# Concept Design and Development of an Electric Go-Kart Chassis for Undergraduate Education in Vehicle Dynamics and Stress Applications

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{T}= 355 MPa. For the shaft material, S355 mild steel was chosen. S355 has a high fracture toughness since it has high plasticity at the conditions of use. For the dynamic strength of the shaft design, the key parameters are inverse bending dynamic strength σ

^{d}

_{−1}= 280 MPa and inverse torsional dynamic strength τ

^{d,t}

_{−1}=180 MPa. In contrast, the material chosen in [16] is AISI 4130, with a yield strength of σ

_{T}= 435 MPa. It also has good weld ability, high fracture toughness, and plasticity, so it is an excellent choice of material for the chassis. It is marked according to AISI, the American-based institution. It is not readily available in Croatia. In [11], AISI 4130 was also selected for the chassis material. In [22], the chassis material was not marked, only the yield strength of 250 MPa was stated, which was close to S235, according to EN 10027-1. In several papers [10,15,18,19], the material chosen was AISI 1018, with a very similar yield strength of 370 MPa. One quite different choice of material, aluminum alloy 6063, was chosen in [13], with a yield strength of around 220 MPa. The difficulty with aluminum alloy involves the additional material in the welding process, i.e., the electrode. Overall, one can argue that the material most chosen for chassis is a mild structural steel, with yield strengths ranging from 250 to 440 MPa, with good weld ability. Hence, our choice of material falls within this range.

#### 2.1. Vehicle Dynamics Modeling

_{d}is the driver’s mass, and m

_{v}is the vehicle mass. The final COG position according to Figure 2 is $L=1.103\mathrm{m},{h}_{\mathrm{CG}}=0.32\text{}\mathrm{m},\text{}{L}_{\mathrm{CG}}=0.62\text{}\mathrm{m}.$ Figure 2 and Figure 3 depict the inertial forces at acceleration, causing redistribution of ground reactions on a vehicle concept design.

_{CG}, and the distance from the front wheels marked by L

_{CG}. The inertial force at braking in a straight trajectory is shown with the red arrow, and the combined weight with the blue arrow.

_{CG}. The inertial forces in Figure 2 were used to determine the normal reaction forces on wheels in the “worst” case scenario, braking in the curved trajectory, to determine loads for the finite element model analysis. The normal inertial force in a curved trajectory was calculated according to

_{com}is the combined driver’s and vehicle’s mass, v is the COG velocity, and r

_{CG}is the COG’s trajectory curvature radius. The tangential inertial force is calculated as

_{11}for longitudinal distance from the contact of the rear left tire to the COG, and B

_{11}for the radial distance from the contact of the rear left tire to the COG, etc. In Figure 4, the nomenclature for the ground reaction forces is, for instance, ${F}_{\mathrm{T}}^{12\mathrm{n}}$ is a friction force on the outer rear tire on the normal line to the combined COG, and ${F}_{\mathrm{T}}^{21\mathrm{t}}$ is a friction force component on the inner front tire on the tangential line to the combined COG. The maximum expected friction force on any given tire, according to the dry friction Coulomb’s law, is ${F}_{\mathrm{T}}\le {F}_{\mathrm{N}}{\mu}_{0}$, where μ

_{0}is the static friction coefficient. The friction force on each contact surface, in Figure 4, is depicted by two components, radial and tangential.

_{11}, yields

_{CG}, yielding

_{CG}= 16 m, h

_{CG}= 0.32 m, v = 10 m/s, L

_{CG}= 0.62 m, m

_{com}= 130 kg, a

^{T}= 1.6 m/s

^{2}, is shown in Table 1. This set of parameters is within the friction coefficient, i.e., for each wheel within the friction cone.

