# Study on the Engagement Characteristics and Control Strategy of High Speed Difference Dry Friction Clutch

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Short Range/Vertical Aircraft Propulsion System

#### 2.1.1. Principle of Short Range/Vertical Aircraft Propulsion System

#### 2.1.2. Test Equipment and Methods

- Turn on the input motor, push the input speed to the corresponding speed, and the stable running time is not less than 5 s.
- Start the friction plate actuator, and the pressure starts to load.
- After the speed of both ends of the clutch is the same, keep it for 5 s, and then retract the mechanical locking actuator.
- Confirm that the mechanical locking continues for 10 s.
- Reduce the input speed.
- Extend the mechanical lock actuator and stabilize for 5 s.
- Unload the friction plate actuator, the pressure is unloaded.
- After the output end stops under the action of inertia, after confirming that the clutch is disengaged, turn off the input end motor so that the motor speed decays to 0 within 10 s.

#### 2.2. Model of Engagement Characteristics of Dry Friction Clutches

#### 2.2.1. Modeling of the Friction Clutch Dynamics

_{e}is the output torque of the engine, T

_{c1}and T

_{c2}are the friction torque transmitted by the clutch, T

_{v}is the load torque borne by the output end of the driven disc, and I

_{e}, I

_{c1}, I

_{c2}, I

_{v}is the rotation of the engine, the main/slave part of the clutch, and the load part respectively. Inertia, c

_{e}, c

_{c1}, c

_{c2}, c

_{v}is the damping coefficient of the engine, the driving disc, the driven disc, and the load part, k

_{ec}is the torsional stiffness from the engine to the active part of the clutch, and k

_{cv}is the torsional stiffness from the clutch driven part to the load part.

_{e}, θ

_{c1}, θ

_{c2}, θ

_{v}are the angular displacements of the engine shaft, the driving disk, the driven disk, and the load part, respectively.

#### 2.2.2. Modeling of the Friction Clutch Temperature Field

^{3}), C

_{p}is the heat capacity of the solid at constant pressure (unit: J/(kg·K)), k is the thermal conductivity of the solid (unit: W/(m·k)), and μ is the velocity field defined by the translation motion sub-node during motion (unit: m/s), Q is the heat source (unit: W/m

^{3}), and ∇T is the temperature gradient.

## 3. Results and Verification

#### 3.1. The Simulation Results of the Engagement Characteristics of Dry Friction Clutch

#### 3.2. The Verification of Dynamics Model and Temperature Model

#### 3.2.1. Dynamic Model

#### 3.2.2. Temperature Model

## 4. Discussion

#### 4.1. The Engagement Characteristics of the Traditional Fixed Slope Engagement Pressure

#### 4.2. The Variable Slope Engagement Pressure Loading

#### 4.2.1. The Engagement Characteristics of the Variable Slope Engagement Pressure Loading

_{1}, k

_{2}, and k

_{3}, and the corresponding change times t

_{1}, t

_{2}. Among them, t

_{1}and t

_{2}are determined by the speed difference w

_{1}and w

_{2}at the time of slope transition, that is, when the relative speed is less than w

_{1}, the slope is k

_{1}. When the relative speed is between w

_{1}and w

_{2}, the slope is changed to k

_{2}, and when it is greater than w

_{2}, the slope is converted to k

_{3}.

_{1}= 300 N/s, k

_{2}= 2141 N/s, k

_{3}= 244 N/s, w

_{1}= 505 rad/s, w

_{2}= 35 rad/s.

#### 4.2.2. The Optimization of the Control Strategy for Variable Slope Pressure Loading

- (1)
- Orthogonal design

_{1}, k

_{2}, k

_{3}, w

_{1}, and w

_{2}are used as the optimization parameters, and the five parameters are all set at three levels. The levels of the experimental factors are shown in Table 4.

_{16}(4

^{5})) and the friction clutch dynamics simulation, the corresponding impact torque and engagement time can be obtained, as shown in Table 5.

_{1}, k

_{2}, k

_{3}, w

_{1}, and w

_{2}on the engagement time and impact torque can be obtained, as shown in Figure 24 and Figure 25.

_{2}> w

_{2}> k

_{1}> k

_{3}> w

_{1}in descending order. With the increase of k

_{2}and k

_{3}, the impact torque increases. With the increase of k

_{1}, the impact torque first decreases and then increases, and reaches the maximum value at 350. With the increase of w

_{2}, the impact torque decreases. The influence of w

_{1}on the impact torque is not obvious.

_{2}> w

_{1}> k

_{1}> w

_{2}> k

_{3}in descending order. With the increase of k

_{1}, k

_{2}, k

_{3}, w

_{1}, w

_{2}the engagement time decreases.

- (2)
- SVR-PSO multi-objective optimization algorithm and results

## 5. Conclusions

- It is found that the faster engagement pressure loading occurs along with the shorter engagement time, the larger impact torque, and the higher temperature. How to decrease simultaneously engagement time and impact torque is important to the high speed difference friction clutch.
- Compared with the traditional fixed-slope engagement pressure loading method, the pro-posed variable-slope engagement pressure loading method can reduce simultaneously the engagement time, temperature rise, and impact torque, which has good application and spread value.
- The proposed SVR-PSO optimization algorithm can obtain the best parameters of the variable-slope pressing force strategy. The optimized Pareto solution can be applied to different working conditions.
- The simulational data show good agreement with the experimental result. It means that the simulation models have high precision and application value.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the short-range/vertical take-off and landing aircraft propulsion system.

**Figure 6.**The Simpack dynamics model of friction clutch. (1) Clutch housing (2) Moving plate (3) Static plate (4) Input shaft (5) Fixed constraints (6) Friction pair restraint (7) Drive constraints.

