Automotive Innovation

, Volume 1, Issue 3, pp 272–280 | Cite as

Parameter Study and Improvement of Gearbox Whine Noise in Electric Vehicle

  • Shouyuan ZhangEmail author


Gearbox whine noise can seriously reduce the interior sound quality in an electric passenger car. In this work, a six-degree-of-freedom (6-DOF) dynamic model of a helical gear system was constructed and the mechanism for generation of whine noise was analyzed. The root cause of the problem was found through noise, vibration and harshness (NVH) testing of the gearbox and the vehicle. A rigid-elastic coupling dynamics model of the reducer assembly was then developed. The accuracy of the model was then validated via modal testing. The structure-borne noise of the reducer under full acceleration conditions was predicted using the acoustic structure coupling model and the rigid-elastic coupling model of the reducer. Gear parameters including the pressure angle, the helix angle and the contact ratio were studied to determine their effects on the whine noise. Gear tooth microgeometry modification parameters were then optimized to reduce the transmission error of the first pair of meshing gears. Finally, the whine noise from the gearbox was eliminated.


Gearbox Whine noise Simulation Electric vehicle 

1 Introduction

The electric vehicle (EV) industry has been developing rapidly over recent years. The noise characteristics of electric vehicles are completely different to those of internal combustion engine (ICE) vehicles. The reducer and auxiliary equipment such as vacuum pumps, electric power steering (EPS) units and high-voltage control units are also important noise sources, when the electric motor generates noise. While the overall noise level of an EV is lower than that of a typical ICE vehicle, noise such as the reducer noise, which may not be noticeable in ICE vehicles, becomes both obvious and annoying in EVs, particularly at low speeds. The sound quality in EVs is dominated by high-order noise, which is induced at high frequencies by the motor and the reducer, while the sound quality in ICE vehicles is characterized by the main engine noise orders in the low-frequency range. The whining noise in EVs with tonality characteristics that come from the reducer is particularly serious because of the low overall sound level, making it more annoying to the occupants.

Yoo et al. performed an in-depth study of the gear whine noise mechanism in automotive transmission systems. 3D vibration measurements of the gear surfaces were performed, and the surface roughness parameters were found to play the most important role in whine noise generation. A target roughness value was therefore proposed to be checked in the production line [1]. Perret-Liaudet et al. built a finite element model of a gearbox and used measured static transmission error data to predict the structure dynamics response on the gearbox. The simulation results were validated using test data. The finite element analysis (FEA) model was then used to identify the main parameters that influenced the whine noise [2]. Meier et al. described the powertrain NVH development process for EV at Daimler and developed a new “whining intensity factor” to evaluate the annoyance caused by tonal noise. Their results showed good correlation with subjective ratings [3]. Abe et al. used the dynamic transmission error and the dynamic bearing force as gear whine noise metrics to compare similar gear designs. The response surface methodology was used to design the gear microgeometry [4]. Rishnaswami et al. improved the whine noise of a new automatic transmission through isolation of the shifter cable and improvements in the sound packaging at the vehicle level. Further improvements were obtained by redesigning the gear set using smaller modules, higher contact ratios and increased backlash at the system level [5]. Shin et al. predicted the vibration levels of a six-speed automatic transmission gearbox using Romax software, and good correlation with experimental results was demonstrated. The whine noise was improved using a planetary gear microgeometry optimization process [6]. Kanase et al. predicted the vibration levels of a manual gearbox housing that was excited by transmission errors. The results of simulations and field tests correlated well. A sensitivity analysis of the whine noise with respect to the bearing preload and the input torque was also performed using the simulation model [7].

Until recently, some research has been conducted on whine noise measurement and prediction of EV reducers [8, 9]. To resolve the whine noise problems of a newly developed EV reducer, a rigid-elastic coupling method that considers gear transmission errors is proposed to predict the radiated noise from a gearbox. A multi-body finite element coupling model of the reducer was constructed to predict the whine noise under full acceleration conditions. The model was validated using modal test results and was then used for parameter study and optimization. The whine noise was subsequently eliminated after improvements were made to the gear microgeometry parameters.

