CHAPTER 6 HEAT DISSIPATION AND TEMPERATURE DISTRIBUTION OF BRAKE LINER USING STEADY STATE ANALYSIS

Transcription

1 131 CHAPTER 6 HEAT DISSIPATION AND TEMPERATURE DISTRIBUTION OF BRAKE LINER USING STEADY STATE ANALYSIS 6.1 INTRODUCTION Drum brakes were the first types of brakes used on motor vehicles. Nowadays, over 100 years after the first usage, drum brakes are still used on the rear wheels of most vehicles. The drum brake is used widely as the rear brake particularly for small car and motorcycle. The leading-trailing shoe design is used extensively as rear brake on passenger cars and light weight pickup trucks. Most of the front-wheel-driven vehicles use rear leadingtrailing shoe brakes. The brake drum of a motorcycle is usually made from cast aluminum and essentially a cylinder sandwiched between the wheel rim and the wheel hub. Within the drum are brake shoe lines with friction material. Both disc and drum brakes work on the same principle: friction and heat. When resistance or force is applied to a turning wheel, the vehicle s brake system causes the wheels to decelerate and finally stop. During this process heat is generated causing the brake temperature to rise. The factors, which determine the vehicle deceleration, are vehicle weight, braking force, coefficient of friction and pressure distribution over the braking surface area. Disc brake components are fully exposed to the atmosphere and hence heat removal is efficient. On the other hand, drum brake components are fully enclosed inside the brake assembly. This may result in comparatively higher temperature with regard to disc brake system under same braking conditions.

2 132 High temperature of the drum brake shoe may cause brake fade and eventually lose effectiveness. Fading is the result of too much heat build-up within the drum. Hence, the drum brakes can only operate as long as they can absorb heat generated by kinetic energy lost due to decelerating the wheels. Once the brake components themselves become saturated with heat, they lose the ability to stop a vehicle. At high temperatures other components of the brake system undergo higher thermal expansion. Since the geometry of the drum brake is more complicated than the disc brake, maintaining the component dimensions at high temperature within the desirable limit is very critical. Thermal expansion of a component beyond a certain limit may interfere with other neighboring components. This may result in the thermal seizure or locking of the drum brake. This, in turn can result in further rise in temperature of the system and consequently, it can trigger the failure of other components. The failure under investigation is the rear drum brake of a spoke wheel in the two-wheeler vehicle observed during high panic braking. Various components of the brake, namely drum brake liner, brake drum, brake shoe were observed to have failed. Figure 6.1 shows the shoe assembly of a brake liner. Figure 6.2 shows model with only brake shoe components modeled without the spokes. Figure 6.1 Brake panel with shoe and liner after cover panel removed

3 MODELING OF DRUM BRAKE ASSEMBLY Creating a linear drum brake assembly model contain three steps viz Pre-processor, Solution and Post-processors. Figure 6.3 shows the finite element model for the coupled drum brake system assembly that contains the main five components which are brake drum, two shoes and two linings (leading and trailing), participating in the friction wear response of a drum brake system. The attached linings to the shoes will be in contact with the drum during braking to produce the friction forces. These leading and trailing shoes can be moved in different direction opposed to each other through action cam and spring movement. The brake panel from one side and the drum from the other side house the brake shoes and drum brake liner. Heat generated due to brake application is dissipated through the panel, brake drum and shoe liner. Figure 6.2 3D Modeling of Shoe brake assembly

4 134 Figure 6.3 Meshing of Shoe brake assembly FEA has become an important and reliable tool to analyze and predict wide range of failure mechanisms in different fields. In the finite element analysis presented below, fatigue is not modeled and ffew assumptions are made in the numerical model. Brake shoes are included in the model and steady state analysis is performed. The properties of brake liner and aluminum alloy are given in Table 6.1 and Table 6.2 (Singh, OP & Jayamathy, M, 2010). Table 6.1 Properties of Brake liner Properties Description Youngs Modulus 0.95 Poisson ratio 0.29 Shear modulus N/m x e 11 Density kg/m Thermal expansion ( ) 1 x 10-4 / 0 K Thermal conductivity (k) 30 w/m 0 K Specific heat 900 J/ kg 0 K

5 135 Table 6.2 Properties of Aluminum alloy Properties Description Youngs Modulus N/m x e 11 Poisson ratio 0.33 Shear modulus N/m x e 11 Density kg/m Thermal expansion ( ) 2.1 x e -5 / 0 K Thermal conductivity (k) 92 w/m 0 K Specific heat 900 J/ kg 0 K Figure 6.4 Vehicle speed versus braking cycle Steady state analysis is justified on the basis of Figure 6.4.Time between the start of nth and start of (n + 1)th braking constitute a cycle. Temperature of the brake drum components is measured after every 10 braking cycle. It is found that the temperature during braking increases and drops when it is accelerated. After certain time of braking the temperature

