# An Experimental Investigation and Numerical Analysis of the Thermal Behavior of a Clutch System Using the Frictional Facing of Functionally Graded Materials

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## Abstract

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## 1. Introduction

## 2. Materials and Methodology

#### 2.1. FGM

#### 2.2. Experimental Procedure

#### 2.3. Numerical Simulation

- The materials are isotropic, and the thermal characteristics of the materials do not depend on temperature.
- Both the actual and the nominal contact areas are the same size.

_{gen.p}is the heat generated by the pressure plate, Q

_{gen.c}—by the clutch disc, and Q

_{gen.p}—by the flywheel. When the radius of the clutch disk (r) is known, the sliding angular speed ($\omega $) r/s may be calculated. The time-dependent angular speed under the linear reduction assumption is as follows:

^{2}K.

- Flywheel: the conditions on the inner and outer disc radii are$${k}_{flywheel}{\frac{\partial T}{\partial r}|}_{r={r}_{i-flywheel}}=h\left[T\left({r}_{i-f},z,t\right)-{T}_{a}\right],\phantom{\rule{0ex}{0ex}}0<\theta <2\pi ,\left({t}_{cushion}/2\right)+{t}_{clutchdisc}\le z\le {t}_{flywheel}+\left({t}_{cushion}/2\right)+{t}_{clutchdisc},\hspace{1em}t\ge 0$$$${k}_{flywheel}{\frac{\partial T}{\partial r}|}_{r={r}_{o-flywheel}}=h\left[T\left({r}_{o-f},z,t\right)-{T}_{a}\right],\phantom{\rule{0ex}{0ex}}0<\theta <2\pi ,\left({t}_{cushion}/2\right)\le z\le {t}_{flywheel}+\left({t}_{cushion}/2\right)+{t}_{clutchdisc},\hspace{1em}t\ge 0$$
- and at the back side of the flywheel, it is$${\frac{\partial T}{\partial z}|}_{z=-\left[{t}_{flywheel}+\left({t}_{cushion}/2\right)+{t}_{clutchdisc}\right]}=h\left[T\left(r,z,t\right)-{T}_{a}\right],\hspace{1em}{r}_{i-flywheel}\le r\le {r}_{o-flywheel},0\theta 2\pi ,\hspace{1em}t\ge {t}_{s}$$
- Pressure plate: the conditions at the inner and outer radii are$${k}_{pressureplate}{\frac{\partial T}{\partial r}|}_{r={r}_{i-pressureplate}}=h\left[T\left({r}_{i-pressureplate},z,t\right)-{T}_{a}\right],\phantom{\rule{0ex}{0ex}}0\theta 2\pi ,\left({t}_{cushion}/2\right)+{t}_{clutchdisc}\le +\left({t}_{cushion}/2\right)+{t}_{clutchdisc}+{t}_{pressureplate},\hspace{1em}t\ge 0$$$${k}_{pressureplate}{\frac{\partial T}{\partial r}|}_{r={r}_{o-pressureplate}}=h\left[T\left({r}_{o-pressureplate},z,t\right)-{T}_{a}\right],\phantom{\rule{0ex}{0ex}}0\theta 2\pi ,\left({t}_{cushion}/2\right)+{t}_{clutchdisc}\le +\left({t}_{cushion}/2\right)+{t}_{clutchdisc}+{t}_{pressureplate},\hspace{1em}t\ge 0$$

## 3. Results and Discussions

#### 3.1. The Heat Transfers of the Pressure Plate and Flywheel

#### 3.2. Radial and Circular Effect on the Temperature

#### 3.3. The Effect of Rotational Speed

_{s}= 0 to minimum values (zero) at the end of the heating phase (slipping time). The reason for obtaining these results is that the heat generated is directly proportional to the sliding speed. The sliding speed of the friction clutches started with a maximum value at the beginning of the heating phase and decreased to zero at the end of the heating phase.

