Mechanical Metamaterials in Mitigating Vibrations in Battery Pack Casings

Abstract

Battery pack casings with a total energy of 12.432 kWh were designed using two types of materials: aluminum alloy and carbon fiber reinforced composite filament based on polyphthalamide or high-performance/high-temperature nylon (PPA-CF). The effectiveness of mechanical metamaterials (lattice and auxetic structures) in mitigating the levels of random vibrations in the battery pack casings was studied using a numerical method. Both structures demonstrate outstanding capabilities with a 97% to 99% reduction in vibration levels in the aluminum casing. However, the capabilities of these structures in mitigating vibration levels in the PPA-CF casing are very limited, in that they can only mitigate approximately 63.8% and 92.8% of the longitudinal vibrations at the top cover of the casing and center of its front and back walls, respectively. Compared to PPA-CF, aluminum alloy shows better vibration mitigation performance with or without structural modification.

1. Introduction

In recent years, owing to the strict control of pollution emissions worldwide, the electric vehicle industry has developed by leaps and bounds. However, compared with conventional combustion engine vehicles, the period of development has been relatively short, leading to technical issues such as the impact of road vibration on battery capacity and battery safety. Safety, being the foremost concern for the public, has prompted manufacturers and research institutes to actively conduct research aimed at mitigating the vibration level of battery pack casings. A device consisting of a pre-compressed spring, a raceway, and a bearing was designed by Zou et al. [1] to customize nonlinear forces. The device could be easily applied to energy harvesting and vibration isolation. Trinh et al. [2] proposed an innovative quasi-zero stiffness oscillation model using pneumatic artificial muscle. This model had potential benefits in engineering applications such as vibration absorbers and vibration isolation.

Among various vibration damping methods, the use of mechanical metamaterials is one of the most common methods that has been reported to mitigate the vibration level of various structures such as wheels, machines, and battery pack casings [3]. Syam et al. [4] presented the design, analysis, and experimental verification of strut-based lattice structures to enhance the mechanical vibration isolation properties of a machine frame. They concluded that a trade-off needed to be made between the frame’s natural frequency and its compressive strength to achieve high vibration isolation efficiency. Gunaydin et al. [5] replaced parallel nylon ligaments within re-entrant and honeycomb lattice structures with chopped and continuous carbon fiber to constitute multi-material lattice configurations. They found that the natural frequency of the multi-material configurations increased from 4% to 18% depending on the configuration and material. Gunaydin et al. [5] ignored the factor of the frame’s compressive strength similar to what had been done by Syam et al. [4].

The vibration reduction of the beam-like lattice structure was studied by Liu et al. [6] using the local nonlinear energy sink (NES) attachment. The results showed that the amplitude of NES response increased when the beam axis deviated from the center position. Monkova et al. [7] investigated the vibration damping properties of 3D-printed body-centered cubic (BCC) lattice structures under harmonic excitation at three employed inertial masses. The experimental results showed that the ability of the lattice structures to dampen mechanical vibration increased with decreasing volume ratio and increasing cell size, inertial mass, and excitation frequency. The frequency response and the damping ratio of the IWP-type triply periodic minimal surface (TPMS) lattice structure was calculated by Zhang et al. [8] using dynamic vibration transfer rate tests. The results showed that increasing the cell size and decreasing the volume fraction could be more beneficial to achieve low-frequency vibration isolation. Based on the findings of Monkova et al. [7] and Zhang et al. [8], it could be concluded that lattice structures with larger cell size and smaller volume fraction could contribute to better vibration isolation performance.

