Open Access
 Issue Int. J. Simul. Multidisci. Des. Optim. Volume 12, 2021 19 9 https://doi.org/10.1051/smdo/2021019 27 August 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

2 Methodology

To perform the analysis, the following data have been collected such as mass (m) of the vehicle 1000 kg, Maximum velocity (u) and minimum velocity (v) of the vehicle considered is 100 km/h and 0 km/h, inner diameter of the brake rotor as 0.240 m, outer diameter of the brake rotor as 0.327 m, coefficient of friction μ as 0.4 and stopping distance of the vehicle as 34 m.

Maximum frictional force is calculated using the following formulae(1)

The maximum kinetic energy attained by the vehicle is given by(2)

Deacceleration of the vehicle is given as(3)

Braking force F is given by considering work done W = wd and work done W = 0.5 mV2 = 12474 N.

Stopping time or braking time is given as(4)

Power generated in one rotor p = Q/t = 347659.914 Watts since Q = kinetic energy.

Heat flux generated φ [24] is given by(5)

The heat generation and heat dissipation in case of disc brake arises due to change of kinetic energy into thermal energy which in turn results in heating of the disc brake and the braking power of the disc brake fades at temperature of 600 K. Hence, the film temperature is calculated considering warping temperature and ambient temperature divided by two in this analysis.

Reynold's number Re is given by(6)

Nusselt's Number, Nu is given by:(7)

Forced convective heat transfer coefficient, h is given by(8)

Before proceeding with the brake rotor design, the crucial brake requirements such as brakes must be strong enough to retard the motion within a minimum brake system, should have anti fade properties so that they should be effective, and the material selection are made to able to withstand mechanical properties and chemical composition must be retained to prevent fading. So, in this research paper, the Static Structural Analysis and Steady State Thermal Analysis will be performed on the designed brake rotor. This analysis has been carried out using two different materials considering above brake rotor properties, Martensitic Stainless Steel and Grey Cast Iron. Both these materials are generally used in the automotive industry because of their high corrosion resistance, ability to retains their mechanical and chemical properties at high temperatures, thermally and electrically stable and affordable costs in the market.

3 Disc brakes

3.1 Design of disc brake system using solid works

The rotor dimensions considered for the analysis is as shown in Table 1 and the corresponding drawing of the rotor is shown in Figure 1. The rotor has been modelled using solid works and the corresponding meshed geometry (fine mesh) considering 152266 nodes and 88791 elements.

Table 1

Rotor dimensions.

 Fig. 12D drawing of Rotor Ventilated disc without bell [24].

4 Results and analysis

4.1 Static structural analysis of disc brake

The static structural analysis has been performed by applying the following boundary conditions. Fixed supports have been marked and a frictional force of 4316.4 N has been applied on the outer surface areas of the brake rotors. This analysis has been carried out for both Martensitic Stainless Steel and Grey Cast Iron and the boundary conditions remains same.

The boundary conditions applied is as shown in Figure 2 and the corresponding equivalent elastic strain, stress, shear stress and total deformation analysis have been performed. Figure 3 shows the equivalent elastic strain for both stainless steel and grey cast iron. From these figures it is observed that the maximum strain in case of stainless steel and grey cast iron is 0.0119 and 0.0131 and the minimum strain in both the material is 2.039 e–5 and 2.690 e–5. The strain observed in case of stainless steel is less as compared to grey cast iron.

Figure 4 shows the equivalent stress for both stainless steel and grey cast iron. From these figures it is observed that the maximum stress on the rotor is 2302.8 MPa and 1429.4 MPa for stainless steel and grey cast iron, respectively. Also, the minimum equivalent stress is 1.983 MPa and 1.642 MPa is observed in case of stainless steel and grey cast iron. From this it is observed that the maximum stress is less in case of grey cast iron as compared to stainless steel and same type of behavior is also observed in the literature [2527].

Figure 5 shows the shear stress for both stainless steel and grey cast iron. From this figure it is observed that maximum shear stress in the rotor in case of stainless steel and grey cast iron is 1101.8 MPa and 681.35 MPa, respectively. Also, the minimum shear stress observed is −1085 MPa for stainless steel and −670.83 MPa for grey cast iron. From this it can be concluded that grey cast iron has performed better as compared to stainless steel from shear stress point of view.

Figure 6 shows the total deformation for rotor in case of stainless steel and grey cast iron is 0.6967 mm and 0.7846 mm. From this it is observed that stainless steel has performed better as compared to grey cast iron. It is also observed from literature review [26] that stainless steel total deformation is less as compared to grey cast iron.

Figure 7 shows the comparison of equivalent strain, stress, shear stress and total deformation for both stainless steel and grey cast iron. From this figure it is observed that equivalent strain and total deformation in case of grey cast iron is 9.96% and 12.6% higher than martensitic stainless steel. Also, it is observed that equivalent stress and shear stress in case of grey cast iron is 38% and 38.1% lower than martensitic stainless steel.

 Fig. 2Boundary Conditions for Static Structural.
 Fig. 3Equivalent Elastic Strain for SS and GCI.
 Fig. 4Equivalent Stress for SS and GCI.
 Fig. 5Shear Stress for SS and GCI.
 Fig. 6Total deformation for SS and GCI.
 Fig. 7Comparison of Equivalent strain, Equivalent stress, Shear stress and Total deformation for SS and GCI.

