# Thermal Analysis of Automobile Drive Axles by the Thermal Network Method

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## Abstract

**:**

## 1. Introduction

## 2. Thermal Analysis of a Two-Axle Automobile Drive Axle

#### 2.1. Thermal Network Model of a Two-Axle Automobile Drive Axle

#### 2.1.1. Thermal Network Diagram of a Two-Axle Automobile Drive Axle

#### 2.1.2. Thermal Balance Equations of a Two-Axle Automobile Drive Axle

_{im}is the thermal resistance between node i and node m (°C/W), R

_{ni}is the thermal resistance between node n and node i (°C/W), m

_{i}is the quality of node i (kg), c

_{i}is the specific heat of node i (J/(kg·K)), ∆τ is the time (s), T

_{i}is the temperature of node i (°C), T

_{m}is the temperature of node m (°C), T

_{n}is the temperature of node n (°C), and Q

_{i}is the thermal production generated by node i (if node i is not the thermal source, Q

_{i}will be zero) (W). Based on the hypothesis in Section 2.1.1, the two-axle automobile drive axle is regarded as the steady state. The temperature stays constant, and ∆T

_{i}/∆τ is zero.

#### 2.2. Thermal Analysis Results of a Two-Axle Automobile Drive Axle

- (1)
- The highest temperatures in the reducer, the motor, and differential are the temperatures of nodes 1, 50, and 14. Notably, the temperature (73.7 °C) of the spindle contacting front-end cover (node 50) is the highest temperature of the two-axle automobile drive axle. The reason is that this part is the uppermost thermal source of the two-axle automobile drive axle, and thermal dissipation is more difficult than in other parts.
- (2)
- The average temperature of the motor is higher than the differential and reducer. The average temperature of the reducer is fiercer than the differential.
- (3)
- The temperature of nodes 1, 5, 14, 18, 19, 38, 42, 43, 46, 50, and 52 are high. These nodes are distributed near the thermal sources of the two-axle automobile drive axle, so these temperatures are higher than others.
- (4)
- The temperature differences among some adjacent nodes are not distinct. However, the temperature differences among different nodes on the shell are apparent.

#### 2.3. Validation of Thermal Network Method

## 3. Effects of Key Factors on Reducing the Temperature

#### 3.1. Structural Effect of an Automobile Drive Axle

#### 3.2. Parameter Effects of an Automobile Drive Axle

#### 3.2.1. Effect of Motor Output Power

#### 3.2.2. Effect of Friction Coefficient among Teeth

- (1)
- During the process of gears, applying more fashioning or developing the process technology to improve the machining precision.
- (2)
- Further polishing gears after manufacturing.
- (3)
- Replacing gears regularly with new ones
- (4)
- Adopting the lubricating material with good lubrication properties to act as an intermediate medium between gears, and replenishing the lubricating material regularly.

#### 3.2.3. Effect of Helical Angle of Gears

#### 3.2.4. Effect of Lubricating Oil Parameter

## 4. Conclusions

- (1)
- The highest temperature (73.7 °C) of the two-axle automobile drive axle is located in the motor. In addition, the average temperature of the motor is higher than the differential and reducer, and the average temperature of the reducer is higher than the differential.
- (2)
- The highest temperature (62.2 °C) of the planetary automobile drive axle is also located in the motor. Compared with the two-axle drive axle, the highest temperature of the planetary drive axle is obviously lower. Therefore, as for the planetary drive axle, the possibility of exceeding the limited dangerous temperature is lower.
- (3)
- The corresponding highest temperatures of the planetary automobile drive axle with the motor power of 14 kW, 22 kW, and 30 kW are 60 °C, 62.2 °C, and 64.74 °C. The corresponding highest temperatures with the friction coefficient of 0.02, 0.04, and 0.06 are 59.74 °C, 60.86 °C, and 62.2 °C. The corresponding highest temperatures with the helical angle of 0°, 10°, and 20° are 62.2 °C, 64.47 °C, and 65.43 °C. The corresponding highest temperatures with the thermal transfer coefficient of 0.1414, 0.2, and 0.3 are 62.2 °C, 63.79 °C, and 65.21 °C. On the premise of ensuring normal operation, the motor output power, the friction coefficient among teeth, the helical angle of the gear, and thermal transfer coefficient of the lubricating oil can be optimized to be lower for reducing the temperature of the automobile drive axle.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Node | Name | Node | Name | Node | Name |
---|---|---|---|---|---|

1 | high-speed axle driving gear | 2 | high-speed axle driven gear | 3 | oil–gas mixture in reducer |

4 | intermediate axle | 5 | cylindrical bearing | 6 | gasket |

7 | fixed sleeve | 8 | bearing clasp | 9 | cover |

10 | box cover | 11 | cover | 12 | lubricating oil in reducer |

13 | high-speed axle | 14 | intermediate axle driving gear | 15 | air |

16 | driven gear | 17 | oil–gas mixture in shell | 18 | side gear |

19 | cylindrical bearing on half axle | 20 | differential box | 21 | planetary gear |

22 | left half axle | 23 | right half axle | 24 | planet pin |

25 | adjuster cover | 26 | drive axle shell | 27 | adjuster gasket |

28 | joint of motor and reducer | 29 | oil–gas mixture in differential | 30 | joint of bearing |

