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HACETTEPE UNIVERSITY

FACULTY OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

OMU 332

VEHICLE COMPONENT DESIGN

PROJECT NO : 2

PROJECT TITLE : NORSTER 600R BRAKE DESIGN

GROUP NAME : EGG

PREPARED BY : Gökhan YAZAR

Gizem ÖZEL

Erkin Barış BİLGİ

DATE : 07.06.2011

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1. STATEMENT OF THE PROBLEM

The problem is to design a front brake system for Norster 600R according to

following considerations:

- Brake force distribution

- Brake distance

- Max. brake temperature requirements

2. INTRODUCTION

Missions of the front brake system design are given below:

- Selection of friction material

- Foundation brake design

- Heat transfer analysis

At this project, we will design a disc brake for front brake system. To design a disc

brake, we must calculate the following system parameters:

- Number of pistons

- Brake cylinder area

- Brake rotor/Brake pad dimensions

- Lining friction material and friction coefficient

- Brake factors

- Front brake line pressure

After all these calculations, disc brake design will be completed with the heat transfer

analysis.

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BRAKE DESIGN

Required Data

Empty and loaded vehicle weight

Static weight distribution: lightly and fully laden

Wheelbase

Center of gravity height: lightly and fully load

Tire and wheel size

Max. speed

Standards

Steps of Design

Selection of Brake Force Distribution

Hydraulics

Design of Foundation Brake

Pedal Assembly

Disc Brake

Drum Brakes

SCHEDULE

Date Submission 1 Submission 2 Submission 3 Submission 4

13.05.11 Selection of Friction Material

20.05.11

Foundation Brake Design

27.05.11

Heat Transfer Analysis

07.06.11

Technical Drawings

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THEORETICAL KNOWLEDGE

General uses of the brakes can be formulated in terms of three basic functions a

braking system must provide:

1. Decelerate a vehicle including stopping.

2. Maintain vehicle speed during downhill operation.

3. Hold a vehicle stationary on a grade.

Deceleration involves the change of the kinetic and potential energy (if any) of a

vehicle into thermal energy. Important factors a brake design engineer must consider

include braking stability, brake force distribution, tire/road friction utilization, braking while

turning, pedal force modulation, stopping distance, in-stop fade and brake wear.

Maintaining vehicle speed on a hill involves the transfer of potential into thermal

energy. Important considerations are brake temperature, lining fade, brake fluid

vaporization in hydraulic brakes and brake adjustment of air brakes.

Holding a vehicle stationary on a grade with the parking brake is mainly a problem of

force transmission between the application lever and the tire. However, since a parking

brake may be used for vehicle deceleration in an emergency, both thermal and vehicle

dynamic factors must be considered by the design engineer.

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DISC BRAKES

The disc brake is the best brake we have found so far. Disc brakes are used to stop

everything from cars to locomotives and jumbo jets. Disc brakes wear longer, are less

affected by water, are self adjusting, self cleaning, less prone to grabbing or pulling and stop

better than any other system around.

The main components of a disc brake are:

The brake pads

The caliper, which contains a piston

The rotor, which is mounted to the hub

Disc Brake Components

Brake Pads: There are two brake pads on each caliper. They are constructed of a metal

"shoe" with the lining riveted or bonded to it. The pads are mounted in the caliper, one on each

side of the rotor. Brake linings used to be made primarily of asbestos because of its heat

absorbing properties and quiet operation; however, due to health risks, asbestos has been

outlawed, so new materials are now being used.

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Brake pads wear out with use and must be replaced periodically. There are many types and

qualities of pads available. The main differences between these types are brake life (how long

the new pads will last) and noise (how quiet they are when you step on the brake). Harder

linings tend to last longer and stop better under heavy use but they may produce an irritating

squeal when they are applied.

Brake Pads

If the lining wears down until to the metal brake shoe, then there will be a "Metal-to-Metal"

condition where the shoe rubs directly against the rotor causing severe damage and loss of

braking efficiency. Some brake pads come with a "brake warning sensor" that will emit a

squealing noise when the pads are worn to a point where they should be changed. This noise

will usually be heard when your foot is off the brake and disappear when you step on the brake.

If you hear this noise, have your brakes checked as soon as possible.