6 136 attains the maximum and maintain the same for subsequent braking. (i.e. after successive brake applications). This value of high temperature causes the wheel hub to expand beyond certain limit. Hence, estimating the maximum thermal expansion under steady state condition is justified. The temperature of wheel rim of reference vehicles fitted with spokes is about 40 0 C only even after 60 brake applications. This indicates that spokes do not conduct heat efficiently due to small contact area at the wheel hub. Heat conduction through the brake shoe to the brake drum panel dominates only after the brake drum temperature shows sign of saturation. It is interesting to note that even after brake shoe temperature reaches a saturation value, the brake drum temperature keeps rising. The rate of temperature rise decreases with time. Table 6.3 gives the test conditions to measure the temperature of brake components after every 10 braking cycle. Table 6.3 Details of test conditions Brake Test Weight of vehicle with rider Velocity of two wheeler Brake applied Brake input Test track No. of braking cycle 6 No. of times brakes applied Temperature reading 180 Kg 60 Km/hr Rear Parameters Maximum before wheel lock Normal road condition 10 times for each temperature measurement Infrared thermometer

7 137 Table 6.4 Parameters used for heat flux calculations Factors Value Drag coefficient,c d 0.4 Projected area, A p (m 2 ) 0.65 Moment of inertia (Spoke wheel) (kgm 2 ) Angular velocity ( ) (rad/s) 46 Drum brake liner area (m 2 ) This temperature distribution is applied as a body force in the linear structural analysis to get the temperature induced thermal expansion. The commercially available software ANSYS 9.0 is used for the analysis. Element Solid 70 is used for the thermal analysis and element Solid 45 is used for the structural analysis. Element size of 2 mm is used for meshing. 6.3 THERMAL BOUNDARY CONDITIONS Heat transfer coefficients (HTC) on the cooling surfaces and heat flux value inside the brake liner are needed to determine the temperature distribution of the brake assembly. Measurements of these two quantities are very difficult due to continuous rotation and complex geometry of the wheel. The Energy balance methodology is used for determining HTC and heat flux (Singh O M 2010) as given in Equation (6.1). ds dt Ff = mc p + ha (T-To) + A T dt dt 4 (6.1) where F f is the braking force (N); S, the braking distance; m, the mass of the brake drum (kg); Cp, the specific heat capacity (J/kg 0 K); T, the temperature of brake drum ( 0 K); A, the area of cooling surface of the brake drum (m 2 ); h, the coefficient of heat transfer between the brake drum and air (W/m 2 0 K); T 0, the

8 138 temperature of surrounding air ( 0 K); t, the braking time (s) and (Stefan Boltzmann constant) = 5.7x10-8 (W/m 2 0 K 4 ). Since the heat transfer by convection is more dominant at low temperature of the drum brake, radiation effect can be neglected (Noyes 1969). Sheridan et al (1988) found that in almost all braking conditions, about 90% of the heat dissipation is by convection and hence radiation effect can be neglected. Noyes et al (1969) developed a thermal model based on the finite difference method and concluded that 65% of the energy is dissipated by convection and 35% as stored thermal energy, energy lost by radiation and conduction to the lining. The measurements were made at the end of 10 stops with vehicle running at 90 km/ hr. The brake drum reaches steady state temperature after successive brake applications. Reaching the steady state temperature depends upon the material compositions of the brake liner. The rate of change of temperature, dt/dt, becomes negligible and radiation loss is neglected. Hence, change in internal energy of the system can be neglected. After removing radiation and internal energy, the equation simplifies, as given in Equation (6.2). ds Ff = ha (T-T o) dt (6.2) E dissipate is the available energy for dissipation into heat. The heat dissipated is calculated using mathematical forms as given in Equations (6.3) and (6.4) below. E dissipate = E lin + E 1 rot + E 2 rot (KE tot + E drag ) (6.3) E dissipate = F f S = 1 2 1/2 MV2 + ( 1 2 I m+ 1 2 I ) (ke tot + F drag S) (6.4)

9 139 where E lin linear kinetic energy of the vehicle, E rot is the kinectic energy due to rotation of wheels, E drag is the energy lost due to vehicle drag, E tot is the vehicles total energy, M is the total mass of the system, I 1 and I 2 are moment of inertia of front and rear wheel,, the angular velocity, F drag is the velocity drag, C d the coefficient of drag and A p is projected area of the vehicle. F drag can be calculated using Equation (6.5): F drag = 1 2 C d A p (6.5) F drag = 1 2 x 0.4 x 0.6 x 2.7 x (16.66 )2 F drag = N Substituting the value of F drag in Equation (6.4), E dissipate = x ( x x 46 2 ) ( x 7473) E dissipate = w Heat flux can be calculated using Equation (6.6): Q flux = E dissipate Area of drum liner (A) x stopping time (t) (6.6) Area of brake liner = m 2 Braking time = 5 Sec Q flux = / x 5 Q flux = W/m 2