#### 3.4. The Effect of Torques

#### 3.5. The Effect of Material

## 4. Conclusions and Remarks

- The results proved that the heat flow was proportional to the disc radius during the sliding time when the lowest temperatures were recorded at the inner disc radius and the highest were recorded at the outer disc radius, with a difference of 5.3%.
- The new FGM (Al–Sic) material has superior thermal behavior compared with the other materials (VH03 and HDS57). The reduction in surface temperatures reached 10% and 14% due to a high heat dissipation feature according to its thermal properties. This proves that FGM is most suitable for use in a dry clutch system.
- Temperature variations were significantly affected by torque, firstly, and secondly, the sliding speed. In general, the maximum temperature approximately occurred in the middle of the sliding period and then decreased to a minimum temperature at the end of the sliding period.
- The results showed that the change in temperature values with radial direction is much higher than in the circumference direction; therefore, the latter is not important, because the maximum difference does not exceed 0.56%.
- The thermal behavior of a clutch disc depends on the choice of several factors:
- Friction material;
- Rotation speed;
- Loading or transmission torque;
- Boundary conditions and loading.

- To estimate the highest temperature that will occur during the sliding phase, the temperature field of the contact surfaces during the start of the engagement operation must be studied. As a result, the clutch system’s stability under a certain thermal condition can be assessed. Automotive experts view this study as crucial to determining the friction clutch’s optimal design and calculating the lifespan of the contacting elements of the clutch system.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

c | Specific heat (J kg^{−1} m^{−1}) |

h | Heat transfer coefficient (W m^{−2} K^{−1}) |

K | Thermal conductivity (W m^{−1} K^{−1}) |

Q | Total heat generation (W) |

q | Nominal value of the specific power of friction (W m^{−2}) |

P | Pressure (Pa) |

r | Radius (m) |

r_{i} | Inner radius (m) |

r_{o} | Outer radius (m) |

r_{m} | Mean radius |

t | Time (s) |

t_{s} | Slip time (s) |

${t}_{clutchdisc}$ | Thickness of clutch disc (m) |

${t}_{cushion}$ | Thickness of axial cushion |

$T$ | Temperature (k) |

T_{a} | Ambient temperature |

${T}_{i}$ | Initial temperature (k) |

Greek Symbols | |

$\theta $ | Temperature rise (k) |

${\theta}_{0}$ | Temperature rise scaling factor (k) |

ρ | Density of metals |

$\alpha $ | Thermal diffusivity (m^{2} s^{−1}) |

µ | Friction coefficient |

Abbreviations | |

FGM | Functionally graded material |

HDS57 | A rigid woven friction material manufactured with draft yarn and aramid fibers |

VH-03 | A woven material with glass fiber, which is reinforced with copper |

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**Figure 9.**(

**a**) The optimal mesh of the clutch system using FGM and (

**b**) the Grid Independence Test for mesh.

**Figure 11.**Temperature distributions applied to different speeds (Torque = 4.5 kg·m). (

**a**). Rotational speed = 680 (rpm) using VH-03. (

**b**). Rotational speed = 860 (rpm) using HDS57. (

**c**). Rotational speed = 1200 (rpm) using FGM.

**Figure 12.**Temperature distribution at a constant torque (3.5 kg·m) for different speed values. (

**a**). Rotational speed = 680 (rpm) using HDS57. (

**b**). Rotational speed = 860 (rpm) using FGM. (

**c**). Rotational speed = 1200 (rpm) using VH-03.

**Figure 13.**Temperature distribution at a constant torque (2.5 kg·m) for different speed values. (

**a**). Rotational speed = 680 (rpm) using FGM. (

**b**). Rotational speed = 860 (rpm) using VH-03. (

**c**). Rotational speed = 1200 (rpm) using HDS57.

**Figure 14.**Temperature distribution at a constant speed (680 rpm) when applying different torques. (

**a**). Torque = 4.5 (kg·m) using VH-03. (

**b**). Torque = 3.5 (kg·m) using HDS57. (

**c**). Torque = 2.5 (kg·m) using FGM.

**Figure 15.**Temperature distribution at a constant speed (860 rpm) when applying different torques. (

**a**). Torque = 4.5 (kg·m) using HDS57. (

**b**). Torque = 3.5 (kg·m) using FGM. (

**c**). Torque = 2.5 (kg·m) using VH-03.

**Figure 16.**Temperature distribution at a constant speed (1200 rpm) when applying different torques. (

**a**). Torque = 4.5 (kg·m) using FGM. (

**b**). Torque = 3.5 (kg·m) using VH-03. (

**c**). Torque = 2.5 (kg·m) using HDS57.

**Figure 17.**A comparison of the maximum temperature distribution of speed (1200 rpm) and torque (4.5 Kg·m) for different materials.

