In the rapidly evolving landscape of the automotive industry, the noise, vibration, and harshness (NVH) performance of electric vehicles (EVs) has become a critical differentiator for manufacturers. Unlike traditional internal combustion engine vehicles, electric vehicles lack the masking effect of engine noise, making high-frequency noises such as gear whine from reducers more perceptible and irritating to passengers. This issue is particularly pronounced in China EV markets, where consumer expectations for comfort are high. In this study, we investigate a specific case of gear whine noise in an electric vehicle reducer, focusing on the first-stage gears during acceleration. Our approach combines experimental testing, simulation analysis, and optimization strategies to identify the root cause and propose effective solutions. The integration of advanced modeling techniques and real-world validation underscores the importance of addressing NVH challenges in the design phase of electric vehicle components.
The gear whine noise was initially identified during full-throttle acceleration tests of the electric vehicle, where a distinct whine was subjectively perceived at a vehicle speed of approximately 110 km/h. To quantify this phenomenon, we conducted NVH testing in accordance with standard protocols, collecting data on sound pressure levels and vibration accelerations. The test setup included sensors positioned at the rear seat area for acoustic measurements and on the reducer housing for vibration analysis, alongside CAN bus data acquisition for motor speed and torque. The results revealed a significant peak in the 26th order sound pressure level at an input speed of 8,280 rpm, corresponding to the first-stage gear meshing frequency. This finding prompted a detailed investigation into the dynamics of the reducer system in the context of electric vehicle applications.
To understand the transmission path of the gear whine noise, we employed a frequency response function analysis using a rigid-flex coupled model of the reducer developed in MASTA software. The model incorporated finite element representations of key components, such as the intermediate shaft, first-stage driven gear, and housing. By applying a unit harmonic dynamic meshing force to the first-stage gears, we simulated the vibration response at the output shaft. The amplitude-frequency response function showed no significant amplification at the whine frequency of 3,588 Hz, indicating that the path from the gears to the reducer housing was not the primary contributor. This led us to focus on the excitation source itself, emphasizing the need for a thorough analysis of gear dynamics in electric vehicle systems.
The excitation source for gear whine is often attributed to transmission error (TE), which represents the deviation between the theoretical and actual positions of gears during meshing. The static transmission error, comprising design and manufacturing components, can lead to dynamic excitations under operational conditions. For the first-stage gears, we calculated the design TE using simulation tools, with the peak-to-peak value expressed as:
$$TE_{pp} = \max(TE) – \min(TE)$$
where TE is defined as the linear error along the line of action:
$$TE = \theta_2 r_2 – \theta_1 r_1$$
Here, $\theta_1$ and $\theta_2$ denote the rotational angles of the driving and driven gears, respectively, while $r_1$ and $r_2$ are their base circle radii. Under the torque condition of 140 N·m at 8,280 rpm, the design TE peak-to-peak value was 0.1154 μm, which is below the typical threshold of 0.3 μm for NVH concerns. Additionally, gear accuracy met ISO 1328 Grade 6 standards, and geometric tolerances were within specifications, ruling out manufacturing defects as the primary cause. This directed our attention to the dynamic response of the system, particularly the interaction between meshing frequency and structural modes.
We performed a dynamic analysis of the reducer to assess the system’s response to TE excitations. The equations of motion for a gear pair can be represented as a four-degree-of-freedom model, including translational and rotational freedoms:
$$m_1 \ddot{y}_1 + c_1 \dot{y}_1 + k_1 y_1 + k_m TE + c_m \dot{TE} = 0$$
$$m_2 \ddot{y}_2 + c_2 \dot{y}_2 + k_2 y_2 + k_m TE + c_m \dot{TE} = 0$$
$$I_1 \ddot{\theta}_1 + (k_m TE + c_m \dot{TE}) r_1 + T_1 = 0$$
$$I_2 \ddot{\theta}_2 + (k_m TE + c_m \dot{TE}) r_2 + T_2 = 0$$
where $m_1$, $m_2$, $I_1$, and $I_2$ are the masses and moments of inertia, $k_1$, $k_2$, $c_1$, and $c_2$ are the support stiffness and damping, and $k_m$ and $c_m$ are the time-varying meshing stiffness and damping. The dynamic meshing force $k_m TE + c_m \dot{TE}$ contains oscillatory components that act as excitation sources. At the whine condition, the first-stage gear meshing frequency coincided with the radial distortion mode frequency of the first-stage driven gear, leading to resonance. This resonance amplified the dynamic TE, resulting in excessive noise emission, a common issue in high-speed electric vehicle applications.