2 Whine Noise Generation Theory and Dynamic Model of Gear System

Whine noise is the response of a gearbox structure to dynamic load excitation, which includes both external and internal excitation. The internal excitation is the main cause of the whine noise and is produced by time-variant meshing stiffness, transmission errors and the impacts of mesh-in and mesh-out processes. The external excitation includes dynamic imbalance, motor torque fluctuations and the time-variant stiffness of the bearing. Reducers with helical gears are widely used in modern EVs. In these helical gears, more than one tooth on each gear meshes simultaneously, and thus they operate more stably than spur gears. However, dynamic axial forces occur in the meshing process. Torsional vibrations will be produced under displacement excitation of the tooth profile error, the time-variant stiffness and other processes. A 6-DOF torsional–bending–axial coupling vibration model of a helical gear system must therefore be developed to analyze the dynamic responses of the gear system under time-variant excitation, as shown in Fig. 1.
Fig. 1

6-DOF dynamic model of helical gear system

Assume here that \( \beta \) denotes the helix angle, and \( e \) is the circumferential relative displacement of the teeth, which is caused by profile errors, tooth pitch errors and tooth elastic deformation. The axial tooth displacement that is caused by internal excitation is
$$ z = e\tan \beta $$
Torsional displacements of the driver gear and the passive gear occur under the application of dynamic loads. \( \theta_{a} \) and \( \theta_{p} \) are the torsional angles of the driver gear and passive gear, respectively. The overall circumferential displacement at the meshing point on the driver and passive sides is, respectively, given by
$$ y_{ac} = e_{a} + \theta_{a} R_{a} $$
where \( e_{a} \) is the circumferential displacement of the driver gear, and
$$ y_{pc} = e_{p} - \theta_{a} R_{a} $$
where \( e_{p} \) is the circumferential displacement of the passive gear.
The axial displacements of the meshing point on the driving and passive sides are, respectively, given by:
$$ z_{ac} = \left( {z_{a} - y_{ac} } \right)\tan \beta $$
$$ z_{pc} = \left( {z_{p} + y_{pc} } \right)\tan \beta $$
The axial and circumferential dynamic excitation forces at the meshing point are, respectively, given by
$$ \begin{aligned} F_{y} & = k_{s} \cos \beta \left( {y_{ac} - y_{pc} - e} \right) \\ & \quad + C_{s} \cos \beta \frac{d}{dt}\left( {y_{ac} - y_{pc} - e} \right) \\ \end{aligned} $$
$$ \begin{aligned} F_{z} & = k_{s} \sin \beta \left( {z_{ac} - z_{pc} - z} \right) \\ & \quad + C_{s} \sin \beta \frac{\text{d}}{{{\text{d}}t}}\left( {z_{ac} - z_{pc} - z} \right) \\ \end{aligned} $$
As a result, the kinetic equations of the system are as follows:
$$ \left\{ {\begin{array}{*{20}l} {m_{a} \ddot{y}_{a} + c_{ay} \dot{y}_{a} + k_{ay} y_{a} = - F_{y} \left( t \right)} \hfill \\ {m_{a} \ddot{z}_{a} + c_{az} \dot{z}_{a} + k_{az} z_{a} = F_{z} \left( t \right)} \hfill \\ {I_{a} \ddot{\theta }_{a} = - T_{a} \left( t \right) - F_{y} \left( t \right)R_{a} } \hfill \\ {m_{p} \ddot{y}_{p} + c_{py} \dot{y}_{p} + k_{py} y_{p} = - F_{y} \left( t \right)} \hfill \\ {m_{p} \ddot{z}_{p} + c_{pz} \dot{z}_{p} + k_{pz} z_{p} = F_{z} \left( t \right)} \hfill \\ {I_{p} \ddot{\theta }_{p} = - T_{a} \left( t \right)i - F_{y} \left( t \right)R_{p} } \hfill \\ \end{array} } \right. $$
Here \( I_{a} \) and \( I_{p} \) are the moments of inertia of the driver gear and the passive gear, respectively; \( T_{a} \) is the driving torque; \( i \) is the transmission ratio; and \( R_{a} \) and \( R_{p} \) are the radii of the pitch circles of the driver gear and the passive gear, respectively.
The matrix form of the equations above is given as:
$$ \left[ m \right]\left\{ {\ddot{\delta }} \right\} + \left[ c \right]\left\{ {\dot{\delta }} \right\} + \left[ k \right]\left\{ \delta \right\} = \left\{ {F\left( t \right)} \right\} $$
where \( \left[ m \right] \), \( \left[ c \right] \) and \( \left[ k \right] \) are the mass matrix, the damping matrix and the stiffness matrix of the gear system, respectively; and \( \left\{ F \right\} \) is the dynamic load matrix composed of the external driving force and the internal force, which are both caused by transmission errors in the operating process.

