# Multi-Objective Optimization and Test of a Tractor Drive Motor

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## Abstract

**:**

## 1. Introduction

## 2. Optimization Parameters of Drive Motor

_{m}defined as the viscous damping coefficient, the functional relationship between ${T}_{\mathrm{max}}$, ${T}_{\mathrm{m}}$, ${\omega}_{\mathrm{max}}$ and ${\omega}_{\mathrm{m}}$ can be established as:

## 3. Design Objective Function of Drive Motor

#### 3.1. Heat Loss Objective Function

_{m}is the power of the driving motor, kW.

#### 3.2. Total Efficiency Function of the Drive System

## 4. Design Constraints of Drive Motor

#### 4.1. Maximum Slot Full Rate Constraints

_{a}is the diameter of the stator core, cm; B

_{m}is the amplitude of the air gap magnetic flux density, T; ${L}_{\mathrm{st}}$ is the length of the stator core, cm; ${k}_{\mathrm{w}}$ is the winding factor; ${k}_{\mathrm{e}}$ is the ratio of ${k}_{\mathrm{ep}}$ and single-phase winding-back EMF coefficient; ${W}_{\mathrm{p}}$ is the number of winding turns; ${a}_{\mathrm{cu}}$ is the number of parallel shares; ${N}_{\mathrm{cu}}$ is the number of single-coil turns; ${A}_{\mathrm{s}}$ is the area of the single stator slot, mm

^{2}; and ${k}_{\mathrm{s}}$ is the full slot rate; ${k}_{\mathrm{ss}}$ is the maximum slot full rate.

#### 4.2. Field-Weakening Speed Regulation Constraints

#### 4.3. Constraints of Torque Reserve Coefficient

_{TN}is the rated traction force of the electric tractor, N; and ${F}_{\mathrm{Ta}}$ is the plow resistance under the working condition, N.

_{0}is the transmission ratio of the central drive-train; ${\eta}_{\mathrm{ky}}$ is the transmission efficiency of the transmission, %; ${\eta}_{0}$ is the transmission efficiency of the central drive-train, %; and ${r}_{\mathrm{q}}$ is the driving radius, m.

#### 4.4. Tractor Rated Power Constraints

## 5. Optimization Algorithm and Example Design

#### 5.1. Optimization Algorithm Design

_{TN}and ${T}_{\mathrm{mT}}$ are introduced into Equation (44) to obtain the constraint equation of ${\omega}_{\mathrm{mT}}$, and the constraint of the motor speed regulating ability is introduced into Equation (36). Then, the design constraint of ${\omega}_{\mathrm{max}}$ is established. From the Sheffield University MATLAB GA toolbox, the two functions that are gacommon.m and gamultiobjsolve could easily be called [27]. Through gacommon.m processing constraint types, the boundary conditions are established. The global solution of heat loss objective Equation (26) and transmission efficiency objective Equation (32) is carried out by gamultiobjsolve. Afterward, the fitness function deviation is determined, and the individual front-end distribution of the solution set of ${D}_{\mathrm{m}}$ and ${T}_{\mathrm{mT}}$ is solved; the optimal solution is selected as the design value of traction motor parameters. The drive motor ${\omega}_{\mathrm{max}}$ is calculated according to Equation (21). Finally, in accordance with the electric tractor’s bus voltage of the drive motor is set, and the other intrinsic parameters of the drive motor are calculated by Equations (14) and (21).

#### 5.2. Optimization Example

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## 6. Control Test

#### 6.1. Test Design

#### 6.2. Comparative Analysis

## 7. Conclusions

- (1)
- This study proposes a multi-objective optimization method for the drive motor of tractors. The objective functions are established based on the heat loss of the drive motor and the total efficiency of the driving system. Considering the inherent characteristics of the motor and the characteristics of the tractor’s working conditions, a mathematical model of constraints is established, and the NSGA-II algorithm is used to design the optimization problem-solving process.
- (2)
- An optimization example is developed, in which the single-target optimization results of the drive motor’s optimal energy efficiency and the optimal mechanical transmission efficiency of the transmission system are taken as the control group for conducting the tractor electric drive system bench control test.
- (3)
- The test results show that for the tractor model in the optimization example, compared with the control group, the proposed multi-objective optimization method can make the overall tractor system efficiency the highest, and the maximum and rated values of the total efficiency ${\eta}_{\mathrm{q}}$ of the drive system of the multi-objective optimization design scheme. Compared with the optimal design scheme with ${\eta}_{\mathrm{me}}$ as a single objective, it is increased by 2% and 1.4%, respectively, and compared with the optimal design scheme with ${\eta}_{\mathrm{tr}}$ as a single objective; it improved by 26.5% and 73.6%, respectively. It can provide an effective calculation method for the motor design problem in the subsequent development of the tractor electromechanical drive system.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Design Method | Multi-Objective Optimization | $\mathbf{Optimization}\mathbf{Aimed}\mathbf{at}{\mathit{\eta}}_{\mathbf{m}\mathbf{e}}$ | $\mathbf{Optimization}\mathbf{Aimed}\mathbf{at}{\mathit{\eta}}_{\mathbf{t}\mathbf{r}}$ |
---|---|---|---|

${P}_{\mathrm{mT}}$/kW | 36.8 | 36.8 | 36.8 |

${T}_{\mathrm{mT}}$/N·m | 216 | 92.5 | 1445 |

${\omega}_{\mathrm{mT}}$ /r·min^{−1} | 1627 | 3800 | 243 |

${\omega}_{\mathrm{max}}$/r·min^{−1} | 2861 | 7500 | 496 |

${k}_{\mathrm{E}}$/V·min·r^{−1} | 0.133 | 0.051 | 0.766 |

${D}_{\mathrm{m}}$/N·m·min·r^{−1} | 0.175 | 0.024 | 5.713 |

${V}_{\mathrm{mT}}$/V | 380 | 380 | 380 |

Equipment | Parameter | Numeric/Type | Production Enterprises |
---|---|---|---|

Two-way battery simulator | Hardware technology | High-power IGBT technology | Xi’an Xunpai |

Input power/V | 380 (Three-phase five-wire AC) | ||

Output power/kW | 100 | ||

Output voltage/V | 670 | ||

Output current/A | −200~200 | ||

Detects the resolution | 15 mA or 15 mV | ||

Mode of communication | CAN, Ethernet | ||

HDT05 torque speed integrated sensor | Rated torque/(N·m) | 2000 | YB2~2000 |

Rated speed/(r/min) | 4000 | ||

Precision/% | $\pm $0.2 | ||

WT333 power analyzer | channel | WT333, Three-channel | Yokogawa, Japan |

Precision/% | 0.2 |

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**MDPI and ACS Style**

Liu, M.; Li, Y.; Zhao, S.; Han, B.; Lei, S.; Xu, L.
Multi-Objective Optimization and Test of a Tractor Drive Motor. *World Electr. Veh. J.* **2022**, *13*, 43.
https://doi.org/10.3390/wevj13020043

**AMA Style**

Liu M, Li Y, Zhao S, Han B, Lei S, Xu L.
Multi-Objective Optimization and Test of a Tractor Drive Motor. *World Electric Vehicle Journal*. 2022; 13(2):43.
https://doi.org/10.3390/wevj13020043

**Chicago/Turabian Style**

Liu, Mengnan, Yanying Li, Sixia Zhao, Bing Han, Shenghui Lei, and Liyou Xu.
2022. "Multi-Objective Optimization and Test of a Tractor Drive Motor" *World Electric Vehicle Journal* 13, no. 2: 43.
https://doi.org/10.3390/wevj13020043