Calipers: There are two main types of calipers: Floating calipers and fixed calipers. There

are other configurations but these are the most popular. Calipers must be rebuilt or replaced

if they show signs of leaking brake fluid.

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Single piston floating calipers are the most popular and also least costly to manufacture

and service. A floating caliper "floats" or moves in a track in its support so that it can center

itself over the rotor. As you apply brake pressure, the hydraulic fluid pushes in two

directions. It forces the piston against the inner pad which in turn pushes against the rotor. It

also pushes the caliper in the opposite direction against the outer pad, pressing it against the

other side of the rotor. Floating calipers are also available on some vehicles with two pistons

mounted on the same side. Two piston floating calipers are found on more expensive cars

and can provide an improved braking "feel".

Brake Caliper

Four Piston Fixed Calipers are mounted rigidly to the support and are not allowed to

move. Instead, there are two pistons on each side that press the pads against the rotor. Four

piston calipers have a better feel and are more efficient, but are more expensive to produce

and cost more to service. This type of caliper is usually found on more expensive luxury and

high performance cars.

Rotor: The disc rotor is made of iron with highly machined surfaces where the brake

pads contact it. Just as the brake pads wear out over time, the rotor also undergoes some

wear, usually in the form of ridges and groves where the brake pad rubs against it. This wear

pattern exactly matches the wear pattern of the pads as they seat themselves to the rotor.

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When the pads are replaced, the rotor must be machined smooth to allow the new pads

to have an even contact surface to work with. Only a small amount of material can be

machined off of a rotor before it becomes unusable and must be replaced. A minimum

thickness measurement is stamped on every rotor and the technician doing the brake job

will measure the rotor before and after machining it to make sure it does not go below the

legal minimum. If a rotor is cut below the minimum thickness, it will not be able to handle

the high heat that brakes normally generate. This will cause the brakes to "fade," greatly

reducing their effectiveness to a point where you may not be able to stop!

Rotor

DRUM BRAKES

The main reason why drum brakes are still used, is cost. While all vehicles produced

for many years have disk brakes on the front, drum brakes are cheaper to produce for the

rear wheels. The other reason is the parking brake system. On drum brakes, adding a

parking brake is the simple addition of a lever, while on disk brakes, we need a complete

mechanism, in some cases, a complete mechanical drum brake assembly inside the disk

brake rotor! Parking brakes must be a separate system that does not use hydraulics.

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Drum brakes consist of a backing plate, brake shoes, brake drum, wheel cylinder,

return springs and an automatic or self-adjusting system. When you apply the brakes, brake

fluid is forced, under pressure, into the wheel cylinder which, in turn, pushes the brake shoes

into contact with the machined surface on the inside of the Drum. When the pressure is

released, return springs pull the shoes back to their rest position. As the brake linings wear,

the shoes must travel a greater distance to reach the drum. When the distance reaches a

certain point, a self-adjusting mechanism automatically reacts by adjusting the rest position

of the shoes so that they are closer to the drum

Drum Brake Components

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OTHER UNITS

Master Cylinder is located in the engine compartment on the firewall, directly in

front of the driver’s seat. A typical master cylinder is actually two completely separate

master cylinders in one housing, each handling two wheels. This way if one side fails, you will

still be able to stop the car. The brake warning light on the dash will light if either side fails,

alerting you to the problem. Master cylinders have become very reliable and rarely

malfunction (fault); however, the most common problem that they experience is an internal

leak. This will cause the brake pedal to slowly sink to the floor when your foot applies steady

pressure. Letting go of the pedal and immediately stepping on it again brings the pedal back

to normal height.

Master Cylinder

Brake Fluid is special oil that has specific properties. It is designed to withstand cold

temperatures without thickening as well as very high temperatures without boiling. (If the

brake fluid should boil, it will cause you to have a spongy pedal and the car will be hard to

stop.) Brake fluid must meet standards that are set by the Department of Transportation

(DOT). Each standard (DOT-3, DOT-4 vs.) has different boiling point. For instance, DOT-3 has

a dry boiling point 205°C and wet boiling point 140°C.

