#
Lightweight Chassis Design of Hybrid Trucks Considering Multiple Road Conditions and Constraints^{ †}

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Modeling the Side Rails

## 3. Cross Members’ Integration and Complete Assembly

^{3}) and the rest of the cross member using aluminum (Young’s modulus = 73 GPa, Poisson ratio = 0.3, density = 2700 kg/m

^{3}).

## 4. Stiffness and Modal Frequency Calculation

**being the vertical displacement):**

_{v}_{v}) and vertical bending stiffness (k

_{v}), these values were obtained for a set of randomly generated designs and compared with the values corresponding to the baseline of truck chassis. Figure 5a,b show the plots of vertical stiffness vs. the mass of the randomly generated and the first vertical bending frequency vs. the mass for the same random designs, respectively. The design marked as ‘Model of interest’, as shown in Figure 5c, had a higher stiffness compared to the baseline truck chassis yet had a significantly lower mass.

## 5. Model Verification

## 6. Suspension Integration

## 7. Static Analysis

- (i)
- Both front wheels in bump event;
- (ii)
- Both rear wheels in bump event;
- (iii)
- Both front tires in pothole event;
- (iv)
- Both rear tires in pothole event;
- (v)
- Maximum breaking condition.

## 8. Mode Detection

## 9. Optimization Framework

^{2}–10

^{3}kg. Hence, if the constraints are not satisfied, the objective function assigns a value ~10

^{6}kg and thus becomes an undesirable design.

^{th}iteration) using Equations (7) and (8), respectively.

_{1}and c

_{2}are known as thrust parameters; $w$ is the inertia weighting parameter of velocity; ${p}^{i}$ and ${p}_{k}^{g}$ are the best particle position (throughout iterative history) and the best swarm position, respectively. In Equation (7) the second term is known as “individual correction” because (${p}^{i}-{x}_{k}^{i}$) is essentially the difference between the particle’s current position and the best position in history. Thus, if the term increases, the particle is attracted more towards the best position. The third term in Equation (7) is called “social correction” as $\left({p}_{k}^{g}-{x}_{k}^{i}\right)$ is the difference between the particle’s position and the best position in the entire swarm, and hence it attracts the particle to the global best. The inertia weight parameter, $w$, decides the influence of the particle’s velocity compared to the personal and social influences, and it decides the optimization convergence rate. The parameter $\Delta t$ is called the time step and is often taken as 1. The values of the parameters as considered in this work are listed in Table 4.

^{5}) was assigned to the objective function corresponding to it. This causes the optimizer to consider the design to be infeasible and thus the particle is discarded from the search space.

## 10. Optimization Results and Discussion

## 11. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Top view and side view of rail; (

**b**) cross section of side rail (consisting of C-section with top and bottom plates).

**Figure 2.**Rails divided into three sections with different thicknesses (shown using different colors).

**Figure 3.**(

**a**) Cross members and relative positions in the structure; (

**b**) medium-fidelity finite element model of the baseline design.

**Figure 4.**(

**a**) Vertical bending deflection under applied load in the middle. (

**b**) Finite Element Model with vertically downward force.

**Figure 5.**(

**a**) Vertical bending stiffness vs. mass for random designs, (

**b**) first vertical bending frequency vs. mass for random designs, and (

**c**) the side rails of the model of interest (lower mass compared to baseline but with high vertical bending stiffness).

**Figure 11.**(

**a**) Reference eigenvector (vertical bending mode) and (

**b**) matching eigenvector from a set of test eigenvectors.

**Figure 16.**(

**a**) Vertical bending frequency vs. structural mass for all designs analyzed and (

**b**) violation vs. structural mass for all designs analyzed during optimization.

**Figure 17.**(

**a**) Optimized design (mass of chassis without suspensions and point masses = 275 kg) (

**b**) thickness distribution of the side rails.

**Figure 18.**Von Mises stress distribution of optimized design for (

**a**) Event #1, (

**b**) Event #2, (

**c**) Event #3, (

**d**) Event #4 and (

**e**) Event #5.

Case | First Torsional Deformation Frequency (Hz) | First Lateral Bending Frequency (Hz) | First Vertical Bending Frequency (Hz) | Vertical Bending Stiffness (N/mm) | Violation Value |
---|---|---|---|---|---|

