# Optimizing Automatic Transmission Double-Transition Shift Process Based on Multi-Objective Genetic Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Modeling of DTS

#### 2.1. Modeling of the Planetary Gear Sets Based on the Lagrange Method

#### 2.2. Modeling of Clutch Friction

#### 2.3. Modeling of the Transmission Input Power

#### 2.4. Modeling of the Transmission Output Power

## 3. Double-Transition Shift Process Analysis

#### 3.1. BL and BM Power on Upshift Process Analysis

#### 3.2. BS and CS Power on Downshift Process Analysis

## 4. Multi-Objective Optimization of DTS

#### 4.1. Strategy One

#### 4.2. Strategy Two

#### 4.3. Strategy Three

#### 4.4. Strategy Four

#### 4.5. Strategy Five

## 5. Conclusions

- (1)
- In this paper, the Lagrange method is used to dynamically model the double-transition shift for heavy-duty mining truck automatic transmission. The vehicle powertrain system and the controller based on the multi-objective genetic algorithm are built-in Matlab/Simulink. The dynamic analysis of two sets of clutches for DTS is carried out.
- (2)
- Obtained in the multi-objective genetic algorithm, the Pareto optimal solution shows that the lowest root mean square of shift jerk and the energy loss of clutches are $4.05{\mathrm{m}/\mathrm{s}}^{-3}$ and $22.4KJ$, respectively.
- (3)
- The simulation results of five strategies of double-transition shift show that overlapping the inertia phases of both clutch groups will cause the fluctuation amplitude of the output torque to increase. On the contrary, the shift jerk can be more stable at ${j}_{\mathrm{max}}\le 14.2{\mathrm{m}/\mathrm{s}}^{-3}$, which is reduced by 56.3%, when the inertial phases are not overlapped. The torque phase overlaps with the inertia phase of another group of clutches, effectively reducing the shift time to about 1.1s and thus decreasing the clutch energy loss by 13.4%, which is $W=27.1KJ$.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Stribeck friction model (

**a**) and clutch friction working modes switching according to different transmitted torques and relative speeds of clutch (

**b**).

**Figure 3.**Multi-objective genetic algorithm diagram (non-dominated sorting genetic algorithm II, NSGA-II).

**Figure 5.**Simulation results of 2–3 power-on double-transition upshift for Strategy 1. (

**a**) Output shaft and clutch torque. (

**b**) Clutch speed and speed ratio. (

**c**) The jerk of shift process. (

**d**) The clutch energy loss of shift process.

**Figure 6.**Simulation results of 2–3 power-on double-transition upshifts for Strategy 2. (

**a**) Output shaft and clutch torque. (

**b**) Clutch speed and speed ratio. (

**c**) The jerk of shift process. (

**d**) The clutch energy loss of shift process.

**Figure 7.**Simulation results of 2–3 power-on double-transition upshift for Strategy 3. (

**a**) Output shaft and clutch torque. (

**b**) Clutch speed and speed ratio. (

**c**) The jerk of shift process. (

**d**) The clutch energy loss of shift process.

**Figure 8.**Simulation results of 2–3 power-on double-transition upshift for Strategy 4. (

**a**) Output shaft and clutch torque. (

**b**) Clutch speed and speed ratio. (

**c**) The jerk of shift process. (

**d**) The clutch energy loss of shift process.

**Figure 9.**Simulation results of 2–3 power-on double-transition upshift for Strategy 5. (

**a**) Output shaft and clutch torque. (

**b**) Clutch speed and speed ratio. (

**c**) The jerk of shift process. (

**d**) The clutch energy loss of shift process.

Gears | CS | BS | CH | BM | BL | BR | Gear Ratio |
---|---|---|---|---|---|---|---|

1 | √ | √ | 4.00 | ||||

2 | √ | √ | 2.67 | ||||

3 | √ | √ | 2.00 | ||||

4 | √ | √ | 1.33 | ||||

5 | √ | √ | 1.00 | ||||

6 | √ | √ | 0.67 | ||||

R1 | √ | √ | −5.00 | ||||

R2 | √ | √ | −3.33 |

Time | BS and CS | BL and BM | ||||
---|---|---|---|---|---|---|

Strategy 1 | Strategy 2 | Strategy 3 | Strategy 4 | Strategy 5 | ||

${t}_{0}\sim {t}_{1}$ | low gear | |||||

${t}_{1}\sim {t}_{2}$ | torque phase | low gear | ||||

${t}_{2}\sim {t}_{3}$ | high gear | inertia phase | torque phase | low gear | ||

${t}_{3}\sim {t}_{4}$ | inertia phase | high gear | inertia phase | torque phase | low gear | |

${t}_{4}\sim {t}_{5}$ | torque phase | high gear | inertia phase | torque phase | low gear | |

${t}_{5}\sim {t}_{6}$ | low gear | high gear | inertia phase | torque phase | ||

${t}_{6}\sim {t}_{7}$ | high gear | inertia phase | ||||

${t}_{7}\sim {t}_{8}$ | high gear |

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**MDPI and ACS Style**

Zhang, H.; Zhao, X.; Yang, J.; Zhang, W. Optimizing Automatic Transmission Double-Transition Shift Process Based on Multi-Objective Genetic Algorithm. *Appl. Sci.* **2020**, *10*, 7794.
https://doi.org/10.3390/app10217794

**AMA Style**

Zhang H, Zhao X, Yang J, Zhang W. Optimizing Automatic Transmission Double-Transition Shift Process Based on Multi-Objective Genetic Algorithm. *Applied Sciences*. 2020; 10(21):7794.
https://doi.org/10.3390/app10217794

**Chicago/Turabian Style**

Zhang, Heng, Xinxin Zhao, Jue Yang, and Wenming Zhang. 2020. "Optimizing Automatic Transmission Double-Transition Shift Process Based on Multi-Objective Genetic Algorithm" *Applied Sciences* 10, no. 21: 7794.
https://doi.org/10.3390/app10217794