Belhocine et al. 2013. Int. J. Vehicle Structures & Systems, 5(1), 15-22 ISSN: 0975-3060 (Print), 0975-3540 (Online) doi: 10.4273/ijvss.5.1.03 © 2013. MechAero Foundation for Technical Research & Education Excellence
Inter nati onal Jour nal of Vehicle Structures & Systems Available online at www.ijvss.maftree.org
Thermo-mechanical Stress Analysis of Disc Brake Rotor Ali Belhocinea and Mostefa Bouchetarab Department of Mechanical Engineering, Oran University of Science and Technology, Algeria. a Corresponding Author, Email:
[email protected]. b Email:
[email protected]
ABSTRACT: This paper presents a thermo-mechanical analysis of dry contact between the brake disc and pads during the braking phase. The simulation strategy is based on computer code ANSYS. The modeling of transient temperature in the disc is used to identify the influence of geometric design of the disc to install the ventilation system in vehicles. A thermostructural analysis is then used to determine the deformation, Von Mises stresses in the disc and the contact pressure distribution in the pads. The results are satisfactory compared to those found in the literature. KEYWORDS: Brake discs; Heat flux; Heat transfer coefficient; Von Mises stress; Contact pressure CITATION: A. Belhocine and M. Bouchetara. 2013. Thermo-mechanical Stress Analysis of Disc Brake Rotor, Int. J. Vehicle Structures & Systems, 5(1), 15-22. doi:10.4273/ijvss.5.1.03 surfaces of the disc and pads results in thermal distortion called coning which was found to be the main cause of judder and disc thickness variation. Ouyang et al [5] found that temperature could also affect the vibration level in a disc brake assembly. Ouyang et al [5] and Hassan et al [6] employed finite element approach to investigate the thermal effects on disc brake squeal using dynamic transient and complex eigenvalue analysis, respectively. The ability of the braking system to bring a vehicle to safe controlled stop is absolutely essential in preventing accidental vehicle damage and personal injury. The braking system is composed of many parts, including friction pads on each wheel, a master cylinder, wheel cylinders, and a hydraulic control system [7]. Disc brake consists of cast-iron disc which rotates with the wheel, caliper fixed to the steering knuckle and brake pads. When the braking process occurs, the hydraulic pressure forces the piston and therefore pads and disc brake are in sliding contact. Set up force resists the movement and the vehicle slows down or eventually stops. Friction between the disc and pads always opposes motion and the heat is generated due to conversion of the kinetic energy [8]. The three-dimensional simulation of thermo-mechanical interactions on the automotive brake, showing the transient thermo-elastic instability phenomenon, is presented for the first time in this academic community [9]. In this work, the thermo-mechanical behaviour of the dry contact between the disc and brake pads at the time of braking phase is modelled using finite element analysis software ANSYS [10]. The numerical simulation of the coupled transient thermal and stress fields is sequentially carried out by thermo-structural coupling method based on ANSYS.
1. Introduction Passenger cars have been one of the essential transportation for people to travel from one destination to another. The braking system represents one of the most fundamental safety-critical components in modern passenger cars. Therefore, the braking system of a vehicle is undeniably important, especially in slowing or stopping the rotation of a wheel by pressing brake pads against rotating wheel discs. Braking performance of a vehicle can significantly be affected by the temperature rise in the brake components. The frictional heat generated on the interface of the disc and the pads can cause high temperature. Particularly, the temperature may exceed the critical value for a given material, which leads to undesirable effects, such as brake fade, local scoring, thermo-elastic instability, premature wear, brake fluid vaporization, bearing failure, thermal cracks and thermally excited vibration [1]. Light weight advanced composite materials for vehicle application has been identified to reduce fuel consumption in the automobile systems. Over 75% of fuel consumption relates directly to the vehicle weight. However, reducing the vehicle weight can improve the cost to performance ratio for the transportation industry. Researchers have shown that the vehicle weight reduction is a promising strategy for improving energy consumption in vehicles, and presents an important opportunity to reduce energy use in the transportation sector [2]. Gao and Lin [3] stated that there is considerable evidence that the contact temperature is an integral factor reflecting the influence of combined effect of load, speed, friction coefficient, thermo physical and durability properties of the materials. Lee and Yeo [4] reported that uneven distribution of temperature at the 15
Belhocine et al. 2013. Int. J. Vehicle Structures & Systems, 5(1), 15-22
swept by a brake pad. 0 is the initial speed of the vehicle. p is the factor of load distribution on the surface of the disc. m is the mass of the vehicle. The loading corresponds to the heat flux on the disc surface. The dimensions and the parameters used in the thermal calculation are given in Table 2.
