# Design and Numerical Analysis of Electric Vehicle Li-Ion Battery Protections Using Lattice Structure Undergoing Ground Impact

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## Abstract

**:**

## 1. Introduction

_{2}emission in 2011–2017 was reduced by 1.6 billion tons and 612 kilotons, respectively [3]. Furthermore, the EV also has a higher efficiency compared to common internal combustion engine vehicle due to electrical components usage and minimal power conversion [4].

## 2. Materials and Methods

#### 2.1. Lattice Models and Definition

#### 2.2. Taguchi Design of Experiment

#### 2.3. Finite Element Analysis

## 3. Optimization Result and Analysis

#### 3.1. Taguchi Optimization

_{i}shows the output value. For each control factor and corresponding levels, the mean and S/N Ratios of the lattice structure’s SEA are averaged, presented in Table 6, and visualized in Figure 7 and Figure 8.

^{°}of α angle. Finally, the last control factor, E or A/B ratio, shows that the S/N ratio reduces and a higher A/B ratio, in which the structure tends to be flatter. Hence, the optimum control factor is E1, A/B ratio of 1. Each control factor optimum parameter is summarized in Table 7.

_{ij}is the average value of control factor i with the optimum level j.

#### 3.2. Analysis of Variance (ANOVA)

_{t}is the sum of response at level t, T is the total sum response, N is total number of runs, and n shows number of repetition.

#### 3.3. Optimization Result and Verification

## 4. Battery Pack Design and Analysis

#### 4.1. Battery Impact Simulation Model

#### 4.2. Results and Discussion

## 5. Conclusions

- The sensitivity analysis using Analysis of Variance results in the contributions of 5 control factors for SEA output. The most sensitive parameter is the relative density (47.73% contribution), followed by height-to-cross section characteristic length – H/C ratio (25.96%), length-to-width – A/B ratio (13.43%), geometry (10.57%), and taper (α) angle (1.25%), with the error contribution of 1.05%. Based on the F-test analysis, all control factors significantly affect the SEA output, with a 95% confidence level;
- The optimum design, with the highest SEA output, based on the Taguchi Orthogonal Array has configuration of the octet-cross geometry structure, with 40% relative density, with a H/C ratio of 1.5, α angle 0
^{°}, and the A/B ratio of 1. The SEA output from this optimum design is 85.47 kJ/kg. - The lattice structure’s optimized model can be applied as the sandwich core in the battery protection system. The lattice structure size is 10 mm by 10 mm by 15 mm, arranged in 18 × 18 × 2 cells. This structure’s total mass is 1722 grams and can maintain the battery deformation for a maximum of 2.7 mm.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

EV | Electric Vehicle |

OHC | Octahedron-Cross |

OC | Octet-Cross |

OT | Octet-Truss |

OTM | Octet-Truss Modified |

DoE | Design of Experiment |

SEA | Specific Energy Absorption |

ANOVA | Analysis of Variance |

DoF | Degree of Freedom |

SS | Sum of Square |

MS | Mean Square |

CAD | Computer-aided Design |

DFSS | Design for Six Sigma |

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**Figure 1.**Four Lattice Structure Cell Model: (

**a**) Octahedron-Cross (OHC). (

**b**) Octet-Cross (OC). (

**c**) Octet-Truss (OT). (

**d**) Octet-Truss-Modified.

**Figure 6.**Ti-6Al-4V Effective Plastic True Stress-Strain Curve [26].

**Figure 14.**Multicell Lattice Structure Configuration: (

**a**) Configuration #1. (

**b**) Configuration #2. (

**c**) Configuration #3.

Control Factors | Level | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | ||

A | Geometry | OHC | OC | OT | OTM |

B | $\rho $ | 10% | 20% | 30% | 40% |

C | H/C Ratio | 0.5 | 1 | 1.5 | 2 |

D | $\alpha $ | 0${}^{\circ}$ | 1.5${}^{\circ}$ | 3${}^{\circ}$ | 4.5${}^{\circ}$ |

E | A/B Ratio | 1 | 1.5 | 2 | 2.5 |

Running No. | Control Factor | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

A (Geometry) | B ($\mathit{\rho}$) | C (H/C) | D ($\mathit{\alpha}$) | E (A/B) | ||||||

