# Numerical Modelling and Multi Objective Optimization Analysis of Heavy Vehicle Chassis

^{*}

## Abstract

**:**

## 1. Introduction

^{®}and ANSYS

^{®}software. The author looked at variables like the position of the center of gravity, the dynamic and manufacture constraints in their design criteria. A multi-objective function was defined which considered mass reduction and chassis stiffness as objectives. They were able to reduce the weight of 3D structure by 5.31 kg [25].

## 2. Methodology

^{®}software. The modelled chassis is then optimized using the Taguchi design of Experiments (D.O.E). The optimization techniques used are the central composite design (CCD) scheme and the optimal space filling (OSF) design. Sensitivity plots and response surface plots are then generated. The critical range of optimized variables is then determined. The equivalent stress, deformation, mass and surface response are evaluated for each design points. The optimization techniques used in this research have not been implemented in chassis design and could be helpful in the development of future chassis designs.

#### 2.1. The Simulation Environment

^{®}V18.1. The interaction with the software is through graphical user interface (GUI). However, the inbuilt language of the software is C++. The chassis is analyzed as a static structure. A finite element model analysis of the chassis is then performed. We initially evaluate the chassis deformations and the stress distributions on a given standard chassis [27]. We then optimize this chassis, in terms of reducing the deformations and the stress distributions, using the Taguchi design of experiments method. The next subsection details the chassis geometry, loading, and boundary conditions.

#### 2.2. Chassis Specifications

#### 2.3. CAD Modelling

^{®}design modeler using the sketch and extrude tool. The dimensions of chassis are taken from literature as per Table 1 [27]. Two longitudinal members and eight lateral members are modeled as shown in Figure 2.

## 3. Results and Discussion

#### 3.1. FE Results on a Standard Chassis

#### 3.2. Optimization of Standard Chassis

^{®}design modeler. These variables are the widths of cross member 1, 2 and 3, as shown in Figure 9 (H6), Figure 10 (H12) and Figure 11 (H14). The width dimensions are tabulated in Figure 12 below. The distance between these cross members is 1461.6 mm and 1724 mm, respectively. The three (3) selected cross sections are from rightmost (front) transverse member of chassis.

#### 3.2.1. Total Deformation

- 58.5 mm (−10%) for cross member 1, 65 mm for member 2 and 65 mm for member 3.
- 65 mm for cross member 1, 65 mm for member 2 and 71.5 mm (+10%) for member 3.

- 60.67 mm (−6.6%) for cross member 1, 65 mm for member 2 and 61.53 (−5.3%) mm for member 3.
- 65 mm for cross member 1, 67.6 mm (+4%) for member 2 and 71.07 (+9.3%) mm for member 3.

#### 3.2.2. Equivalent Stress

- 65 mm for cross member 1, 71.5 mm (+10%) for member 2 and 65 mm for member 3.
- 65 mm for cross member 1, 65 mm for member 2 and 71.5 mm (+10%) for member 3.

- 58.933 mm (−9.3%) for cross member 1, 60.667 mm (−6.7%) for member 2 and 65.867 mm (+1.5%) for member 3.
- 62.4 mm (−1.4%) for cross member 1, 61.533 mm (−5.3%) for member 2 and 70.2 mm (+8%) for member 3.

#### 3.2.3. Solid Mass

- 70.2 mm (+8%) for cross member 1, 65.867 mm (1.34%) for member 2, 69.333 mm (+6.7%) for member 3.

#### 3.2.4. Surface Response

#### Equivalent Stresses Surface Response

#### Mass Surface Response

#### 3.2.5. Sensitivity

## 4. Conclusions

## 5. Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**A ladder chassis frame (truck) view [6].

**Figure 13.**The example points of a Central Composite Circumscribed design with three input parameters [29].

**Figure 14.**Optimal space filling design (OSF) [31].

**Figure 16.**Equivalent stress vs. design points (

**a**) for CCD scheme (

**b**) for optimal space filling design.

**Figure 18.**Response surface plot of equivalent stress vs. cross member 1 and cross member 2 (

**a**) for CCD scheme, and (

**b**) for optimal space filling (OSF) design.

**Figure 19.**Response surface plot of equivalent stress vs. cross member 2 and cross member 3 (

**a**) for CCD scheme, and (

**b**) for optimal space filling design.

**Figure 20.**Equivalent stress cross member 1 (

**a**) for CCD scheme, and (

**b**) for optimal space filling (OSF) design.

**Figure 21.**(

**a**) Equivalent stress vs. cross member, (

**a**) 3 in case of CCD scheme, and (

**b**) 2 in case of optimal space filling design.

**Figure 22.**Three-dimensional response surface plot of solid mass (

**a**) for CCD scheme (

**b**) for optimal space filling design.

**Figure 23.**Solid mass vs. cross member 1 (

**a**) for CCD scheme, and (

**b**) for optimal space filling design.

**Figure 24.**Solid mass vs. cross member 3 (

**a**) for CCD scheme, and (

**b**) for optimal space filling design.

**Table 1.**Specifications of TATA 1612 chassis [27].

Vehicle Name | TATA 1612 |
---|---|

Frame Section | C type (116 mm × 25 mm × 5 mm) |

Front Overhang (a) | 740 mm |

Rear Overhang (c) | 1400 mm |

Wheel Base (b) | 6670 mm |

Total Load acting on chassis | 257,022 N |

Load acting on each beam | 128,511 N/Beam |

Stress produced on the beam (σ) | 3297.422 N/mm^{2} |

Material of Chassis | St 52 E |

Variable Name | Lower Bound | Upper Bound |
---|---|---|

Cross Member 1 | 58.5 mm | 71.5 mm |

Cross Member 2 | 58.5 mm | 71.5 mm |

Cross Member 3 | 58.5 mm | 71.5 mm |

A | B | C | D | E | F | G | |
---|---|---|---|---|---|---|---|

1 | Name | P5 - cross_member1 (mm) | P6 - cross_member2 (mm) | P7 - cross_member3 (mm) | P3 - Equivalent Stress Max (MPa) | P4 - Total Deformation Max (mm) | P8 - Solid Mass (kg) |

