# Design, Development and FE Thermal Analysis of a Radially Grooved Brake Disc Developed through Direct Metal Laser Sintering

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Development of Disc Brake by DMLS

## 3. Previous Studies on Thermal Analysis of Disc Brake

^{2}in 4.5 s. For the analysis, speed of the car reduced from 33.34 to 0 m/s, within 4.5 s. Single stop cycle of braking was used for thermal and structural analysis since material regains its original elastic condition after brake force is removed. Lopez et al. [11] made several assumptions to simplify thermal analysis complexity and output surface temperature was measured experimentally and compared with FE analysis [12,13]. Heat dissipated through brake disc surface during application of brake and heat flux applied to surface was considered with and without radial grooves. Huajiang et al. [14] considered heat transfer convection only after brake application was completed and car accelerated to regain its original speed. These areas include an effective surface area for applying braking pressure with and without radial grooves on disc surface. The remaining surface area of the disc was considered insulated for the purpose of comparison of surface temperatures with and without grooves under the brake pressure of 1 MPa.

## 4. Temperature Distributions in Disc Brake

_{f}is in Watts; hc is the convection heat transfer coefficient; Input parameters and dimensions of brake discs are tabulated in Table 5, Acd and Acp are the contact surface area of the disc and pads, respectively, in m

^{2}; Ts is surface temperature of brake disc; and Ta is ambient air temperature in °C. Heat transfer coefficient is applied to brake discs as heat flux boundary condition. Thus, increasing the rate of heat transfer from surface brake discs reduces disc surface temperature on total surface area of the brake discs [20].

^{3}) is given by $=1.225\text{}\mathrm{Kg}/{\mathrm{m}}^{3}$, where ${\mathrm{m}}_{\mathrm{a}}$ is the mass flow rate of air (m

^{3}/s) and ${\mathrm{V}}_{\mathrm{avge}}$ is the average air velocity (m/s). Convective heat transfer coefficient at different air velocities are obtained from the formula [21].

_{cd}is disc surface swept by brake pad (m

^{2}), ε

_{p}is factor load distributed on brake disc surface, m is mass of vehicle (kg), g = 9.81 is acceleration of gravity (m/s

^{2}), V

_{0}is initial speed of vehicle (m/s), and ad is the deceleration of the vehicle (m/s

^{2}).The disc brake groove passage and sector chosen for numerical analysis are shown in Figure 1. The dimensions of grooves on disc surface are 3.5 mm by 2.5 mm each, with outer and inner diameters as 240 mm and 120 mm, respectively. Heat transfer coefficient ${\mathrm{h}}_{\mathrm{C}}$ associated with laminar flow for radial and non-radial grooves on brake discs was calculated for Re < 2.4 × 10

^{5}, where do is outer diameter of discs mm, Re is Reynolds number, and Ka is thermal conductivity of air, W/m °C. Experimental validation was done on modified brake disc with and without radial grooves brake using non-contact thermometer Fluke-561, Infrared thermometer, which can measure contact and ambient temperatures. IR thermometer is used to measure hot moving energized, hard-to-reach objects instantly. Experimental results are given in Table 6 for generation of heat on disc surfaces. Disc surface temperatures increase with increasing braking time for different disc design configurations.

## 5. Experimental Validations

## 6. Results and Discussions

#### 6.1. Nodal Temperatures and Contact Pressure

#### 6.2. Von Mises and Stress

^{2}while with grooves is 137.076 N/mm

^{2}. A significant reduction has been observed from ANSYS results. At higher speeds, the von Mises and stress are likely increased because of more frictional heat generated at the time of maximum braking time and pressure applied. The Transient finite element simulation gives variation of temperature distribution with respect to time as shown in Figure 12.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${\mathrm{M}}_{\mathrm{v}}$ | is total mass of vehicle |

${\mathrm{V}}_{\mathrm{i}}$ | Initial speed of vehicle |

${\mathrm{K}}_{\mathrm{e}}$ | Kinetic Energy |

${\mathsf{\gamma}}_{\mathrm{p}}$ | Heat partition coefficient |

${\mathsf{\xi}}_{\mathrm{ep}},{\text{}\mathsf{\xi}}_{\mathrm{ed}}$ | Thermal Effusivity of pad and Disc. |