1 | 1 | [OHC] | 1 | [10%] | 1 | [0.5] | 1 | [0${}^{\circ}$] | 1 | [1] |

2 | 1 | [OHC] | 2 | [20%] | 2 | [1] | 2 | [1.5${}^{\circ}$] | 2 | [1.5] |

3 | 1 | [OHC] | 3 | [30%] | 3 | [1.5] | 3 | [3${}^{\circ}$] | 3 | [2] |

4 | 1 | [OHC] | 4 | [40%] | 4 | [2] | 4 | [4.5${}^{\circ}$] | 4 | [2.5] |

5 | 2 | [OC] | 1 | [10%] | 2 | [1] | 3 | [3${}^{\circ}$] | 4 | [2.5] |

6 | 2 | [OC] | 2 | [20%] | 1 | [0.5] | 4 | [4.5${}^{\circ}$] | 3 | [2] |

7 | 2 | [OC] | 3 | [30%] | 4 | [2] | 1 | [0${}^{\circ}$] | 2 | [1.5] |

8 | 2 | [OC] | 4 | [40%] | 3 | [1.5] | 2 | [1.5${}^{\circ}$] | 1 | [1] |

9 | 3 | [OT] | 1 | [10%] | 3 | [1.5] | 4 | [4.5${}^{\circ}$] | 2 | [1.5] |

10 | 3 | [OT] | 2 | [20%] | 4 | [2] | 3 | [3${}^{\circ}$] | 1 | [1] |

11 | 3 | [OT] | 3 | [30%] | 1 | [0.5] | 2 | [1.5${}^{\circ}$] | 4 | [2.5] |

12 | 3 | [OT] | 4 | [40%] | 2 | [1] | 1 | [0${}^{\circ}$] | 3 | [2] |

13 | 4 | [OTM] | 1 | [10%] | 4 | [2] | 2 | [1.5${}^{\circ}$] | 3 | [2] |

14 | 4 | [OTM] | 2 | [20%] | 3 | [1.5] | 1 | [0${}^{\circ}$] | 4 | [2.5] |

15 | 4 | [OTM] | 3 | [30%] | 2 | [1] | 4 | [4.5${}^{\circ}$] | 1 | [1] |

16 | 4 | [OTM] | 4 | [40%] | 1 | [0.5] | 3 | [3${}^{\circ}$] | 2 | [1.5] |

Variable | Noise | ||
---|---|---|---|

Increasing | Nominal | Reducing | |

Impactor velocity (m/s) | 5.25 | 5 | 4.75 |

Relative Density | ρ × 1.05 | ρ | ρ × 0.95 |

Variable | Value | Unit |
---|---|---|

Density [25] | 4428.79 | kg/m^{3} |

Young’s Modulus [25] | 116.52 | GPa |

Yield Strength [26] | 932.22 | MPa |

Poisson’s Ratio [25] | 0.31 | |

Cowper-Symonds Constant: D [27] | 200 | |

Cowper-Symonds Constant: q [27] | 15 |

Running No. | Noise; SEA (kJ/kg) | Average (kJ/kg) | S/N Ratio (dB) | ||
---|---|---|---|---|---|

