# An Effect of a Carbon-Containing Additive in the Structure of a Friction Material on Temperature of the Wet Clutch Disc

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−2}K

^{−1}. A computer simulation of the friction process taking into account the thermomechanical contact of the working elements of the multidisc clutch with thermoelastic instability effect was carried out in the article [19]. An attempt to identify the features of the hot spots generation process in a wet multi-disc clutch was made in the paper [20]. The results obtained on the basis of the thermoelastic contact model were compared with the corresponding experimental data.

- (1)
- development of effective 2D and 3D computational models with the use FEM to determine the temperature of the friction clutch;
- (2)
- carrying out a comparative analysis of the temperature fields obtained by means of both models with the same friction work done;
- (3)
- investigating the effect of a carbon-containing additive in the structure of the new four friction materials on the temperature mode of the clutch.
- (4)

## 2. Friction Materials

_{10}), which contained 20% of the additive in the form of elemental graphite GE-1, pencil graphite GP-1 and foundry coke powder of various fractions C-1 and C-2.

## 3. Experiment

^{−1}.

^{−1}K

^{−1}, while after graphitization is equal to 0.58–1.34 W m

^{−1}K

^{−1}. For example, the thermal conductivity of graphite determined by the spatial orientation of the layers can be 233 W m

^{−1}K

^{−1}, while pure copper is equal to 400 W m

^{−1}K

^{−1}[37].

## 4. Numerical Model

^{®}software by using the Heat Transfer Module [38]. Additionally, in order to determine the friction work done ${W}_{i}$ (Figure 7), special tools, namely Global ODEs (ordinary differential equations) and DAEs (differential-algebraic equations) from Mathematics module were incorporated.

## 5. Numerical Analysis

## 6. Conclusions

- (1)
- the highest thermal conductivity and specific heat has the material no. 2, while the lowest values of the quantities has the material no. 3;
- (2)
- the highest coefficient of friction appears for the steel disc combined with the friction material no. 4, and the lowest for steel disc and friction material no. 1;
- (3)
- the estimation of the maximum clutch temperature can be carried out with sufficient accuracy using a 2D model, which allows for the reduction of labor losses at the preparatory stage and computational time. The single simulation case carried out on the workstation with CPU Intel
^{®}Xeon^{®}E5-2698 v4 @ 2.20GHz; RAM 64 GB (DDR4) lasted approximately 40 s, and 2200 s, when using 2D and 3D models, respectively. On the other hand, the determination of the temperature field in the elements of the friction clutch is better to carry out with the use of the 3D model; - (4)
- At the same total friction work done during a single clutch engagement, the lowest temperature was achieved when using friction material no. 1, and the highest for material no. 4. Also, the use of these materials resulted in the longest and shortest periods of frictional sliding, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${A}_{a}^{(2D)}$ | nominal contact surface area in the 2D model (${\mathrm{m}}^{2}$) |

${A}_{a}^{(3D)}$ | nominal contact surface area in the 3D model (${\mathrm{m}}^{2}$) |

${f}_{i}$ | coefficient of friction of the $i-th=1,2,3,4$ friction material (dimensionless) |

${I}_{0}$ | braking torque of the rotating masses ($\mathrm{kg}{\mathrm{m}}^{2}$) |

$h$ | heat transfer coefficient ($\mathrm{W}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$) |

${p}_{0}^{(2D)}$ | contact pressure in the 2D model (MPa) |

${p}^{(3D)}$ | contact pressure in the 3D model (MPa) |

$P$ | clamping force of the clutch elements (N) |

${Q}_{i}$ | friction power of the $i-th=1,2,3,4$ friction material (W) |

$r$ | radial coordinate (m) |

${r}_{p},{R}_{p}$ | inner and ouer radius of the friction path, respectively (m) |

${r}_{eq}$ | equivalent radius of the contact region (m) |

$t$ | time (s) |

${t}_{end}$ | total time of the process equal to 90 s (s) |

${t}_{s,i}$ | braking time of the $i-th=1,2,3,4$ friction material (s) |

$T$ | temperature (°C) |

${T}_{a}$ | initial/ambient temperature (°C) |

${W}_{0}$ | kinetic energy of the system (J) |

${W}_{i}$ | work of friction of the $i-th=1,2,3,4$ friction material (J) |

$z$ | axial coordinate (m) |

Greek Symbols | |

$\omega $ | angular velocity ($\mathrm{rad}{\mathrm{s}}^{-1}$) |

${\omega}_{0}$ | initial angular velocity ($\mathrm{rad}{\mathrm{s}}^{-1}$) |

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**Figure 7.**Time profiles of the power ${Q}_{i}$ and the work ${W}_{i}$, $i=1,2,3,4$ of friction during braking.