**Figure 13.**Temperature curve of conventional fixed slope. (

**a**) Engagement pressure rise time is 8 s (

**b**) Engagement pressure rise time of 10 s.

**Figure 14.**Temperature field simulation results (engagement pressure rise time is 10 s). (

**a**) Overall temperature field (

**b**) Friction plate (

**c**) Clutch housing.

**Figure 23.**Results of variable slope pressure loading. (

**a**) Main/driven disk speed curve (

**b**) Torque curve (

**c**) Temperature curve.

Physical and Mechanical Properties | Numeric Value |
---|---|

density/(g·cm^{−3}) | 1.76 |

tensile strength/MPa | 55.7 |

compressive strength/MPa | 68.8 |

bending strength/MPa | 72.9 |

Interlayer shear strength/MPa | 7.6 |

Thermal conductivity W/(m·K) | 100 |

Properties | Friction Plate | Steel |
---|---|---|

Thermal conductivity | 100 W/(m·K) | 46 W/(m·K) |

Specific heat capacity | 1800 J/(kg·K) | 300 J/(kg·K) |

Density | 753 kg/m^{3} | 7800 kg/m^{3} |

Loading Mode | Engagement Time (s) | Impact Torque (Nm) | Maximum Temperature (°C) |
---|---|---|---|

up time is 8 s | 6.5 | 539 | 215 |

up time is 10 s | 8 | 529 | 234 |

variable-slope | 5.9 | 523 | 184 |

Factor | Horizontal | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

k1 (N/s) | 150 | 200 | 260 | 350 |

k2 (N/s) | 1500 | 2000 | 2500 | 3000 |

k3 (N/s) | 200 | 300 | 400 | 500 |

w1 (rad/s) | 400 | 430 | 480 | 510 |

w2 (rad/s) | 10 | 20 | 30 | 40 |

Order Number | k_{1}(N/s) | k_{2}(N/s) | k_{3}(N/s) | w_{1}(Rad/s) | w_{2}(Rad/s) | T (s) | M (N·m) |
---|---|---|---|---|---|---|---|

1 | 150 | 1500 | 200 | 400 | 10 | 12 | 529 |

2 | 150 | 2000 | 300 | 430 | 20 | 9 | 534 |

3 | 150 | 2500 | 400 | 480 | 30 | 6.5 | 542 |

4 | 150 | 3000 | 500 | 510 | 40 | 5 | 548 |

5 | 200 | 1500 | 300 | 480 | 40 | 9 | 508 |

6 | 200 | 2000 | 200 | 510 | 30 | 6.4 | 524 |

7 | 200 | 2500 | 500 | 400 | 20 | 8.7 | 551 |

8 | 200 | 3000 | 400 | 430 | 10 | 7 | 573 |

9 | 260 | 1500 | 400 | 510 | 20 | 7.7 | 522 |

10 | 260 | 2000 | 500 | 480 | 10 | 6.8 | 545 |

11 | 260 | 2500 | 200 | 430 | 40 | 7.2 | 527 |

12 | 260 | 3000 | 300 | 400 | 30 | 7.4 | 555 |

13 | 350 | 1500 | 500 | 430 | 30 | 8.9 | 519 |

14 | 350 | 2000 | 400 | 400 | 40 | 8.2 | 523 |

15 | 350 | 2500 | 300 | 510 | 10 | 5.2 | 559 |

16 | 350 | 3000 | 200 | 480 | 20 | 5.2 | 565 |

Order Number | k_{1}(N/s) | k_{2}(N/s) | k_{3}(N/s) | w_{1}(Rad/s) | w_{2}(Rad/s) | Time (s) | Actual Time (s) | Fractional Error (%) | Impulsive Torque (N·m) | Actual Impact Torque (N·m) | Fractional Error (%) | Maximum Temperature (°C) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 260 | 1635 | 412 | 489 | 40 | 7.2 | 7.9 | 8.9 | 513 | 512 | 0.2 | 202 |

2 | 300 | 2639 | 249 | 510 | 15 | 5.1 | 5 | 2 | 557 | 560 | 0.5 | 181 |

3 | 287 | 2486 | 229 | 503 | 36 | 5.5 | 5.5 | 0 | 536 | 534 | 0.4 | 175 |

4 | 279 | 1847 | 253 | 485 | 38 | 6.8 | 7.3 | 6.8 | 518 | 514 | 0.8 | 198 |

5 | 303 | 1896 | 247 | 492 | 36 | 6.4 | 6.9 | 7.2 | 521 | 514 | 1.4 | 201 |

6 | 300 | 2141 | 244 | 505 | 35 | 5.9 | 6 | 1.7 | 528 | 523 | 1 | 188 |

average error | 4.4 | average error | 0.72 |

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**MDPI and ACS Style**

Zhu, C.; Chen, Z.; Shi, Z.; Zhang, Y.
Study on the Engagement Characteristics and Control Strategy of High Speed Difference Dry Friction Clutch. *Machines* **2023**, *11*, 407.
https://doi.org/10.3390/machines11030407

**AMA Style**

Zhu C, Chen Z, Shi Z, Zhang Y.
Study on the Engagement Characteristics and Control Strategy of High Speed Difference Dry Friction Clutch. *Machines*. 2023; 11(3):407.
https://doi.org/10.3390/machines11030407

**Chicago/Turabian Style**

Zhu, Chu, Zhi Chen, Zongcai Shi, and Yingdong Zhang.
2023. "Study on the Engagement Characteristics and Control Strategy of High Speed Difference Dry Friction Clutch" *Machines* 11, no. 3: 407.
https://doi.org/10.3390/machines11030407