**Figure 18.**The diagnostic plots of parameter effects: (

**a**) Main effect plot of means and (

**b**) the main effect of SN ratios.

Layer | Al | Sic |
---|---|---|

1 | 93% | 7% |

2 | 96.5% | 3.5% |

3 | 100% | 0% |

Composition | FGM (Al–Sic) | FGM (Al-Ni) [19] |
---|---|---|

Max. value | 110 HV | 95 HV |

Material | FGM | HDS57 | VH-03 | |
---|---|---|---|---|

AL | Sic | |||

Density (kg/m^{3}) | 2770 | 3100 | 1700 | 2100 |

Thermal conductivity (W/m·K) | 160 | 120 | 0.23 | 0.30 |

Specific Heat (J/kg·K) | 923.5 | 750 | 1350 | 1368 |

Property | First Layer | Second Layer | Third Layer |
---|---|---|---|

Density (kg/m^{3}) | 2793.1 | 2781.55 | 2770 |

Thermal conductivity (W/m·K) | 157.2 | 158.6 | 160 |

Specific Heat (J/kg·K) | 911.355 | 917.4275 | 923.5 |

Coefficient of Friction | 0.52494 | 0.49385 | 0.47 |

Variable | Values |
---|---|

Angular speed (rpm) | 1200, 860, 680 |

Torque (kg·m) | 4.5, 3.5, 2.5 |

Frictional material types | FGM, HDS57, VH-03 |

Test No. | Rotational Speed (rpm) | Torque (kg·m) | Material Type |
---|---|---|---|

1 | 680 | 2.5 | FGM |

2 | 680 | 3.5 | HDS57 |

3 | 680 | 4.5 | VH-03 |

4 | 860 | 3.5 | FGM |

5 | 860 | 4.5 | HDS57 |

6 | 860 | 2.5 | VH-03 |

7 | 1200 | 4.5 | FGM |

8 | 1200 | 2.5 | HDS57 |

9 | 1200 | 2.5 | VH-03 |

Source | DF | Adj SS | Adj MS | F-Value | p-Value | Contributions % |
---|---|---|---|---|---|---|

Angular speed (rpm) | 2 | 694.85 | 347.423 | 68.15 | 0.014 | 40.11 |

Type of friction material | 2 | 17.68 | 8.842 | 1.73 | 0.366 | 1.02 |

Torque (kg·m) | 2 | 1009.52 | 504.762 | 99.02 | 0.010 | 58.27 |

Error | 2 | 10.20 | 5.098 | |||

Total | 8 | 1732.25 | ||||

R-sq | R-sq(adj) | |||||

99.41% | 97.65% |

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**MDPI and ACS Style**

Jabbar, N.A.; Hussain, I.Y.; Abdullah, O.I.; Mohammed, M.N.
An Experimental Investigation and Numerical Analysis of the Thermal Behavior of a Clutch System Using the Frictional Facing of Functionally Graded Materials. *Designs* **2023**, *7*, 125.
https://doi.org/10.3390/designs7060125

**AMA Style**

Jabbar NA, Hussain IY, Abdullah OI, Mohammed MN.
An Experimental Investigation and Numerical Analysis of the Thermal Behavior of a Clutch System Using the Frictional Facing of Functionally Graded Materials. *Designs*. 2023; 7(6):125.
https://doi.org/10.3390/designs7060125

**Chicago/Turabian Style**

Jabbar, Nasr A., Ihsan Y. Hussain, Oday I. Abdullah, and M. N. Mohammed.
2023. "An Experimental Investigation and Numerical Analysis of the Thermal Behavior of a Clutch System Using the Frictional Facing of Functionally Graded Materials" *Designs* 7, no. 6: 125.
https://doi.org/10.3390/designs7060125