#### 2.2. Vehicle Power Train

^{−1}. The chosen wheels with a diameter of 255 mm would have an angular speed at the limit speed ${v}_{\mathrm{L}}={\omega}_{\mathrm{w}}D/2\Rightarrow {\omega}_{\mathrm{w}}=2{v}_{\mathrm{L}}/D=2\cdot 15.85/0.255\approx 124.3{\mathrm{s}}^{-1}.$ This leads to a rotational speed of ${n}_{\mathrm{w}}={\omega}_{\mathrm{w}}/\left(2\pi \right)=124.3/\left(2\pi \right)=19.785{\text{}\mathrm{s}}^{-1}=1187{\text{}\mathrm{min}}^{-1}.$ To reduce the rotational speed from the motor to the wheel, a simple chain drive is presumed. The transmission ratio should be $i={n}_{\mathrm{m}}/{n}_{\mathrm{w}}=4600/1187=3.875={z}_{\mathrm{w}}/{z}_{\mathrm{m}}.$ z

_{w}stands for the number of teeth on the rear shaft chain gear, and z

_{m}stands for the number of teeth on the motor chain gear. If the motor chain gear is chosen with 13 teeth, then the rear shaft chain gear should have ${z}_{\mathrm{w}}=3.875\cdot 13=50$. The chain that could be used to drive the vehicle has a pitch of at least 8 mm, for “reason” of the minimum pitch diameter of the small chain gear, following the diameter of the sleeve for the motor shaft. Such a chain gear would have a pitch diameter ${r}_{2\mathrm{w}}=4/\mathrm{sin}\left(0.5\cdot 360/50\right)=63.7\text{}\mathrm{mm}=0.0637\mathrm{m}$. The force acting on the chain gear on the rear shaft is ${F}_{ch}=1600\xb70.9/\left(124.3-0.0637\right)=181.9\text{}\mathrm{N}$.

_{k}

^{b}stands for the stress concentration factor at bending, the upper index “t” stands for torsion, and “a” for axial load case. Further on, ${\sigma}_{\mathrm{a}}^{\mathrm{b}}$ is the bending induced normal stress amplitude, ${\sigma}_{\mathrm{a}}^{\mathrm{a}}$ is the axial load induced stress amplitude, ${\tau}_{\mathrm{a}}^{\mathrm{t}}$ is the torsion induced stress amplitude, while all stress components with lower index “m” are mean values of, respectively, depicted stress components. The Soderberg criterion is chosen as the simplest and most conservative condition in the form of:

_{1}and k

_{2}, respectively, [37]. ${\sigma}_{-1}^{\mathrm{d}}$ stands for inverse dynamic bending strength [29,37], ${\sigma}_{\mathrm{T}}$ stands for yield strength, and f

_{s}the chosen safety factor. These dynamic strength conditions use the stress components transformed into equivalent stresses, as shown in Equation (12). It is one of the best suited explicit equations for the case of combined non-proportional stress components (i.e., one stress component changing with time, differently from other stress components).

_{bI}= 20.15 Nm, M

_{bII}= 51.5 Nm, M

_{tII}= 10.4 Nm.

^{d}

_{−1}= 280 MPa, and an inverse torsional dynamic strength of σ

^{d,t}

_{−1}=180 MPa.

## 3. Finite Element Analysis

## 4. Tube Wall Stability Analysis (Buckling)

## 5. Design of Electrical System

#### 5.1. Energy Demand

#### 5.2. Battery System Modeling

_{4}Ti

_{5}O

_{12}—“lithium titanate”) and LFP (Li Fe Po

_{4}—“lithium iron phosphate”). These two types do not burn or explode compared to the other cells considered. The number of cycles for both types is large, and the range of operating temperatures of the cells is also very wide and sufficient to operate in the initially assumed conditions. Comparing LTO and LFP cells, the biggest difference, and also the disadvantage of LTO cells, is their high cost.

