In the rapid development of the new energy vehicle industry, pure electric vehicles have gradually become the mainstream trend due to their zero emissions, low energy consumption, and comfortable driving experience. However, the removal of the traditional internal combustion engine and its masking noise sources significantly increases the sensitivity of the entire vehicle to noise, vibration, and harshness (NVH) performance. Particularly during energy regenerative coasting, the electric drive axle transmission system is prone to whining noise and structural vibration, which severely degrade the subjective quality and ride comfort. Among the critical subsystems of the electric drive axle, the dynamic meshing characteristics of the gear transmission have a decisive influence on NVH performance. Our research focuses on a specific type of pure electric pickup truck that exhibited abnormal vibration and noise during the energy regenerative coasting phase. Through systematic analysis and optimization, we aim to improve the NVH behavior of the electric drive axle, with special emphasis on the role of helical gear modification.
To identify the root cause of the abnormal noise, we first conducted on-vehicle vibration and noise tests. The electric drive axle in this study consists of an electric motor, a motor shaft, a first-stage helical gear pair, a second-stage helical gear pair, and a differential gear set. The complaint speed range was identified between 3500 and 5500 r/min during energy recovery. We installed an accelerometer on the axle housing to collect vibration signals and a microphone fixed on the chassis approximately 10 cm above the axle to capture radiated noise. The sampling frequency was set to 25.6 kHz. The tests were performed under three typical regenerative coasting conditions: low, medium, and high energy recovery, corresponding to torque ranges of 0–27 Nm, 37–65 Nm, and 73–102 Nm, respectively. The motor speed gradually decreased from 9500 r/min to 2000 r/min during the tests.
Using order tracking analysis, we processed the noise signals from the three conditions. The resulting colormaps revealed a prominent energy enhancement at the 27th order in all three cases. This order corresponds to the meshing frequency of the first-stage helical gear pair, where the number of teeth on the driving gear is 27. The strong energy band along the 27th order indicated that the first-stage helical gear pair was the primary excitation source for the abnormal vibration and noise. Particularly under the low energy recovery condition, the noise amplitude reached its maximum. The phenomenon suggested that the helical gear pair exhibited periodic impact characteristics during meshing, leading to an unstable dynamic response. Therefore, we decided to perform tooth surface modification on this helical gear pair to improve contact properties and reduce transmission error fluctuations, thereby suppressing the 27th order excitation and enhancing the overall NVH performance of the electric drive axle system.
To understand the meshing behavior of the helical gear pair under load, we developed a rigid-flexible coupled dynamic model using MASTA software. The model incorporated the flexibility of the axle housing, shafts, and support bearings, and treated the first-stage helical gears as flexible bodies whose modal properties were imported via finite element substructuring. This approach enabled a fully coupled analysis of structural deformation and gear meshing. The input boundary conditions were set to match the real vehicle test conditions, with constant motor torque at the input side and a fixed damping support at the output side to simulate the wheel-end regenerative state. A nonlinear transient dynamic solver was employed to capture the dynamic response and transmission error, with adaptive time steps based on the meshing period. The original helical gear pair had already undergone some modification during design, as listed in Table 1.
| Parameter | Driving gear | Driven gear |
|---|---|---|
| Normal module (mm) | 2 | 2 |
| Number of teeth | 27 | 98 |
| Helix angle (°) | 28.5 | 28.5 |
| Hand of helix | Right | Left |
| Pitch circle diameter (mm) | 62.64 | 227.36 |
| Normal pressure angle (°) | 18 | 18 |
| Face width (mm) | 42.5 | 40.5 |
| Accuracy grade | 6 | 6 |
| Crowning modification (μm) | 6 | 6 |
| Helix angle modification (μm) | 5 | -10 |
| Profile crowning (μm) | 3 | 5 |
| Pressure angle modification (μm) | -3 | 6 |
Based on the simulation model, we extracted the tooth contact characteristics and transmission error of the first-stage helical gear pair under the three energy recovery conditions. The transmission error is defined as the deviation between the theoretical and actual angular displacement of the driven gear when the driving gear rotates through a certain angle. It can be expressed as:
$$ \delta = r_1(\theta_2 – \theta_2′) – r_2(\theta_1 – \theta_1′) $$
where \( r_1 \) and \( r_2 \) are the pitch circle radii of the driving and driven helical gears, respectively; \( \theta_1 \) and \( \theta_2 \) are the instantaneous angular displacements; and \( \theta_1′ \) and \( \theta_2′ \) are the initial angular displacements. Under the low energy recovery condition, the maximum contact pressure on the tooth surface was 653.52 MPa, and the peak-to-peak transmission error was only 0.0983 μm. In this condition, the tooth load and elastic deformation were relatively small, leading to low mesh stiffness and significant backlash effects, which made the system more sensitive to disturbances and prone to generating vibration and noise. Under medium and high energy recovery conditions, the contact pressure increased to 883.22 MPa and 1583.35 MPa, respectively, with corresponding peak-to-peak transmission errors of 0.147 μm and 0.272 μm. As the load increased, tooth elastic deformation and mesh stiffness also increased, gradually eliminating backlash effects and stabilizing the dynamic response, which resulted in lower noise energy. However, under all three conditions, we observed edge contact characteristics with uneven load distribution along the tooth width direction. This non-uniform load distribution caused periodic variations in mesh stiffness, which was a major contributor to transmission error fluctuations. Therefore, further tooth surface modification was necessary to reduce the transmission error peak-to-peak value and improve the NVH performance.