High-Fidelity Model | 3.45 | 12.57 | 24.26 | 4027 | N/A |

Shell Element (Element Size 12.5 mm) | 3.29 | 10.64 | 25.34 | 4168 | 0.010944 |

Shell Element (Element Size 15 mm) | 3.27 | 10.58 | 25.16 | 4182 | 0.01012 |

Shell Element (Element Size 17.5 mm) | 3.21 | 10.57 | 25.31 | 4154 | 0.00991 |

Shell Element (Element Size 20 mm) | 3.21 | 10.54 | 25.121 | 4125 | 0.009498 |

Wheel -> | Front Left | Front Right | Back Left | Back Right | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Direction -> | X | Y | Z | X | Y | Z | X | Y | Z | X | Y | Z |

Front Both Bump | 0 | 0 | 1.75 | 0 | 0 | 1.75 | 0 | 0 | 1 | 0 | 0 | 1 |

Rear Both Bump | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1.75 | 0 | 0 | 1.75 |

Front Both Pot Hole | 0.75 | 0 | 1.75 | 0.75 | 0 | 1.75 | 0 | 0 | 1 | 0 | 0 | 1 |

Rear Both Pot Hole | 0 | 0 | 1 | 0 | 0 | 1 | 0.75 | 0 | 1.75 | 0.75 | 0 | 1.75 |

G-Stop Forward | 0.4 | 0 | 1 | 0.4 | 0 | 1 | 0.4 | 0 | 1 | 0.4 | 0 | 1 |

**Table 3.**Modal assurance criteria (MAC) values of test eigenvectors with respect to reference eigenvectors (see Figure 4b).

Natural Frequencies (Hz) | Normalized MAC Value |
---|---|

3.969 | 8.80 × 10^{−8} |

10.57 | 1.22 × 10^{−6} |

22.23 | 1.10 × 10^{−4} |

25.43 | 2.23 × 10^{−1} |

26.14 | 5.00 × 10^{−3} |

27.31 | 5.68 × 10^{−5} |

30.08 | 8.23 × 10^{−5} |

31.94 | 1.00 |

33.63 | 7.50 × 10^{−3} |

PSO Parameter | Value |
---|---|

$w$ | 0.78 |

${c}_{1}$ | 2 |

${c}_{2}$ | 2 |

$\Delta t$ | 1 |

Properties | Baseline Model | Optimized Model |
---|---|---|

Mass (Kg) | 317 | 275 |

First Bending Frequency (Hz) | 25.12 | 20.5 |

Bending Rigidity (N/mm) | 4125 | 268 |

Violation Parameter (Stress) | 0.0094 | 0.0086 |

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**MDPI and ACS Style**

De, S.; Singh, K.; Seo, J.; Kapania, R.K.; Ostergaard, E.; Angelini, N.; Aguero, R.
Lightweight Chassis Design of Hybrid Trucks Considering Multiple Road Conditions and Constraints. *World Electr. Veh. J.* **2021**, *12*, 3.
https://doi.org/10.3390/wevj12010003

**AMA Style**

De S, Singh K, Seo J, Kapania RK, Ostergaard E, Angelini N, Aguero R.
Lightweight Chassis Design of Hybrid Trucks Considering Multiple Road Conditions and Constraints. *World Electric Vehicle Journal*. 2021; 12(1):3.
https://doi.org/10.3390/wevj12010003

**Chicago/Turabian Style**

De, Shuvodeep, Karanpreet Singh, Junhyeon Seo, Rakesh K. Kapania, Erik Ostergaard, Nicholas Angelini, and Raymond Aguero.
2021. "Lightweight Chassis Design of Hybrid Trucks Considering Multiple Road Conditions and Constraints" *World Electric Vehicle Journal* 12, no. 1: 3.
https://doi.org/10.3390/wevj12010003