# Thermal-Fluid-Solid Coupling Simulation and Oil Groove Structure Optimization of Wet Friction Clutch for High-Speed Helicopter

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## Abstract

**:**

## 1. Introduction

## 2. Thermal-Fluid-Solid Coupling Modeling and Simulation

#### 2.1. Working Principle of Wet Clutch

#### 2.2. Drag Torque Mathematical Model

_{1}, the thickness of the oil layer is δ

_{1}, and the angle of the non-radial oil groove area is approximated. θ

_{2}, in which the thickness of the oil layer in the non-oil groove area is δ

_{2}, the thickness of the oil layer in the annular groove area is δ

_{3}. According to the incompressibility and continuity of the lubricating oil, the pressure distribution in the θ

_{1}and θ

_{2}regions can be obtained as:

_{1}is the highest pressure at the boundary line of the non-oil groove area of θ

_{1}and θ

_{2}; p

_{2}is the highest pressure at the boundary line of the annular groove area of θ

_{1}and θ

_{2}; p

_{0}is determined by boundary conditions; μ is the dynamic viscosity of lubricating oil; ω is the rotational speed of the dual plate.

_{1}, carry out the circumferential force analysis on the micro-unit body, and establish the equilibrium equation:

_{1}, v = rω). Therefore:

_{1}is

_{2}non-oil groove area r is:

_{a1}and r

_{a2}are the inner and outer diameters of each annular region in the non-oil groove area of θ

_{2}. Therefore, the drag torque in the non-oil groove area of θ

_{2}is:

_{2}is:

_{b1}and r

_{b2}are the inner and outer diameters of each annular groove in the area of θ

_{2}. Then, the drag torque in the annular groove area of θ

_{2}can be obtained as:

#### 2.3. Thermal-Fluid-Solid Coupling Simulation of Compound Oil Groove

_{1}and b

_{2}are the width of radial and annular grooves, respectively, l is the spacing between two annular grooves. The simulation results show that the drag torque of group A is smaller, but the temperature rise is higher. In group B, the number of oil grooves is increased, so the heat dissipation capacity is stronger, and the drag torque is larger.

## 3. Taguchi Experiment Design and Simulation Results Analysis

#### 3.1. Design of Simulation Experiments by Taguchi Method

#### 3.2. Simulation Results and Analysis of Taguchi Experiment

#### 3.2.1. Simulation Results of Taguchi Method

_{m}of each group of experiments could be obtained, and the results are shown in Table 4. Taguchi method takes signal-to-noise ratio (S/N) as the evaluation index to measure the target parameters. The maximum signal-to-noise ratio is the optimal target parameter under the given conditions, and the influence degree of each parameter can be reflected by its numerical value. The flow chart of oil groove structure parameter optimization for wet friction clutch is as shown in Figure 9.

#### 3.2.2. Influence of Oil Groove Structure Parameters on Drag Torque

#### 3.2.3. Influence of Oil Groove Structure Parameters on Maximum Temperature

## 4. Multi-Objective Optimization Algorithm and Verified Simulation

#### 4.1. Non-Dominated Neighborhood Immune Algorithm

_{m}.

- (1)
- Initialization

_{0}), dominated antibody group, activity antibody group and clone antibody group are generated in this procedure. Where, the size of primary antibody group is n

_{D}.

- (2)
- Update dominant groups

_{t}) are recognized in this procedure. All dominant antibodies are copied to form the temporary dominant antibody group (DT

_{t+1}).

- (3)
- Select based on nondominated neighbor

_{t+1}is not more than n

_{D}, DT

_{t+1}is set as D

_{t+1}. Otherwise, the crowding distance between the all individuals in the DT

_{t+1}is calculated to arrange individuals in descending order. The top-n

_{D}individuals in the first group form D

_{t+1}according to the crowding distance in descending order. If D

_{t}is not more than n

_{A}, A

_{t}is set as D

_{t}. Otherwise, the top-n

_{D}individuals in the first group form A

_{t}according to the crowding distance in descending order.

- (4)
- Proportional clone

_{t}) is obtained through applying proportional clone on A

_{t}.

- (5)
- Recombination and hypermutation

_{t}) is reorganized and hyper mutated. C is set as new clone group (C

_{t}) and go to step 2.