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The brake fluid reservoir is on top of the master cylinder. Most cars today have a

transparent reservoir so that you can see the level without opening the cover. The brake

fluid level will drop slightly as the brake pads wear. This is a normal condition and no cause

for concern. If the level drops noticeably over a short period of time or goes down to about

two thirds full, brakes should be checked as soon as possible. Brake fluid must maintain a

very high boiling point .Exposure to air will cause the fluid to absorb moisture which will

lower that boiling point.

Brake Lines: The brake fluid travels from the master cylinder to the wheels through a

series of steel tubes and reinforced rubber hoses. Rubber hoses are only used in places that

require flexibility, such as at the front wheels, which move up and down as well as steer. The

rest of the system uses non-corrosive seamless steel tubing with special fittings at all

attachment points. If a steel line requires a repair, the best procedure is to replace the

complete line. If this is not practical, a line can be repaired using special splice fittings that

are made for brake system repair. Usage of the brass “compression” fittings or copper

tubing to repair a brake system is dangerous and illegal.

Proportional Valve: These valves are mounted between the master cylinder and the

rear wheels. They are designed to adjust the pressure between the fronts and rear brakes

depending on how hard you are stopping. The shorter you stop, the more of the vehicle's

weight is transferred to the front wheels, in some cases, causing the rear to lift and the front

to dive. These valves are designed to direct more pressure to the front and less pressure to

the rear the harder you stop. This minimizes the chance of premature lockup at the rear

wheels.

Pressure Differential Valve: This valve is usually mounted just below the master

cylinder and is responsible for turning the brake warning light on when it detects a

malfunction. It measures the pressure from the two sections of the master cylinder and

compares them. Since it is mounted ahead of the proportioning or equalizer valve, the two

pressures it detects should be equal. If it detects a difference, it means that there is probably

a brake fluid leak somewhere in the system.

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Combination valve: It is simply a proportioning valve and a pressure differential valve

that is combined into one unit.

Combination Valve (Sliding Caliper)

The power brake booster is mounted on the firewall directly behind the master

cylinder and, along with the master cylinder, is directly connected with the brake pedal. Its

purpose is to amplify the available foot pressure applied to the brake pedal so that the

amount of foot pressure required to stop even the largest vehicle is minimal. Power for the

booster comes from engine vacuum. The automobile engine produces vacuum as a by-

product of normal operation and is freely available for use in powering accessories such as

the power brake booster. Vacuum enters the booster through a check valve on the booster.

The check valve is connected to the engine with a rubber hose and acts as a one-way valve

that allows vacuum to enter the booster but does not let it escape. The booster is an empty

shell that is divided into two chambers by a rubber diaphragm. There is a valve in the

diaphragm that remains open while your foot is off the brake pedal so that vacuum is

allowed to fill both chambers. When you step on the brake pedal, the valve in the

diaphragm closes, separating the two chambers and another valve opens to allow air in the

chamber on the brake pedal side. This is what provides the power assist.

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Power Brake Booster

Power boosters are very reliable and cause few problems of their own; however,

other things can contribute to a loss of power assist. In order to have power assist, the

engine must be running. If the engine stalls or shuts off while you are driving, you will have a

small reserve of power assist for two or three pedal applications but, after that, the brakes

will be extremely hard to apply and you must put as much pressure as you can to bring the

vehicle to a stop.

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3. DESIGN CALCULATIONS

Total Braking Distance

Total braking distance for the case of the maximum speed of the vehicle is assumed

120 m and to provide that a deceleration value is calculated. The total travelled distance

during braking is calculated by formulas on below;

Where;

Calculations are made in Matlab and the result is;

4.1785 m/s2

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Actuating Force, Braking Torque, Normal Pressure, Effective Radius, Force Location

Material Friction

Coefficient(f)

Maximum

Pressure(Pmax ,MPa)

Max. Instantaneous

Temp.(°C)

Max. Continuous

Temp.(°C)

Rigid

Molded

Asbestos

0.31-0.49

5.2

500-750

230-350

Normal Force to the Pads

Brake Torque

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Equivalent(effective) Radius

Force Location

Where;

ri=inner diameter of the pad

ro=outer diameter of the pad

Ѳ1, Ѳ2=caliper angles

f =friction coefficient

Uniform wear assumption

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Thermal Analysis

Absorbed energy by the brake assembly;