2. Heat flux entering the disc In the case of disc brake, the effective friction between the pads and the disc are extremely complex due to the present time brake pads and their composite structure [11]. The heat distribution between the brake disc and the pads is mostly dependent on the material characteristics, in particular, density d,p, thermal conductivity kd,p, specific heat Cd,p. Where subscripts d and p represent disc and pads respectively. The disc material is gray cast iron with high carbon content [15] and possesses good thermo-physical characteristics. The brake pad has an isotropic elastic behaviour. Thermomechanical characteristics of these materials for pad and disc as adopted in this simulation are given in Table 1. Table 1: Thermo-elastic properties used in simulation
Material Properties Thermal conductivity, k (w/m.°C) Density, (kg/m3) Specific heat, c (J/Kg. °C) Poisson’s ratio, Thermal expansion, (10-6 / °C) Elastic modulus, E (GPa) Coefficient of friction, Operation Conditions Angular velocity, (rad/s) Hydraulic pressure, P (MPa)
Pad 5 1400 1000 0,25 10 1 0,2
Disc 57 7250 460 0,28 10,85 138 0,2
Fig.1: Application of heat flux over disc face Table 2: Parameters of automotive brake application
Parameter Inner disc diameter, mm Outer disc diameter, mm Disc thickness, mm Disc height, mm Vehicle mass m, kg Initial speed 0 , km/h Deceleration a, m/s2 Effective rotor radius ,mm Rate distribution of the braking forces, % Factor of charge distribution of the disc p Surface disc swept by the pad Ad, mm2
157.89 1
The heat quantities, Qd,p, generated by the disc and the pads can be given by the following relationship [12]:
Qd Qp
d k d Cd
(1)
p k pC p
As the braking disc is not entirely covered by the friction pads, the ratio between the disc surface Sd and the pad surface Sp is considered in the computation. The ratio of heat division between the disc and pads is given by:
Q S c d d Qp S p
d k d Cd S d p k pC p S p
3. Thermal analysis and CFD modelling Transient heat conduction in three dimensional heat transfer problem is governed by the following differential equation [16]:
(2)
q y q z q T Q C p x dx dy dz dt
Considering the heat quantity, Q, generated during the friction, the heat quantities distributed to the pads and the disc are given by:
d Q c (1 c )
(3)
p Q (1 c )
(4)
1 mgv0 z 1 2 Ad p
(6)
Where qx, qy and qz are conduction heat fluxes in x, y and z-directions, respectively. Cp is the specific heat, ρ is the specific mass. Q is internal heat generation rate per unit volume. T is the temperature that varies with the coordinates as well as the time t. The conduction heat fluxes can be written in the form of temperature using Fourier's law. Assuming constant and uniform thermal properties, the relations are:
The brake disc absorbs most part of the heat, usually more than 90% [13], through the effective contact surface of the friction coupling. Considering the complexity of the problem and limited data processing, the effect of pads is represented by an entering heat flux as shown in Fig.1. The initial heat flux q0 entering the disc is calculated by the following formula [14]:
q0
Value 66 262 29 51 1385 28 8 100.5 20 0.5 35993
q x k x
T T T , q y k y , q z k z dx dy dz
(7)
Where kx, ky and kz are thermal conductivity in x, y and z-directions, respectively. Heat transfer boundary conditions consist of several heat transfer modes that can be written in different forms. The boundary conditions frequently encountered are as follows [17, 18]:
(5)
Where z = a/g is breaking effectiveness with a being the deceleration of the vehicle and g is acceleration of gravity. is the distribution rate of the braking forces between the front and rear axle. Ad is the disc surface 16
Ts T1 x, y, z, t
(8)
qs h(Ts T )
(9)
Belhocine et al. 2013. Int. J. Vehicle Structures & Systems, 5(1), 15-22
Where T1 is the specified surface temperature. qs is the specified surface heat flux (positive into a surface). h is the convective heat transfer coefficient. Ts and T∞ are the temperatures of unknown surface and convection. The finite volume method consists of three stages starting with the formal integration of the governing equations of fluid flow over the finite control volumes of the solution domain. Then discretisation, involving the substitution of a variety of finite-difference-type approximations for the terms in the integrated equation representing flow processes such as convection, diffusion and sources. This converts the integral equation into a system of algebraic equations, which can then be solved using iterative methods [19]. The control volume integration distinguishes the finite volume method from other CFD methods. The statements resulting from this step express the ‘exact’ conservation of the relevant properties for each finite cell volume. This gives a clear relationship between the numerical analogue and the principles governing the flow. To enable the modeling of a rotating disc, rotating reference frame technique that is available in ANSYS is used. For the preparation of the mesh of CFD model, various surfaces of the disc, as shown in Fig. 2, are generated using ICEM CFD. Linear tetrahedral elements are used for mesh generation with 30717 nodes and 179798 elements. An irregular mesh, as shown in Fig. 3, is used.