Increased | Nominal | Decreased | |||

1 | 16.42 | 16.19 | 16.02 | 16.21 | 24.19 |

2 | 35.28 | 34.15 | 33.04 | 34.15 | 30.66 |

3 | 53.32 | 51.24 | 48.24 | 50.93 | 34.12 |

4 | 55.63 | 50.30 | 48.34 | 51.42 | 34.18 |

5 | 23.60 | 22.49 | 21.94 | 22.68 | 27.10 |

6 | 23.31 | 22.77 | 21.82 | 22.63 | 27.08 |

7 | 79.77 | 73.49 | 66.03 | 73.10 | 37.20 |

8 | 91.99 | 89.63 | 87.56 | 89.73 | 39.05 |

9 | 29.76 | 28.83 | 26.99 | 28.53 | 29.08 |

10 | 46.60 | 42.54 | 42.73 | 43.96 | 32.84 |

11 | 19.66 | 18.08 | 16.07 | 17.94 | 24.99 |

12 | 53.40 | 52.12 | 49.52 | 51.68 | 34.25 |

13 | 16.38 | 15.39 | 14.18 | 15.32 | 23.66 |

14 | 39.65 | 37.89 | 33.83 | 37.13 | 31.34 |

15 | 57.87 | 56.24 | 54.87 | 56.33 | 35.01 |

16 | 39.80 | 37.65 | 35.65 | 37.70 | 31.50 |

Total | 1948.30 | - | - |

Variable | Index | Mean (kJ/kg) | S/N RAtio (dB) |
---|---|---|---|

A | 1 | 38.18 | 30.79 |

2 | 52.03 | 32.61 | |

3 | 35.53 | 30.29 | |

4 | 36.62 | 30.38 | |

B | 1 | 20.68 | 26.01 |

2 | 34.47 | 30.48 | |

3 | 49.57 | 32.83 | |

4 | 57.63 | 34.75 | |

C | 1 | 23.62 | 26.94 |

2 | 41.21 | 31.76 | |

3 | 51.58 | 33.40 | |

4 | 45.95 | 31.97 | |

D | 1 | 44.53 | 31.75 |

2 | 39.29 | 29.59 | |

3 | 38.82 | 31.39 | |

4 | 39.73 | 31.34 | |

E | 1 | 51.56 | 32.77 |

2 | 43.37 | 32.11 | |

3 | 35.14 | 29.78 | |

4 | 32.29 | 29.40 |

Control Factor | Level | Description | Value |
---|---|---|---|

A | 2 | Geometry | Octet-Cross |

B | 4 | ρ | 40% |

C | 3 | H/C Ratio | 1.5 |

D | 1 | α | 0^{°} |

E | 1 | A/B Ratio | 1 |

Variable | DOF | SS | Contribution | MS | F | Significance |
---|---|---|---|---|---|---|

A | 3 | 2138.19 | 10.57% | 712.73 | 106.98 | Significant |

B | 3 | 9659.32 | 47.73% | 3219.77 | 483.31 | Significant |

C | 3 | 5254.40 | 25.96% | 1751.47 | 262.90 | Significant |

D | 3 | 253.26 | 1.25% | 84.42 | 12.67 | Significant |

E | 3 | 2718.77 | 13.43% | 906.26 | 136.03 | Significant |

Error | 32 | 213.18 | 1.05% | 6.66 | ||

Total | 47 | 20,237.12 | 100% |

Parameter | Noise | ||
---|---|---|---|

Increase | Nominal | Decrease | |

Volume (mm^{3}) | 10,014.24 | 9473.54 | 8943.15 |

Mass (g) | 44.36 | 41.97 | 39.62 |

Total EA (J) | 3931.29 | 3553.12 | 3293.07 |

SEA (kJ/kg) | 88.62 | 84.66 | 83.12 |

Parameters | Existing Model | Estimated | Verification | Difference | ||
---|---|---|---|---|---|---|

Value | Gain | Value | Gain | |||

Mean SEA (kJ/kg) | 40.59 | 94.97 | 54.38 | 85.47 | 44.88 | 9.51 |

S/N Ratio (dB) | 31.02 | 41.21 | 10.19 | 38.63 | 7.61 | 2.58 |

**Table 11.**Jellyroll Material Properties [13].

Variable | Value |
---|---|

Density | 2.721 × 10^{−6} kg/mm^{3} |

Young’s Modulus | 0.5 GPa |

Configuration | Dimension (mm × mm × mm) | Plies | Mass (g) |
---|---|---|---|

1 | 10 × 10 × 15 | 1 | 861 |

2 | 14 × 14 × 21 | 1 | 1232 |

3 | 10 × 10 × 15 | 2 | 1722 |

Master Part | Slave Part |
---|---|

Impactor | Top Sandwich Layer |

Impactor | Lattice Core |

Impactor | Bottom Sandwich Layer |

Impactor | Battery Housing |

Lattice Core | Lattice Core |

Top Sandwich Layer | Lattice Core |

Bottom Sandwich Layer | Lattice Core |

Battery Skin | Battery Housing |

Top Sandwich Layer | Battery Housing |

Floor Panel | Battery Housing |

Battery Jellyroll | Battery Skin |

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**MDPI and ACS Style**

Pratama, L.K.; Santosa, S.P.; Dirgantara, T.; Widagdo, D.
Design and Numerical Analysis of Electric Vehicle Li-Ion Battery Protections Using Lattice Structure Undergoing Ground Impact. *World Electr. Veh. J.* **2022**, *13*, 10.
https://doi.org/10.3390/wevj13010010

**AMA Style**

Pratama LK, Santosa SP, Dirgantara T, Widagdo D.
Design and Numerical Analysis of Electric Vehicle Li-Ion Battery Protections Using Lattice Structure Undergoing Ground Impact. *World Electric Vehicle Journal*. 2022; 13(1):10.
https://doi.org/10.3390/wevj13010010

**Chicago/Turabian Style**

Pratama, Leonardus Kenny, Sigit Puji Santosa, Tatacipta Dirgantara, and Djarot Widagdo.
2022. "Design and Numerical Analysis of Electric Vehicle Li-Ion Battery Protections Using Lattice Structure Undergoing Ground Impact" *World Electric Vehicle Journal* 13, no. 1: 10.
https://doi.org/10.3390/wevj13010010