Where;

m=vehicle mass

V1=vehicle maximum speed

k= correction factor of rotating masses and (R=wheel radius) equals to:

Mass of Brake Disc

Where;

ρ=density of the disc material

rdisc =disc radius

t=thickness of the rotor

The temperature rise of the brake assembly

Where;

E=absorbed energy by the brake assembly

Cp=specific heat capacity

m=mass of the brake parts

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Overall coefficient of heat transfer

hCR = hr + fv hc

Where;

hr = radiation component of hCR

hc = convective component of hCR

fv = ventilation factor

Maximum temperature of brake assembly

Tmax = +

Where;

A=Lateral surface area and equals to: A=4 *π* rdisc2

T=disc temperature

=ambient temperature

Tmax- =Temperature Rise

W= mdisc

t1=3600/24=150s (assumption is made according to example 16.5 from Shigley)

At the calculation of the maximum temperature rise for the brake assembly the

equations which are above, were used. According to results (see 4.RESULTS part) maximum

temperature rise is about 135-140 °C which is very below of the critical temperature of the

selected material, and so required conditions for thermal considerations are satisfied.

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4. RESULTS

Notation

h_max: Max. Height of the Vehicle

mu: Coefficient of Friction Between Tires and Road

g: Gravitational Coefficient

f_r: Rolling Resistance Coefficient

i_t_1: First Gear Ratio

i_d: Differential Ratio

NRD: Nominal Rim Diameter

NSW: Nominal Section Width

PHI: Aspect Ratio

K: Dimensionless Constant, 0.96 for Radial Automobile Tires

m_unl: Unladen Mass

gama: Rotating Mass Factor

m_eq_unl: Equivalent Mass

m_pass: Passenger Mass

v_tank: Fuel Tank Volume

ro_RON95: Density of RON95

m_fuel_max: Fuel Mass (Full Tank)

m_lug: Mass of Additional Luggage

m_add: Total Mass of Additional Factors

m_tot: Total Mass

i: Brake Force Distribution Factor

W: Weight of the Vehicle-Laden

dmax: Maximum Deceleration

d: Dimensionless Deceleration

F_f: Front Braking Force

THETA: Caliper Angle Difference

R_w: Tire Rolling Radius

T_bf: Front Braking Torque

T: Braking Torque on One Side of the Wheel

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MU: Coefficient of Friction for Rigid Molded Asbestos Pads

R_r: Rotor Radius for 14 in Rim Diameter

R_o: Outer Radius of Pad

R_i: Inner Radius of Pad

R_eff: Effective Radius

F: Actuating Force

P_a: Largest Normal Pressure

Tot_Area: Total Piston Area

Pis_Area: Allowable Piston Area for Ro-Ri=35 mm

Pis_Num: Piston Number

k: Correction Factor for Rotating Masses

V1: Initial Velocity

m: Laden Mass of Vehicle

Eb: Energy Absorbed by Brake

ro_disc: Density of Disc Material

R_disc: Radius of Brake Disc

t: Thickness of Brake Disc

m_disc: Mass of the Brake Disc

Cp: Specific Heat Capacity

delta_T: Temperature Rise

Tamb: Temperature of Ambient

t1: Brake was used 24 times per hour

hr: Radiation Component of Heat Transfer Coefficient

hc: Convective Component of Heat Transfer Coefficient

MAS: Mean Air Speed

fv: Multiplying Factor

hcr: Overall Heat Transfer Coefficient

A: Lateral Surface Area

Tmax: Maximum Temperature

Temp_Rise: Calculated Temperature Rise

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Matlab Output

-Total Braking Distance and Maximum Deceleration

dmax =4.1785

dtot =120.0011

We made our calculations according to dmax=4.0000

-Actuating Force, Braking Torque, Normal Pressure, Equivalent Radius, Force Location

(Output data is tabulated)

Assumptions:

P_hyd= 9000 kPa

Piston Number =2

R_o=R_r(rotor)-20 mm

R_o – R_i = 35 mm

Theta =600

R(rotor) (mm)

R(outer) (mm)

R(inner) (mm)

R(effective) (mm)

Fd (N) F(normal) (N)

Pa (MPa)

Piston Area

(mm^2)

# of Piston

Piston Radii (mm)

122.5 102.5 67.5 85 6425.4 8031.8 1.9479 446.2103 2 11.9178

125 105 70 87.5 6241.8 7802.3 1.8246 433.4615 2 11.7463

127.5 107.5 72.5 90 6068.5 7585.6 1.7128 421.4209 2 11.5820

130 110 75 92.5 5904.4 7380.6 1.6110 410.0311 2 11.4244

132.5 112.5 77.5 95 5749.1 7186.3 1.5180 399.2408 2 11.2731

135 115 80 97.5 5601.7 7002.1 1.4328 389.0039 2 11.1276

We decided to use red colored dimensions and values.