The constructed CFD models were solved using ANSYS-CFX [20]. Periodic boundary conditions are applied on the section sides. As the brake disc is made from sand casted grey cast iron, the disc model is attached to an adiabatic shaft whose axial length spans that of the domain. Air around the disc is considered to be 20 °C. Open boundaries with zero relative pressure were used for the upper, lower and radial ends of the domain. Material data were taken from ANSYS material data library for air at 20 °C. Reference pressure was set to be 1 atm, turbulence intensity low and turbulent model used was k-ε. Fig. 4 shows the CFD model of the disc brake and boundary conditions. Symmetric wall air
Outlet Air at 20 °C Disc
Input
Adiabatic wall air
Fig.4: Disc brake CFD model
The airflow through and around the brake disc was analysed using the ANSYS CFX. This solver automatically calculates the heat transfer coefficient at the wall boundary. The heat transfer coefficients for convection were calculated and organized in such a way, that they could be used as a boundary condition in thermal analysis. Average heat transfer coefficient calculated for all disc using ANSYS CFX Post is shown in Fig. 5. The variation of heat transfer coefficient in the non stationary mode for the full and ventilated disc designs are shown in Figs. 6 and 7. The introduction of the ventilation system directly influences the heat transfer coefficient for the same surface as this result in a reduction in wall-fluid temperature difference.
Fig 2: Definition of surfaces of the ventilated disc
Fig. 5: Distribution of heat transfer coefficient on a ventilated disc in the stationary case Fig.3: Irregular mesh in the wall
17
-2
-1
Coefficient of transfer h [W.m .°C ]
Belhocine et al. 2013. Int. J. Vehicle Structures & Systems, 5(1), 15-22 120 110 100 90 80 70 60 50 40 30 20 10 0 -0.5
maximum temperature of the disc is approximately 60 °C lesser than the full disc case. It is noted that ventilation in the design of the discs of brake gives a better system of cooling.
SC1 SC2 SC3 SC4 SF1 SF3 ST2 ST3 ST4 SV1 SV2 SV3 SV4
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Time [s]
Fig. 6: Variation of heat transfer coefficient (h) of various surfaces for a full disc in the non-stationary case 250 SC1 SC2 SC3 SF1 SF3 SPV1 SPV2 SPV3 SPV4 ST1 ST2 ST3 ST4 SV1 SV2 SV3 SV4
-1
200
-2
Coefficient of transfer h [W m °C ]
225
175 150 125 100 75 50 25 0 -0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
(a) Full disc (172103 nodes and 114421 elements)
4.0
Time [s]
Fig. 7: Variation of heat transfer coefficient (h) of various surfaces for a ventilated disc in transient case (b) Ventilated disc (154679 nodes and 94117 elements)
4. Initial conditions and simulation
Fig. 8: Finite element meshing of the disc brake
The mesh of the full and ventilated disc using isoparametric tetra-hedral elements with 10 nodes is shown in Fig. 8. The boundary conditions are applied using ANSYS Multiphysics Workbench by choosing the mode of first simulation of the all parts, and by defining their physical properties. These conditions constitute the initial conditions of the simulation. After fixing these parameters, boundary conditions associated with each surface are introduced. The total time of simulation is set as 45s with a 0.25s increment of initial time. The minimum and maximum time increments are set to 0.125s and 0.5s respectively. Initial temperature of the disc is set to 60 °C. The values of the heat transfer coefficients (h) obtained for each surface as shown in Figs. 6 and 7 are used. The values of entering heat flux obtained by ANSYS-CFX code are used. Figs. 9 and 10 show the variation in the temperature according to time during the simulation. From the first step, the variation in the temperature shows a great growth which is due to the speed of the physical course of the phenomenon during braking, namely friction, plastic micro-distortion of contact surfaces. For the full disc, the temperature reaches its maximum value of 401.55 °C at t = 1.8839s. It is noted that the interval of 0 to 3.5s represents the forced convection phase. After 3.5s, the free convection lasts until the end of the simulation. In the case of the ventilated disc, the
(a) Full disc
(b) Ventilated disc Fig. 9: Variation of peak temperature vs. Time step
18
Belhocine et al. 2013. Int. J. Vehicle Structures & Systems, 5(1), 15-22
dimensional tetrahedral element with 10 nodes (solid 187) for the disc and pads. There are about 185901 nodes and 113367 elements in the finite element model as shown in Fig. 12.
