CFD Analysis and Comparison of Different Ventilation Geometries for Brake Discs

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1 CFD Analysis and Comparison of Different Ventilation Geometries for Brake Discs Vijay Gautam DTU, Delhi, India Ananya Bhardwaj DTU, Delhi, India Rahul Sharma DTU, Delhi, India Abstract: It is the primary objective of design engineers to reduce weight and maximize safety and performance of the automotive components. A significant research in the domain of improving brake disc heat dissipation is being carried out as it is one of the most crucial components of any automobile. The aim of the present research is to establish a systematic process for simulating and optimizing air-cooling of a solid brake disc (without internal vanes) used in a motorbike through CFD analysis, comparing cooling performance of different geometries like through-holes, radial slots and other ventilation geometries. The heat generated during a stop by sudden application of brakes, the worst condition of design is estimated from kinetic energy dissipation and its distribution in both the wheels. The conditions used for finite element analysis are similar to estimated running conditions found using OPTIMUMLAP software i.e. average rotational speed and also the translational velocity of the car are used to define the boundary conditions in the simulations. The heat transfer coefficient is estimated and compared using an unsteady RANS simulation using ANSYS FLUENT software. Through iterative simulations, the heat transfer coefficient is significantly enhanced by more than 50 percent for slotted disc geometry as compared to a disc design without slots. Keywords Disc brake, Finite element analysis, Heat transfer coefficient, heat dissipation, ventilation geometry M I. INTRODUCTION ost modern automobiles are heavily reliant on the usage of disc braking system and therefore proper and efficient design of brake discs becomes imperative for vehicle performance and passenger safety. As much as 99% of the vehicle kinetic and potential energy is converted to heat during brake application, this heat is dissipated through the ventilated disc [1]. Inadequate dissipation of heat through the discs causes excessive heat build-up which leads to abnormal operation of the brakes due to brake fade, excessive pad or rotor wear and thermal judder. Previous numeric and experimental studies have contributed towards optimum design of disc brake. Evaluation of transient temperatures produced in disc brakes was done by Newcomb [2] which led him to suggest using temperature distribution in further studies. Sparse solver ADINA was utilized by Hohman et al. [3] to carry out Finite Element Analysis of the disc and drum brakes. Contact situations were taken as the focus area where friction was the major factor, results included deformation, stress distribution, contact pressure during sticking and sliding friction. Gao [4] used 3D thermo-mechanical coupling model to analyze the transient temperature field and thermal fatigue fracture of the disc. Hwang and Wu [1] contributed by studying the thermal-mechanical characteristics of ventilated disc brake during brake operation. It was observed that thermal expansion was adversely affected when nonaxisymmetric contact pressure was applied which resulted in non-axisymmetric temperature fields. The thermal stress and strain matched accordingly to the temperature distribution. Another similar study by Adamowicz and Grzes [5] involved 3D FEA to obtain temperature distribution from which it was inferred that at the initial point of braking the temperature of the disc rises sharply and then becomes stagnant at some lower temperature. An inverse algorithm based on conjugate gradient method for estimating the space and time dependent heat flux was developed by Yang and Chan [6], they also conducted numerical studies to confirm the results of the proposed method. Numerical investigation of the transient heat conduction problem of friction and its effect on temperature field and thermal stresses for metal-ceramic pad and cast iron disc was done by Yevtushenko and Kuciej [7]. Compressive stresses in the disc were induced due to localized intensive frictional heating at the contact surfaces and after initiation of braking crack would initiate due to the tensile normal stresses developed in the disc. Simulation and analysis of 3D transient temperature field of brake disc under downhill