-Thermal Considerations, Temperature Rise

m_tot =1.5353e+003

F_f = 4.1151e+003

R_w =265.4400

T_bf =546.1615

T =273.0807

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k =1.1500

V1 =26.3889

m = 1.5353e+003

Eb = 6.1475e+005

ro_disc = 7800

R_disc = 130

t = 30

m_disc =12.4237

Cp =500

delta_T =98.9630

Tamb = 25

t1 = 150

hcr = 53.6000

A =0.2124

W = 12.4237

beta =0.0018

Tmax = 155.2711

Temp_Rise =130.2711

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5. DISCUSSION

This project presents the outline of the front brake design for Norster 600R. It is

concluded that hydraulic brake system in all car are same with little different in components

structure like pad materials and rotor material. The researches on brake pad materials

stated that commercial composition of the pad cannot be concluded whether is preferable

to contain organic or semi metallic brake pads contain more copper. Both organic and semi-

metallic may contain copper although specific amounts will depend on the manufacturer.

Found that contact areas also increase as wear develops. This corresponds to the reduction

of roughness values of the pad surface.

For the dimensions of the brake system components general assumptions are made

according to Brake Design and Safety (R.Limpert).The most important criteria for the rotor

and inherently for the other parts is the rim diameter of the wheel. Reducing the rotor width

and a ventilated design achieve reduce in weight and also improvement of cooling

characteristics.

After the specifications of the dimensions of the brake assembly parts, actuating

force, braking torque, equivalent radius and force location values were calculated and there

is no critical values are observed for the selected material. And then, thermal analysis was

done for the brake system and the maximum temperature rise in case of a hard braking

condition was calculated. Results show that, there is no risk of overheating and possibility of

hazardous condition with respect to material properties.

Finally, engineering drawings were made by using Catia for the parts which were

designed. In engineering drawing, was not entered into details and the other parts such as

bolts, pistons etc. were not shown. Drawings of the main components which are rotor,

caliper and pads were done and general dimensions of the part were indicated in the

drawings.

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6. APPENDIX

Matlab Input Codes

-Total Braking Distance and Maximum Deceleration

tr=1.2; %reaction time ta=0.1; %application time tb=0.18; %deceleration rise vo=95/3.6; %max. velocity dt=120; %total braking distance

dtot=0; dmax=10.0; %dmax(max. deceleration) when total braking distance=120 m

while(dtot<120) d1=vo*(tr+ta); d2=vo*tb-(dmax/6)*(tb^2); d3=(vo^2)/(2*dmax)-vo*tb/2+dmax*(tb^2)/8; dtot=d1+d2+d3; %total braking distance dmax=dmax-0.0001; end

% dmax and corresponding total braking distance dmax dtot

-Actuating Force, Braking Torque, Normal Pressure, Equivalent Radius, Force Location

