# Research on Regenerative Braking of Pure Electric Mining Dump Truck

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Principle Analysis of Regenerative Braking Control System

## 3. System Model and Control Strategy

#### 3.1. Drive Motor, Battery and Regenerative Braking Force Model

#### 3.1.1. Drive Motor Mechanics Model

#### 3.1.2. Battery Model

#### 3.1.3. Regenerative Braking Force Model

#### 3.2. Vehicle Dynamics Model

#### 3.2.1. Normal Reaction Force on the Front and Rear Wheels of the Vehicle when Braking

#### 3.2.2. Front and Rear Axle Braking Force Distribution

- (1)
- The front and rear wheels are both locked and dragged.
- (2)
- The front wheels are locked and dragged first, and then the rear wheels are locked and dragged.
- (3)
- The rear wheels are locked and dragged first, and then the front wheels are locked and dragged.

#### 3.3. Regenerative Braking Strategy

#### 3.3.1. Vehicle Speed based Braking Strategy

#### 3.3.2. I Curve based Braking Strategy

#### 3.3.3. Regeneration Braking Strategy based on β Line

#### 3.3.4. Maximizing Front Axle Braking Force Strategy ${\mathrm{F}}_{\mathrm{fmax}}$

## 4. Simulation Analysis

#### 4.1. Simulation of Different Braking Strength on Horizontal Road at Maximum Vehicle Speed

_{0}= 15 km/h at full load and no load, braking with braking strength z = 0.05, z = 0.1 and z = 0.15 (Because the vehicle speed is low, the braking strength of the road drive cycle is smaller than 0.15, the vehicle reserves the mechanical brake, during emergency braking, pure mechanical braking is adopted and the brake is safe and reliable. Therefore, the case which the braking strength z > 0.15 is not discussed).

#### 4.1.1. Comparison of Braking Energy Recovery

#### 4.1.2. Comparison of Braking Force Distribution

#### 4.2. Simulation of Road Drive Cycle

#### 4.2.1. Comparison of Braking Energy Recovery

#### 4.2.2. Vehicle Energy Consumption and Battery SOC Changes

_{r}) is large. Figure 13 shows the braking power demand when the vehicle is fully loaded on roads with different rolling resistance coefficients. It can be seen that when the rolling resistance coefficient is large, the vehicle kinetic energy (F

_{a}) and potential energy (F

_{i}) are mainly used to overcome the road rolling resistance (F

_{r}) when braking or downhill. At this time, the recoverable energy is limited, as shown in Figure 13a. When the road surface is improved and the rolling resistance coefficient is reduced, more vehicle kinetic energy and potential energy can be recovered. See Figure 13b. Wind resistance (F

_{w}) is negligible compared to rolling resistance.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 9.**Different strategies recover energy at full load. (

