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Scott Kuznarsky
17 April 2011
Honors Senior Design
SAE Formula Hybrid
Brake and Brake Pedal Design
Abstract
The design goals of the brake team for the SAE Formula Hybrid car was to be able to
have the capability of locking all four wheels and stopping the vehicle in a straight line. Also we
wanted to make the brake pedals adjustable for different drivers and stop the car from maximum
speed in less than five seconds. For this the team, with the help of Dr. Gross, read and
understood the vast equations and concepts that govern the braking systems of moving vehicles.
Using these equations and the knowledge learned in the classroom, one could find out the forces
required to stop the car and design the brake system around these calculated forces. Rotors,
calipers, master cylinders, brake pedals, gas pedals, and other braking components were designed
to fit the needs of the car. The following report will briefly cover the overall design of the brake
system and then go into detail about pedal design and pedal assembly, the part of the project that
I designed for my senior honors project.
Introduction
Today the automotive industry is looking to expand its horizons and discover new ways
to propel cars. In the past few years there have been numerous technological advancements in the
area of alternative fuels for cars. One such advancement comes in the form of a car that runs on
gas as well as electricity; a hybrid car. The University of Akron has started to contribute to this
research and joined a competition for the cause, the SAE Formula Hybrid Car. The goal of the
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team is to design a car that runs solely on an electric motor, eliminating the need for gas. For this
project I chose to be a part of the brake team; our objective is to design and build the brakes and
brake system that can stop the car.
Design Criteria
When one starts a design for a product the first thing that needs to be understood are the
goals and the design criteria that needs to be met. The team members of the SAE Formula
Hybrid brake team decided to use the rules outlined in the SAE Formula Hybrid Competition as
the initial design criteria and set a few goals to meet our own challenges. The following are the
required rules for the braking system of the car per Formula SAE rules:
1. The brake system must be capable of locking all four (4) wheels during the test specified.
2. If a regenerative brake system is used, up to the first 50% of brake pedal travel may be
dedicated to activating regenerative or other advanced braking systems, but the remaining
travel must mechanically activate the hydraulic system. Regenerative braking may
continue into the latter portion of the pedal travel.
3. Unarmored plastic brake lines are prohibited.
4. The braking systems must be protected with scatter shields from failure of the drive train
or from minor collisions.
5. The brake system will be dynamically tested and must demonstrate the capability of
locking all four (4) wheels and stopping the vehicle in a straight line at the end of an
acceleration run specified by the brake inspectors.
6. Brake over-travel switch must be installed on the car. This switch must be installed so
that in the event of brake system failure such that the brake pedal over travels, the switch
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will be activated and must shut down all drive systems and must trip the accumulator
isolation relays.
These rules were used as a base line for the goals of the brake team. The team goals set for the
design were as follows:
1. Brakes can stop the car from full speed to zero in five (5) seconds.
2. Design the pedals so that they can be adjusted to different size drivers.
3. Pedal assembly designed to withstand 2000 N of force.
4. Brake pedal designed so that only 67 lbs of force is needed to apply the brakes.
5. Brake pedal travel is only 4 inches.
These goals provided the team with a sense of worth and an achievement to strive for. Once the
goals were set, the design stage was able to be started.
Design
In order to start the design of the brake system the weight of the vehicle needs to be
known. To begin the design, each team estimated the weight of the components that they would
use. Once the estimations were made, the brake team had an estimated total weight for the car
and the brakes could be designed. For this the brake team utilized some literature on brake
design that was provided by our advisor. First, the team calculated the effective mass of the
vehicle during the application of the brakes. When the brakes are applied load transfer occurs;
this means that more weight is on the front of the car than on the back because of the
deceleration force. Then, using the help of an excel spreadsheet, the brake forces required on the
front and rear tires could be calculated. Once these forces were known, the team decided to
design the rotors, calipers and the master cylinders needed to apply this force. After these
components were designed, the pedals and pedal assembly could be designed.
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Using the knowledge gained in the classroom and some references provided by Dr.
Gross, the concept of a brake system was understood. After reading chapter 8 of a provided
handout titled “Disc Brake System with Two Master Cylinders” the pedal system could be
designed. For the pedal system, the main components that needed to be designed were the brake
pedal, accelerator pedal, balance bar, and brake over-travel switch. Also, another important
aspect of the design was to incorporate the pedal system to make it fit within the frame of the car
and also have the capability to be adjusted; fitting drivers of different height.
Before the brake pedal can be designed one needs to understand how the brake pedal
works with the master cylinders and the entire braking systems. The figures below shows a
schematic of how the brake pedal and the brake components interact.