31 | motor spindle | 32 | oil–gas mixture in motor | 33 | air |

34 | front-end of motor | 35 | after end of motor | 36 | air |

37 | stator yoke | 38 | base layer of motor cabinet | 39 | air-cooled air duct |

40 | upper layer of motor cabinet | 41 | stator winding | 42 | stator tooth |

43 | air gap | 44 | superstratum of rotor | 45 | rotor guide rod |

46 | substratum of rotor | 47 | axle of motor | 48 | axle contact rear-end cover |

49 | bearing near rear-end cover | 50 | axle contact front-end cover | 51 | bearing near front-end cover |

52 | axle of motor | 53 | rear-end cover | 54 | front-end cover |

55 | air |

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

Motor output power [kW] | 22 |

Phase voltage [V] | 380 |

Load current [A] | 19 |

Speed [rpm] | 1300 |

Number of poles | 4 |

Stator slot number | 48 |

Rotor slot number | 38 |

Number of the stator winding in parallel | 1 |

Number of the lead wound | 1 |

Stator outer diameter [cm] | 38.9 |

Stator inner diameter [cm] | 24.99 |

Rotor outer diameter [cm] | 24.82 |

Rotor inner diameter [cm] | 8.72 |

Core length [cm] | 17.45 |

Airgap length [cm] | 0.0834 |

Insulation layer thickness [cm] | 0.03 |

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

Sun gear teeth number | 19 |

Planetary gear teeth number | 66 |

Inner ring gear teeth number | 152 |

Gear modulus | 1.25 |

Teeth profile angle [°] | 20 |

Spiral angle [°] | 0 |

Tooth width of sun gear [cm] | 4.6 |

Tooth width of planetary gear [cm] | 4.6 |

Tooth width of inner ring gear [cm] | 7 |

Root radius of sun gear [cm] | 1.096 |

Addendum radius of sun gear [cm] | 1.377 |

Base radius of sun gear [cm] | 1.115 |

Pitch radius of sun gear [cm] | 1.201 |

Root radius of planetary gear [cm] | 3.968 |

Addendum radius of planetary gear [cm] | 4.25 |

Base radius of planetary gear [cm] | 3.876 |

Pitch radius of planetary gear [cm] | 4.173 |

Root radius of inner ring gear [cm] | 9.656 |

Addendum radius of inner ring gear [cm] | 9.375 |

Base radius of inner ring gear [cm] | 8.927 |

Pitch radius of inner ring gear [cm] | 9.5 |

Coefficient of friction among teeth | 0.06 |

Kinematic viscosity of lubricating oil [m^{2}/s] | 0.000006 |

Thermal conductivity coefficient of lubricating oil [W/m×k] | 0.1414 |

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

Modulus of bevel gear [cm] | 0.5 |

Main bevel gear teeth number | 10 |

Side gear teeth number | 16 |

Radius of main bevel gear [cm] | 2.5 |

Bevel gear tooth width coefficient | 0.33 |

Tooth width of bevel gear [cm] | 0.825 |

Diameter of main bevel gear [cm] | 5 |

Diameter of side gear [cm] | 8.3 |

Transmission ratio of main bevel gears | 1.6 |

Length of gear meshing line [cm] | 0.1 |

Pressure angle of bevel gear [°] | 20 |

Contact ratio | 1 |

Gear oil film thickness [cm] | 0.1 |

Average diameter of bevel gear indexing circle [cm] | 4.175 |

Friction coefficient of bevel gear | 0.05 |

Tangential pressure angle of bevel gear [°] | 23.96 |

Inner diameter of differential inner cylindrical bearing [cm] | 6 |

Friction coefficient of bearing | 0.002 |

Point 1 | Point 2 | Point 3 | Point 4 | Point 5 | |
---|---|---|---|---|---|

Temperature in TNM (°C) | 45.9 | 39.5 | 38.0 | 45.7 | 52.4 |

Temperature in experimentation (°C) | 46.6 | 34.9 | 35.7 | 51.2 | 51.7 |

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**MDPI and ACS Style**

Ning, X.; Chen, M.; Zhou, Z.; Shu, Y.; Xiong, W.; Cao, Y.; Shang, X.; Wang, Z.
Thermal Analysis of Automobile Drive Axles by the Thermal Network Method. *World Electr. Veh. J.* **2022**, *13*, 75.
https://doi.org/10.3390/wevj13050075

**AMA Style**

Ning X, Chen M, Zhou Z, Shu Y, Xiong W, Cao Y, Shang X, Wang Z.
Thermal Analysis of Automobile Drive Axles by the Thermal Network Method. *World Electric Vehicle Journal*. 2022; 13(5):75.
https://doi.org/10.3390/wevj13050075

**Chicago/Turabian Style**

Ning, Xinfei, Mingzhang Chen, Zijian Zhou, Yuwen Shu, Wei Xiong, Yang Cao, Xuebing Shang, and Zixi Wang.
2022. "Thermal Analysis of Automobile Drive Axles by the Thermal Network Method" *World Electric Vehicle Journal* 13, no. 5: 75.
https://doi.org/10.3390/wevj13050075