NVH performance optimization scheme of electric drive reduction box based on dynamic simulation

Aiming at the NVH problem of a new energy MPV electric drive gearbox, a finite element model of the gearbox gear shaft system multi-body dynamics and shell structure dynamics was established to analyze the shell harmonic response in the resonance frequency band under the constraint mode and bearing internal load conditions. Compared with the NVH bench verification test, the simulation results of the initial scheme showed that the relative error of the resonance frequency was -7.21%, and the maximum relative error of the vibration velocity amplitude was 10.53%. The simulation modeling was reasonable and the results were clearly directed.

With the rapid development of electric vehicles in recent years, the requirements for vibration and noise of electric drive assemblies including drive motors, controllers and reducers are getting higher and higher. For box-type power structures that contain power sources inside, in actual working processes, due to frequent changes in working conditions, components with greater flexibility may vibrate. During the operation of the electric drive assembly, the specific stator and rotor structures of the drive motor generate order torque pulsations, which are transmitted to the reducer housing through the gear shaft and bearings, causing the housing to vibrate and radiate noise to the outside, seriously affecting the quality of the vehicle and user experience. Therefore, it is necessary to analyze the noise generation mechanism and influencing factors of the reducer, and try to avoid possible NVH problems through vibration reduction and noise reduction design in the early stage of design. In the later stage of design, the vibration of the reducer is effectively controlled through engineering means, the noise level is reduced, and the comfort of the whole vehicle is improved.

Research shows that the main sources of gear system noise are: dynamic excitation of gear system meshing, vibration of prime mover (engine, motor, etc.), vibration of working mechanism and load change, etc. During the NVH performance evaluation of a new energy MPV, the customer complained that there was an obvious 36th-order noise problem of ~2274Hz near the half-axle position of the rear housing of the electric drive assembly reduction box, corresponding to the motor speed of ~3790rpm, and proposed NVH performance optimization requirements.

Based on the initial scheme of gearbox dynamics modeling and simulation, this paper conducts shell constraint mode and harmonic response analysis at resonant frequency, designs NVH bench test, verifies the accuracy of the current model, and proposes shell optimization scheme for simulation verification. By reducing the amplitude of surface vibration velocity in the key vibration area and the maximum vibration area of ​​the shell, the goal of vibration reduction and noise reduction of the electric drive assembly is achieved.

1 Mechanical structure vibration theory

The system is "forced" to vibrate due to continuous external excitation. Its vibration characteristics depend not only on the characteristics of the system itself, but also on the characteristics of the excitation. The differential equation of forced vibration motion of a single-degree-of-freedom damped mechanical system under the action of a simple harmonic excitation force is:

(1)

make

Substituting into equation (1), we get:

(2)

Differential equation (2) is a second-order linear non-homogeneous differential equation with constant coefficients. Its general solution can be expressed as the sum of the general solution x1(t) of the second-order linear homogeneous differential equation with constant coefficients and the special solution x2(t) of equation (2):

x=x1(t)+x2(t)

(3)

In the formula, x1(t) represents the free vibration of the damping system. In the case of small damping, this is a decaying vibration, which is meaningful in a short period of time after the start of vibration and will decay as time goes by. When only the continuous constant amplitude vibration in the forced vibration is studied, x1(t) can be ignored.

x2(t) represents the forced vibration in the damping system and is called the steady-state solution of the system. From the property that the non-homogeneous term of the differential equation is a sine function, it can be seen that the form of the special solution is also a sine function, and its frequency is the same as the excitation frequency. Therefore, the special solution can be set as:

x2(t)=Bsin(ωt-ψ)

(4)

Where B is the amplitude of the forced vibration; Ψ is the phase angle of the displacement lagging behind the exciting force.

Substituting x2(t) and its first-order and second-order derivatives into equation (2), we can solve for B and Ψ:

(5)

(6)

make

have to:

(7)

(8)

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2 Initial scheme modeling, simulation and experimental verification 2.1 Gearbox dynamics modeling

2.1.1 Multi-body dynamics modeling of gear shaft system

In the gear transmission analysis software MASTA, a multi-body dynamics simulation model including shafts, gears and bearings is established, as shown in Figure 1. Based on the boundary conditions of the vehicle NVH performance evaluation, the bearing loads of the input shaft, intermediate shaft and output shaft of the reduction gearbox are calculated under the conditions of motor speed of 3790 rpm and output power of 45 kW.

2.1.2 Shell structure dynamics modeling

In the finite element analysis software ABAQUS, a dynamic finite element model of the gearbox housing structure including the front and rear housings is established, as shown in Figure 2. The motor end face and the gearbox suspension hole are constrained, and the first 6-order housing constraint modes are calculated. Based on the resonance frequency of 2274 Hz provided by the vehicle NVH performance evaluation, the housing harmonic response analysis under bearing load excitation in the resonance band range of 1800 to 2800 Hz is performed, and the calculation frequency interval is 10 Hz.

Figure 1 Multi-body dynamics model of gearbox gear system

Fig.1 MBS model of gear train

Figure 2 Dynamic finite element model of shell structure

Fig.2 FEA model of gear box housing

2.2 Dynamics simulation results

2.2.1 Constrained modal analysis

The first six-order shell constraint modes are shown in Figure 3, where the first-order natural frequency is 2 208 Hz, and the vibration mode is the axial breathing deformation of the lower end face of the output bearing seat of the rear shell. The second-order natural frequency is 2 613 Hz, and the vibration mode is the axial breathing deformation of the right end face of the output bearing seat of the rear shell. The third-order natural frequency is 2 752 Hz, and the vibration mode is the axial breathing deformation of the left end face of the input bearing seat of the front shell. The fourth-order natural frequency is 2 960 Hz, and the vibration mode is the axial breathing deformation of the right end face of the middle bearing seat of the rear shell and the right end face of the output bearing seat. The fifth-order natural frequency is 3 317 Hz and the sixth-order natural frequency is 3 474 Hz, both of which are local vibration modes of the shell with low noise sensitivity.

First mode, natural frequency 2 108 Hz

Second mode, natural frequency 2 613 Hz

The third mode, natural frequency is 2752 Hz

Fourth mode, natural frequency 2 960 Hz

Fifth mode, natural frequency 3 317 Hz

Sixth mode, natural frequency 3 474 Hz

Figure 3 The first 6 shell constraint modes

Fig.3 Constraint modal of gear box housing

2.2.2 Harmonic response analysis

The resonance frequency of the harmonic response shell is 2110 Hz, which is consistent with the constraint mode result. The vibration velocity cloud diagram of the rear shell surface is shown in Figure 4. The maximum vibration area of ​​the shell is the lower end surface of the output shaft bearing seat, node 2312, and the velocity amplitude is 11.41 mm/s.

During the forced vibration of the shell, the unconstrained large plane and thin-walled structure contributes the most to the radiated noise. Considering the sensor layout space for the subsequent NVH bench test, the intermediate shaft bearing seat node 4304 and the output shaft bearing seat node 9395 are marked and defined as the key vibration area of ​​the shell. In the resonance band range of 1800-2800 Hz, the velocity amplitude-frequency characteristic curves of different areas of the rear shell are shown in Figure 5. The vibration velocity amplitude of the intermediate bearing seat is 6.30 mm/s, and the vibration velocity amplitude of the output shaft bearing seat is 2.91 mm/s.

2.3 Simulation model test verification

2.3.1 NVH bench verification test