2018 3rd International Conference on Electrical, Control and Automation Engineering (ECAE 2018)

ISBN: 978-1-60595-080-8

Study on Load Spectrum Extraction Method of Battery Pack Fixture Point

in Frequency Domain

Yun-kai GAO and Bo FENG*

School of Automotive Studies, Tongji University, China, 201804

*Corresponding author

Keywords: Load spectrum, Frequency domain method, Random vibration, Virtual iteration, Battery pack.

Abstract. A method to obtain load spectrum of battery pack fixture point in frequency domain is

proposed. The multi-body dynamics model of the vehicle is established, and virtual iteration is carried

out with the road load spectrum collected on the proving ground test as the target signal, and the

random load spectrum of the connection points between suspension system and body is obtained. The

time domain signals of the connection points are converted into frequency domain signals, and

random response analysis is carried out to obtain the acceleration PSD matrices of the body

monitoring points and the battery pack fixture points. The PSD of monitoring point calculated by the

frequency domain method is compared with the measured signal PSD. The results show that the

calculated values are in good agreement with the measured values, therefore, this method is very

effective to some extent. The proposed load spectrum extraction method in frequency domain also has

reference value for the fatigue load spectrum extraction of other connecting parts of vehicle body.

Introduction

The vehicle is subjected to the random loads from road surface during driving because of the

unevenness of the pavement [1]. In recent years, the electric vehicles are developing rapidly. As

battery pack is the most important part of the energy supply system of electric vehicle, its fatigue

performance under complex random loads affects the safety of the vehicle a lot. Therefore, the

acquisition of the fatigue load spectrum of battery pack fixture point has important engineering

significance.

For the performance requirements of battery pack structure under random vibration, there are GB/T

31467.3-2015, SAE J2380 and other standards at home and abroad. Based on the SAE J2380

standard, Wang Wenwei et al. carried out fatigue analysis on the battery pack with the use of standard

load spectrum [2]. However, the fatigue characteristics of the battery pack structure in real working

condition cannot be obtained by the standard vibration test. At present, there are few studies on the

fatigue characteristics of the battery pack under real road excitation, and most of them are carried out

in time domain. Chen Qi obtained the driving force and driving displacement of battery pack through

virtual iteration based on the measured load spectrum of the battery pack in urban road conditions,

which were used as the excitation to the fatigue simulation [3].

The random load test can simulate the actual random load accurately. Power spectral density

function is the basis for loading the random load test. Therefore, the acquisition of the frequency

domain load spectrum of battery pack fixture point is significant. Youngwoo Choi et al. proposed a

uniaxial vibration fatigue test method with weighted power spectral density as excitation, which

proved that the method can reflect the real road conditions well and shorten the fatigue test cycle [4].

Based on the six-component force signals of the wheel spindle centers, Bishop et al. performed a

random response analysis on the finite element truck model to obtain the frequency domain load

spectrum of the spare wheel bracket and verified its effectiveness [5]. However, there are few studies

on the methods of extracting the load spectrum of battery pack fixture point in frequency domain at

home and abroad.

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The objective of this paper is an electric vehicle. Based on the road spectrum collected on the

proving ground test, virtual iteration and the frequency domain load spectrum extraction method are

carried out to obtain the PSD matrices of the body monitoring points and the battery pack fixture

points. The effectiveness of the frequency domain load spectrum extraction method is verified by

comparing the PSD of the body monitoring point with the PSD of the measured signal. The calculated

PSD matrix at the battery pack fixture points can completely describe the loads cascading in

frequency domain, which provides a basis for the random vibration fatigue test of the battery pack

under the corresponding road conditions.

Acquisition of the Load Spectrum of Vehicle Body

Virtual Iteration

According to the connectivity of the suspension system as well as the geometric and mechanical

parameters of the vehicle, an accurate multi-body dynamics model of the vehicle is established. Then

the vehicle body is made flexible, and the rigid-flexible coupling model of the vehicle is shown as

Figure 1.

Figure 1. Rigid-flexible coupling model.

Figure 2 shows the road load data collected on the shortwave road, which is used as the target signal

for virtual iteration. Based on the rigid-flexible coupling model of the vehicle, the vertical

displacements of the spindle centers, which will be the driving signal for the dynamic analysis, is

obtained by virtual iteration.

Figure 2. Accelerations of the front spindle centers.

The quality of virtual iteration needs to be evaluated. Waveform comparison, relative RMS error

and pseudo damage ratio are common methods to evaluate the quality of virtual iteration [6]. The

results are shown in the figures. The time and frequency domain waveforms of vertical acceleration at

left front spindle center are shown in Figure 3 and Figure 4, respectively. The relative RMS error is

compared as shown in Figure 5. The damage ratio curve is shown in Figure 6. It is obvious that the

time domain and frequency domain waveforms both coincide very well, in addition, the relative RMS

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error and damage ratio are within a reasonable range. The iterative result of the target signal is highly

consistent with the test.

