|---|
| Number of Teeth | 26 | 81 | 23 | 76 |
| Meshing Order | 26 | 26 | 7.38 | 7.38 |
To determine the root cause of the whine, I first examined the transmission paths. The vibration data from the reducer housing showed a peak at the 26th order, indicating that the noise originated from the reducer itself rather than external paths. I then performed a frequency response analysis using a multibody dynamics model of the reducer, which included flexible components such as the intermediate shaft, first-stage wheel, and housing. The model was built using commercial software, and a unit harmonic dynamic meshing force was applied to the first-stage gears. The resulting acceleration response at the output shaft measurement point showed no significant amplification at 3,588 Hz, with the nearest peak at 3,360 Hz. This ruled out the transmission path from the gears to the housing as the primary cause of amplification, suggesting that the issue lay with the excitation source itself.
Next, I analyzed the excitation sources, starting with the static transmission error (TE). Transmission error is a key indicator of gear NVH performance, representing the deviation between the theoretical and actual positions of the meshing gears. For a pair of gears, the TE in the line of action can be expressed as:
$$TE = \theta_2 r_2 – \theta_1 r_1$$
where \( \theta_1 \) and \( \theta_2 \) are the rotational angles of the pinion and wheel, and \( r_1 \) and \( r_2 \) are their base circle radii. Alternatively, in terms of angular error:
$$TE = \theta_2 – \frac{\theta_1 Z_1}{Z_2}$$
Simulations of the design TE peak-to-peak value under the operating torque of 140 N·m (corresponding to 8,280 rpm) yielded a result of 0.1154 μm, which is below the typical threshold of 0.3 μm for whine noise. This indicated that the design TE was not the primary contributor. Additionally, the gears were manufactured with grinding processes and met ISO 1328 Grade 6 accuracy standards, with no significant geometric deviations or assembly issues found during tolerance checks. Thus, I shifted focus to the dynamic behavior of the system.
A dynamic response analysis of the reducer was conducted using a rigid-flexible coupled model. The equations of motion for the gear pair can be represented by a 4-degree-of-freedom system:
$$m_1 \ddot{y}_1 + c_1 \dot{y}_1 + k_1 y_1 + k_m TE + c_m \dot{TE} = 0$$
$$m_2 \ddot{y}_2 + c_2 \dot{y}_2 + k_2 y_2 + k_m TE + c_m \dot{TE} = 0$$
$$I_1 \ddot{\theta}_1 + (k_m TE + c_m \dot{TE}) r_1 + T_1 = 0$$
$$I_2 \ddot{\theta}_2 + (k_m TE + c_m \dot{TE}) r_2 + T_2 = 0$$
where \( m_1, m_2 \) are masses, \( I_1, I_2 \) are moments of inertia, \( k_1, k_2 \) and \( c_1, c_2 \) are support stiffness and damping, and \( k_m, c_m \) are the time-varying meshing stiffness and damping. The dynamic meshing force \( k_m TE + c_m \dot{TE} \) contains alternating components that excite vibrations. Under the 26th order excitation at 3,588 Hz, the simulation revealed a localized resonance in the first-stage wheel, characterized by radial distortion mode. The system modal analysis identified a mode at 3,546 Hz (27th order) with a similar shape, and the frequency deviation of 1.2% suggested overlap. To confirm this, I performed a free modal analysis of the first-stage wheel using finite element software, considering the constraint from the intermediate shaft. The results, summarized in Table 2, showed that the 3rd and 4th elastic modes were radial distortion modes with frequencies close to 3,590 Hz, aligning with the meshing frequency at the whine condition.