Zhang and Yang [9] studied the dynamic performance of a novel lightweight auxetic cellular vibration isolation base consisting of re-entrant hexagonal honeycombs. The excellent vibration isolation performance of the auxetic cell-based structure was achieved by increasing the Poisson’s ratio of the re-entrant honeycombs and decreasing their relative density. Pyskir et al. [10] designed a locally resonant auxetic metamaterial for vibration isolation by combining different mechanisms such as auxetism, local resonances, and buckling. They found large bandgaps for the resonant case and strong isolation properties were confirmed by the experimental data. The outcomes of Zhang and Yang [9] and Pyskir et al. [10] proved that auxetic structures with larger Poisson’s ratio and bandgaps had higher vibration mitigation capability. Scarpa and Bianchi [11] described the vibration transmissibility behavior of auxetic and conventional foams under low- and high-amplitude vibrations. The auxetic foam exhibited higher dynamic stiffness and enhanced viscous dissipation characteristics when subjected to nonlinear vibration loading. Kim et al. [12] presented novel spindle holders that were fabricated using auxetic materials for spindle vibration mitigation. They confirmed that an auxetic material-based spindle holder could effectively suppress spindle vibration when the spindle was machined or idled. The results of Scarpa and Bianchi [11] and Kim et al. [12] confirmed that auxetic structures were effective in mitigating nonlinear vibration loading. The damping capacity of manufactured auxetic NiTi components was evaluated by Nespoli et al. [13] using the loss factor index and the amount of energy dissipated per cycle. The results showed that the damping capacity of the auxetic NiTi cell took advantage of electropolishing, and was superior to that of traditional materials.

It can be seen that most of the reported studies on the vibration issue were conducted using samples of mechanical metamaterials, whereas none directly applied mechanical metamaterials to the real battery pack casings. Therefore, in the present study, the effects of lattice and auxetic structures on the vibration level of a battery pack casing are investigated through numerical methods to gain insight into the actual vibration condition of the casing of a battery pack of an electric vehicle when it is undergoing random vibration.

2. Methodologies

2.1. Battery Pack Casing

The geometries of the original, lattice, and auxetic battery pack casings are shown in Figure 1. The lattice [14] and auxetic structures [15] were only applied on the top cover, front wall, and back wall to reduce the vibration level while maintaining the structural strength of the battery pack casings. The side wall thickness and wall thicknesses of both the top cover and bottom base of the casings were 3.5 mm and 5 mm, respectively, based on the optimum vibration damping design from Pal et al. [16]. The battery pack casing can accommodate 120 units of NMC 811 cells (Grepow, Shenzhen, China) in a 3P40S arrangement. The cell capacity and cell voltage were 28 Ah and 3.7 V, respectively. Therefore, the pack capacity, pack voltage, and pack total energy were 84 Ah, 148 V, and 12.432 kWh, respectively.

2.2. Numerical Set-Up

The simulation was conducted using Abaqus/CAE 2024 software. Two types of materials were simulated in this study: aluminum and PPA-CF. Aluminum is an aluminum alloy (AlSi10Mg) with a density ($\rho$) of 2700 kg/m³, a Young’s modulus (E) of 70 Gpa, and a Poisson’s ratio ($\nu$) of 0.275. The properties of PPA-CF are listed in

Table 1. Properties of PPA-CF [18]. G is the shear modulus.

Properties	Value
$\rho$ (kg/m3)	1200
El (MPa)	6945
Et (MPa)	2977
Ev (MPa)	2977
${\nu }_{lt}$	0.33
${\nu }_{lv}$	0.33
${\nu }_{tv}$	0.4
Glt (MPa)	3000
Glv (MPa)	3000
Gtv (MPa)	1063

. A total of 25 reference points (RPs) were placed on the outer wall of the casing for data capture as shown in Figure 2. In the present study, the x-axis, y-axis, and z-axis are referred as the longitudinal (l), vertical (v), and transverse (t) directions, respectively. Four steps were created in the numerical model: modal analysis, x-longitudinal vibration, y-vertical vibration, and z-transverse vibration. The power spectral density (PSD) profiles of the latter three steps are entered based on the data from ISO 12405-2 [17] and are shown in

Table A1. PSD profile of the x-longitudinal step [17].

Frequency (Hz)	PSD (g2/Hz)
5	0.0125
10	0.03
20	0.03
200	0.00025

,

Table A2. PSD profile of the y-vertical step [17].

Frequency (Hz)	PSD (g2/Hz)
5	0.05
10	0.06
20	0.06
200	0.0008

and

Table A3. PSD profile of the z-transverse step [17].

Frequency (Hz)	PSD (g2/Hz)
5	0.01
10	0.015
20	0.015
50	0.01
200	0.0004

in Appendix A. The total weight of the 120 units of battery cells was 46.44 kg, which was assigned as a uniformly distributed point mass in the numerical model. The cover and bottom parts of the casing were attached together by assigning a tie constraint between them. A pinned boundary condition was assigned to the six bolt holes.

3. Results and Discussion

3.1. Aluminum Casing

The results of the modal analysis are presented in

Table 2. Natural frequencies of the three different aluminum battery pack casings.