h_max = 1.4; %[m] Max. Height of the Vehicle(ASSUMPTION) mu = 0.85; %[] Coefficient of Friction Between Tires and Road(ASSUMPTION) g = 9.81; %[m/s^2] Gravitational Coefficient f_r = 0.055; %[] Rolling Resistance Coefficient(ASSUMPTION) i_t_1 = 3.818; %[] First Gear Ratio i_d = 4.412; %[] Differential Ratio NRD=14*24.5; %[mm] Nominal Rim Diameter NSW=175; %[mm] Nominal Section Width PHI=0.60; %[] Aspect Ratio K=0.96; %[] Dimensionless Constant,0.96 for Radial Automobile Tires m_unl = 532; %[kg] Unladen Mass gama = 1.03+0.0016*(i_t_1*i_d)^2; %[] Rotating Mass Factor(ASSUMPTION) m_eq_unl = m_unl*(1+gama); %[] Equivalent Mass m_pass = 80*2; %[kg] Passenger Masw(95%Percentile(ASSUMPTION) v_tank = 32; %[l] Fuel Tank Volume ro_RON95 = 0.7431; %[kg/l] Density of RON95 [THUMMADETSAK] m_fuel_max = v_tank*ro_RON95; %[kg] Fuel Mass (Full Tank)(ASSUMPTION) m_lug = 30; %[kg] Mass of Additional Luggage(ASSUMPTION) m_add = m_pass+m_fuel_max+m_lug; %[kg] Tot.Mass of Add. Factors(ASSUMPTION) m_tot=m_eq_unl+m_add; %[kg] Total Mass i=0.6701; %[] Brake Force Distribution Factor W=m_tot*g; %[N] Weight of the Vehicle-Laden dmax=-4; %[m/s^2] Maximum Deceleration d=-(dmax/g); %[] Dimensionless Deceleration F_f=i*W*d %[N] Front Braking Force THETA=60*pi/180; %[rad] Caliper Angle Difference R_w=K*((NRD/2)+PHI*NSW) %[mm] Tire Rolling Radius

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T_bf=(F_f*R_w/1000)/2 %[Nm] Front Braking Torque T=T_bf/2 %[Nm] Braking Torque on One Side of the Wheel MU=0.40; %[]Coefficient of Friction for Rigid Molded Asbestos Pads

(ASSUMPTION) for 0.31-0.49

for R_r=122.5:2.5:135 %[mm] Rotor Radius for 14 in Rim Diameter R_o=R_r-20 %[mm] Outer Radius of Pad! 20mm(ASSUMPTION) R_i=R_o-35 %[mm] Inner Radius of Pad! 40mm(ASSUMPTION) R_eff=(R_o+R_i)/2 %[mm] Effective Radius F_d=(2*T)/(R_eff/1000) %[N] F=T/(MU*(R_eff/1000)) %[N] Actuating Force P_a=F/(THETA*(R_o-R_i)*R_i) %[MPa] Largest Normal Pressure P_hyd=9000*10^3 %[Pa] Hydraulic Pressure Pis_Num=2 %[] Piston Number Tot_Area=(F/P_hyd)*10^6 %[mm^2] Total Piston Area Pis_Area=Tot_Area/2 %[mm^2] Allowable Piston Area for Ro-Ri=35 mm R_pis=sqrt(Pis_Area/pi) %[mm] Piston Radius end

-Thermal Considerations, Temperature Rise (rest part of the code)

%% Thermal Analysis k=1.15 %[] Correction Factor for Rotating Masses (Assumption)(1.05-1.15

for passenger cars in high gears) V1=95/3.6 %[m/s] Initial Velocity m=m_tot %[kg] Laden Mass of Vehicle Eb=(k*m*V1^2)/2 %[J] Energy Absorbed by Brake ro_disc=7800 %[kg/m^3] Density of Disc Mat.(Steel(Assumption(7750-8050) R_disc=130 %[mm] Radius of Brake Disc (Assumption) t=30 %[mm] Thickness of Brake Disc (Assumption)(Minimum value

of the thickness is 28.1mm for ventilation brakes)

m_disc=ro_disc*pi*R_disc^2*t*10^-9 %[kg] Mass of the Brake Disc Cp=500 %[J/kg*C] Specific Heat Capacity delta_T=Eb/(m_disc*Cp) %[C] Temperature Rise Tamb=25 %[C] Temperature of Ambient

%% Tmax-Tamb=300 %[C] First Assumption for Temperature Rise t1=60^2/24; %[s] Brake was used 24 times per hour (Assumption) hr=27.5; %[W/m^2*C] Radiation Component of Heat Transfer

Coefficient(Shigley Figure 16.24a) hc=7.5; %[W/m^2*C] Convective Component of Heat Transfer

