# CFD-Based Investigation of Lubrication and Temperature Characteristics of an Intermediate Gearbox with Splash Lubrication

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## Abstract

**:**

## 1. Introduction

## 2. Cooling Mechanism

## 3. Experimental Setup

## 4. Numerical Setup

#### 4.1. Volume of Fluid (VOF) Multiphase Model and Governing Equations

_{oil}is the volume fraction of oil, ρ

_{oil}is the oil density, and

**u**is the velocity vector.

_{oil}is the property of oil, φ

_{air}is the property of air, and α

_{air}is the volume fraction of air.

_{f}is the fluid density, μ is the fluid dynamic viscosity, k

_{f}is the thermal conductivity of the fluid,

**u**is the velocity vector, p is the pressure,

**F**is the external force, T is the temperature, E is the energy, and k

_{s}is the thermal conductivity of the solid.

#### 4.2. Multiple Reference Frames (MRF) Model

_{w}is the rotational speed of the roller, n is the rotational speed of the inner ring, D

_{w}is the mean diameter of the roller, α is the bearing contact angle, and d is the pitch diameter of the bearing.

#### 4.3. Computational Model and Mesh

#### 4.4. Boundary Conditions

_{s}is the sliding power loss, f is the friction coefficient, F

_{n}is the average normal load, and v

_{s}is the average sliding speed.

_{r}is the rolling power loss, v

_{r}is the average rolling speed, h is the thickness of the elastohydrodynamic lubrication (EHL) oil film, b is the tooth width, ε

_{α}is the gear end face coincidence degree, and β

_{b}is the helix angle of the gear base circle.

_{ch}is the churning power loss, f

_{g}is the gear infiltration factor, υ is the kinematic viscosity of the lubricating oil at the operating temperature, n

_{s}is the gear rotational speed, D is the component diameter, b is the tooth width, R

_{f}is the tooth surface roughness factor, β is the spiral angle, and A

_{g}is the arrangement coefficient.

_{1}and Q

_{2}, respectively, are:

^{2}·K).

## 5. Results and Discussion

#### 5.1. Experimental Results

#### 5.2. Flow Field

#### 5.3. Lubrication and Temperature Characteristics of Gears

#### 5.3.1. Lubrication Characteristics of Gears

#### 5.3.2. Temperature Characteristics of Gears

_{1}, while that at the larger end and the spoke is at an acute angle θ

_{2}. The heat at the acute angle concentrates easily, and the heat dissipation effect at the acute angle is worse than that at the obtuse angle. As shown in Figure 15c,d, a large convective heat transfer coefficient corresponds to a low gear tooth surface temperature. The average temperature of the tooth surface at an azimuth angle of 0–90° or 270–360°, which is close to the gear meshing area, is high, while that at an azimuth angle of 180–225° is low. The tooth surface temperature of the driving gear is higher than that of the driven gear because the heat output per unit area of the driving gear is larger.

#### 5.4. Lubrication and Temperature Characteristics of Bearings

#### 5.4.1. Lubrication Characteristics of Bearings

#### 5.4.2. Temperature Characteristics of Bearings

## 6. Conclusions and Future Work

- The maximum relative error between the experimental and simulation results of the wall temperature of the casing and end covers was 10.636%. The relative error between the experimental and simulation results of the oil temperature in the oil pool was 3.180%. The oil temperature satisfied the limit requirement (<110 °C), and the oil content met the engineering application standard. The results indicate that CFD simulations can accurately predict the temperature distribution of an intermediate gearbox with splash lubrication.
- In splash lubrication, large amounts of lubricating oil are splashed onto the tooth surface near the gear meshing area to lubricate and cool it, because the gear meshing area experiences the highest amount of frictional heat generation. A large convective heat transfer coefficient corresponds to a low gear tooth surface temperature. The tooth surface temperature of the driving gear is higher than that of the driven gear, because the heat output per unit area of the former is higher.
- The lubricating oil flows in the direction of rotation of the roller. Rollers with a large convective heat transfer coefficient have a lower temperature. The convective heat transfer coefficient of the roller wall is largely related to the lubrication environment of the roller, including the oil distribution inside the bearing cavity and the flow rate. Therefore, the convective heat transfer coefficient and temperature of the rollers are not determined solely by the oil volume fraction of the roller wall.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Arrangement of measuring points. 1 and 2—measuring points on the end cover near the input bearing; 3, 4, 5, and 6—measuring points on the end cover near the output bearing; 7, 8, 9, 10, 11, and 12—measuring points on the wall of the casing.