Battery Pack Casing	Mode 1 (Hz)	Mode 2 (Hz)	Mode 3 (Hz)
Original	54	92	97
Lattice	216	233	264
Auxetic	205	226	232

. The first three modes of the original aluminum casing range from 54 Hz to 97 Hz. With the structural modification provided by the lattice and auxetic structures, the first three modes of the lattice and auxetic aluminum casings are increased to above 200 Hz. Mode shape 1 of the three aluminum casings are shown in Figure 3. These results verify the effectiveness of the lattice and auxetic structures in mitigating vibrations in aluminum casings because it is well known from various standards and studies that the frequency range of road vibration is normally below 150 Hz [19]. Figure 4 shows the longitudinal displacement of the three different aluminum casings at 15 Hz. The displacement patterns of the casing for battery pack at 15 Hz were selected for presentation because the displacement peaks of the three aluminum casings are found in this frequency region (see Figure 5). It can be observed from Figure 4 that under the same contour limits and same deformation scale factor, the deformation pattern that exists on the original aluminum casing is no longer observed on either the lattice or auxetic aluminum casings. The vibration levels of different reference points at the wall center of each aluminum casing are shown in Figure 5. Not all data from the 25 reference points are presented for brevity. It is found that for the original aluminum casing, the displacement peaks at all reference points occur at around 20 Hz and 93 Hz. As the vibration levels of the lattice and auxetic aluminum casings are about 100 times lower than that of the original aluminum casing, the vibration levels of these two aluminum casings are presented separately in Figure 5f,g, respectively. It is found that the displacement peaks at all reference points of both modified aluminum casings occur at around 16 Hz.

Figure 6 shows the vertical deformation patterns of the three aluminum casings at 15 Hz. Again, the original aluminum casing deformed vertically at its bottom wall but this bottom wall deformation was not present in either the lattice or auxetic aluminum casings. The same phenomenon is observed for the longitudinal displacement (compare Figure 5 and Figure 7) where the vibration levels of the lattice and auxetic aluminum casings are 100 times lower than those of the original aluminum casing. In addition, the displacement peaks at all reference points are shifted from 54 Hz (original battery pack) to 16 Hz with the implementation of the lattice and auxetic structures. From Figure 8a, it is found that the location of maximum transverse displacement is the same for both longitudinal and vertical displacements—the bottom wall of the original aluminum casing. A Similar phenomenon to that observed for the vertical and longitudinal directions is observed for the transverse direction where the displacement peaks at all reference points are shifted from 96 Hz to 16 Hz (both lattice and auxetic aluminum casings) with about 100 times lower vibration levels (see Figure 9), except at RPs 7, 9, 17, and 19. The displacement peaks of these four reference points still occur at 96 Hz and 16 Hz as with the other reference points; however, the vibration levels of the lattice and auxetic aluminum casings at these four locations are 10 to 100 times higher than those for the same RPs on the original aluminum casing, as shown in Figure 10, respectively, for frequencies below 100 Hz. These four reference points are actually located below the casing’s extension for mounting the bolts (see Figure 2). Therefore, it can be concluded that the lattice and auxetic structures enhance the vibration levels in the areas below the aluminum casing’s extension and in the direction parallel with the aluminum casing’s extension. Overall, the lattice and auxetic structures are able to mitigate about 97% to 99% of vibration level in three directions, as shown in

Table 3. Vibration mitigation capabilities of the lattice and auxetic aluminum casings in 3 directions.

Battery Pack Casing	Longitudinal (%)	Vertical (%)	Transverse (%)
Lattice	97.7	98.9	99.0
Auxetic	97.1	98.7	97.9

. Note that the results in transverse direction exclude the findings at RPs 7, 9, 17, and 19.

3.2. PPA-CF Battery Pack Casings

The natural frequencies of the three PPA-CF casings are presented in

Table 4. Natural frequencies of the three different PPA-CF casings.

