As the key component of a hybrid electric vehicle (HEV), the dynamic performance of the power coupling mechanism is found to have a significant effect upon the vibration and noise of the whole vehicle. In this paper, a dynamic model with rigid and flexible bodies of a double planetary gear power coupling mechanism is established. Then, the characteristics of the bearing constraining forces in time domain and frequency domain are simulated and analysed. At the same time, the finite element model of the housing of the power coupling mechanism is established. Then, the vibration response of the housing is analysed under the excitation of the bearing constraining forces, and the vibration displacement of the housing surface is obtained. Furthermore, based on the vibration displacement of the housing surface, a prediction model of housing radiating noise is established. Then, the radiating noise characteristics of the housing and the acoustic contribution of each panel are analysed. Finally, the free damping structure and new stiffener structure are adopted to optimize the rear end cover of the housing. The optimization model based on the vibration acceleration of the rear end cover surface is established by applying K-S function and response surface method. Then, the optimization model is solved by applying the sequential quadratic programming to obtain the optimal structure of the housing. The optimization results demonstrate that the acoustic power level after optimization is decreased by 3.94 dB, 3.92 dB, 5.59 dB, and 2.84 dB at frequencies of 770 Hz, 870 Hz, 1650 Hz, and 2480 Hz, respectively. Therefore, the optimization effect of the housing structure is obvious, and this can be the theoretical basis and reference for reducing the vibration and noise of the power coupling mechanism.
It is known that the power of HEV is coupled, switched, and output by a power coupling mechanism which is composed of the power coupling system (gear pairs, transmission shafts, bearings, etc.), the structural system (housing), motors, the electrical control system, and other subsystems. As one of the key components of HEV, the dynamic performance of the power coupling mechanism has a great influence on the powertrain and even the whole vehicle [
In all types of the power coupling mechanism used in HEV, the double planetary gear power coupling mechanism is widely used because of its properties of small size, light weight, strong bearing capacity, and high transmission efficiency [
At present, the research about HEV is mainly concentrated on the control strategy [
In this paper, a double planetary gear power coupling mechanism is taken as the research object. Its multibody dynamic model of the power coupling system is established. Then, the characteristics of the bearing constraining forces of the power coupling system in time domain and frequency domain under power switching condition are simulated and analysed. At the same time, the vibration response and radiating noise of the power coupling mechanism housing are analysed. Finally, the optimal design of the housing structure is discussed.
The 3D solid model of each component of the power coupling system is built with software UG, and then the assembly model is established [
Assembly model of the power coupling system.
Gear parameters of the front and rear planet rows.
Parameters | Front planet row | Rear planet row | ||||
---|---|---|---|---|---|---|
Sun | Planets | Internal gear | Sun | Planets | Internal gear | |
Tooth number | 30 | 23 | 78 | 22 | 18 | 58 |
Face width (mm) | 27.5 | 25 | 25 | 50 | 35 | 35 |
Direction | Left | Right | Right | Left | Right | Right |
Module (mm) | 1 | 1.5 | ||||
Pressure angle | 20° | 20° | ||||
Helix angle | 25° | 30° |
Gear parameters of the first and second reduction mechanisms.
Parameters | First reduction mechanism | Second reduction mechanism | ||
---|---|---|---|---|
Driving gear | Driven gear | Driving gear | Driven gear | |
Tooth number | 54 | 55 | 24 | 77 |
Face width (mm) | 30 | 30 | 25 | 25 |
Direction | Right | Left | Right | Left |
Module (mm) | 2.5 | 2 | ||
Pressure angle | 20° | 20° | ||
Helix angle | 30° | 30° |
It can be seen from Figure
After the solid modelling in software UG, the solid model of the power coupling system is input into the software ADAMS in which the material properties of each component of the system are defined. In order to define the motion relationships among the components, the constraint relation is applied, including revolute joints and fixed joints. The constraint relation is as follows: firstly, the engine input shaft, rotor of motor MG1, rotor of motor MG2, composite mechanism, first reduction gear shaft, and second reduction gear shaft are connected to the ground separately with revolute joints. The planet gears of the front planet row are connected to the planet carrier separately with revolute joints. The planet gears of the rear planet row are connected to the planet carrier separately with revolute joints. Secondly, the engine input shaft is connected to the planet carrier of the front planet row with a fixed joint. The rotor of motor MG1 and the sun gear of the front planet row are connected to the MG1 input shaft separately with fixed joints. The rotor of motor MG2 and the sun gear of the rear planet row are connected to the MG2 input shaft separately with fixed joints. The planet carrier of the rear planet row is connected to the ground with a fixed joint. The internal gear ring of the front planet row, the internal gear ring of the rear planet row, and the outer gear ring of the composite mechanism are connected to the composite mechanism separately with fixed joints.
At the same time, the contact parameters of the gear pairs are defined. In addition, since the input shafts from the engine and two motors are prone to elastic deformation, they are treated as flexible bodies [
Dynamic model with rigid and flexible components.