3 Whine Noise Prediction and Improvement

3.1 Reducer Model

Whine noise is radiated through the gearbox, so the structural design and the stiffness of the gearbox are both important. To enable accurate prediction of the whine noise, a finite element model of the gearbox housing was developed.

The gearbox is made from an aluminum alloy. The basic size of each of the meshed elements is 2 mm. CTETRA solid elements were used to form the FEA model. The model contained a total of 510,715 elements. The left and right sides of the gearbox were connected using CBEAM elements to simulate bolt connections. The macro gear parameters of the reducer are shown in Table 1. The 3D solid models of the bevel gears and the shafts used in the reducer were imported into LMS Virtual Motion software and were assembled together to form the multi-body dynamics model shown in Fig. 2.
Table 1

Macro gear parameters of the reducer


Number of teeth

Normal module

Normal pressure angle (°)

Helix angle (°)

Tooth width (mm)

Overlap contact ratio

1st gear pair







2nd gear pair







Fig. 2

Finite element model of the gearbox housing (left); multi-body dynamics model of the gears (middle); flexible-rigid coupling model of the reducer (right)

The FEA model of the gearbox housing was then imported into Virtual Motion to construct the rigid-elastic coupling dynamics model of the reducer. The shaft ends were connected to the gearbox using BUSHING elements to simulate the bearings. The radial and axial stiffness of the bushings were obtained via stiffness testing, while the rotational stiffness was set to zero to allow rotation. A massless dummy part was constructed between the ground and driver gear shafts. The dummy part and the shaft were connected using a revolute joint. The driving angular velocity was imposed on the reducer input shaft, and the torque load was exerted on the output shaft. This setup is used to avoid redundant constraints in the system. The constraints of the gearbox were built in the same locations as those used in the reducer bench test for ease of comparison between the simulation and test results. The contact between the gear teeth was simulated using the nonlinear vibration model presented by Cai [10] to allow precise calculation of the dynamic meshing force and the time-variant meshing stiffness. The effects of simultaneous meshing of multiple teeth on the dynamic characteristics of the reducer are also considered in the Cai model. The kinematic equations that were used for the contact simulation are given as follows:
$$ \begin{aligned} & m\ddot{x} + c\dot{x} + \sum\limits_{i = 1}^{n} {f_{i} } \left( {x,t} \right) = p_{s} \\ & f_{i} \left( {x,t} \right) = k_{i} \left( {x,t} \right)\left[ {x_{s} + x + e_{i} \left( t \right)} \right] \\ \end{aligned} $$
where \( m \) is the equivalent mass; \( n \) is the number of teeth meshing simultaneously; \( c \) is the mesh stiffness; \( f_{i} \left( {x,t} \right) \) is the internal dynamic excitation force; \( p_{s} \) is the external load or driving force; \( k_{i} \left( {x,t} \right) \) is the time-variant stiffness; \( x_{s} ,\,\,x \) are the static and dynamic displacement deviations, respectively; and \( e_{i} \left( t \right) \) is the tooth profile error.

The rigid-elastic coupling model of the reducer that was built is shown in Fig. 2.

3.2 Reducer Assembly Model Validation

Initially, the Craig–Bampton modal analysis of the reducer assembly was performed using the above rigid-elastic coupling model. The advantage of the Craig–Bampton method is that it considers the effects of both the internal boundary conditions and the load. The residual flexibility modes were used together with a truncated set of fixed-interface normal modes in this method. Use of this combination tends to give more accurate results than the free–free condition modal analysis method. The Craig–Bampton modal analysis method in NX Nastran software was used to obtain the dynamic response characteristics of the reducer under realistic working conditions. The first bending modal shape color map obtained is shown in Fig. 3.
Fig. 3

Color map of first bending modal shape and modal testing of the reducer assembly

Modal testing was conducted to validate the effectiveness of the coupling reducer assembly model. The modal tests were performed on the reducer assembly, which includes the gear shafts, the bearings and the gearbox housing. The reducer assembly was hung using an elastic cord under free–free conditions. The constrained mode under the gear gravity load and the bearing constraint were then measured. Thirty measurement points were set up over the gearbox housing surface to capture the modal shape. Ten three-directional accelerometers were used to measure the dynamic responses that were caused by hammer impacts. The measurement points were divided into three groups. The responses at these measuring points were obtained with a fixed hammer impact position. The test process is illustrated in Fig. 3.