${\mathrm{A}}_{\mathrm{cp}},{\text{}\mathrm{A}}_{\mathrm{cd}}\text{}$ | Friction contact area of pad and Disc. |

${\mathrm{Q}}_{\mathrm{Total}}$ | Heat flux on contact area. |

${\mathrm{Q}}_{\mathrm{disc}},{\text{}\mathrm{Q}}_{\mathrm{Pad}}$ | Heat flux into the disc and pad. |

${\mathrm{Q}}_{\mathrm{f}}$ | Convective heat transfer |

Ts | Surface temperature of brake disc. |

Ta | Ambient air temperature in °C. |

Ø | coverage sector of braking forces |

$\mathrm{Z}$ | Braking Effectiveness. |

g | Acceleration of gravity |

${\mathrm{m}}_{\mathrm{a}}$ | Mass flow rate of air |

${\mathrm{V}}_{\mathrm{avge}}$ | Average air velocity |

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**Figure 2.**3D-CAD geometries: (

**a**) without Radial grooves; (

**b**) with radial grooves; and (

**c**) optimal dimensions and areas of grooves.

**Figure 4.**SEM of brake disc surface subjected to High Temperature Region (HTR) at: (

**a**) R = 50 mm; and (

**b**) R = 100 mm.

**Figure 6.**CAD model of brake disc and pad with (

**a**) 6, (

**b**) 9 and (

**c**) 18 radial grooves on disc surface.

**Figure 9.**Nodal temperatures at braking pressure of 1 MPa, without and with grooves on disc surfaces.

**Figure 10.**Thermal Deformation at Braking Pressure of 1 MPa, without and with grooves on disc surfaces.

**Figure 13.**Fitted line plot for Temperature and heat flux and main effect plots for disc temperatures.

**Figure 15.**Variation of heat flux with different speed, surface temperatures and contour plots for surface temperature range at different heat flux.