10 140 Figure 6.5 shows heat flux as input given to the FEA. Table 6.5 shows heat flux value of the asbestos brake lining and flyash based brake lining to predict temperature distribution and thermal expansion of brake drum. Figure 6.5 FEA analysis of Heat flux as input Table 6.5 Heat flux input to different brake liners S.No Brake liner Heat Flux (W/m 2 ) 1 Asbestos brake lining FG FG FG FG FG

11 STRUCTURAL BOUNDARY CONDITION AND VALIDATION IN FEA Thermal expansion behaviour of drum brake components is complex due to the presence of various components. To determine the thermal expansion using Ansys 9, some region of the drum brake has to be fixed i.e. displacement equal to zero has to be specified to avoid rigid body motion, though in actual condition, every component undergoes some degree of thermal expansion depending upon their temperatures. The boundary condition is validated with FEA. During experiments, brake is applied at the rear end of the wheel and temperatures of the brake drum are measured when the vehicle is completely stopped. So there will be some delay in measurement of the readings resulting in lower reading of temperature. Figure 6.6 (a) shows maximum thermal expansion of 0.19 mm for asbestos based brake liner. Figures 6.7 (a), 6.8 (a), 6.9 (a), 6.10 (a) and 6.11 (a) show maximum thermal expansion of mm, mm, 0.429, mm and mm of non-asbestos based brake liners. Figures 6.6 (b) show the temperature of asbestos based brake liner and Figures 6.7(b), 6.8(b), 6.9(b), 6.10 (b) and 6.11 (b) show the temperature distribution of non-asbestos based brake liners.

12 142 Figure 6.6(a) Contours of total thermal expansion (mm) of aluminum alloy brake drum with asbestos brake liner Figure 6.6(b) The predicted temperature ( 0 K) distribution of aluminum alloy brake drum with asbestos brake liner

13 143 Figure 6.7(a) Contours of total thermal expansion (mm) of aluminum alloy brake drum with brake liner - FG-1 Figure 6.7(b) The predicted temperature ( 0 K) distribution of aluminum alloy brake drum with brake liner - FG-1

14 144 Figure 6.8(a) Contours of total thermal expansion (mm) of aluminum alloy brake drum with brake liner- FG-2 Figure 6.8(b) The predicted temperature ( 0 K) distribution of aluminum alloy brake drum with brake liner - FG-2

15 145 Figure 6.9(a) Contours of total thermal expansion (mm) of aluminum alloy brake drum with brake liner- FG-3 Figure 6.9(b) The predicted temperature ( 0 K) distribution of aluminum alloy brake drum with brake liner - FG-3

16 146 Figure 6.10(a) Contours of total thermal expansion (mm) of aluminum alloy brake drum with brake liner - FG-4 Figure 6.10(b) The predicted temperature ( 0 K) distribution of aluminum alloy brake drum with brake liner -FG-4

17 147 Figure 6.11(a) Contours of thermal expansion (mm) of aluminum alloy brake drum with brake liner -FG-6 Figure 6.11(b) The predicted temperature ( 0 K) distribution of aluminum alloy drum brake with brake liner - FG-6

18 148 The average heat transfer coefficients (HTC) are determined by using the correlation, which is approximate. The brake components such as rim and spoke are not included in the FEA. Heat flux calculations are done assuming constant heat generation is constant and it depends upon the steady state temperature attained by the individual brake liner. However heat supplied to the brake drum is not constant but decreases linearly with time. Considering the simplification of the problem, the FEA model predicts results and can be reasonably accepted. In structural analysis, center of the brake shoe is a constraint in axial direction (Kukutschova, 2009 and Filip 2010). Thermal analysis of the brake drum is performed independently using the temperature obtained from the experiments. Brake liner FG-3 and FG-5 give almost heat flux generated during experiments and therefore FG-5 is not considered for analysis. The minimum expansion is due to the air flow over the brake drum and the heat is removed due to convection. The maximum temperature distribution of K occurs in the brake liner FG-6, whereas the maximum temperature distribution of K occurs in asbestos brake liner. The thermal expansion values are beyond 0.50 mm of specified limit in these locations. On the other hand, the corresponding thermal expansion and temperature distribution of brake drum components caused by the asbestos brake liner were low when compared to non asbestos organic based brake liner due to lesser amount of heat flux generated during braking. This FEA method is adopted, as it is very difficult to measure these expansions during actual running conditions.

19 SUMMARY 1. FEA reveals that steady state temperature attained in nonasbestos organic brake liner is fairly high when compared with asbestos brake liner. 2. Thermal expansion of the aluminum alloy brake drum with non-asbestos organic brake liner is high when compared to asbestos organic brake liner due to more heat generated during braking.