- (6)
- End.

#### 4.2. Verification of the Structure Parameters from the Multi-Objective Optimization

## 5. Verification of the Thermal-Fluid-Solid Coupling Simulation of Compound Oil Groove

## 6. Conclusions

_{m}by 2.00~5.40% and reduces M by 4.34–12.22%. Furthermore, the Pareto optimal solution set of NNIA has high accuracy and strong reliability, and oil groove parameters can be set for specific performance requirements.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 15.**Test rig for drag torque [16]. ➀ clutch disc, ➁ disc bracket, ➂ driving motor, ➃ glass plate, ➄ precision thread, ➅ valve, ➆ housing, ➇ force sensor.

**Figure 16.**Comparison of drag torque experiment results and simulation results [16].

Parameters | Data |
---|---|

Working speed n [rpm] | 2450 |

Diameter of the inlet d0 [mm] | 182 |

Diameter of the outlet d1 [mm] | 245 |

Clearance δ [mm] | 0.5 |

Oil feeding flow rate Q [kg/s] | 0.1 |

Lubricating oil temperature T0 [°C] | 58 |

Wall temperature T1 [°C] | 50 |

Convective heat transfer coefficient of separator disc h2 [W/(m2·°C)] | 1890 |

Convective heat transfer coefficient of friction disc h1 [W/(m2·°C)] | 380 |

Parameter of Lubricating Oil | Value | Unit |
---|---|---|

Density ρ | 880 | kg/m^{3} |

Dynamic viscosity μ | 96.8 | mPa·s |

Specific heat volume C | 1900 | J/(kg·°C) |

Thermal conductivity λ | 0.144 | W/(m·°C) |

No. | m | b_{1}/mm | b_{2}/mm | l/mm | M/(N·m) | Tm/°C |
---|---|---|---|---|---|---|

A | 8 | 8 | 2.5 | 2.0 | 12.08 | 75.20 |

B | 12 | 8 | 1.5 | 2.5 | 12.50 | 74.03 |

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

Number of radial grooves | m | 6 | 8 | 10 | 12 |

Radial groove width [mm] | b1 | 2 | 4 | 6 | 8 |

Annular groove width [mm] | b2 | 1.5 | 2 | 2.5 | 3 |

Annular groove spacing [mm] | l | 1.5 | 2 | 2.5 | 3 |

Parameters | m | b_{1} | b_{2} | l |
---|---|---|---|---|

1 | 21.97 | 21.84 | 21.95 | 21.81 |

2 | 21.95 | 21.91 | 21.90 | 21.68 |

3 | 21.47 | 21.73 | 21.66 | 21.90 |

4 | 21.84 | 21.75 | 21.73 | 21.84 |

Delta | 0.49 | 0.19 | 0.29 | 0.22 |

Rank | 1 | 4 | 2 | 3 |

Parameters | m | b_{1} | b_{2} | l |
---|---|---|---|---|

1 | −37.44 | −37.50 | −37.48 | −37.55 |

2 | −37.51 | −37.51 | −37.53 | −37.46 |

3 | −37.53 | −37.51 | −37.47 | −37.47 |

4 | −37.52 | −37.49 | −37.52 | −37.53 |

Delta | 0.09 | 0.03 | 0.06 | 0.09 |

Rank | 2 | 4 | 3 | 1 |

m | b_{1}/mm | b_{2}/mm | l/mm | |
---|---|---|---|---|

M | 10 | 6 | 2.5 | 2 |

T_{m} | 6 | 8 | 2.5 | 2 |

Parameters | ||
---|---|---|

G_{max} | maximum number of generations | 50 |

n_{D} | maximum size of dominant population | 30 |

n_{A} | maximum size of active population | 40 |

n_{C} | size of clone population | 60 |

bu | the upper boundary of variable | [12,8,3,3] |

bd | the nether boundary of variable | [6,2,1.5,1.5] |

DG_{max+1} | final approximate Pareto-optimal set |

No. | m | b_{1}/mm | b_{2}/mm | l/mm | S/mm^{2} | M/N·m | T_{m}/°C |
---|---|---|---|---|---|---|---|

