# Gear Ratio Optimization of a Multi-Speed Transmission for Electric Dump Truck Operating on the Structure Route

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## Abstract

**:**

## 1. Introduction

## 2. Modeling and Analysis of Electric Dump Truck

#### 2.1. Dynamics of the Transmission

#### 2.2. Battery Model

#### 2.3. Powertrain System

## 3. Shift Schedule and Gear Ratio Optimization

#### 3.1. Shift Schedule

#### 3.2. Gear Ratio Optimization

#### 3.3. The Objective Function

#### 3.4. Inequality Constraints

## 4. Simulation Results

#### 4.1. Driving Cycle Analysis

#### 4.2. Optimization Results

#### 4.3. Performance Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Vehicle model schematic (acc, acceleration signal; dec, deceleration signal; SOC, state of charge).

**Figure 2.**The layout of the transmission: (

**a**) Schematic diagram; and (

**b**) the designed transmission in SolidWorks ( MG, motor/generator; 1, drive motor; 2, 1st sun gear (S1); 3, 1st planet gear (C1); 4, 1st brake (B1); 5, 1st ring gear (R1); 6, worm shaft; 7, worm gear; 8, 2nd ring gear (R2); 9, 2nd planet gear (C2); 10, 2nd sun gear (S2); 11, 2nd brake (B2)).

**Figure 3.**The relationship between the battery internal resistance (per cell) and state of charge(SOC).

**Figure 14.**Simulation results: (

**a**) velocity comparison; (

**b**) road grade; (

**c**) SOC curve; (

**d**) pedal position of acceleration and brake; and (

**e**) gear control sequence.

**Figure 17.**Operating point distribution on the motor efficiency map of the EDT with a single speed transmission.

**Figure 18.**Operating point distribution on the motor efficiency map of the EDT with a two-speed transmission.

Parameter | Symbol | Value |
---|---|---|

Vehicle mass | ${m}_{1}$ | 20,000 kg |

Load mass | ${m}_{2}$ | 28,000 kg |

Full load mass | m | 48,000 kg |

Wheel radius | r | 0.74 m |

Maximum speed | ${u}_{max}$ | 60 km/h |

Maximum ascendable grade | G | 40% |

Coefficient of rolling resistance | $f$ | 0.017 |

Coefficient of air resistance | ${C}_{d}$ | 0.8 |

Main reducer ratio | ${i}_{g0}$ | 7.3 |

Face area | $A$ | 5 m^{2} |

Battery capacity | ${C}_{a}$ | 220 Ah |

Maximum motor speed | ${n}_{max}$ | 4000 rpm |

Maximum motor torque | ${T}_{max}$ | 5000 Nm |

Gear | B1 | B2 |
---|---|---|

1st gear | engaged | disengaged |

2nd gear | disengaged | engaged |

Null | disengaged | disengaged |

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## Share and Cite

**MDPI and ACS Style**

Tan, S.; Yang, J.; Zhao, X.; Hai, T.; Zhang, W. Gear Ratio Optimization of a Multi-Speed Transmission for Electric Dump Truck Operating on the Structure Route. *Energies* **2018**, *11*, 1324.
https://doi.org/10.3390/en11061324

**AMA Style**

Tan S, Yang J, Zhao X, Hai T, Zhang W. Gear Ratio Optimization of a Multi-Speed Transmission for Electric Dump Truck Operating on the Structure Route. *Energies*. 2018; 11(6):1324.
https://doi.org/10.3390/en11061324

**Chicago/Turabian Style**

Tan, Senqi, Jue Yang, Xinxin Zhao, Tingting Hai, and Wenming Zhang. 2018. "Gear Ratio Optimization of a Multi-Speed Transmission for Electric Dump Truck Operating on the Structure Route" *Energies* 11, no. 6: 1324.
https://doi.org/10.3390/en11061324