# Model-Based Estimation of Transmission Gear Ratio for Driving Energy Consumption of an EV

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## Abstract

**:**

## 1. Introduction

_{2}emission levels below the reference value for 2020 [6].

## 2. Mathematical Models

#### 2.1. Vehicle Dynamics

#### 2.2. Traction Motor Model

#### 2.3. Simulation Model

## 3. Model Validation

^{2}. It was limited by motor rated torque, as the maximum traction force was lower than the limited traction force due to tire slip. The vehicle travel distance was also estimated for this acceleration and was determined as 188.7 m.

## 4. Simulation Results

## 5. Numerical Study on Energy Consumption

#### 5.1. Transmission Configuration and Gear Ratio

#### 5.2. Vehicle Power Demand

#### 5.3. Vehicle Energy Consumption

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$\ddot{x}$ | Longitudinal vehicle acceleration |

ICE | internal combustion engine |

HEV | hybrid electric vehicle |

BEV | battery electric vehicle |

EV | electric vehicle |

${F}_{tr}$ | traction force |

${F}_{aero}$ | aerodynamic force |

${F}_{roll}$ | rolling resistance |

${m}_{equiv}$ | equivalent vehicle mass |

${M}_{mot}$ | traction motor output torque |

${i}_{tr}$ | transmission ratio |

${\eta}_{tr}$ | mechanical efficiency |

${r}_{d}$ | wheel dynamic radius |

${F}_{tr\left(max\right)}$ | maximum traction force |

${\mu}_{x}$ | tire friction coefficient |

${F}_{z}^{front}$ | vertical load on the driving axle |

${C}_{d}$ | drag coefficient |

$S$ | vehicle frontal area |

${\rho}_{air}$ | air density |

V | vehicle speed |

${C}_{r}$ | rolling friction coefficients |

$k$ | rolling speed coefficient |

$m$ | vehicle mass |

${P}_{tr}$ | traction power |

${E}_{tr}$ | driving energy |

${P}_{loss}$ | power loss |

${M}_{ref}$ | rated torque |

${\omega}_{ref}$ | maximum speed of the motor |

${P}_{el}$ | electric power |

${E}_{el}$ | energy consumption |

${n}_{mot}$ | motor speed |

${C}_{m}$ | mass correction coefficient |

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**Figure 4.**Vehicle acceleration vs. time and vehicle speed vs. time for acceleration from 0 to 100 km/h.

**Figure 6.**Cumulative energy consumption vs. transmission second gear ratio for different switching speed over WLTC.

**Figure 7.**Motor electric and mechanical power vs. time for WLTC in the case of a single speed gearbox.

**Figure 8.**Motor electric and mechanical power vs. time for NEDC in the case of a single speed gearbox.

**Figure 9.**Motor electric and mechanical power vs. time for FTP-75 in the case of a single speed gearbox.

Parameters | Designation | |
---|---|---|

Motor rated power (kW) | ${P}_{ref}$ | 80 |

Motor rated torque (Nm) | ${M}_{ref}$ | 280 |

Motor maximum speed (rpm) | ${n}_{ref}$ | 10,300 |

Cooper losses coefficient (−) | ${k}_{c}$ | 0.14 |

Iron losses coefficient (−) | ${k}_{i}$ | 2.3 |

Windage losses coefficient (−) | ${k}_{w}$ | 6 × 10^{−7} |

Constant losses (−) | $C$ | 500 |

Parameters | WLTC | NEDC | FTP-75 |
---|---|---|---|

Duration (s) | 1800 | 1180 | 1874 |

Stops duration (s) | 235 | 241 | 241 |

Distance (km) | 23.26 | 11.02 | 17.77 |

Maximum speed (km/h) | 131.3 | 120 | 91.1 |

Average speed (km/h) | 46.5 | 33.6 | 34.2 |

Maximum acceleration (m/s^{2}) | 1.66 | 1.11 | 1.48 |

Minimum acceleration (m/s^{2}) | −1.5 | −1.39 | −1.48 |

Parameters | Designation | |
---|---|---|

Type of EV | BEV | |

Aerodynamic drag coefficient | ${C}_{d}$ | 0.28 |

Frontal area (m^{2}) | $S$ | 2.19 |

Rolling friction coefficient | ${C}_{r}$ | 0.0083 |

Rolling speed coefficient | $k$ | 1 × 10^{−5} |

Vehicle mass (kg) | $m$ | 1645 |

Mass correction coefficient | ${C}_{m}$ | 1.1 |

Motor rated power (kW) | ${P}_{r}$ | 80 |

Motor rated torque (Nm) | ${M}_{r}$ | 254 |

Motor rated speed (rpm) | ${n}_{r}$ | 3000 |

Motor maximum speed (rpm) | ${n}_{max}$ | 10,000 |

Maximal speed (km/h) | 144 | |

Acceleration time (s) | 0–100 km/h | 11.5 |

Transmission ratio | ${i}_{tr}$ | 8.19 |

Wheel rolling radius (m) | ${r}_{roll}$ | 0.315 |

Transmission mechanical efficiency (-) | ${\eta}_{tr}$ | 0.95 |

Parameters | WLTC | WLTC | NEDC | NEDC | FTP-75 | FTP-75 |
---|---|---|---|---|---|---|

Single Speed Gearbox | Dual Speed Gearbox | Single Speed Gearbox | Dual Speed Gearbox | Single Speed Gearbox | Dual Speed Gearbox | |

Total energy per cycle (kWh) | 3.173 | 3.079 | 1.415 | 1.389 | 2.235 | 2.184 |

Average power (kW) | 6.35 | 6.16 | 4.32 | 4.23 | 4.29 | 4.19 |

Specific energy (kWh/km) | 0.136 | 0.132 | 0.129 | 0.126 | 0.126 | 0.123 |

CPU time (ms) | 1.426 | 1.705 | 1.325 | 1.541 | 1.551 | 1.746 |

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**MDPI and ACS Style**

Hinov, N.; Punov, P.; Gilev, B.; Vacheva, G.
Model-Based Estimation of Transmission Gear Ratio for Driving Energy Consumption of an EV. *Electronics* **2021**, *10*, 1530.
https://doi.org/10.3390/electronics10131530

**AMA Style**

Hinov N, Punov P, Gilev B, Vacheva G.
Model-Based Estimation of Transmission Gear Ratio for Driving Energy Consumption of an EV. *Electronics*. 2021; 10(13):1530.
https://doi.org/10.3390/electronics10131530

**Chicago/Turabian Style**

Hinov, Nikolay, Plamen Punov, Bogdan Gilev, and Gergana Vacheva.
2021. "Model-Based Estimation of Transmission Gear Ratio for Driving Energy Consumption of an EV" *Electronics* 10, no. 13: 1530.
https://doi.org/10.3390/electronics10131530