**a**) Based on vehicle speed; (

**b**) based on I curve; (

**c**) based on β line; (

**d**) based on ${F}_{\mathrm{fmax}}$.

**Figure 10.**Different strategies recover energy at no load. (

**a**) Based on vehicle speed; (

**b**) based on I curve; (

**c**) based on β line; (

**d**) based on ${F}_{\mathrm{fmax}}$.

**Figure 11.**Different strategy braking force distribution at full load and no load. (

**a**) Based on vehicle speed; (

**b**) based on I curve; (

**c**) based on β line; (

**d**) based on ${F}_{\mathrm{fmax}}$.

**Figure 13.**Power requirements for braking with different rolling resistance coefficients (full load, uphill) (

**a**) f = 0.04; (

**b**) f = 0.02.

Parameters | Value |
---|---|

Vehicle curb mass ($m1$) | 45,000 kg (Include batteries) |

Load capacity ($m2$) | 55,000 kg |

Center of mass height (${h}_{g}$) | 1.8 m (Full load), 1.5 m (No load) |

Wheelbase ($L$) | 6 m |

Front wheelbase ($a$) | 2.45 m (Full load), 1.78 m (No load) |

Rear wheelbase ($b$) | 3.55 m (Full load), 4.72 m (No load) |

Wheel radius ($r$) | 0.95 m |

Rolling resistance coefficient ($f$) | 0.04 |

Ground adhesion coefficient ($\phi $) | 0.6 |

Motor rated power (${P}_{\mathrm{e}}$) | 200 kW |

Number of motors ($N$) | 2 (Four-wheel drive) |

Strategy | Braking Strength | ||||||
---|---|---|---|---|---|---|---|

z = 0.05 | z = 0.1 | z = 0.15 | |||||

Full Load | No Load | Full Load | No Load | Full Load | No Load | ||

Speed based | Energy covered | 17.7 | 0.0 | 310.1 | 117.9 | 392.3 | 163.4 |

Vehicle Kinetic energy * | 868.1 | 390.6 | 868.1 | 390.6 | 868.1 | 390.6 | |

Proportion [%] | 2.0% | 0.0% | 35.7% | 30.2% | 45.2% | 41.8% | |

I curve | Energy covered | 56.5 | 0.0 | 411.4 | 165.4 | 517.5 | 221.7 |

Vehicle Kinetic energy * | 868.1 | 390.6 | 868.1 | 390.6 | 868.1 | 390.6 | |

Proportion [%] | 6.5% | 0.0% | 47.4% | 42.3% | 59.6% | 56.8% | |

β line | Energy covered | 56.5 | 0.0 | 411.3 | 165.0 | 517.4 | 221.0 |

Vehicle Kinetic energy * | 868.1 | 390.6 | 868.1 | 390.6 | 868.1 | 390.6 | |

Proportion [%] | 6.5% | 0.0% | 47.4% | 42.2% | 59.6% | 56.6% | |

${F}_{\mathrm{fmax}}$ | Energy covered | 105.0 | 21.4 | 445.3 | 199.9 | 383.1 | 232.9 |

Vehicle Kinetic energy * | 868.1 | 390.6 | 868.1 | 390.6 | 868.1 | 390.6 | |

Proportion [%] | 12.1% | 5.5% | 51.3% | 51.2% | 44.1% | 59.6% |

Strategy | Working Condition | |||
---|---|---|---|---|

Full Load | No Load | Total | ||

Speed based | Energy covered | 361.4 | 420.7 | 782.1 |

Vehicle Kinetic | 740.0 | 2778.0 | 3518.0 | |

Proportion [%] | 48.8% | 15.1% | 22.2% | |

I curve | Energy covered | 501.6 | 783.5 | 1285.1 |

Vehicle Kinetic | 740.0 | 2778.0 | 3518.0 | |

Proportion [%] | 67.8% | 28.2% | 36.5% | |

β line | Energy covered | 501.6 | 783.0 | 1284.6 |

Vehicle Kinetic | 740.0 | 2778.0 | 3518.0 | |

Proportion [%] | 67.8% | 28.2% | 36.5% | |

${F}_{\mathrm{fmax}}$ | Energy covered | 591.8 | 1464.3 | 2056.1 |

Vehicle Kinetic | 740.0 | 2778.0 | 3518.0 | |

Proportion [%] | 80.0% | 52.7% | 58.4% |

Strategy | Motor Regenerative Braking Efficiency | |||
---|---|---|---|---|

Full Load | No Load | |||

Front | Rear | Front | Rear | |

Vehicle speed | 60.76% | 69.79% | 36.02% | 2.41% |

I curve | 68.16% | 75.42% | 44.95% | 8.11% |

β line | 74.68% | 69.43% | 50.60% | 0.42% |

${F}_{\mathrm{fmax}}$ | 85.53% | 0.00% | 57.65% | 0.00% |

Strategy | Energy Consumed | Improvement Ratio (Compared to No Regeneration)% | ||
---|---|---|---|---|

Full Load (Uphill) | No Load (Downhill) | Total | ||

No Regenerative | 145850 | 42795 | 188645 | 0.00% |

Vehicle speed | 145630 | 41011 | 186641 | 1.06% |

I curve | 145630 | 40811 | 186441 | 1.17% |

β line | 145630 | 40811 | 186441 | 1.17% |

${F}_{\mathrm{fmax}}$ | 145580 | 40128 | 185708 | 1.56% |

Strategy | Energy Consumed | Improvement Ratio (Compared to No Regeneration) % | ||
---|---|---|---|---|

Full Load (Uphill) | No Load (Downhill) | Total | ||

No regenerative | 100290 | 28852 | 129142 | 0.00% |

Vehicle speed | 98902 | 24096 | 122998 | 4.76% |

I curve | 98812 | 23785 | 122597 | 5.07% |

β line | 98812 | 23785 | 122597 | 5.07% |

${F}_{\mathrm{fmax}}$ | 98665 | 23078 | 121743 | 5.73% |

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**MDPI and ACS Style**

Zhang, W.; Yang, J.; Zhang, W.; Ma, F.
Research on Regenerative Braking of Pure Electric Mining Dump Truck. *World Electr. Veh. J.* **2019**, *10*, 39.
https://doi.org/10.3390/wevj10020039

**AMA Style**

Zhang W, Yang J, Zhang W, Ma F.
Research on Regenerative Braking of Pure Electric Mining Dump Truck. *World Electric Vehicle Journal*. 2019; 10(2):39.
https://doi.org/10.3390/wevj10020039

**Chicago/Turabian Style**

Zhang, Wei, Jue Yang, Wenming Zhang, and Fei Ma.
2019. "Research on Regenerative Braking of Pure Electric Mining Dump Truck" *World Electric Vehicle Journal* 10, no. 2: 39.
https://doi.org/10.3390/wevj10020039