The modal frequency, the modal damping and the modal shapes were identified using the PolyMAX method [11] with a relatively small frequency band. A comparison between the results of the simulations and tests for the first five modes is shown in Table 2.
Table 2

Comparison of modal parameter results between simulations and tests


Simulation (Hz)

Test (Hz)

Damping ratio (%)





















The maximum modal frequency difference between the simulation and test results is less than 5%, which demonstrates the effectiveness of the rigid-elastic coupling model of the reducer assembly. Therefore, the model can be used for further prediction of whine noise characteristics.

3.3 Whine Noise Prediction and Problem Root Cause Analysis

Inner and outer acoustic finite element models that envelop the gearbox housing were built for whine noise prediction, as shown in Fig. 4.
Fig. 4

Inner and outer acoustic finite element models enveloping the gearbox housing

The transmission errors (TEs) of the first and second meshing gears were used as the excitation when computing the structure-borne noise of the reducer that is radiated under the wide-open throttle (WOT) condition. The TEs of the meshing gears were measured. The results for the first pair of gears are as shown in Fig. 5.
Fig. 5

a Transmission error test setup; b results for the first pair of gears

Figure 5 shows the first three harmonic orders of the TEs and the peak-to-peak TEs under driving and coasting conditions. The maximum peak-to-peak TE is 2.5 μm, which is small when compared with that of similar reducers. However, the radiated noise is high, particularly at higher frequencies. The radiated noise was measured 1 m away from the reducer surface in a benchmark test at a driving torque of 280 N m under the full acceleration condition. Vehicle testing was also performed to acquire the sound level received at the position of the driver’s right ear. This position was measured on a smooth asphalt road under the WOT condition. The driving torque that was input to the reducer was 280 N m. The measurement results are illustrated in Fig. 6.
Fig. 6

a Reducer benchmark test setup; b color map of the original reducer radiation noise; c overall and 25th-order noise of the original reducer measured 1 m away from its surface in benchmark testing; d the same parameters at the driver’s right ear position in vehicle testing

It is shown that 25th-order noise, which was caused by the first driving gear, contributes most strongly to the overall noise level. The 25th-order sound level is almost equal to the overall sound level measured in the benchmark test. In the vehicle tests, the maximum 25th-order noise was 60 dB (A), which is just 3 dB (A) lower than the overall noise. Other important noise source orders include the 8.85th, the 17.7th order and the 48th order. The first two orders are caused by the second gear pair. The 48th order comes from the electromagnetic noise of the motor. The goal of this work is to remove the highest order of the noise so noise orders other than the 25th were not included in the simulation. The difference between the noise of a specific order and the overall noise should be large enough to be able to eliminate whine noise as a rule of thumb. To improve the first driving gear, the main factors that influence the radiated noise must be determined. The macro parameters, including the pressure angle, the helix angle and the contact ratio, were studied to determine the sensitivities to radiated noise via simulations using the validated reducer assembly model.

The multi-body dynamic analysis of the original reducer was performed at a driving torque of 280 N m under full acceleration conditions. These were the same conditions that were used in the laboratory. The transient forces and torques of the bearings that support the gear axis were acquired in the time domain. These forces and torques were then translated into the frequency domain. The frequency spectrum of the bearing forces was then used as the excitation for simulation of the reducer structure-borne noise. The noise frequency spectrum was acquired at a position 1 m away from the gearbox housing. The whine noise prediction results are shown in Fig. 7.
Fig. 7

The noise frequency spectrum color map on the top of the reducer 1 m away from its surface

The results show that the 25th-order noise is the most prominent noise order within the color map plot. This order is the main contributor to the overall noise and is thus the root cause of the whine noise problem. The simulation results are consistent with the test results, thus confirming the effectiveness of the simulation method. The acoustic reducer assembly model is therefore suitable for use in further parameter studies.

