brakes
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Transcript of brakes
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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