# Integrated Thermal and Dynamic Analysis of Dry Automotive Clutch Linings

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Dynamics

#### 2.1. Damping Coefficients

^{th}mode and ${\omega}_{n}$ is its natural radiancy. The natural frequency of the system is obtained by solving the eigenvalue problem:

#### 2.2. Engine and Resistive Torques

#### 2.3. Friction Torque

## 3. Thermal Analysis

## 4. Measurement of Coefficient of Friction and Thermal Transport Properties

## 5. Combined Thermal-Dynamic Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Equivalent Pin-on-Disc Condition | Clutch Condition | |||
---|---|---|---|---|

Test Time (s) | Speed (m/s)/(RPM) | Load (kg) | Clamp Load (N) | Flywheel Speed (m/s) |

30 | 10.1/2412 | 0.21 | 400 | 10.1 |

37 | 8.3/1972 | 0.48 | 900 | 8.3 |

55 | 5.5/1311 | 1.12 | 2250 | 5.5 |

82 | 3.7/878 | 2.00 | 3750 | 3.7 |

110 | 2.7/656 | 2.66 | 5000 | 2.7 |

210 | 1.4/342 | 3.72 | 7000 | 1.4 |

1257 | 0.2/57 | 5.32 | 10,000 | 0.2 |

**Table A2.**Thermal transport properties for new and worn clutch lining material [21].

Material Thermal Properties | Condition | |
---|---|---|

New | Worn | |

Thermal conductivity (W/mK) | 0.652 ± 0.13 | 0.353 ± 0.17 |

Specific heat (J/kg·K) | 542 ± 35 | 614 ± 39 |

Thermal diffusivity (m^{2}/s) | 8.3 × 10^{−7} ± 0.3 × 10^{−7} | 4.6 × 10^{−7} ± 0.35 × 10^{−7} |

Parameters | Values | Unit |
---|---|---|

Torsional inertia, I_{1} | 1 | kg/m^{2} |

Torsional inertia, I_{2} | 0.3 | kg/m^{2} |

Torsional inertia, I_{3} | 0.045 | kg/m^{2} |

Torsional inertia, I_{4} | 0.0015 | kg/m^{2} |

Torsional inertia, I_{5} | 0.0028 | kg/m^{2} |

Torsional inertia, I_{6} | 0.0022 | kg/m^{2} |

Torsional inertia, I_{7} | 0.035 | kg/m^{2} |

Torsional inertia, I_{8} | 0.5 | kg/m^{2} |

Torsional inertia, I_{9} | 60 | kg/m^{2} |

Torsional inertia, I_{10} | 0.5 | kg/m^{2} |

Torsional inertia, I_{11} | 60 | kg/m^{2} |

Damping coefficient, c_{1} | 50 | N.m.s./rad |

Damping coefficient, c_{2} | 26 | N.m.s./rad |

Damping coefficient, c_{3} | 50 | N.m.s./rad |

Damping coefficient, c_{4} | 450 | N.m.s./rad |

Damping coefficient, c_{5} | 125 | N.m.s./rad |

Damping coefficient, c_{6} | 625 | N.m.s./rad |

Damping coefficient, c_{7} | 125 | N.m.s./rad |

Stiffness coefficient, k_{1} | 20,000 | N.m/rad |

Stiffness coefficient, k_{2} | 15,000 | N.m/rad |

Stiffness coefficient, k_{3} | 20,000 | N.m/rad |

Stiffness coefficient, k_{4} | 180,000 | N.m/rad |

Stiffness coefficient, k_{5} | 50,000 | N.m/rad |

Stiffness coefficient, k_{6} | 250,000 | N.m/rad |

Stiffness coefficient, k_{7} | 50,000 | N.m/rad |

First gear ratio | 3.5 | - |

Differential gear ratio | 4.25 | - |

Wheel radius, R_{w} | 0.34 | m |

Vehicle mass, m_{v} | 2500 | kg |

Coefficient of rolling resistance, μ_{r} | 0.015 | - |

Density of air, d_{a} | 1.2922 | kg/m^{3} |

Effective vehicle frontal area, A_{v} | 2.8 | m^{2} |

Aerodynamic drag coefficient, C_{d} | 0.37 | - |

Inner radius of clutch, r_{i} | 0.0925 | m |

Outer radius of clutch, r_{o} | 0.135 | m |

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

Density of pressure plate and flywheel | 7200 | kg/m^{3} |

Specific heat of pressure plate and flywheel | 360 | J/kg·K |

Thermal Conductivity of pressure plate and flywheel | 55 | W/mK |

Number of friction surfaces, Z | 2 | - |

Inner radius of friction material | 0.1 | m |

Outer radius of friction material | 0.145 | m |

Inner radius of pressure plate | 0.1 | m |

Outer radius of pressure plate | 0.145 | m |

Inner radius of flywheel | 0.013 | m |

Outer radius of flywheel | 0.150 | m |

Thickness of friction lining | 0.01 | m |

Thickness of flywheel | 0.05 | m |

Thickness of pressure plate | 0.055 | m |

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**Figure 1.**Schematic representation of the extended 9-DOF clutch dynamic model to the whole vehicle drivetrain system.

**Figure 5.**Predicted variations of angular displacement, angular velocity and angular acceleration for the new friction lining material during clutch engagement.

**Figure 6.**Predicted variations of displacement, angular velocity, and angular acceleration for the worn friction lining material during clutch engagement.

**Figure 7.**Predicted clutch system temperature rises for a single engagement for (

**a**) new and (

**b**) worn friction linings.

**Figure 8.**Predicted temperature rise due to consecutive series of engagements for the clutch system with (

**a**) new and (

**b**) used friction lining materials.

**Table 1.**Variation of the coefficient of friction with slip speed, $v$, for new and worn clutch lining materials [21].

Disc Temperature | Linear Regressed Equation for New Friction Material | Linear Regressed Equation for Worn Friction Material |
---|---|---|

20 °C | $0.48\u20130.0210v$ | $0.32\u20130.00189v$ |

40 °C | $0.49\u20130.0191v$ | $0.32\u20130.00452v$ |

60 °C | $0.48\u20130.0178v$ | $0.31\u20130.00761v$ |

90 °C | $0.47\u20130.0167v$ | $0.34\u20130.00436v$ |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Gkinis, T.; Rahmani, R.; Rahnejat, H.
Integrated Thermal and Dynamic Analysis of Dry Automotive Clutch Linings. *Appl. Sci.* **2019**, *9*, 4287.
https://doi.org/10.3390/app9204287

**AMA Style**

Gkinis T, Rahmani R, Rahnejat H.
Integrated Thermal and Dynamic Analysis of Dry Automotive Clutch Linings. *Applied Sciences*. 2019; 9(20):4287.
https://doi.org/10.3390/app9204287

**Chicago/Turabian Style**

Gkinis, Theofilos, Ramin Rahmani, and Homer Rahnejat.
2019. "Integrated Thermal and Dynamic Analysis of Dry Automotive Clutch Linings" *Applied Sciences* 9, no. 20: 4287.
https://doi.org/10.3390/app9204287