3.4 Sensitivity Study of Gear Parameters Influencing Whine Noise

To eliminate the whine noise, a sensitivity study of the gear parameters, including the normal pressure angle, the helix angle and the contact ratio, was performed. The reducer was simulated at a constant speed of 3000 rpm under a torque load of 178 N m; these are the typical conditions that cause whine noise. Different gear parameters were used to obtain the radiation noise at a distance of 1 m away from the reducer surface in the frequency domain.

The influence of the normal pressure angle on the shape of the gear tooth is illustrated in Fig. 8a.
Fig. 8

Results of gear macro parameters study. a Gearbox radiation noise (A-weighted) at different pres- 312 sure angles of (15.5°) (dashed line), (18.5°) (solid line) 313 and (21.5°) (dotted line) 314. b Gearbox radiation noise (A-weighted) at different helix 315 angles of −20° (dotted line), 24° (solid line) and 28° 316 (dashed line) 317. c Gearbox radiation noise (A-weighted) at different over- 318 lap contact ratios of −1.9 (solid line), 2.0 (dotted line) 319 and 2.2 (dashed line)

The root width of the gear tooth becomes larger if the normal pressure angle is larger, which causes the anti-bending strength to increase. However, the contact ratio, which varies inversely with the pressure angle, is then reduced. As a result, the contact strength is reduced, although this reduction is offset somewhat by an accompanying increase in the radius of curvature of the involute. The radiation noise characteristics of the reducer under the WOT condition with a 178 N m load when different pressure angles are used for the simulation are shown in Fig. 8a. Variation of the addendum modification factor has the same effect on the gear tooth shape. Increasing the addendum modification would also cause the bending strength of the tooth to increase. The contact ratio decreases accordingly, which tends to cause the whine noise to increase.

At the lower pressure angle (15.5°), the radiation noise is in the 1–3 dB (A) range, which is lower than that which occurs at the original pressure angle (18.5°). The radiation noise at the higher pressure angle (21.5°) is in the 1–2 dB (A) range, which is higher than that which occurs at the original pressure angle, particularly within the 3000–5000 rpm speed range. The whine noise is perceived to be more annoying in the high speed range than at low speeds in EVs. Therefore, appropriate reduction in the pressure angle will be helpful in reducing the gearbox whine noise.

The gear helix angle was studied to determine its effect on the reducer whine noise. An interaction was observed between the helix angle and the module. Increasing the helix angle requires a corresponding reduction in the module to maintain the same reference diameter. Increasing the helix angle will also increase the number of meshing teeth and improve the axial contact ratio, which in turn increases the contact strength of the teeth. However, the transverse contact ratio decreases, which results in smaller teeth and reduction in the bending strength.

Figure 8b shows the A-weighted structure-borne noise level of the reducer under the 178 N m load at different helix angles. The noise level was measured at a location 1 m away from the reducer surface. The radiation noise of the reducer with the 20° gear helix angle is 2–3 dB higher than that of the original reducer with a 24° helix angle in the 3000–5000 rpm speed range. However, the noise of the reducer with the 28° helix angle is 1–3 dB lower than that of the original reducer over the full speed range. The simulation results show that reducers with appropriately large helix angles show better NVH performances.

The overall contact ratio is a vital factor in reducing the gear whine noise. This ratio is expected to be high to provide a good load carrying capacity and good NVH performance. However, it is not the case that a higher ratio provides better performance. In this paper, different overlap contact ratio values are used to determine the radiation noise of the reducer under the 178 N m torque load. The results are shown in Fig. 8c. The noise level of the reducer with the overlap contact ratio of 2.2 is 1–3 dB (A) lower than that with the contact ratio of 1.918. The noise level in the case of the overlap contact ratio of 2.0 is the lowest among the three cases and was 3–5 dB (A) lower than that of the original reducer. This indicates that having an overlap contact ratio with an integer value is helpful in further reducing the structure-borne noise radiation.