2 braking conditions was conducted by Zhang and Xia [8]. Observations were made which indicated that density of the heat flux increases with increase in friction radius and the temperature gradient in the radial direction is a significant factor. Enhancement of braking performance can be done by efficient cooling of brake discs by accentuating heat dissipation to maintain temperatures within the operating range for the brake pads. Rejection of heat by brake discs is through conduction to the wheel hub, radiation and convection to the surroundings. Optimum design of ventilation geometry can improve brake disc cooling as convection is largely responsible for heat dissipation in normal conditions. A systematic approach for obtaining the optimum geometry through the example of an open wheel race-car which comprises of a 4mm thick plate type disc brake will be presented in this paper. Simulation and prediction of the heat generated and dissipation rate in the brake discs will be conducted through the use of computer aided engineering. To obtain realistic results proper and efficient use of CAD is required to circumvent its limitations. The main aim of this paper is to arrive at a method which can provide accurate results of convective heat transfer coefficient using Computational Fluid Dynamics (CFD) and also to maximize it by testing iterations of varied ventilation geometries. The estimated coefficient will then be used to predict peak temperatures and cooling time. In a race-car which is pushed to the limits of performance through repetitive and heavy braking, employing the use of the most efficient and fastest cooling design of brake disc is imperative. II. METHODOLOGY It is assumed for the purpose of analysis that 100% of the kinetic and potential energy of the vehicle is converted to heat at the disc pad interface to design for maximum case. The front brakes are required to provide more braking torque due to occurrence of forward load transfer during brake operation when the vehicle is moving forward; the load transfer is calculated manually using vehicle operation parameters. The average convective heat transfer coefficient is determined on the basis of a CFD analysis using the average translational and rotational speed of the disc to model the airflow. Transient simulation is carried out to determine peak temperature and rate of cooling; this is done by using the heat determined through calculation distributed for the duration of a stop taken as heat power input for the simulation. This paper is concerned with the simulation of a student built formula race-car. The goal is to minimize un-sprung mass, meaning the area of the disc has to be kept as low as possible to minimize weight while using the design which is the best possible geometry for maximizing the heat transfer coefficient. A. OptimumLap Log Data Optimumlap software is utilized to obtain the average translational velocity and the rotational velocity of the disc (from average car speed) and the heaviest braking zone by processing telemetry information from the racecar during movement around the track. The values obtained are further utilized in the CFD analysis. Fig. 1 illustrates a typical speed vs elapsed distance plot. Fig. 1. Speed vs. Distance graph obtained from Optimumlap B. Brake Disc Geometric Design Constraints while designing the disc include the limited space at the wheel hub assembly and the pre-selected brake caliper, accordingly the diameter of the brake disc is set at Ø175mm and thickness at 4 mm. Brake disc materials is AISI 410 which is a martensitic stainless steel. From initial analysis it was determined that increasing the number of holes and slots provided a positive increment to the convective heat transfer coefficient but also increased the physical stresses induced during brake operation. Designs were again tested and only those which had induced stress value of less than or equal to 500 MPa were used for subsequent analysis. The designs are illustrated in Fig. 2. Fig. 2. Different ventilation geometries tested in simulations

3 C. Ventilation through Slotted and Drilled geometries Ventilation geometries provide multiple benefits, first they help to improve the heat transfer coefficient as more surface area is exposed, forced convection due to internal airflow is introduced and also the un-sprung mass is reduced as well. Drilled, slotted and curved vanes are some of the generally used geometries. They are designed keeping in mind a maximum stress value of 400 N/mm2 and are tested in ANSYS structural, excessive material removal is avoided to maintain thermal storage capacity and avoid failure and distortion through thermal stresses. D. Finite Element Strength Assessment ANSYS Static Structural was used to simulate real time braking and analyze the induced stress as shown in Fig. 3. Maximum deceleration of vehicle was assumed as 1.8g, taking this into account during brake calculations of load transfer the maximum brake torque required was determined to be 345Nm applied through the brake disc-pad interface on the disc while its mounts were set as a fixture as shown in Fig. 3. F. Average Heat Transfer Determination ANSYS FLUENT software is used to determine the convective heat transfer coefficient distribution over the surface geometry. Optimumlap simulation is used to obtain the values of the average rotational velocity and the average translational velocity which are then used as inputs for the airflow around the disc. The computation of the Heat Transfer coefficient of the brake disc was done using ANSYS FLUENT. A conjugate heat transfer setup was created by importing disc geometry and creating a fluid domain around it. Different setups with varying amount of elements ranging from to 2.5 million elements were created to get mesh independent solution. Tetrahedral elements populating the mesh for CFD analysis are shown in Fig. 4. Fig. 4. Illustration of the mesh generated for the CFD simulation Fig. 3. Structural Stress analysis of drilled disc E. Evaluation of Load Power and Heat Power Load transfer takes places during brake operation as a result more brake torque is required at the front wheels which results in increased heat generation at the front as compared to the rear. Deceleration, height of centre of gravity and static weight distribution can be used to determine the load transfer. Ratio of dynamic loads is found to be 75% front and 25% rear when taking in to account a deceleration of 1.6g. Reduction in the potential and kinetic energies is used to calculate the total heat energy generated during the heaviest braking zone (100-30kph). Peak temperatures are found using the amount of energy dissipated over the stop and the heat transfer coefficient obtained through CFD analysis and also by applying the heat power found from the energy equivalence to the brake disc for the duration of the stop. For efficient use of computational resources a plane parallel to the face of the disc and at the center of the thickness was used. In order to set the brake disc as rotating domain, rotational velocity was given to the air boundary around the disc. An inlet velocity was given to the air domain to simulate lateral movement of the brake disc. Fig. 5 illustrates the airflow around the disc. Table 1 provides the input parameters of the CFD analysis. Fig. 5. Velocity of the air medium around the brake disc for CFD simulation

