# Performance Comparison of Pure Electric Vehicles with Two-Speed Transmission and Adaptive Gear Shifting Strategy Design

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## Abstract

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## 1. Introduction

- (1)
- A partition gear-shifting strategy combining the economic and dynamic performances of pure electric vehicle two-speed transmission was designed, and fuzzy logic was utilized to adjust the partition shifting strategy online.
- (2)
- Via comparison, the influence of the two-speed transmission on the economic and dynamic performances of the pure electric vehicle was revealed.
- (3)
- A few contributions to the application of automatic transmission in the field of passenger pure electric vehicles are provided.

## 2. Powertrain Structure and System Modeling

#### 2.1. Battery Modeling

_{out}is [30]:

_{oc}refers to the open circuit voltage, I

_{bat}denotes the battery’s output current, and R

_{int}represents the internal resistance.

_{d}is the discharge power of the battery and P

_{c}is the charge power of the battery. The table lookup relationship between P

_{d}, P

_{c}, and battery SOC is shown in Figure 3a,b, respectively. Furthermore, the following relationship can be obtained by substituting Equation (1) into Equation (2):

_{int}is the initial SOC and C

_{0}is the battery capacity.

#### 2.2. Electric Motor Model

_{m}is:

_{g}is:

_{m}denotes the electric motor efficiency, T

_{m}and n

_{m}refer to the torque and speed of the motor, respectively, P

_{req}refers to the required power, and P

_{m}and P

_{g}represent the output power of the motor, respectively. The motor selected a permanent magnet synchronous motor (PMSM), and the efficiency of the motor is shown in Figure 4.

#### 2.3. Transmission Model

_{1}, the second gear transmission ratio i

_{2}, the key parameters of the vehicle are shown in Table 1, the Structure of 2DCT is shown in Figure 5.

_{m}denotes the rotational inertia of the motor output shaft and clutch drive shaft; ω

_{m}means the angular speed of the output shaft of the motor; b

_{m}is the rotational damping coefficient of the motor output shaft; and T

_{c}

_{1}and T

_{c}

_{2}represent the torque transferred by clutch C

_{1}and C

_{2}, respectively.

_{c}

_{1}, J

_{c}

_{2}represent the rotational inertia of the driven part of C

_{1}and C

_{2}, respectively; ω

_{c}

_{1}, ω

_{c}

_{2}are the angular velocities of C

_{1}and C

_{2}, respectively; b

_{c}

_{1}, b

_{c}

_{2}are the rotational damping coefficients of driven shafts of C

_{1}and C

_{2}, respectively; and T

_{1}, T

_{2}are the output torque of the clutch driven shafts, respectively. The clutch output torque is:

_{n}is the pressure applied to the clutch; and μ is the friction coefficient of the clutch friction plate. The dynamic balance equation of the clutch output is:

_{0}indicates the output torque of transmission.

_{w}is the rotational inertia of the drive shaft section, ω

_{w}is the rotational damping coefficient of the drive shaft section, and T

_{f}is the total resistance torque applied to the wheel.

#### 2.4. Longitudinal Dynamics Model of Vehicle

_{rq}is the driving torque demand, η

_{t}is the efficiency of transmission, m is the mass of the vehicle, g is the gravity acceleration, f is the coefficient of rolling resistance, α is the angle of the road slope, A is the frontal area of the vehicle, v is the velocity of the vehicle, C

_{d}is the drag coefficient, and δ is the coefficient of rotational mass conversion.

_{w}is the rotational inertia of the wheel and J

_{f}is the moment of inertia of the flywheel.

## 3. Gear-Shifting Strategy

#### 3.1. Economic Gear-Shifting Strategy

#### 3.2. Dynamic Gear-Shifting Strategy

#### 3.3. Gear-Shifting Strategy Online Modification

## 4. Comparison and Verification

#### 4.1. Comparison of Vehicle Economic Performance

#### 4.2. Comparison of Vehicle Dynamic Performance

#### 4.3. Rig Testing

_{z}, F

_{f}, F

_{g}, F

_{a}, and F

_{i}are the driving resistance, the rolling resistance, the slope resistance, the air resistance, and the acceleration resistance, respectively.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 8.**Membership functions of the input and output variables in fuzzy rules of economic shifting strategy.