2 | 1 | 65 | 65 | 65 | 3280.49 | 347.4546 | 214.6414 |

3 | 2 | 58.5 | 65 | 65 | 3264.454 | 347.8886 | 209.9142 |

4 | 3 | 71.5 | 65 | 65 | 3520.136 | 347.1296 | 219.3685 |

5 | 4 | 65 | 58.5 | 65 | 3273.633 | 347.7588 | 209.9142 |

6 | 5 | 65 | 71.5 | 65 | 3527.463 | 346.9958 | 219.3685 |

7 | 6 | 65 | 65 | 58.5 | 3259.301 | 343.9264 | 209.9142 |

8 | 7 | 65 | 65 | 71.5 | 3220.32 | 340.7808 | 219.3685 |

9 | 8 | 59.71528 | 59.71528 | 59.71528 | 3345.578 | 341.9918 | 203.1113 |

10 | 9 | 70.28472 | 59.71528 | 59.71528 | 3433.409 | 341.7593 | 210.798 |

11 | 10 | 59.71528 | 70.28472 | 59.71528 | 3439.451 | 341.5502 | 210.798 |

12 | 11 | 70.28472 | 70.28472 | 59.71528 | 3313.501 | 341.1359 | 218.4847 |

13 | 12 | 59.71528 | 59.71528 | 70.28472 | 3466.476 | 342.1991 | 210.798 |

14 | 13 | 70.28472 | 59.71528 | 70.28472 | 3231.431 | 341.758 | 218.4847 |

15 | 14 | 59.71528 | 70.28472 | 70.28472 | 3293.051 | 341.7089 | 218.4847 |

16 | 15 | 70.28472 | 70.28472 | 70.28472 | 3464.079 | 341.2692 | 226.1714 |

A | B | C | D | E | F | G | |
---|---|---|---|---|---|---|---|

1 | Name | P5 - cross_member1 (mm) | P6 - cross_member2 (mm) | P7 - cross_member3 (mm) | P3 - Equivalent Stress Max (MPa) | P4 - Total Deformation Max (mm) | P8 - Solid Mass (kg) |

2 | 1 | 69.33333 | 68.46667 | 60.66667 | 3494.398 | 345.0904 | 217.1625 |

3 | 2 | 63.26667 | 69.33333 | 59.8 | 3237.664 | 341.5257 | 212.7505 |

4 | 3 | 59.8 | 66.73333 | 68.46667 | 3352.964 | 344.4751 | 214.6414 |

5 | 4 | 68.46667 | 59.8 | 67.6 | 3498.669 | 345.3408 | 215.2717 |

6 | 5 | 58.93333 | 60.66667 | 65.86667 | 3507.02 | 347.0544 | 207.7082 |

7 | 6 | 71.06667 | 63.26667 | 63.26667 | 3348.538 | 348.8975 | 216.5322 |

8 | 7 | 66.73333 | 62.4 | 58.93333 | 3249.308 | 342.5268 | 209.5991 |

9 | 8 | 70.2 | 65.86667 | 69.33333 | 3320.901 | 343.0932 | 222.2048 |

10 | 9 | 65.86667 | 64.13333 | 64.13333 | 3286.35 | 348.261 | 214.0111 |

11 | 10 | 65 | 67.6 | 71.06667 | 3469.519 | 341.1595 | 220.9442 |

12 | 11 | 61.53333 | 71.06667 | 65 | 3478.07 | 347.1521 | 216.5322 |

13 | 12 | 60.66667 | 65 | 61.53333 | 3506.208 | 351.4384 | 208.9688 |

14 | 13 | 64.13333 | 58.93333 | 62.4 | 3305.275 | 350.4504 | 207.7082 |

15 | 14 | 67.6 | 70.2 | 66.73333 | 3475.766 | 345.3902 | 221.5745 |

16 | 15 | 62.4 | 61.53333 | 70.2 | 3236.134 | 342.5801 | 214.0111 |

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**MDPI and ACS Style**

Agarwal, A.; Mthembu, L.
Numerical Modelling and Multi Objective Optimization Analysis of Heavy Vehicle Chassis. *Processes* **2021**, *9*, 2028.
https://doi.org/10.3390/pr9112028

**AMA Style**

Agarwal A, Mthembu L.
Numerical Modelling and Multi Objective Optimization Analysis of Heavy Vehicle Chassis. *Processes*. 2021; 9(11):2028.
https://doi.org/10.3390/pr9112028

**Chicago/Turabian Style**

Agarwal, Abhishek, and Linda Mthembu.
2021. "Numerical Modelling and Multi Objective Optimization Analysis of Heavy Vehicle Chassis" *Processes* 9, no. 11: 2028.
https://doi.org/10.3390/pr9112028