Due to the lack of the experiment bench, all the results obtained in the following sections are from simulation using commercial software. In order to make sure the correctness of model, the solid model of the double planetary gear power coupling mechanism has been accurately established in software UG. In addition, the material properties and constraint relation has been accurately defined in software ADAMS. Since the input shafts from the engine and two motors are prone to elastic deformation, they are treated as flexible bodies in software ADAMS. Therefore, the error of the model is already very small, and all the simulation results should be reliable.
Road tests are done on HEV, and Table
Data obtained in road tests.
Working conditions |
|
|
|
|
|
|
SOC (%) |
---|---|---|---|---|---|---|---|
Pure electric drive condition | 30 | 0 | 2250 | 16.75 | −2220 | 0 | 49.5 |
Engine starts under the pure electric drive condition | 30 | 0∼800 | 2250 | 45∼8 | −2218∼662 | 0∼27.6 | 47 |
Low-speed cruising condition | 30 | 1220 | 2205 | −9.25 | 2247 | −6.25 | 45 |
High-speed cruising condition | 80 | 1408 | 6010 | −9.95 | −923 | −20.1 | 51.3 |
It is known that the engine needs to start and stop frequently during the operation of HEV, especially when the pure electric drive mode is switched to the combined drive mode of engine and motor, the vibration and noise caused by transient impact from power switching is particularly obvious. Therefore, the dynamic characteristics of power coupling system are analysed by choosing the power switching mode of the HEV as the simulation condition, during which the engine starts under the pure electric drive condition.
According to the data in Table
Time histories and frequency spectra of bearing constraining forces. (a) Engine input shaft bearing. (b) MG1 input shaft bearing. (c) Composite mechanism bearing. (d) MG2 input shaft bearing. (e) First reduction gear shaft bearing. (f) Second reduction gear shaft bearing.
As the vibration excitation sources of housing, bearing constraining forces directly affect the vibration and radiating noise of the power coupling mechanism. Therefore, it is necessary to analyse the time histories and frequency spectra of bearing constraining forces. The related analysis is as follows.
From Figures
It is known that the composite mechanism needs to not only couple the speed and torque of the power sources, but also bear the transient impact generated when the power of the front planet row is switched, so its dynamic characteristics are quite complex. Figure
Under the chosen working condition, the gear-mesh frequency of the rear planet row is 825 Hz according to Equation (
As shown in Figure
In addition, the impact of the power switching from the front planet row on the reduction gear assembly is very small. It can be seen from Figures
With the help of software UG, the housing model of the power coupling mechanism is established, as shown in Figure
Housing of the power coupling mechanism.
Finite element model of the housing.
The housing is bolted to the frame. The degrees of freedom of the surface nodes at each fixed support are all constrained, as shown in Figure
Fixed support of the housing.
The modal superposition method [
The vibration displacement response of housing surface when the frequencies are the first 10 natural frequencies of housing mode and the peak frequencies of the bearing constraining forces, respectively, is analysed and discussed. The results are as follows.
Firstly, since the excitation of gear-mesh and the thin-wall characteristics of housing itself, the maximum vibration displacement at each analysed frequency occurs mainly on the end cover of the front planet row, the end cover of the rear planet row, and the bearing seats of the front planet row housing. The vibration of the whole housing is mainly presented as the local deformation. The vibration displacement response at each analysed frequency is in good agreement with the excitation of the bearing constraining forces.
Secondly, the maximum vibration displacement response of the end cover of the rear planet row appears in the third-order natural frequency (870 Hz), while the end cover of the front planet row obtains the maximum vibration displacement response when the frequency is the fourth-order natural frequency (1005 Hz), as shown in Figures
Vibration response of the housing surface. (a) The 3rd natural frequency (870 Hz). (b) The 4th natural frequency (1005 Hz).
Acoustic boundary element method (BEM) is a commonly used method in acoustics calculation. Compared with the acoustic finite element method, it is more flexible and intuitive. In addition, the analytical method and numerical method are used comprehensively in the boundary element method, so this method has the advantages of low dimension, wide range, and high computational efficiency.
In this paper, the acoustic boundary element method is used with software LMS Virtual.Lab to simulate the housing radiating noise. The acoustic boundary element model of the housing is established with the software LMS Virtual.Lab, as shown in Figure
BEM model of the housing.
In software LMS Virtual.Lab, the reference sound pressure is set as
Frequency spectrum of radiating acoustic power.
It can be seen from Figure
Figure
Sound pressure levels of the housing surface. (a) 770 Hz. (b) 830 Hz. (c) 870 Hz. (d) 1010 Hz. (e) 1650 Hz. (f) 2480 Hz.
The housing is divided into four acoustic panels, as shown in Figure
Panel division of the housing.
In this paper, the acoustic contribution of each panel is calculated based on the approach of acoustic transfer vector (ATV). The range of calculated frequencies is 400–3000 Hz, and the step frequency is 10 Hz.