3.5 Whine Noise Improvement

The transmission error of the meshing teeth has a significant influence on the whine noise. The contact pot and the peak-to-peak transmission error of each gear pair were optimized using Romax software to minimize the noise that was radiated. The optimized parameters used for modification of the tooth microgeometry are given in Table 3. A gear grinding technique and 6th-grade precision is required in gear manufacturing. The crowning modification must be smooth and must be located around the center area of the tooth. The optimized backlash is in the 0.05–0.08 mm range. Kinematic simulations of the gears were performed for various load cases. The contact point under the 182 N m load and the transmission error values under different load conditions are shown in Fig. 9.
Table 3

Profile modification scheme for the first gear pair

Modification method

Lead slope relief

Lead crowning

Profile crowning

Parabolic tip

Modification amount

− 8 μm

3 μm

5 μm

2.8 μm

Fig. 9

a Contact points of the two sides under test with a 182 N m load; b transmission errors of the first meshing gears

The contact point is located uniformly around the central area of the tooth. There is no bias load during the operating process, and the gears mesh well. The maximum peak-to-peak TE value is 0.25 µm which is one-tenth of the maximum TE of the original reducer. The prototype reducer was manufactured using the microgeometry parameters given above to verify the actual improvement effects. First, the contact point experiments were conducted in both the forward and backward rotational directions under various loads. The results measured under a torque load of 182 Nm are shown in Fig. 9 and showed good consistency with the simulation results. The test results show that the contact point occurs in the middle of the tooth surface and covers more than 90% of the surface area. The prototype operates fairly well, which indicates that there is no bias load under these operating conditions. The NVH benchmark testing of the optimized reducer was performed in a sound absorption chamber to obtain the near-field noise radiation. The frequency spectrum color map plot of the noise when measured 1 m away from the reducer surface is as shown in Fig. 10. The reducer was tested under a 280 N m load using full acceleration conditions ranging from 900 to 6000 rpm. The reducer was also installed on a vehicle, and the NVH test was performed again.
Fig. 10

a Color map plot of reducer radiation noise after transmission error optimization in benchmark test; b overall and 25th-order noise levels at the driver’s right ear position during vehicle testing

In the color map plot that was plotted after transmission error optimization, there is no dominant noise order in the 0–6000 rpm speed range. The overall noise is reduced by 2–3 dB (A). The 25th-order noise is 12–28 dB (A) lower than the overall noise, which indicates that the 25th-order component no longer makes a significant contribution to the overall noise. The maximum sound pressure level of the 25th order is reduced from 60 dB (A) to 50 dB (A) in the vehicle tests, as shown in Fig. 10. The measurement results show that the attempts to improve the radiation noise of the reducer are successful, particularly for the 25th-order component. The root cause of the whine noise has thus been eliminated. In vehicle-based subjective assessment tests, no obvious whine noise was observed in the cabin under the WOT condition.

4 Conclusions

A whine noise problem occurs in electric passenger cars in the full acceleration case. NVH testing and transmission error testing of the vehicle’s reducer were performed. The root cause of the whine noise problem was identified through further analysis. A rigid-elastic coupling model of the reducer was developed. A Craig–Bampton modal analysis of the reducer assembly, including the gear shafts, the bearings and the gearbox housing, was performed. The modal simulation results were validated via modal testing of the reducer assembly. An acoustic-structural finite element model of the reducer was then developed on the basis of the validated reducer coupling model. Gear parameters including the pressure angle, the helix angle and the contact ratio were studied to clarify their effects on the gearbox structure-borne noise. Microgeometry modification was also performed to reduce the transmission error of the first meshing gears, and the whine noise was ultimately greatly improved. The main conclusions that were drawn are as follows:
  1. 1.

    The finite element dynamic model of the gearbox developed here is suitable for accurate prediction of the structure-borne noise under different load conditions. NVH performance assessment and optimization of the reducer is thus possible before the prototype is manufactured.

  2. 2.

    Acoustic simulations of the gearbox were performed using various gear parameters. The results showed that a reduction in the pressure angle combined with increases in the helix angle and the overlap contact ratio provided favorable conditions for gearbox noise reduction. The noise decreases further when an overlap contact ratio with an integer value is used.

  3. 3.

    Microgeometry modification of the first meshing gears was also performed. The peak-to-peak transmission error was reduced by 90%. The results of NVH benchmark testing of the reducer showed that the 25th-order sound level was reduced dramatically in the 0–6000 rpm speed range. The overall sound level in the near field is reduced by 2–3 dB (A). The 25th-order sound level was 12–28 dB (A) lower than the overall sound level. Finally, the gearbox whine noise was greatly improved after the gear optimization process.




This work was supported by the State New Energy Vehicle Research Center and Beijing Electric Vehicle Co., Ltd.


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Copyright information

© China Society of Automotive Engineers (China SAE) 2018

Authors and Affiliations

  1. 1.Beijing Electric Vehicle Co., LTDBeijingChina

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