**Figure 9.**Characteristic maps of fuzzy logic in economic shifting strategy: (

**a**) Fuzzy logic for speed, acceleration and adjustment; (

**b**) Fuzzy logic for pedal opening, acceleration and adjustment.

**Figure 10.**Membership functions of the input and output variables in fuzzy rules of dynamic shifting strategy.

**Figure 11.**Characteristic maps of fuzzy logic in dynamic shifting strategy: (

**a**) Fuzzy logic for speed, pedal change rate and adjustment; (

**b**) Fuzzy logic for pedal opening, pedal change rate and adjustment.

**Figure 13.**Vehicle speed tracking and gearshifts trajectories: (

**a**) NEDC driving cycle; (

**b**) Gear position; (

**c**) UDDS driving cycle; (

**d**) Gear position; (

**e**) WLTC driving cycle; (

**f**) Gear position.

**Figure 14.**Motor efficiency in three driving cycles: (

**a**) Efficiency under NEDC driving cycle; (

**b**) Efficiency under UDDS driving cycle; (

**c**) Efficiency under WLTC driving cycle.

**Figure 15.**Battery SOC curves in three driving cycles: (

**a**) NEDC driving cycle; (

**b**) UDDS driving cycle; (

**c**) WLTC driving cycle.

**Figure 16.**Braking recovery energy curves in three driving cycles: (

**a**) NEDC driving cycle; (

**b**) UDDS driving cycle; (

**c**) WLTC driving cycle.

**Figure 17.**Acceleration time at different road slopes: (

**a**) Acceleration time from 0 to 100 km/h at 0% slope; (

**b**) Acceleration time from 0 to 50 km/h at 0% slope; (

**c**) Acceleration time from 0 to 100 km/h at 4% slope; (

**d**) Acceleration time from 0 to 50 km/h at 4% slope; (

**e**) Acceleration time from 0 to 100 km/h at 6% slope; (

**f**) Acceleration time from 0 to 50 km/h at 6% slope.

Item | Parameter | Unit | Value |
---|---|---|---|

Vehicle | Vehicle mass (EVT) | kg | 1758 |

Vehicle mass (EV) | kg | 1730 | |

Rolling resistance coefficient | 0.0083 | ||

Rotating mass conversion factor | 1.08 | ||

Air resistance coefficient | 0.28 | ||

Vehicle frontal area | m^{2} | 2.1 | |

Dynamic radius of the wheel | m | 0.31 | |

Battery | Rated capacity | Ah | 88.24 |

Battery voltage | V | 340 | |

Motor | Peak power | kw | 110 |

Peak speed | r/min | 12,000 | |

Peak torque | Nm | 230 | |

Transmission | First gear ratio | 3 | |

Second gear ratio | 1.19 | ||

Final Drive | Final drive ratio (EVT) | 3.91 | |

Final drive ratio (EV) | 8.28 |

Drive Cycle | Vehicle Type | Final SOC (%) | Braking Recovery Energy (kJ) |
---|---|---|---|

NEDC | EVT | 65.89 | 578.69 |

EV | 65.88 | 572.64 | |

UDDS | EVT | 65.47 | 908.43 |

EV | 65.38 | 844.60 | |

WLTC | EVT | 60.16 | 1131.90 |

EV | 59.97 | 957.15 |

Slope | Vehicle Type | 0~100 km/h (s) | 0~50 km/h (s) |
---|---|---|---|

0% | EVT | 9.45 | 3.72 |

EV | 11.19 | 5.48 | |

4% | EVT | 10.97 | 4.17 |

EV | 13.32 | 6.57 | |

6% | EVT | 11.98 | 4.45 |

EV | 14.81 | 7.37 |

Vehicle Type | Max Slope | Max Speed |
---|---|---|

EVT | 36% | 228 km/h |

EV | 25% | 169 km/h |

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## Share and Cite

**MDPI and ACS Style**

He, B.; Chen, Y.; Wei, Q.; Wang, C.; Wei, C.; Li, X.
Performance Comparison of Pure Electric Vehicles with Two-Speed Transmission and Adaptive Gear Shifting Strategy Design. *Energies* **2023**, *16*, 3007.
https://doi.org/10.3390/en16073007

**AMA Style**

He B, Chen Y, Wei Q, Wang C, Wei C, Li X.
Performance Comparison of Pure Electric Vehicles with Two-Speed Transmission and Adaptive Gear Shifting Strategy Design. *Energies*. 2023; 16(7):3007.
https://doi.org/10.3390/en16073007

**Chicago/Turabian Style**

He, Bolin, Yong Chen, Qiang Wei, Cong Wang, Changyin Wei, and Xiaoyu Li.
2023. "Performance Comparison of Pure Electric Vehicles with Two-Speed Transmission and Adaptive Gear Shifting Strategy Design" *Energies* 16, no. 7: 3007.
https://doi.org/10.3390/en16073007