Figure
Color map of the panel acoustic power contribution.
It is suggested in acoustic contribution analysis of panels that the optimization of housing structure should give priority to the rear end cover. It is known that ribs can affect the vibration and radiating noise of a housing [
Stiffener structure before and after optimization. (a) Before optimization. (b) After optimization.
As shown in Figure
Structural design variables.
Considering the function and rationality of the housing structure, following constraint conditions are given to the design variables
Another constraint condition is that the mass
It is known from Section
Locations of 4 typical nodes.
The K-S function is used to condense the maximum acceleration values of 4 typical nodes into a valid value which can reflect the vibration acceleration of the whole rear end cover. As a comprehensive index to describe the vibration characteristics of the whole rear end cover, this valid value can be written as
Considering design variables, constraint conditions, and objective function, the optimization model of the rear end cover [
Response surface method (RSM) is a method for describing the relationship between input variables and response of complex systems by reasonably selecting test points and using a series of deterministic tests to fit the equation of state [
Define
According to constraint conditions,
Sample points and vibration acceleration levels.
Number |
|
|
|
|
---|---|---|---|---|
1 | 7 | 3 | 6 | 147.233 |
2 | 6.5 | 3 | 6 | 147.886 |
3 | 7 | 2.5 | 6 | 148.703 |
4 | 7 | 3 | 5.5 | 147.742 |
5 | 7.5 | 3 | 6 | 146.642 |
6 | 7 | 3.5 | 6 | 145.727 |
7 | 7 | 3 | 6.5 | 146.761 |
Although the expressions of Equations (
Therefore, Equation (
In order to test the accuracy of the fitting function, the sample points in the range of design variables are randomly selected for special point test. Table
Comparison of fitting values and simulation results.
Special points | Fitting values (dB) | Simulation results (dB) | The relative errors (%) |
---|---|---|---|
(6, 3, 6) |
148.601 | 143.645 | +3.45 |
(6, 4, 4) |
150.031 | 143.214 | +4.76 |
(7, 2, 4) |
159.055 | 152.717 | +4.15 |
(7, 4, 6) |
146.405 | 150.762 | −2.89 |
(8, 4, 6) |
145.285 | 139.536 | +4.12 |
(8, 4, 8) |
143.619 | 136.196 | +5.45 |
It can be seen from Table
Sequential quadratic programming (SQP) [
The optimization process starts with the initial value. The optimization process and data are shown in Table
Results of each iteration.
Iterative step |
|
|
|
Target value |
---|---|---|---|---|
0 | 7.0000 | 3.0000 | 6.0000 | 147.2330 |
1 | 6.1039 | 4.0000 | 6.8156 | 146.8684 |
2 | 6.2398 | 3.5657 | 7.6846 | 145.2662 |
3 | 6.1890 | 3.4263 | 9.1849 | 144.5284 |
4 | 6.1085 | 3.4639 | 10.0000 | 144.2302 |
5 | 6.0870 | 3.5098 | 10.0000 | 144.2184 |
6 | 6.0841 | 3.5160 | 10.0000 | 144.2183 |
Figures
Iterative process of objective function.
Iterative process of design variables.
From Figure
Figure
Based on the optimal solution of the optimization model, the acoustic boundary element model is reestablished. The radiating acoustic power level of the housing after optimization is calculated and compared with that before optimization, as shown in Figure
Acoustic power level before and after optimization.
The target problem of our study is to reduce the vibration and noise of the double planetary gear power coupling mechanism. In order to solve the target problem, we design a new rear end cover. It can be seen from Figure
In this paper, the vibration response and radiating noise of the power coupling mechanism housing are analysed and discussed. At the same time, an optimization model of the housing rear end cover is established and solved to obtain the optimal structure of the housing. The main conclusions can be summarized as follows: The vibration of the whole housing is mainly presented as local deformation. The maximum vibration displacement of the front end cover appears at the fourth-order natural frequency (1005 Hz), while the rear end cover has bigger vibration displacement when the frequencies are 768 Hz, 870 Hz, and 1650 Hz, respectively. The vibration response of the whole housing surface is in good accordance with the excitation of the bearing constraining forces. The housing radiating noise has a good correspondence with the vibration response. The radiating acoustic power of the housing is bigger when the frequencies are 770 Hz, 870 Hz, 1010 Hz, 1650 Hz, and 2480 Hz, respectively. At the same time, based on the approach of acoustic transfer vector, the acoustic contributions of four panels of the housing are analysed, and the rear end cover (panel 4) is found to have the largest acoustic contribution. The housing acoustic power level after optimization is decreased by 3.94 dB at 770 Hz, decreased by 3.92 dB at 870 Hz, decreased by 5.59 dB at 1650 Hz, and decreased by 2.84 dB at 2480 Hz. Therefore, the optimization effect is obvious in reducing the vibration and radiating noise of the power coupling mechanism housing.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was financially supported by National Natural Science Foundation of China (51575238).