4 TABLE I. Parameter Solvers Turbulence Model Wall Functions Brake Disc initial temperature Air Brake Disc rotational velocity Air Velocity CFD SETTINGS Value Coupled flow, energy Realizable k-ɛ Alt y+ wall treatment 400K Incompressible ideal gas 460 rad/s 10 m/s Fig. 7. Simulation Result of transient thermal showing peak temperature achieved by the Brake Disc after a stop from 100Km/h to 30Km/h Fig. 6. Heat transfer coefficient distribution, peak values of coefficient are obtained at the edges while it is lower for the faces The surface integral of the area-weighted average of the heat transfer coefficients of boundaries between the disc and the air surrounding it were calculated by utilizing the gradient of the heat transfer coefficient across the entire surface of the disc, the simulation outcome is illustrated in Fig. 6. G. Thermal Transient Analysis Initial thermal analysis is aimed at obtaining the peak temperature of the disc during stop; this is done by applying the heat power over the surface of the disc in contact with the pad during brake operation and inputting the average heat transfer coefficient in the analysis. The sum of kinetic energy of translation and rotation of the car weighing 300Kg with driver, decelerating to 30 km/h from 100 km/h was equated to the heat energy generated. The total energy was distributed over the duration of the stop obtained from the Optimumlap speed data to determine the heat power from the heat energy obtained earlier. Ambient air temperature of 22 degrees Celsius was taken as the initial disc temperature and convection was applied over the entire disc surface with the average heat transfer coefficient as found through CFD. Fig. 7 illustrates the CFD result. Peak temperature values are tabulated in Table 2. Fig. 1. Results of transient thermal analysis showing temperature after 5 seconds of running after a peak temperature of 673K. This image shows a drop of 17 K for the drilled geometry for ventilation. Analysis of the cooling of the brakes during 5 seconds of straight run after reaching peak temperature of 673 K in a stop is done separate from the first analysis, Fig. 8 illustrates this simulation. Ambient air temperature is kept at 295K and the entire face of the brake disc is under convection. The results are tabulated in Table 2. III. RESULT AND DISCUSSION Four different geometries; blank, drilled, slotted and drilled and slotted were made to undergo simulations with similar setup. Comparison of their heat transfer coefficients is done along with simulation at peak temperatures. Prior stress analysis using ANSYS Structural was done to all four geometries to ensure the validity of their mechanical performance under load. The conclusions drawn from the study should be looked at while considering the fact that there are inherent limitations to software based analyses and therefore the results obtained are only an indication of real world performance and not the actual values which would be present in a real world practical scenario.

5 Furthermore computer based simulations will be followed by real world experiments in the next stage of the study for further validation. The experiments would be conducted on the university formula student car itself using type-k rubbing style thermocouple to monitor the brake disc temperatures and with the use of data-loggers to obtain and record data for analysis. TABLE II. Design type for ventilation RESULTS OF CFD AND TRANSIENT THERMAL SIMULATIONS Average Heat Transfer Coefficient (W/m 2 ) Peak temperatures after stop (Kelvin) Blank Disc Drilled Disc Slotted Disc Slotted and Drilled Disc Temperature drop after 5 seconds of driving (Kelvin) References [1] P. Hwang and X. Wu, "Investigation of temperature and thermal stress in ventilated disc brake based on 3D thermo-mechanical coupling model," Journal of mechanical science and technology, vol. 24, pp , [2] T. Newcomb, "Transient temperatures attained in disk brakes," British Journal of Applied Physics, vol. 10, p. 339, [3] C. Hohmann, et al., "Contact analysis for drum brakes and disk brakes using ADINA," Computers & Structures, vol. 72, pp , [4] C. Gao and X. Lin, "Transient temperature field analysis of a brake in a non-axisymmetric three-dimensional model," Journal of Materials Processing Technology, vol. 129, pp , [5] A. Adamowicz and P. Grzes, "Analysis of disc brake temperature distribution during single braking under non-axisymmetric load," Applied Thermal Engineering, vol. 31, pp , [6] Y.-C. Yang and W.-L. Chen, "A nonlinear inverse problem in estimating the heat flux of the disc in a disc brake system," Applied Thermal Engineering, vol. 31, pp , [7] A. Yevtushenko and M. Kuciej, "Temperature and thermal stresses in a pad/disc during braking," Applied Thermal Engineering, vol. 30, pp , [8] J. Zhang and C. G. Xia, "Research of the transient temperature field and friction properties on disc brakes," in Advanced Materials Research, 2013, pp IV. CONCLUSIONS The conclusions drawn from the simulations in this study are as follows: Slotted geometry exhibited the highest average heat transfer coefficient of convection while the blank geometry had the least. Edges had greater value of heat transfer coefficient as compared to the side faces. The disc pad interface is the dominant contributor to temperature change during heavy braking, convection here plays little role. Slotted geometry peak temperature was higher than that of drilled geometry and blank geometry showcased the lowest value of peak temperature. The peak temperature values of the four geometries can be explained by the fact that as material is removed there is less contact of the discs with the brake pad where heat generation takes place and because heat power remains same for all geometries heat concentration is higher in geometries where material is removed and peak temperature increases proportionally. It is found that when discs are exposed to cool air after braking period the discs with the greatest convective heat transfer coefficient cools down the quickest. It can inferred that the usage of the geometry which cools the fastest would be utilized to maximize brake cooling and provide the least possible values of average temperature around the track.