4.2 Steady state thermal analysis of disc brake

In case of braking system when brakes are applied, frictional heat is generated in the brake rotor due to which high temperatures are encountered. This frictional heat due to high temperature causes non-uniform spatial distribution called as hot spotting which contributes to fatigue and wear and in turn cracks [28,29]. This heat needs to be dissipated across the brake rotor to withstand repetitive braking conditions. So, in steady state thermal analysis [30], the overall temperature distribution and total heat flux is calculated. The boundary conditions for steady state thermal analysis [31,32] is as shown in Figure 8. Once the boundary conditions are applied then temperature and total heat flux analysis have been performed. The frictional force between the disc and pad have been studied considering steady state thermal analysis [33].

Figure 9 shows the comparison of temperature distribution for Stainless steel and Grey cast iron. From this figure it is observed that the maximum temperature is 300 °C in both the cases of stainless steel and grey cast iron and the minimum temperature is 244.25 °C and 270.95 °C in case of stainless steel and grey cast iron respectively.

Figure 10 shows the comparison of total heat flux for stainless steel and grey cast iron. From this figure it is observed that the total heat flux value is 0.4629 W/mm2 and 0.50468 W/mm2 for stainless steel and grey cast iron. From this figure it can be concluded that heat transfer is more in case of grey cast iron as compared to stainless steel. Similarly, the minimum total heat flux is 0.0008081 W/mm2 and 0.00102 W/mm2 for stainless steel and grey cast iron respectively.

Figure 11 shows the comparison of temperature and total heat flux for stainless steel and grey cast iron. From this figure it is observed that minimum temperature in case of grey cast iron is 10.9% higher as compared to stainless steel. Whereas total heat flux (amount of heat dissipation) in case of grey cast iron is 9.02% higher as compared to stainless steel. Hence it can be concluded that gray cast iron provided good thermal and mechanical behavior [26,34]. The steady state thermal analysis of disc brake system indicates that if the temperature and friction are higher then the efficiency of the brake system reduces which has been justified in other references [35].

 Fig. 8Boundary conditions for steady state thermal analysis.
 Fig. 9Comparison of temperature distribution for SS and GCI.
 Fig. 10Comparison of Total Heat Flux for SS and GCI.
 Fig. 11Comparison of temperature and heat flux for SS and GCI.

5 Conclusion

In this research paper design and analysis of 17-inch brake rotor has been performed. The modelling is done using solid works and the analysis have been performed using Ansys considering static structural analysis and steady state thermal analysis. In case of static structural analysis, the maximum strain, stress, shear stress and total deformation has been studied whereas in case of steady state thermal analysis, total temperature and heat flux analysis have been studied. From this the following conclusions can be drawn.

• From static structural analysis it is observed that, the maximum strain and total deformation is less in case of stainless steel as compared to grey cast iron whereas maximum stress is less in case of grey cast iron in comparison with stainless steel. Also, the shear stress is less in case of grey cast iron as compared to stainless steel.

• From static structural analysis it is observed that equivalent strain and total deformation in case of grey cast iron is 9.96% and 12.6% higher than martensitic stainless steel whereas equivalent stress and shear stress in case of grey cast iron is 38% and 38.1% lower than martensitic stainless steel.

• From steady state thermal analysis, it can be concluded that the temperature distribution remains same in case of both stainless steel and grey cast iron whereas the heat distribution (Total heat flux) is more in case of grey cast iron as compared to stainless steel. It is observed that minimum temperature in case of grey cast iron is 10.9% higher as compared to stainless steel. Also, the total heat flux is 9.02% higher in case of grey cast iron as compared to stainless steel.

• From this analysis it can be concluded that both the materials have a similar price range in the market and stainless steel is having a slight advantage over grey cast iron because of its higher corrosion properties. Grey cast iron has a better option since it has better thermal stability which is considered most important in design of high-speed brake rotor.

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Cite this article as: Anil Babu Seelam, Nabil Ahmed Zakir Hussain, Sachidananda Hassan Krishanmurthy, Design and analysis of disc brake system in high speed vehicles, Int. J. Simul. Multidisci. Des. Optim. 12, 19 (2021)

All Tables

Table 1

Rotor dimensions.

All Figures

 Fig. 12D drawing of Rotor Ventilated disc without bell [24]. In the text
 Fig. 2Boundary Conditions for Static Structural. In the text
 Fig. 3Equivalent Elastic Strain for SS and GCI. In the text
 Fig. 4Equivalent Stress for SS and GCI. In the text
 Fig. 5Shear Stress for SS and GCI. In the text
 Fig. 6Total deformation for SS and GCI. In the text
 Fig. 7Comparison of Equivalent strain, Equivalent stress, Shear stress and Total deformation for SS and GCI. In the text
 Fig. 8Boundary conditions for steady state thermal analysis. In the text
 Fig. 9Comparison of temperature distribution for SS and GCI. In the text
 Fig. 10Comparison of Total Heat Flux for SS and GCI. In the text
 Fig. 11Comparison of temperature and heat flux for SS and GCI. In the text

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