Figure 1: Brake Pedal with Brake System
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Figure 2: Brake Pedal with two views
From the figure, a and b are the distance from the pivot point to the end of the pedal and master
cylinder connection respectively. Also, in the second figure, one can see how the balance bar of
the brake system works. The balance bar dictates how much force is applied to each master
cylinder; in turn the brake force given to each set of tires. The ratio of a over b is known as the
mechanical advantage and this is calculated from the following equations:
(1)
(2)
(3)
(4)
(5)
*Note: all terms are defined in Figure 3*
From the earlier design stages a few quantities are known and this allows one to solve for the
needed quantities in order to design the brake pedal and pedal system. First equation (1), the
pressure in the front brake lines, and equation (2), the pressure in the rear brake lines can be
solved for because all of the quantities in those equations are known values. After these
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quantities were calculated, equations (3) and (4) could now be solved for; the force on the front
master cylinder and the force on the rear master cylinder respectively. Then assuming all the
quantities in equation (5) are known from previous design choices and known values, the
mechanical advantage is found. However, before the pedal is designed with this mechanical
advantage, a few more calculations had to be made that checked whether or not the mechanical
advantage was acceptable for the design. To do this the travel relationships are checked by
making sure that the following equations hold true:
(6)
(7)
(8)
Equation (6) and equation (7) are equations that check the displaced volume of the front master
cylinder and the rear master cylinder respectively, and the displaced volume of the calipers. If
these two equations were not satisfied, then adjustments to the design were made by choosing
different sized master cylinders. Finally equation (8) was used to confirm that the pedal travel or
foot travel was acceptable. Again, if the inequality was not satisfied corrections to the design
were made until the relationship held true. To perform these calculations an excel spread sheet
was compiled. This spreadsheet allowed for quick changes in the values which would make the
design process much easier. Also, to check the values entered in the initial spreadsheet, hand
calculations were made to confirm the correctness of the spreadsheet that was created. The
following figure shows the spreadsheet that was created to produce the desired design values.
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For two master cylinders:
The Following Quantities Are Assumed Known
Quantity
Symbol
Normal Force - Front
Normal Force - Rear
Coefficient of Tire friction
Coefficient of Brake Friction
Coefficient of Caliper Friction
Maximum Foot Force
Radius of Front Tire
Radius of Rear Tire
Area of Front Master Cylinder
Area of Rear Master Cylinder
Area of Front Caliper
Area of Rear Caliper
Radius of Front Caliper
Radius of Rear Caliper
Travel of Front Caliper
Travel of Rear Caliper
Maximum Foot Travel
Front Master Cylinder Travel
Rear Master Cylinder Travel
Value
Units
FNF
781.25 lbs
FNR
218.75 lbs
μtire
2.25
μbrak
2
μCP
0.5
(Ff oot )MAX
67
lbs
RFT
10
in
RRT
10
in
AFMC
0.306796 in2
ARMC 0.306796 in2
in2
AFCP
4.8
in2
ARCP
2.4
RFCP
4
in
RRCP
3.69 in
SFCP
0.0200 in
SRCP
0.02 in
(Sf oot )MAX
4
in
SFMC
1.3
in
SRMC
1.3
in
H/L (height COG over Length car)
H/L
0.125
Hydraulic fluid (gage) pressure in front brake lines
and front MC
PFF =
406.901 psi
Hydraulic fluid (gage) pressure in rear brake lines
and rear MC
PFR =
247.0077 psi
Force on front master cylinder
Force on rear master cylinder
FFMC =
FRMC =
124.8357 lb
75.78101 lb
Mechanical Advantage (a/b)
M = (a/b) 2.994279
Check to see if Eqn 33 and 39 hold:
AFMC * SFMC > 4*AFCP*SFCP
SRMC * ARMC > 4*ARCP*SRCP
0.398835
0.398835
>
>
0.384
0.192
4
>
3.892563
Sf oot > a/b * (LF *SRMC +LR *SFMC )/(LF +LR )
Guesses for LF and LR
FFCP=
FFRP=
Braking Force (Normal Forces x Tire Coefficient of
Friction x Safety Factor of 1.5)
F total from calcs
LF =
LR =
4 in.
2 in.
3906.25 lbs
1185.637 lbs
3000
5091.887
Figure 3: Excel Spreadsheet for Design Calculations
After all of the equations were satisfied and to the discretion of the brake team, the next
step in the process was to design a brake pedal that would meet the required criteria of the
calculations; that is to have a mechanical advantage of three. In order to save time and money,
the team felt it was in the best interest to select and order a brake pedal from a supplier; in this
case Wilwood Racing. The particular brake pedal that was ordered had a larger mechanical
advantage than the design required but the team decided to adjust the mechanical advantage upon
installation. Also, this particular pedal has a balance bar built in that can be adjusted so that the
brake force for the front and the rear of the car can be adjusted. The accelerator pedal was also
ordered from Wilwood Racing because it would save time and money in the overall design of the
car. The following figures show a drawing of the brake pedal and accelerator pedal that was
ordered. Also, the brake over travel switch needed to be installed somewhere on the brakes that
would shut off they system if the brake pedal traveled too far. For this the team decided to use a
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simple toggle switch that would be mounted on the brake pedal mount. When the pedal travels
far enough, it will mechanically flip the toggle switch, cutting off the system.