To optimize the helical gear modification parameters, we employed an orthogonal experimental design approach. Based on existing literature and the specific characteristics of our helical gear pair, we selected four modification parameters as factors: crowning modification (A), helix angle modification (B), profile crowning (C), and pressure angle modification (D). These parameters were defined on the driving gear, and the same modifications were applied to the driven gear to reduce the number of factors. The total modification amount was the sum of the modifications on both gears, and the modification side was set to the left flank, which is the actual contact surface during meshing. The ranges of each parameter were determined based on tooth surface inspection reports, as shown in Table 2.
| Factor | Modification parameter | Lower limit | Upper limit |
|---|---|---|---|
| A | Crowning modification | 2 | 12 |
| B | Helix angle modification | -15 | 15 |
| C | Profile crowning | 2 | 10 |
| D | Pressure angle modification | -8 | 8 |
We conducted the orthogonal experiment using the low energy recovery condition as the baseline, and evaluated two key performance indicators: peak-to-peak transmission error and maximum tooth contact pressure. The results of the nine orthogonal experiments are listed in Table 3.
| Scheme | A (μm) | B (μm) | C (μm) | D (μm) | Transmission error peak-to-peak (μm) | Max contact pressure (MPa) |
|---|---|---|---|---|---|---|
| 1 | 2 | -15 | 2 | -8 | 0.0689 | 835.5 |
| 2 | 2 | 0 | 6 | 0 | 0.0780 | 582.6 |
| 3 | 2 | 15 | 10 | 8 | 0.1096 | 620.2 |
| 4 | 7 | -15 | 6 | 8 | 0.1123 | 584.5 |
| 5 | 7 | 0 | 10 | -8 | 0.0926 | 630.3 |
| 6 | 7 | 15 | 2 | 0 | 0.1098 | 565.1 |
| 7 | 12 | -15 | 10 | 0 | 0.2021 | 652.2 |
| 8 | 12 | 0 | 2 | 8 | 0.0851 | 697.4 |
| 9 | 12 | 15 | 6 | -8 | 0.0905 | 633.8 |
Through range analysis of the orthogonal experiment results, we identified the optimal combination of modification parameters that minimized the transmission error peak-to-peak value: crowning modification = 2 μm, helix angle modification = 0, profile crowning = 2 μm, and pressure angle modification = -8 μm. This combination corresponds to scheme 1 in Table 3, which yielded the lowest transmission error peak-to-peak among all schemes. We then applied this optimized modification to our rigid-flexible coupled dynamic model and recalculated the tooth contact characteristics and transmission error under the three energy recovery conditions.
The results showed a significant improvement in load distribution. The tooth contact pressure became more uniform along the meshing line, greatly suppressing the concentrated loads that previously caused meshing impacts. Under the low, medium, and high energy recovery conditions, the maximum contact pressure decreased to 537.67 MPa, 735.50 MPa, and 1235.42 MPa, respectively. Compared with the original design, these values were reduced by 17.73%, 16.73%, and 21.97%. The edge stress peaks were notably alleviated. Meanwhile, the peak-to-peak transmission error also improved substantially, reaching 0.0629 μm, 0.102 μm, and 0.208 μm for the three conditions, representing reductions of 36.01%, 30.61%, and 23.53% relative to the original values. Such reductions directly contribute to lower excitation levels in the overall system.
To validate the effectiveness of the optimized helical gear modification in real-world conditions, we manufactured new helical gear pairs with the optimized modifications using precision CNC gear grinding technology. The modification was applied to both the driving and driven gears with the same parameters. The manufacturing process for these modifications is well-established in modern gear production, requiring only minor additions to existing precision grinding steps, which has a limited impact on cost. We then installed the new gears into the same electric drive axle and conducted on-vehicle tests under the same three energy recovery conditions.
The colormaps obtained from the post-optimization tests clearly showed a noticeable reduction in the 27th order noise. Through order slice processing, we extracted the noise curves at the 27th order before and after optimization. Within the complaint speed range (3500–5500 r/min), the maximum noise amplitudes under the low, medium, and high energy recovery conditions decreased by 12 dB(A), 7 dB(A), and 4 dB(A), respectively. These improvements confirm that the proposed helical gear modification scheme effectively reduces the whining noise and enhances the NVH performance of the electric drive axle system in the complaint operating conditions.
In summary, we have demonstrated through a systematic approach combining experimental testing, dynamic modeling, orthogonal optimization, and real-vehicle validation that tooth surface modification of helical gear pairs is a highly effective strategy for mitigating vibration and noise in electric drive axles during energy regenerative coasting. The reduction in transmission error peak-to-peak values by up to 36% and the corresponding decrease in noise amplitudes by up to 12 dB(A) highlight the importance of careful modification design. This work provides valuable engineering insights for the noise and vibration reduction design of electric drive axle transmission systems, particularly for pure electric vehicles where NVH performance is critical to customer satisfaction.
We note that the optimal modification parameters identified in this study are specific to the helical gear geometry and load conditions of this particular electric drive axle. However, the methodology—combining experimental identification of problematic orders, rigid-flexible coupled simulation, orthogonal experimental design for modification optimization, and subsequent validation—can be generalized to other helical gear systems facing similar NVH issues. Future work may explore the influence of manufacturing tolerances, gear wear over time, and the interaction between multiple gear stages to further refine the modification strategy.