(a) Full disc at t= 1.8839 s, Tmax=401.66 °C
Fig.11. Boundary conditions and loading imposed on the disc-pads
(b) Ventilated disc at t=1.8506 s, Tmax=346.44 °C
Fig.12. Refined mesh of the disc-pads
Fig. 10: Temperature distribution
Fig.13. gives the distribution of the total distortion in the whole (disc-pads) for various time steps of the simulation. The deformation scale varies from 0µm with 284.55µm. The value of the maximum displacement is at t = 3.5 s which corresponds to the time of braking. The deformation distribution increases with time for the friction tracks, crown external and the cooling fins of the disc. uring a braking, the maximum temperature depends entirely on the heat storage capacity of disc (on particular tracks of friction). This deformation will generate a un-symmetry of the disc following the temperature rise which will result in an umbrella shaped deformation. Fig.14. presents the Von Mises stress distribution for various time steps of the simulation. The scale of stress values varies from 0MPa to 495.56MPa. The maximum stress from the thermo-mechanical coupling is very significant than that obtained from the dry mechanical analysis under the same conditions. A strong constraint on the level of the bowl of the disc is observed. The disc is fixed to the hub of the wheel by screws preventing its movement in the presence of the disc rotation, torsion stress and shears generated at the level of the bowl created the stress concentrations. The repetition of this behaviour will involve risks of rupture on the level of the disc bowl.
5. Coupled thermo-mechanical analysis The purpose of this analysis is to predict the temperatures and corresponding thermal stresses in the brake disc when the vehicle is subjected to sudden high speed stops [21]. A commercial front disc brake system consists of a rotor that rotates about the axis of a wheel, a caliper–piston assembly where the piston slides inside the caliper, which is mounted to the vehicle suspension system, and a pair of brake pads. When hydraulic pressure is applied, the piston is pushed forward to press the inner pad against the disc and simultaneously the outer pad is pressed by the caliper against the disc [22]. In a real car disc brake system, the brake pad surface is not smooth at all. Abu Bakar and Ouyang [23] adjusted the surface profiles using measured data of the surface height and produced a more realistic model for brake pads. Fig.11 shows the finite element model and boundary conditions of the model composed of a disc and two pads. The initial temperature of the disc and pads is 20℃, and the surface convection condition is applied at all surfaces of the disc and the convection coefficient (h) of 5 W/m2C is applied at the surface of the two pads. The FE mesh is generated using three19
Belhocine et al. 2013. Int. J. Vehicle Structures & Systems, 5(1), 15-22
(a) t = 1.7271 s
(b) t = 3.5 s
(c) t = 30 s
(d) t = 45 s Fig. 13: Total distortion distribution
(a) t = 1.7271 s
(b) t = 3.5 s
(c) t = 30 s
(d) t = 45 s Fig. 14: Von Mises stress distribution
20
Belhocine et al. 2013. Int. J. Vehicle Structures & Systems, 5(1), 15-22
Due to thermal deformation, contact area and pressure distribution also change. Thermal and mechanical deformations affect each other strongly and simultaneously Contact analysis of the interfacial pressure in a disc brake without considering thermal effects was carried out in the past [24]. Brake squeal analysis includes a static contact analysis as the first part of the complex eigenvalue analysis [25 and 26]. Fig. 15 shows the contact pressure distribution in the friction interface of the inner pad taken for at various times of simulation. For this distribution the scale varies from 0 MPa to 3.3477 MPa. The maximum value of pressure is at t = 3.5 s which corresponds to the null rotational speed. It is also noticed that the maximum contact pressure is located on the edges of the pad of the entry and goes down towards the exit from the friction area. This pressure distribution is almost symmetrical compared to the groove. It has the same tendency as that of the distribution of the temperature because the highest area of the pressure is located in the same regions. At the time of the thermo-mechanical coupling, the pressure variation leads to the non-axisymmetric temperature field. This affects the thermal dilation and leads to a variation of the contact pressure distribution.