To validate this hypothesis, we conducted modal analysis on the first-stage driven gear using Altair HyperWorks software. The gear was modeled with constraints simulating its assembly onto the intermediate shaft, and free and constrained modal frequencies were extracted. The radial distortion modes were identified as the primary contributors to the resonance. The table below summarizes the first five elastic modal frequencies of the driven gear in its original design:
| Elastic Mode Order | Modal Frequency (Hz) |
|---|---|
| 1 | 3,064 |
| 2 | 3,087 |
| 3 | 3,590 |
| 4 | 3,592 |
| 5 | 4,529 |
As shown, modes 3 and 4 correspond to radial distortion at frequencies close to the whine frequency of 3,588 Hz. This alignment confirmed that the gear whine was driven by resonance, necessitating design modifications to shift the modal frequencies away from the excitation range. In the context of electric vehicle development, such dynamic interactions are critical to address for ensuring superior NVH performance.
We proposed two optimization schemes to alter the radial distortion mode of the first-stage driven gear: one involving web thinning and another with web thickening. The web thickness was reduced from 11 mm to 10 mm in the first scheme, while in the second, it was increased to 16 mm. The rim thickness was also adjusted accordingly to maintain structural integrity. Modal simulations were repeated for these designs, and the results are compared below:
| Design Scheme | Web Thickness (mm) | Rim Thickness (mm) | Radial Distortion Mode Frequency (Hz) |
|---|---|---|---|
| Original | 11 | 8.73 | 3,590-3,592 |
| Web Thinning | 10 | 6.20 | 3,143 |
| Web Thickening | 16 | 8.73 | 4,294-4,295 |
The web thinning scheme lowered the modal frequency, while web thickening significantly increased it, demonstrating the sensitivity of modal characteristics to geometric changes. Subsequent NVH tests on the electric vehicle equipped with these designs revealed that the web thickening scheme effectively mitigated the whine noise, with the 26th order sound pressure level remaining below 36.2 dB(A) across the operating range. In contrast, the web thinning scheme exacerbated the issue, producing a higher peak at a lower speed. This underscores the importance of modal frequency positioning in electric vehicle reducer design.
Further validation was conducted on a dynamometer test bench to explore higher speed conditions. For the web thickening scheme, the resonance peak shifted to 9,920 rpm, corresponding to a frequency of 4,298.7 Hz, which aligns with the simulated modal frequency. The dynamic transmission error under various torque conditions was also analyzed, as summarized in the following table:
| Torque (N·m) | Original Design TE (μm) | Web Thinning TE (μm) | Web Thickening TE (μm) |
|---|---|---|---|
| 110 | 0.102 | 0.101 | 0.103 |
| 140 | 0.115 | 0.114 | 0.116 |
| 165 | 0.125 | 0.124 | 0.126 |
The minimal variation in TE values across designs confirms that the whine reduction was primarily due to the avoidance of resonance rather than changes in static transmission error. This insight is vital for optimizing electric vehicle powertrains, where dynamic effects often dominate NVH behavior.
In conclusion, our study demonstrates that gear whine in electric vehicle reducers can stem from resonance between meshing frequency and structural modes, particularly radial distortion of gears. By employing comprehensive simulation and testing, we identified the root cause and validated optimization strategies that shift modal frequencies. The web thickening design proved effective in eliminating the whine, highlighting the value of modal analysis in the development of quiet and efficient electric vehicles. As the China EV market continues to grow, such methodologies will be essential for meeting stringent NVH standards and enhancing consumer satisfaction. Future work could explore advanced materials and control strategies to further refine gear dynamics in high-performance electric vehicle applications.