1 | 6 | 2 | 1.5 | 1.5 | 12,807 | 12.84 | 75.70 |

2 | 6 | 4 | 2.0 | 2.0 | 12,592 | 12.53 | 73.78 |

3 | 6 | 6 | 2.5 | 2.5 | 12,086 | 12.54 | 74.02 |

4 | 6 | 8 | 3.0 | 3.0 | 12,020 | 12.26 | 74.54 |

5 | 8 | 2 | 2.0 | 2.5 | 12,804 | 12.70 | 74.78 |

6 | 8 | 4 | 1.5 | 3.0 | 14,357 | 13.13 | 75.10 |

7 | 8 | 6 | 3.0 | 1.5 | 12,180 | 12.19 | 75.10 |

8 | 8 | 8 | 2.5 | 2.0 | 11,566 | 12.08 | 75.20 |

9 | 10 | 2 | 2.5 | 3.0 | 12,363 | 11.63 | 74.57 |

10 | 10 | 4 | 3.0 | 2.5 | 12,261 | 12.05 | 76.20 |

11 | 10 | 6 | 1.5 | 2.0 | 12,518 | 11.63 | 74.57 |

12 | 10 | 8 | 2.0 | 1.5 | 11,518 | 12.09 | 75.70 |

13 | 12 | 2 | 3.0 | 2.0 | 12,592 | 12.30 | 74.95 |

14 | 12 | 4 | 2.5 | 1.5 | 11,831 | 12.18 | 75.10 |

15 | 12 | 6 | 2.0 | 3.0 | 12,856 | 12.45 | 76.67 |

16 | 12 | 8 | 1.5 | 2.5 | 12,068 | 12.50 | 74.03 |

No. | Simulation Data | Pareto-Optimal Set | Improvement | ||
---|---|---|---|---|---|

M/(N·m) | T_{m}/°C | M/(N·m) | T_{m}/°C | ||

1 | 12.18 | 75.10 | 12.13 | 73.64 | −2.00% of T_{m} |

2 | 12.84 | 75.70 | 12.79 | 72.57 | −4.31% of T_{m} |

3 | 12.45 | 76.67 | 12.54 | 72.74 | −5.40% of T_{m} |

4 | 12.50 | 74.04 | 11.98 | 74.06 | −4.34% of M |

5 | 12.84 | 75.70 | 11.56 | 75.64 | −6.22% of M |

6 | 13.13 | 75.10 | 11.70 | 75.08 | −12.22% of M |

Parameters | M/(Nm) | T_{m}/°C | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

No. | m | b_{1} | b_{2} | l | S | Simulation | Predicted | error | Simulation | Predicted | error |

1 | 6 | 3.59 | 2.40 | 1.67 | 12,829 | 12.85 | 12.68 | 1.38% | 72.92 | 72.62 | 0.41% |

2 | 12 | 4.10 | 2.40 | 2.81 | 12,182 | 12.10 | 11.87 | 1.93% | 74.63 | 74.41 | 0.30% |

Parameters | ρ (kg/m^{3}) | r_{1} (mm) | r_{2} (mm) | μ (Pa s) | Q (L/min) |
---|---|---|---|---|---|

Values | 870 | 70.6 | 84.25 | 0.053 | 1.0 |

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## Share and Cite

**MDPI and ACS Style**

Tan, W.; Chen, Z.; Li, Z.; Yan, H.
Thermal-Fluid-Solid Coupling Simulation and Oil Groove Structure Optimization of Wet Friction Clutch for High-Speed Helicopter. *Machines* **2023**, *11*, 296.
https://doi.org/10.3390/machines11020296

**AMA Style**

Tan W, Chen Z, Li Z, Yan H.
Thermal-Fluid-Solid Coupling Simulation and Oil Groove Structure Optimization of Wet Friction Clutch for High-Speed Helicopter. *Machines*. 2023; 11(2):296.
https://doi.org/10.3390/machines11020296

**Chicago/Turabian Style**

Tan, Wuzhong, Zhi Chen, Zhizuo Li, and Hongzhi Yan.
2023. "Thermal-Fluid-Solid Coupling Simulation and Oil Groove Structure Optimization of Wet Friction Clutch for High-Speed Helicopter" *Machines* 11, no. 2: 296.
https://doi.org/10.3390/machines11020296