**Figure 8.**Temperature evolutions for four frictional material on the contact surface $z=0$ at equivalent radius $r={r}_{eq}$: (

**a**) during braking; (

**b**) during braking and subsequent cooling. Solid curves—2D model; dashed curves—3D model.

**Figure 9.**Temperature distributions for four materials along the radial variable $r$ on the contact surface $z=0$ in: (

**a**) stop time moments $t={t}_{s,i}$, $i=1,2,3,4$; (

**b**) last moment of time ${t}_{end}=90\mathrm{s}$. Solid curves—2D model; dashed curves—3D model.

**Figure 10.**Temperature distributions for four materials in axial direction $r$ at radius $r=45\mathrm{mm}$ in: (

**a**) stop time moments $t={t}_{s,i}$, $i=1,2,3,4$; (

**b**) last moment of time ${t}_{end}=90\mathrm{s}$. Solid curves—2D model; dashed curves—3D model.

**Figure 11.**Temperature distributions on the surface of friction at the time ${t}_{\mathrm{max},i}$, $i=1,2,3,4$ of reaching the maximum temperature for four frictional materials: (

**a**,

**b**) ${t}_{\mathrm{max},1}=4.16\mathrm{s}$; (

**c**,

**d**) ${t}_{\mathrm{max},2}=3.45\mathrm{s}$; (

**e**,

**f**) ${t}_{\mathrm{max},3}=2.72\mathrm{s}$; (

**g**,

**h**) ${t}_{\mathrm{max},4}=2.35\mathrm{s}$. Model 2D—(

**a**,

**c**,

**e**,

**g**); model 3D—(

**b**,

**d**,

**f**,

**h**).

**Figure 12.**Isotherms in a plane $rz$ at the time ${t}_{\mathrm{max},i}$, $i=1,2,3,4$ of reaching the maximum temperature for four frictional materials: (

**a**,

**b**) ${t}_{\mathrm{max},1}=4.16\mathrm{s}$; (

**c**,

**d**) ${t}_{\mathrm{max},2}=3.45\mathrm{s}$; (

**e**,

**f**) ${t}_{\mathrm{max},3}=2.72\mathrm{s}$; (

**g**,

**h**) ${t}_{\mathrm{max},4}=2.35\mathrm{s}$. Model 2D—(

**a**,

**c**,

**e**,

**g**); model 3D—(

**b**,

**d**,

**f**,

**h**).

**Table 1.**Influence of the type of carbon-containing additive on thermophysical properties and coefficient of friction.

No. | Additive | Thermal Conductivity $\mathbf{W}{\mathbf{m}}^{-1}{\mathbf{K}}^{-1}$ | Specific Heat $\mathbf{J}{\mathbf{kg}}^{-1}{\mathbf{K}}^{-1}$ | Mass Density $\mathbf{kg}{\mathbf{m}}^{-3}$ | Thermal Diffusivity ${\mathbf{mm}}^{2}{\mathbf{s}}^{-1}$ | Specific Heat Capacity $\mathbf{MJ}{\mathbf{m}}^{-3}{\mathbf{K}}^{-1}$ | Coefficient of Friction Dimensionless |
---|---|---|---|---|---|---|---|

1 | GP-1 | 28.1 | 1189.2 | 6059 | 3.9 | 7.2 | 0.035 |

2 | GE-1 | 44 | 2514.9 | 5832 | 3 | 15 | 0.045 |

3 | C-1 | 13.6 | 438.3 | 5171 | 6 | 2.3 | 0.05 |

4 | C-2 | 18.8 | 701.2 | 5362 | 5 | 3.7 | 0.06 |

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

contact pressure, ${p}_{0}^{(2D)}$ $\mathrm{MPa}$ | 4 |

initial angular velocity, ${\omega}_{0}$ $\mathrm{rad}{\mathrm{s}}^{-1}$ | 235.6 |

braking torque of the rotating masses, ${I}_{0}$ $\mathrm{kg}{\mathrm{m}}^{2}$ | 0.7 |

inner radius of the friction path, ${r}_{p}$ $\mathrm{mm}$ | 30 |

outer radius of the friction path, ${R}_{p}$ $\mathrm{mm}$ | 47.5 |

initial/ambient temperature, ${T}_{a}$ °C | 20 |

heat transfer coefficient, $h$ $\mathrm{W}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$ | 600 |

Type of Quadratic Lagrange Elements | Friction Material | Steel Plate | Steel Disc | Assembly |
---|---|---|---|---|

quadrilateral elements | 175 | 376 | 940 | 1491 |

tetrahedral elements | 69,014 | 69,946 | 129,267 | 268,227 |

Model | ${\mathit{T}}_{\mathbf{max}}$ | ${\mathit{T}}_{\mathbf{max}}$ | ${\mathit{T}}_{\mathbf{max}}$ | ${\mathit{T}}_{\mathbf{max}}$ |
---|---|---|---|---|

1 | 2 | 3 | 4 | |

2D | 115.6 °C | 118.4 °C | 137.9 °C | 145.1 °C |

3D | 113.7 °C | 117.2 °C | 136.1 °C | 143.5 °C |

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**MDPI and ACS Style**

Yevtushenko, A.; Grzes, P.; Ilyushenko, A.; Liashok, A.
An Effect of a Carbon-Containing Additive in the Structure of a Friction Material on Temperature of the Wet Clutch Disc. *Materials* **2022**, *15*, 464.
https://doi.org/10.3390/ma15020464

**AMA Style**

Yevtushenko A, Grzes P, Ilyushenko A, Liashok A.
An Effect of a Carbon-Containing Additive in the Structure of a Friction Material on Temperature of the Wet Clutch Disc. *Materials*. 2022; 15(2):464.
https://doi.org/10.3390/ma15020464

**Chicago/Turabian Style**

Yevtushenko, Aleksander, Piotr Grzes, Aleksander Ilyushenko, and Andrey Liashok.
2022. "An Effect of a Carbon-Containing Additive in the Structure of a Friction Material on Temperature of the Wet Clutch Disc" *Materials* 15, no. 2: 464.
https://doi.org/10.3390/ma15020464