# Optimization Method of Speed Ratio for Power-Shift Transmission of Agricultural Tractor

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Research Object

- The transmission features shift gears that operate independently of one another, allowing for full power-shifting capabilities.
- Depending on the gear distribution, some or all the gears in the transmission may have a structural influence on each other, enabling either partial or full power-shifting functionality.

#### 2.2. Optimization Method

#### 2.2.1. Speed Characteristics of Agricultural Tractors

#### 2.2.2. Optimization Based on Genetic Algorithm

_{d}is the fuel consumption per unit mileage (L), Q

_{z}is the total fuel consumption (L), S

_{z}is the mileage in a calculation cycle (km), P is the engine power (kW), b

_{e}is the specific fuel consumption (g/(kW·h)), v is the tractor speed (km/h), ρ

_{d}is the fuel density (kg/L), g is the gravitational constant (N/kg), n

_{e}is the engine speed (rpm), r is the radius of the drive wheel (m), i

_{t}is the speed ratio, T

_{e}is the engine torque (N·m), X is the parameters to be optimized, y is the total time (s), respectively.

_{t}

_{1}to i

_{t}

_{16}are the total speed ratios of each gear from 1 to 16 gears, respectively.

_{1}to i

_{16}) of the entire transmission can be expressed by Equation (5). The optimization variables for forward gears are expressed by Equation (6).

_{a}

_{1}to i

_{a}

_{4}are the speed ratios of each gear in the front gearbox, respectively; i

_{b}

_{1}to i

_{b}

_{4}are the speed ratios of each gear in the rear gearbox, respectively.

_{em}is the rated engine speed.

## 3. Modeling and Simulation

## 4. Results and Discussion

_{t}) based on the engine speed, equivalent wheel radius, and speed ratio of each gear. This paper establishes the stable engine speed range as 850–2200 rpm and the driving wheel radius as 0.95 m. Using these parameters, the tractor speed ranges for all forward gears were calculated and presented in Figure 10.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic of agricultural tractor powertrain layout [9].

**Figure 2.**The speed statistics of a tractor throughout its life cycle from Resch and Renius [26].

**Figure 3.**The linear coordinate diagram of the speed usage frequency in the whole life cycle of the agricultural tractor.

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

Rated power of engine (kW) | 175 |

Rolling radius of wheels (m) | 0.95 |

Mass of tractor weight (kg) | 9000 |

Mechanical efficiency of drive system | 0.87 |

Speed Ratio | Value | Speed Ratio | Value | Speed Ratio | Value | Speed Ratio | Value |
---|---|---|---|---|---|---|---|

i_{t}_{1} | 394 | i_{t}_{5} | 121 | i_{t}_{9} | 82.6 | i_{t}_{13} | 56.4 |

i_{t}_{2} | 244.7 | i_{t}_{6} | 110 | i_{t}_{10} | 75.1 | i_{t}_{14} | 40.3 |

i_{t}_{3} | 152.9 | i_{t}_{7} | 100 | i_{t}_{11} | 68.3 | i_{t}_{15} | 25.2 |

i_{t}_{4} | 133.1 | i_{t}_{8} | 90.9 | i_{t}_{12} | 62.1 | i_{t}_{16} | 15.7 |

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**MDPI and ACS Style**

Li, B.; Pan, J.; Li, Y.; Ni, K.; Huang, W.; Jiang, H.; Liu, F.
Optimization Method of Speed Ratio for Power-Shift Transmission of Agricultural Tractor. *Machines* **2023**, *11*, 438.
https://doi.org/10.3390/machines11040438

**AMA Style**

Li B, Pan J, Li Y, Ni K, Huang W, Jiang H, Liu F.
Optimization Method of Speed Ratio for Power-Shift Transmission of Agricultural Tractor. *Machines*. 2023; 11(4):438.
https://doi.org/10.3390/machines11040438

**Chicago/Turabian Style**

Li, Baogang, Jinbo Pan, Yuhuan Li, Kun Ni, Wanyou Huang, Hanjun Jiang, and Fuhao Liu.
2023. "Optimization Method of Speed Ratio for Power-Shift Transmission of Agricultural Tractor" *Machines* 11, no. 4: 438.
https://doi.org/10.3390/machines11040438