| Mode Number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Frequency (Hz) | 3,064 | 3,087 | 3,590 | 3,592 | 4,529 |
| Mode Shape | Bending | Bending | Radial Distortion | Radial Distortion | Torsional |
Based on these findings, I concluded that the whine noise was caused by the coincidence of the first-stage gear meshing frequency with the radial distortion modal frequency of the first-stage wheel. This resonance amplified the dynamic transmission error, leading to excessive dynamic meshing forces and audible whine. To mitigate this, I proposed two design modifications to alter the modal characteristics of the first-stage wheel: one with a thinner web and another with a thicker web. The original design had a web thickness of 11 mm and a rim thickness of 8.73 mm; the thinner web design reduced the web to 10 mm and the rim to 6.2 mm, while the thicker web design increased the web to 16 mm, keeping the rim unchanged. These changes aimed to shift the radial distortion mode frequency away from the critical meshing frequency range.
I conducted modal simulations for both new designs using the same finite element approach. The results, presented in Tables 3 and 4, show that the thinner web design lowered the radial distortion mode frequencies to around 3,143 Hz, whereas the thicker web design raised them to approximately 4,294 Hz. This demonstrated that web thickness significantly influences the modal properties, which is crucial for electric car applications where weight and space constraints are common in China EV designs.
| Mode Number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Frequency (Hz) | 3,074 | 3,075 | 3,143 | 3,143 | 4,219 |
| Mode Shape | Bending | Bending | Radial Distortion | Radial Distortion | Torsional |
| Mode Number | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Frequency (Hz) | 3,534 | 3,536 | 4,294 | 4,295 | 5,380 |
| Mode Shape | Bending | Bending | Radial Distortion | Radial Distortion | Torsional |
To validate these simulations, I performed NVH tests on the electric car with the modified gears. For the thinner web design, the 26th order resonance peak shifted to 7,320 rpm (3,172 Hz), with a sound pressure level of 47 dB(A), indicating worsened whine. In contrast, the thicker web design showed no significant whine up to 120 km/h, with a maximum sound pressure level of 36.2 dB(A) at 3,345 rpm. Further testing on a dynamometer for the thicker web design revealed a resonance peak at 9,920 rpm (4,298.7 Hz), which matches the simulated modal frequency of 4,294 Hz. A comparison of the design TE peak-to-peak values across the designs, as shown in Table 5, confirmed that the differences were minimal and within acceptable limits, reinforcing that the whine was due to dynamic effects rather than static TE.
| Design | 110 N·m | 140 N·m | 165 N·m |
|---|---|---|---|
| Original | 0.112 | 0.1154 | 0.118 |
| Thinner Web | 0.111 | 0.114 | 0.117 |
| Thicker Web | 0.113 | 0.116 | 0.119 |
The correlation between the NVH test results and modal simulations, summarized in Table 6, validates the initial hypothesis. For each design, the measured resonance frequency closely matched the simulated radial distortion modal frequency, with deviations of less than 1%. This consistency underscores the importance of modal analysis in addressing gear whine in electric car reducers, especially for China EV models where NVH standards are stringent. The thicker web design successfully eliminated the whine by elevating the modal frequency beyond the common operating range, demonstrating that increasing the radial distortion modal frequency is an effective strategy for noise control.
| Design | Resonance Speed (rpm) | Resonance Frequency (Hz) | Simulated Modal Frequency (Hz) | Deviation (%) |
|---|---|---|---|---|
| Original | 8,280 | 3,588 | 3,590 | 0.06 |
| Thinner Web | 7,320 | 3,172 | 3,143 | 0.9 |
| Thicker Web | 9,920 | 4,298.7 | 4,294 | 0.11 |
In conclusion, this study highlights the critical role of gear modal properties in managing whine noise in electric car reducers. Through a combination of NVH testing, dynamic simulation, and structural optimization, I identified and resolved a resonance-induced whine issue in a China EV model. The findings emphasize that, beyond traditional factors like transmission error and gear accuracy, dynamic resonances must be considered in the design phase. The thicker web solution proved effective, and this approach can be extended to other electric car applications to enhance NVH performance. Future work could explore additional geometric modifications or material changes to further optimize gear dynamics for the evolving China EV market.