Battery Pack Casing	Mode 1 (Hz)	Mode 2 (Hz)	Mode 3 (Hz)
Original	5.0	5.3	5.6
Lattice	2.3	2.5	2.8
Auxetic	2.2	2.4	2.5

. In contrast with the results obtained from aluminum casings, the implementation of lattice and auxetic structures on the PPA-CF casing did not increase the natural frequency of the original PPA-CF casing. The two mechanical metamaterials decreased the natural frequency of the original PPA-CF casing from approximately 5 Hz to as low as 2.2 Hz. The longitudinal displacements of the three PPA-CF casings at 5.5 Hz are presented in Figure 11. The frequency of 5.5 Hz is the peak frequency of the original casing at most reference points as shown in Figure 12. The original PPA-CF casing (see Figure 11a) deforms only at the center of the front and back walls rather than deforming uniformly over the bottom of the casing, similar to the situation with the original aluminum casing (see Figure 4a). This phenomenon could be due to the rotation of the fibers in the longitudinal direction in the present study. In addition to at 5.5 Hz, peak vibrations of the original battery pack also occurred at approximately 8.5 Hz as shown in Figure 12. In the longitudinal direction, lattice and auxetic structures could mitigate vibration levels in certain areas by approximately 63.8% and 92.8%, respectively, namely, RPs 1, 2, 3, 4, 5, 12, 13, 14, 22, 23, and 24. These areas are located on the top cover and at the center of the front and back walls where the maximum deformation occurs (see Figure 11). For all other regions, both the lattice and auxetic structures enhance vibration levels significantly (see Figure 12b,d).

The deformation patterns of the three PPA-CF casings at 5.8 Hz due to vertical vibration are shown in Figure 13. The lattice structure significantly enhances the levels of vertical vibration of the PPA-CF casing, where its top, bottom, and both side-walls deform obviously compared to the other two casings. A more intuitive presentation of this phenomenon is shown in Figure 14. The simulation results showed that both mechanical metamaterials enhanced the vertical vibration levels over the entire casing (all RPs). Vibration peaks of the lattice and auxetic PPA-CF casings for battery pack occur at 5.8 Hz and 5.6 Hz, respectively. The frequencies of 5.8 Hz and 5.6 Hz correspond to the 9th and 8th modes of the natural frequency of the PPA-CF lattice and auxetic casings, respectively. This implies that the vertical PSD vibration profile (see Table A2 in the Appendix A) coincides with the natural frequency of the PPA-CF lattice and auxetic casings and resonance occurred. In the transverse direction, the maximum deformations occur at the center of both side walls of all three PPA-CF casings as shown in Figure 15. This finding is different from that found with the original aluminum casing, where transverse deformation was uniformly distributed over the bottom part of the casing (see Figure 8a). These findings can be attributed to the fact that the aluminum casing is composed of homogeneous material but the PPA-CF casing is not. Overall, the lattice and auxetic structures are only able to mitigate the transverse vibration levels at certain areas below 8 Hz. These areas included RPs 11, 21, and 25 for the lattice structure and RPs 3, 7, 8, 9, 17, 18, and 19 for the auxetic structure, as shown in Figure 16. The transverse vibration mitigation areas of the auxetic casing are largely concentrated around the center of both side walls (see Figure 2) with an overall reduction in vibration levels of 39.8%.

4. Conclusions

In this study, the effects of lattice and auxetic structures in mitigating the vibration level of aluminum and PPA-CF battery pack casings under random vibration conditions were studied using a numerical method. The results show that both structures increase the natural frequencies of the aluminum casing to above 200 Hz. The deformation of the original aluminum casing is uniformly distributed over its bottom part during longitudinal and transverse vibrations but concentrated at the center of its bottom wall during vertical vibration. With higher natural frequencies, the lattice and auxetic aluminum casings can mitigate approximately 97% to 99% of the vibration levels in all three directions, except for some small areas under the casing’s extension in the transverse direction.

Lattice and auxetic structures lower the natural frequencies of the PPA-CF casings to about 2.2 Hz to 2.8 Hz. Consequently, these mechanical metamaterials significantly enhanced the vertical vibration levels over the entire PPA-CF casing. They can only mitigate the longitudinal vibration levels of the PPA-CF casing at its top cover and center front and back walls, and by about 63.8% and 92.8% for the lattice and auxetic structures, respectively. The auxetic structure manages to mitigate the transverse vibration level (39.8%) around the center of both side walls of the PPA-CF casing. It can be concluded that both mechanical metamaterials are effective in mitigating vibration levels of an aluminum battery pack casing. Compared to PPA-CF, aluminum alloy is a better material choice for battery pack casings with or without structural modification.