Coefficient(Shigley Figure 16.24a) MAS=12; %[m/s] Mean Air Speed !!!Assumption fv=6; %[] Multiplying Factor(Shigley Figure 16.24b) hcr=hr+fv*hc; %[W/m^2*C] Overall Heat Transfer Coefficient A=4*pi*R_disc^2*10^-6; %[m^2] Lateral Surface Area W=m_disc; %[kg] Mass of the Brake Disc beta=(hcr*A)/(W*Cp); %[1/s] Tmax=Tamb+(delta_T/exp(-beta*t1)); %[C] Maximum Temperature Temp_Rise=Tmax-Tamb; %[C] Calculated Temperature Rise % First Assumption is not valid

%% Tmax-Tamb=143.5295 %[C] Second Assumption for Temperature Rise t1=60^2/24; %[s] Brake was used 24 times per hour (Assumption) hr=12; %[W/m^2*C] Radiation Component of Heat Transfer

Coefficient(Shigley Figure 16.24a)

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hc=7.2; %[W/m^2*C] Convective Component of Heat Transfer

Coefficient(Shigley Figure 16.24a) MAS=12; %[m/s] Mean Air Speed (Assumption)(Shigley Example 16.5) fv=6; %[] Multiplying Factor(Shigley Figure 16.24b) hcr=hr+fv*hc; %[W/m^2*C] Overall Heat Transfer Coefficient A=4*pi*R_disc^2*10^-6; %[m^2] Lateral Surface Area W=m_disc; %[kg] Mass of the Brake Disc beta=(hcr*A)/(W*Cp); %[1/s] Tmax=Tamb+(delta_T/exp(-beta*t1)); %[C] Maximum Temperature Temp_Rise=Tmax-Tamb; %[C] Calculated Temperature Rise %Second Assumption is not valid

%% Tmax-Tamb=131.3444 %[C] Third Assumption for Temperature Rise t1=60^2/24; %[s] Brake was used 24 times per hour(Assumption) hr=11.1; %[W/m^2*C] Radiation Component of Heat Transfer

Coefficient(Shigley Figure 16.24a) hc=7.1; %[W/m^2*C] Convective Component of Heat Transfer

Coefficient(Shigley Figure 16.24a) MAS=12; %[m/s] Mean Air Speed (Assumption)(Shigley Example 16.5) fv=6; %[] Multiplying Factor(Shigley Figure 16.24b) hcr=hr+fv*hc; %[W/m^2*C] Overall Heat Transfer Coefficient A=4*pi*R_disc^2*10^-6; %[m^2] Lateral Surface Area W=m_disc; %[kg] Mass of the Brake Disc beta=(hcr*A)/(W*Cp); %[1/s] Tmax=Tamb+(delta_T/exp(-beta*t1)); %[C] Maximum Temperature Temp_Rise=Tmax-Tamb; %[C] Calculated Temperature Rise %Third Assumption is not valid

%% Tmax-Tamb=130.3379 %[C] Fourth Assumption for Temperature Rise t1=60^2/24 %[s] Brake was used 24 times per hour(Assumption) hr=11; %[W/m^2*C] Radiation Component of Heat Transfer

Coefficient(Shigley Figure 16.24a) hc=7.1; %[W/m^2*C] Convective Component of Heat Transfer

Coefficient(Shigley Figure 16.24a) MAS=12; %[m/s] Mean Air Speed !!!Assumption(Shigley Example 16.5) fv=6; %[] Multiplying Factor(Shigley Figure 16.24b) hcr=hr+fv*hc %[W/m^2*C] Overall Heat Transfer Coefficient A=4*pi*R_disc^2*10^-6 %[m^2] Lateral Surface Area W=m_disc %[kg] Mass of the Brake Disc beta=(hcr*A)/(W*Cp) %[1/s] Tmax=Tamb+(delta_T/exp(-beta*t1)) %[C] Maximum Temperature Temp_Rise=Tmax-Tamb %[C] Calculated Temperature Rise %Fourth Assumption is valid because the assumption and the calculated

temperature rise is close enough to each other. %Actual temperature rise=130.2711

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7. REFERENCES

Shigley's Mechanical Engineering Design 8th Edition (R.G.Budynas, J.K.Nisbett)

Brake Design and Safety 2nd Edition (Rudolf Limpert)

OMÜ-332 Lecture Notes

Performance of Road Vehicles (Prof. Dr. Y.Samim Ünlüsoy)

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CAT DRAWINGS

Disc

Caliper

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Brake Pad

Brake Assembly