Metal | Wt % |
---|---|

Ni | 17–19 |

Co | 8.5–9.5 |

P/S | Max. 0.01 |

Mo | 4.5–5.2 |

Ti | 0.6–0.8 |

Al | 0.052–0.15 |

C | Max. 0.03 |

Cr/Cu % | Max. 0.5 |

Fe | Balance |

Physical Properties | |
---|---|

1. Typical accuracy: | 0–20 µm |

2. Age hardening shrinkage: | 0.08% |

3. Smallest wall thickness: | 0.3–0.4 mm |

4. Relative density | 100% |

5. Specific density | 8–8.1 g/cm^{3} |

6. Surface roughness Ra | 4–6.5 µm |

7. Surface roughness Rz | 20 µm |

Mechanical Properties | |

1. Ultimate tensile strength: | 2050 ± 100 MPa |

2. Ultimate tensile strength (y) | 1100 ± 100 MPa |

3. Hardness | 50–56 HRC |

4. Tensile—Young’s Modulus | 180,000 ± 20,000 MPa |

Thermal Properties | |

1. Thermal conductivity | 20 ± 1 W/m °C |

2. Specific heat capacity | 450 ± 20 J/kg °C |

3. Operating temperature: | 400 °C |

1. DSC Test Methods | ASTM E1269-05 |

2. Temperature Range | Ambient to 1100 °C. |

3. Temperature Accuracy | ±0.2 K |

4. Temperature Precision | ±0.02 K |

5. Furnace-temperature Resolution | ±0.00006 K |

6. Heating Rate | 0.02 to 300 K/min |

7. Cooling Rate | 0.02 to 50 K/min |

8. Calorimetric Resolution | 0.01 μ W |

9. Measuring Environment | Nitrogen. |

10. TG Measurement range | ±400 mg |

11. Scanning rate | 0.01 °C to 150 °C/min |

12. Sensitivity | 0.2 μg. |

Properties | Disc | Brake Pad |
---|---|---|

Young’s modulus (N/mm^{2}) | 180,000 ± 20,000 MPa | 1500 |

Density (kg/m^{3}) | 8–8.1 g/cm^{3} | 2595 |

Poisson’s ratio | 0.3 | 0.25 |

Thermal conductivity, W/m °C | 20 ± 1 W/m °C | 1.212 |

Ultimate tensile strength, N/mm^{2} | 2050 ± 100 MPa | - |

Coefficient of friction | 0.35 | 0.35 |

Specific heat (J/kg °C) | 450 ± 20 J/kg °C | 1465 |

External Brake disc Radius, mm | 120 |

Internal Brake disc Radius, mm | 60 |

Internal radius of pad, mm | 60 |

External radius of pad, mm | 120 |

Brake pad thickness, mm | 12 |

Brake disc Thickness, mm | 24 |

Brake disc Height, mm | 49 |

Initial speed v, Km/h | 30 |

Mass of Vehicle m, Kg. | 1385 |

The cover angle of pad (in degrees), 20% | 650 |

Deceleration ad, m/s^{2} | 8 |

Vent thickness, mm | 6 |

Brake Disc Effective Radius, R effective, mm | 100 |

Factor of Swept distribution of the disc, ${\mathsf{\epsilon}}_{\mathrm{p}}$ | 0.5 |

Surface disc swept by the pad A cd, mm^{2} | 33,912 |

Contact Pressure P, MPa | 1 |

Heat partition coefficient ${\mathsf{\gamma}}_{\mathrm{p}}$ | 0.95 |

Thermal Effusivity for Brake Pad. | $2645.7$ |

Thermal Effusivity for Brake Disc. | $8971.3$ |

Time | ${\mathbf{a}}_{\mathbf{d}}$ | $\varnothing $ | m | g | V0 | z | A cd | ${\mathit{\epsilon}}_{\mathit{p}}$ | $\left(1-\varnothing \right)$ | $\mathbf{g}\mathbf{m}\mathbf{z}{\mathbf{V}}_{0}$ | 2 A cd ε_{p} | Heat Flux |
---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | 8 | 0.2 | 1385 | 9.8 | 33.34 | 0.8 | 0.033 | 0.5 | 0.8 | 369,407.2 | 0.03 | 4.925 |

1 | 8 | 0.2 | 1385 | 9.8 | 27.7 | 0.8 | 0.033 | 0.5 | 0.8 | 307,615.7 | 0.03 | 4.101 |

2 | 8 | 0.2 | 1385 | 9.8 | 22.2 | 0.8 | 0.033 | 0.5 | 0.8 | 246,269.8 | 0.03 | 3.283 |

3 | 8 | 0.2 | 1385 | 9.8 | 16.6 | 0.8 | 0.033 | 0.5 | 0.8 | 184,591.6 | 0.03 | 2.461 |

4 | 8 | 0.2 | 1385 | 9.8 | 11.1 | 0.8 | 0.033 | 0.5 | 0.8 | 123,134.9 | 0.03 | 1.641 |

5 | 8 | 0.2 | 1385 | 9.8 | 5.5 | 0.8 | 0.033 | 0.5 | 0.8 | 60,903.0 | 0.03 | 0.812 |

Disc Brake with 6-Grooves ${\mathbf{A}}_{\mathbf{c}\mathbf{d}}=0.03637{\mathbf{m}}^{2}$ | Ts, °C | Disc Brake with 9-Grooves ${\mathbf{A}}_{\mathbf{c}\mathbf{d}}=0.037602{\mathbf{m}}^{2}$ | Ts, °C | Disc Brake with 18-Grooves ${\mathbf{A}}_{\mathbf{c}\mathbf{d}}=0.041292{\mathbf{m}}^{2}$ | Ts, °C | |
---|---|---|---|---|---|---|