**Figure 5.**Moving reference frames of the computational model: (

**a**) moving reference frame for gears; (

**b**) moving reference frame for bearings.

**Figure 9.**Flow chart of the coupled thermal-fluid approach. (MRF model refers to multiple reference frames (MRF) model, and VOF model refers to volume of fluid (VOF) multiphase model.)

**Figure 12.**Flow field distribution characteristics: (

**a**) fluid velocity volume rendering; (

**b**) vortex core region.

**Figure 15.**Temperature characteristics of gears: (

**a**) convective heat transfer coefficient of driving gear tooth surface; (

**b**) temperature of driving gear tooth surface; (

**c**) temperature characteristics of driving gear tooth surface; (

**d**) temperature characteristics of driven gear tooth surface.

**Figure 16.**Lubrication characteristics of bearing rollers: (

**a**) azimuth angle of rollers; (

**b**) oil volume fraction of small rollers; (

**c**) oil volume fraction of big rollers.

**Figure 18.**Temperature characteristics of bearing rollers: (

**a**) convective heat transfer coefficient of rollers; (

**b**) temperature of rollers; (

**c**) temperature characteristics of small rollers; (

**d**) temperature characteristics of big rollers.

**Figure 19.**Temperature characteristics of raceways: (

**a**) convective heat transfer coefficient of inner ring; (

**b**) temperature of inner ring; (

**c**) convective heat transfer coefficient of outer ring; (

**d**) temperature of outer ring.

Parameter | Driving Gear | Driven Gear |
---|---|---|

Hand of spiral | RH | LH |

Number of teeth | 35 | 46 |

Module (mm) | 3.8 | 3.8 |

Face width (mm) | 28 | 28 |

Pressure angle (°) | 20 | 20 |

Mean spiral angle (°) | 35 | 35 |

Shaft angle (°) | 128 |

Parameter | Value |
---|---|

Number of rollers | 22/25 |

Inner diameter (mm) | 55 |

Outer diameter (mm) | 90 |

Width (mm) | 40 |

Experimental Parameter | Value |
---|---|

Input rotational speed (r/min) | 5000 |

Input torque (Nm) | 286.5 |

Oil immersion depth (mm) | 17 |

Oil density (kg/m^{3}) | 875.15 (at 60 °C) |

Oil dynamic viscosity (kg/m·s) | 0.0251 (at 60 °C) |

Measured Point | Temperature (°C) |
---|---|

1 | 99 |

2 | 99 |

3 | 88 |

4 | 88 |

5 | 88 |

6 | 88 |

7 | 93 |

8 | 90 |

9 | 88 |

10 | 88 |

11 | 87 |

12 | 80 |

Number of Mesh Elements | Air Flow Rate of the Air Vent (kg/s) | |
---|---|---|

Mesh 1 | 3,361,947 | 0.1334 |

Mesh 2 | 6,432,064 | 0.1106 |

Mesh 3 | 10,589,597 | 0.1052 |

Mesh 4 | 15,206,765 | 0.1031 |

Temperature (°C) | Oil Density (kg/m^{3}) | Oil Kinematic Viscosity (mm^{2}/s) |
---|---|---|

40 | 879.84 | 66.63 |

50 | 877.20 | 42.24 |

60 | 875.15 | 28.71 |

70 | 873.62 | 20.02 |

80 | 872.56 | 14.82 |

90 | 871.96 | 11.22 |

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**MDPI and ACS Style**

Lu, F.; Wang, M.; Pan, W.; Bao, H.; Ge, W.
CFD-Based Investigation of Lubrication and Temperature Characteristics of an Intermediate Gearbox with Splash Lubrication. *Appl. Sci.* **2021**, *11*, 352.
https://doi.org/10.3390/app11010352

**AMA Style**

Lu F, Wang M, Pan W, Bao H, Ge W.
CFD-Based Investigation of Lubrication and Temperature Characteristics of an Intermediate Gearbox with Splash Lubrication. *Applied Sciences*. 2021; 11(1):352.
https://doi.org/10.3390/app11010352

**Chicago/Turabian Style**

Lu, Fengxia, Meng Wang, Wenbin Pan, Heyun Bao, and Wenchang Ge.
2021. "CFD-Based Investigation of Lubrication and Temperature Characteristics of an Intermediate Gearbox with Splash Lubrication" *Applied Sciences* 11, no. 1: 352.
https://doi.org/10.3390/app11010352