(a) t = 1.7271 s
(b) t = 3.5 s
(c) t = 40 s
(d) t = 45 s
resistance. The analysis results showed that the temperature and stress fields in the process of braking phase were fully coupled. The temperature, Von Mises stress, total deformations of the disc and contact pressures of the pads increase as the thermal stresses are added to the mechanical stress. The calculation results are satisfactory with commonly found investigations in the literature. It would be interesting to solve the thermomechanical problem in disc brakes with an experimental study to validate these numerical results with reality. REFERENCE: [1] A.R. Abu Bakar, H. Ouyang, L.C. Khai and M.S. Abdullah. 2010. Thermal analysis of a disc brake model considering a real brake pad surface and wear, Int. J. Vehicle Structures & Systems, 2(1), 20-27. http://dx.doi. org/10.4273/ijvss.2.1.04. [2] M.A. Maleque, A.A. Adebisi and Q.H. Shah. 2012. Energy and cost analysis of weight reduction using composite brake rotor, Int. J. Vehicle Structures & Systems, 4(2), 69-73. http://dx.doi.org/10.4273/ ijvss.4.2.06. [3] H. Gao and X.Z. Lin. 2002. Transient temperature field analysis of a brake in a non-axisymmetric threedimensional model, J. Materials Processing Technology, 129, 513-517. http://dx.doi.org/10.1016/S0924-0136(02) 00622-2. [4] S. Lee and T. Yeo. 2000. Temperature and coning analysis of brake rotor using an axisymmetric finite element technique, Proc. 4th Korea-Russia Int. Symp. Science & Technology, 3, 17-22. [5] H. Ouyang, A.R. AbuBakar and L. Li. 2009. A combined analysis of heat conduction, contact pressure and transient vibration of a disc brake, Int. J. Vehicle Design, 51(1/2), 190-206. http://dx.doi.org/10.1504/IJVD.2009.027121. [6] M.Z. Hassan, P.C. Brooks, and D.C. Barton. 2009. A predictive tool to evaluate disc brake squeal using a fully coupled thermo-mechanical finite element model, Int. J. Vehicle Design, 51(1/2), 124-142. http://dx.doi.org/ 10.1504/IJVD.2009.027118. [7] Sivarao, M. Amarnath, M.S.Rizal and A.Kamely. xxx. An investigation toward development of economical brake lining wear alert system, Int. J. Engineering & Technology, 9(9), 251-256. [8] M. Kuciej and P. Grzes. 2011. The comparable analysis of temperature distributions assessment in disc brake obtained using analytical method and FE model, J. KONES Powertrain and Transport, 18(2), 235-250. [9] C. Cho and S. Ahn. 2001. Thermo-elastic analysis for chattering phenomenon of automotive disc brake, Int. J. KSME, 15(5), 569-579. [10] L. Zhang, Q. Yang, D. Weichert and N. Tan. 2009. Simulation and analysis of thermal fatigue based on imperfection model of brake discs, Proc. Appl. Math. Mech., 9, 533-534. http://dx.doi.org/10.1002/pamm. 200910239. [11] Frein à Disques et Garnitures de Frein à Disques, 4th Edition, 01.07.1993, Fiche U.I.C 541-3. [12] E. Saumweber. 1969. Temperaturberechnung in Bremsscheiben Fürein Beliebiges Fahrprogramm, Leichtbau der Verkehrsfahrzeuge, Augsburg. [13] C. Cruceanu. 2007. Frâne Pentru Vehicule Feroviare, Matrixrom, Bucureşti.
Fig. 15: Contact pressure distribution in the inner pad
6. Conclusions In this paper, the analysis of the thermo-mechanical behaviour of the dry contact between the brake disc and pads during the braking process is detailed. We have shown that the ventilation system plays an important role in cooling discs and provides a good high temperature 21
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[22] M. Nouby and K. Srinivasan. 2009. Parametric studies of disc brake squeal using finite element approach, J. Mekanikal, 29, 52-66. [23] A.R. Abu Bakar and H. Ouyang. 2008. Wear prediction of friction material and brake squeal using the finite element method, Wear, 264(11-12), 1069-1076. http://dx.doi.org/ 10.1016/j.wear.2007.08.015. [24] M. Tirovic and A.J. Day. 1991. Disc brake interface pressure distribution, Proc. IMechE, Part D: J. Automobile Engineering, 205, 137-146. http://dx.doi.org /10.1243/PIME_PROC_1991_205_162_02. [25] H. Ouyang, Q. Cao, J.E. Mottershead and T. Treyde. 2003. Vibration and squeal of a disc brake: modelling and experimental results, Proc. IMechE, Part D: J. Automobile Engineering, 217, 867-875. http://dx.doi.org/ 10.1243/095440703769683270. [26] Y.S. Lee, P.C. Brooks, D.C. Barton and D.A. Crolla. 2003. A predictive tool to evaluate disc brake squeal propensity Part 1: The model philosophy and the contact problem, Int. J. Vehicle Design, 31, 289-308. http://dx.doi. org/10.1504/IJVD.2003.003360.
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