Qo, W/mm^{2} | Qo, W/mm^{2} | Qo, W/mm^{2} | ||||

1. | 3.383 | 36.61 | 3.272 | 35.87 | 2.979 | 34.02 |

2. | 4.060 | 38.97 | 3.927 | 38.05 | 3.576 | 35.82 |

3. | 4.736 | 41.27 | 4.581 | 40.22 | 4.171 | 37.62 |

4. | 5.413 | 43.60 | 5.235 | 42.40 | 4.768 | 39.43 |

5. | 6.089 | 45.92 | 5.889 | 44.57 | 5.363 | 41.23 |

6. | 6.766 | 48.25 | 6.544 | 46.75 | 5.959 | 43.04 |

7. | 7.443 | 50.58 | 7.199 | 48.93 | 6.556 | 44.84 |

8. | 8.119 | 52.90 | 7.853 | 51.10 | 7.151 | 46.64 |

9. | 8.797 | 55.23 | 8.509 | 53.28 | 7.749 | 48.45 |

10. | 9.472 | 57.55 | 9.162 | 55.45 | 8.343 | 50.25 |

11. | 10.14 | 59.88 | 9.817 | 57.63 | 8.939 | 52.06 |

12. | 10.82 | 62.18 | 10.470 | 59.80 | 9.535 | 53.86 |

13. | 11.50 | 64.53 | 11.125 | 61.98 | 10.131 | 55.67 |

14. | 12.17 | 66.85 | 11.779 | 64.15 | 10.726 | 57.47 |

15. | 12.85 | 69.16 | 12.433 | 66.33 | 11.322 | 59.27 |

16. | 13.53 | 71.51 | 13.089 | 68.51 | 11.919 | 61.08 |

3D-Printed Materials | Maraging Steel |
---|---|

Total time of simulation | 45 s |

Initial temperature of the disc | 60 °C |

Increment of initial time | 0.25 s |

Minimal Time Increment | 0.5 s |

Maximal Time Increment | 0.125 s |

Parameters | Without Groove | With Groove |
---|---|---|

Nodal temperature | 77 °C | 70 °C |

Thermal Deformation | 0.979336 mm | 0.433938 mm |

Vonmises Stress | 202.123 N/mm^{2} | 137.076 N/mm^{2} |

With Groove | Without Groove | |||
---|---|---|---|---|

Vo, m/s | Experiment, Temp, (°C) | FEA, Temp, (°C) | Experiment, Temp, (°C) | FEA, Temp, (°C) |

27.78 | 34.02 | 33.5 | 38.37 | 41.15 |

33.34 | 35.82 | 33.8 | 41.05 | 36.59 |

38.89 | 37.62 | 34.6 | 43.72 | 38.24 |

44.45 | 39.43 | 36.2 | 46.39 | 41.36 |

50.00 | 41.23 | 38.0 | 49.07 | 43.58 |

55.56 | 43.04 | 39.3 | 51.74 | 47.21 |

61.12 | 44.84 | 41.5 | 54.42 | 48.96 |

66.67 | 46.64 | 50.1 | 57.09 | 52.24 |

72.24 | 48.45 | 46.8 | 59.77 | 55.23 |

77.78 | 50.25 | 45.4 | 62.44 | 58.51 |

83.34 | 52.06 | 50.4 | 65.12 | 59.54 |

88.89 | 53.86 | 52.8 | 67.79 | 61.27 |

94.45 | 55.67 | 56.2 | 70.47 | 66.98 |

100.0 | 57.47 | 58.5 | 73.14 | 69.45 |

105.5 | 59.27 | 54.1 | 75.81 | 72.12 |

111.1 | 61.08 | 70.0 | 78.49 | 77.25 |

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## Share and Cite

**MDPI and ACS Style**

Sayeed Ahmed, G.M.; Algarni, S.
Design, Development and FE Thermal Analysis of a Radially Grooved Brake Disc Developed through Direct Metal Laser Sintering. *Materials* **2018**, *11*, 1211.
https://doi.org/10.3390/ma11071211

**AMA Style**

Sayeed Ahmed GM, Algarni S.
Design, Development and FE Thermal Analysis of a Radially Grooved Brake Disc Developed through Direct Metal Laser Sintering. *Materials*. 2018; 11(7):1211.
https://doi.org/10.3390/ma11071211

**Chicago/Turabian Style**

Sayeed Ahmed, Gulam Mohammed, and Salem Algarni.
2018. "Design, Development and FE Thermal Analysis of a Radially Grooved Brake Disc Developed through Direct Metal Laser Sintering" *Materials* 11, no. 7: 1211.
https://doi.org/10.3390/ma11071211