Figure 3. Time domain waveform.

Figure 4. Frequency domain waveform.

Figure 5. Relative RMS error.

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Figure 6. Damage ratio curve.

Muti-body Dynamics Analysis

Muti-body dynamics analysis is carried out with the vertical displacement of spindle center which was

obtained from the last iteration as the input signal, and the force (or torque) signals of six degrees of

freedom for each connection point is obtained. The front suspension of the EV is a MacPherson

suspension, the rear suspension is a torsion beam suspension, and there are 16 connection points

between body and chassis.

Figure 7 shows the force signals at the connection point between body and left front shock absorber.

It can be seen that the force in the Z direction is large and the force in the X and Y directions is small.

The Z-direction force maximum is about 3786N, and the minimum value is about 309N, which is

conforming to the actual working conditions.

Figure 7. Force signals of shock absorber connection point.

Load Spectrum Extraction Method in Frequency Domain

Random Vibration Theory

In the multi-excitation stationary stochastic process, if there are n excitation channels, the stochastic

response S(f) will be calculated as follows [7]:

*

1 1

( ) ( ) ( )n n

a ab b

a b

S f H f G f H f

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Where, a and b: the ath

and the bth

excitation channels; Gab(f): the corresponding element in the

power spectral density function matrix; Hb(f): the transfer function corresponding to the bth

excitation

channel; H*

a (f): the conjugate complex of the transfer function.

S(f) can be displacement response, velocity response, acceleration response, or stress response. The

stress response can be further applied to vibration fatigue analysis, and the displacement, velocity or

acceleration response PSD matrix can be used for frequency domain load transfer calculation [5].

Load Spectrum Extraction in Frequency Domain

The 96 channels of signal of the body connection points obtained by virtual iteration, are converted

into a PSD matrix. The response of the finite element model of the vehicle body under unit load is

obtained by inertial relief [8, 9], and the frequency response analysis is used to obtain the transfer

function of each channel. Based on the PSD matrix and the transfer function of each channel, the

acceleration PSD matrix of the body monitoring points and the PSD matrix of the battery pack fixture

points are calculated by random response analysis. The monitoring points are close to the connection

points of vehicle body and shock absorbers, and there are 14 battery pack fixture points, as shown in

Figure 8.

Figure 8. The positions of Monitoring points and battery pack fixture points.

The vertical acceleration PSD of the No. 1 fixture point is shown as Figure 9. The maximum peak is

about 0.17 g2/Hz, which appears near 2.5 Hz. It is known from the analysis that this peak is mainly

derived from the road surface excitation. Smaller peaks appear near 27 Hz and 36 Hz, which is mainly

due to the structural characteristics of the vehicle body.

Figure 9. Vertical acceleration PSD.

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Validation

The waveform comparison between the calculated and measured values of monitoring points is

shown in the figure 10. Obviously, the peak values of the calculated values and the measured values

both appear near 2 Hz. The main influence frequencies are all within 5 Hz, and the trend is consistent

and the peak values are close. The pseudo damage ratios between the calculated values and the

measured values are shown in Table 1, which are all between 0.5 and 2.

(a) Left front monitoring point (b) Right front monitoring point

(c) Left rear monitoring point (d) Right rear monitoring point

Figure 10. Waveform comparison.

It can be concluded that the waveforms of the calculated value and the measured value coincide

well, and the damage ratio is within a reasonable range, which proves that the method to obtain load

spectrum in frequency domain is effective.

Table 1. Damage ratio.

Monitoring point Left front Right front Left rear Right rear

Damage ratio 0.57 0.91 1.68 1.79

Conclusion

A method for extracting the load spectrum of battery pack fixture points in frequency domain is

proposed. Based on the road spectrum collected on the proving ground test, the virtual iteration and

signal processing technology are used to obtain the PSD matrix at the connection points of the vehicle

body. The random response analysis is applied to obtain the PSD matrices of the battery pack fixture

points and the body monitoring points. By comparing the waveform and damage ratio between the

calculated value and the measured value of the monitoring point, it can be concluded that the

waveform between the calculated value and the measured value coincide well, and the damage ratio is

within a reasonable range, which proves that the method to obtain load spectrum in frequency domain

is effective.

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The obtained PSD matrix can be the boundary condition for the battery pack durability test. The

proposed load spectrum extraction method is applicable for complex finite element model. At the

same time, the method has reference value for the load spectrum extraction of other connecting parts

of the vehicle body.

References

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