_{N}= 14 ⋅ 3.6 = 50.4 V. According to the go-kart standard, driving with maximum power can take 10–20 min. For further design of the power supply, the chosen energy capacity is 1.6 kWh (E = 1600 Wh). Since one battery has an approximate or expected capacity of 3 Ah, this means that one serial “package” has the same energy capacity E

_{1}:E

_{1}= 50.4 V·3 Ah = 151.2 Wh. Thus, when designed, ten of such packages should be connected in parallel and then the energy capacity would be ten times more, equal to E

_{10}= 1512 Wh. This is close to the planned power consumption and is also within some geometric parameters that are suitable for mounting on chassis tubes. Details of the battery holder box and the design of the battery cell inter-connections are shown in Figure 15.

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Geometry in calculating the redistribution of forces in a curved trajectory at vehicle acceleration.

**Figure 7.**Chassis geometry modeled for the finite element analysis: (

**a**) isometric “real” view; (

**b**) chassis tubes and plates.

**Figure 10.**Results of analysis, with respect to equivalent stress for the finest mesh (von Mises stress).

**Figure 11.**Sub-modeling of the most stressed joint: (

**a**) geometry of the chassis, part view; (

**b**) view of joint sub-model mesh based on solid elements; (

**c**) von Mises stress distribution in the sub-model.

**Figure 12.**The size of the solid elements compared to the cross-sectional thickness of the tube wall: (

**a**) coarsest mesh; (

**b**) medium mesh; (

**c**) finest mesh.

**Figure 13.**Sub-modeling of the most stressed joint–stub axle in the steering mechanism: calculated factor of safety (FOS).

**Figure 15.**Battery system concept design: (

**a**) cell placement in a holder box; (

**b**) box with the cover attached to the chassis distribution as the basis for the sub-modeling view; (

**c**) lower battery cell inter-connecting plate view; (

**d**) upper battery cell inter-connecting plate view.

F_{N}^{11}/N | F_{N}^{12}/N | F_{N}^{21}/N | F_{N}^{22}/N |
---|---|---|---|

65.1 | 551.3 | 292.5 | 366.3 |

Case | F_{N}^{11}/N | F_{N}^{12}/N | F_{T}^{11n}/N | F_{T}^{12n}/N | F_{T}^{11t}/N | F_{T}^{12t}/N |
---|---|---|---|---|---|---|

1 | 65.1 | 551.3 | 31.2 | 155.3 | 14.9 | 80.1 |

2 | 506.23 | 506.23 | 0 | 0 | 510.12 | 510.12 |

3 | 358.3 | 558.3 | 0 | 0 | 0 | 0 |

Position, x, mm | 15 | 35 | 120 | 642.5 | 677.5 | 770 |

Diameter, d/mm | 15.1 | 17.3 | 19.2 | 22.3 | 23.9 | 19.1 |

Li-Ion Type | Specific Energy (Wh/kg) | Energy Density (Wh/L) | Cycle Life |
---|---|---|---|

NCA | 220–260 | 600 | 500 |

NMC | 150–220 | 580 | 1000–2000 |

Li Fe Po_{4} | 90–160 | 325 | >2000 |

Li_{4} Ti_{5} O_{12} | 60–110 | 177 | 3000–7000 |

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**MDPI and ACS Style**

Mihalić, T.; Hoster, J.; Tudić, V.; Kralj, T.
Concept Design and Development of an Electric Go-Kart Chassis for Undergraduate Education in Vehicle Dynamics and Stress Applications. *Appl. Sci.* **2023**, *13*, 11312.
https://doi.org/10.3390/app132011312

**AMA Style**

Mihalić T, Hoster J, Tudić V, Kralj T.
Concept Design and Development of an Electric Go-Kart Chassis for Undergraduate Education in Vehicle Dynamics and Stress Applications. *Applied Sciences*. 2023; 13(20):11312.
https://doi.org/10.3390/app132011312

**Chicago/Turabian Style**

Mihalić, Tihomir, Josip Hoster, Vladimir Tudić, and Toni Kralj.
2023. "Concept Design and Development of an Electric Go-Kart Chassis for Undergraduate Education in Vehicle Dynamics and Stress Applications" *Applied Sciences* 13, no. 20: 11312.
https://doi.org/10.3390/app132011312