Figure 4: Accelerator and Brake Pedal
After the pedals were ordered, there was another requirement of the design that needed to
be fulfilled; the layout of the pedal system. Knowing that the car would not be covered with a
shell, the brake team had to come up with a platform to mount the brake, accelerator pedal,
accelerator, master cylinders, and brake over travel switch. This platform would act as the floor
for the car and needed to withstand the forces applied by the driver. When designing the platform
the following constraints were considered:
1. The dimensions of the frame where the driver’s feet sat.
2. The dimensions of the brake components.
3. Overall comfort of the driver.
4. Pedal assembly be able to withstand 2000 N of force.
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The platform had to be small enough to fit within the cockpit of the frame and large enough to
mount all of the brake components. Also, the plate had to be installed so that the driver would be
comfortable when driving the car; it was also desired, from the earlier goals, that the brake
pedals be adjustable.
In order to complete this design, a ¼ in thick aluminum plate was chosen to be the
mounting plate for the brake components. This material was chosen because of its high strength
properties and its light weight. However, this aluminum plate couldn’t just be mounted directly
to the frame; to accomplish this part of the design two long and narrow steel strips were used.
The steel that was used was ¼ inch thick and 1 ½ inches wide and cut to two feet in length.
These steel strips would be mounted via welds parallel on either side of the driver in the cockpit
where the driver’s feet were located. Each steel strip was designed so that it had eight holes in it
which the aluminum plate could be mounted on. The amount of holes in the aluminum and steel
made it possible so that the whole aluminum mounting plate could be slid forward or back in the
cockpit; allowing the pedals to be adjusted for different drivers. The following figure shows the
complete pedal assembly modeled in SolidWorks. This model was inserted into the model of the
frame that was provided by the frame team to ensure the pedal assembly would fit.
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Figure 5: Model of Brake Pedal Assembly
This model allowed the team to get an idea of how the pedal system would fit within the car.
After it was determined that the assembly would fit, the components could be machined and
assembled. Also, other concerns that needed to be addressed were the placement of the brake
over travel switch and the heel supports for the driver. It was decided upon production that the
team would come up with the best idea for heel supports that would add to the comfort of the
driver. The team members agreed that the best way to do this would to install a strip of
aluminum that would run across the front edge of the aluminum plate. This would allow the
driver’s heel to rest up against something so that he would feel less fatigue in his leg muscles
during the competition.
In order to see if the pedal brake pedal could withstand 2000 N of force, the team used
their knowledge gained in the class “Analysis of Mechanical Components” and the textbook
“Shigley’s Mechanical Engineering Design.” Using the following equations and assuming that
the pedal behaved like a cantilever beam with a 2000 N (450 lbs) force on the end, the strength
of the pedal was verified.
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(9)
(10)
(11)
(12)
From this calculation, the max stress that occurs because of the force on the pedal was found to
be 7.232 kpsi. After looking up the mechanical properties of the aluminum pedal, the ultimate
tensile strength was 47 kpsi. Since the max stress calculated in the pedal is less than that of the
tensile strength, it can be concluded that for an emergency stop, the pedal can with stand the
2000 N of force.
Also, before attaching the steel strips to the chassis, an analysis of the weld process was
performed. The weld had to be strong enough in order to withstand 2000 N of force that the
driver could potentially exert on the pedal assembly. Using “Shigley’s Mechanical Engineering
Design” 8th edition text book one could find out whether or not the weld would hold up. The
equations in chapter nine were followed and the following equations were used:
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
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Using these equations and knowing the dimensions of the weld along with a force of 450 lbs
(2000 N), the shear force was calculated to be 3.82 kpsi. This assumes that there are six one inch
welds along the side of the steel strips. Then this value was compared to values of the
allowables, 18.6 kpsi allowable in the weld and 22.8 kpsi allowable in the steel strip. Since the
shear force generated is less than both allowables, the weld is safe and will withstand the 2000 N
of force.
Production
With this, all of the design aspects of the brakes were completed; the next step was to
machine any parts that were not purchased and to mount all of the components in the car. Using
the machine shop in the basement of Auburn Science and Engineering Building, the team used
aluminum and steel that was donated by an employer of a member of the team to manufacture
the mounting plate and strips. The other components of the brakes that were machined were the
four brake rotors. The rotors were machined using the vertical ban saw and the lathe in the
machine shop. All other components were ordered from various suppliers.
Conclusion
After all of the parts were machined, the components could be mounted and assembled to
the car. Using the drawings and help from other groups, the brakes were installed in the Formula
Hybrid Car. This whole process was a great experience that allowed us to use our ingenuity and
apply skills and knowledge learned in the classroom to design and build a brake system for a car.
The true test of the system and the car will come during the competition during finals week May
1st through the 7th. However, the team was informed that because of issues that arose during
production and other issues that were out of the team’s hands, we will not be able to go to
competition. This may deter the team but the new goal is to have a working rolling chassis by the
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end of the semester. Overall the experience of designing the brake pedal system required a lot of
critical thinking and ingenuity
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Bibliography
Budynas, R., & Nisbett, K. Shigley’s Mechanical Engineering Design. 8th ed. New York:
McGraw-Hill Science, 2006..
Disc Brake System with Two Master Cylinders. Provided by Dr. Gross. 2010.
*Note: Hand calculations can be found in the appendix of SAE Formula Hybrid Complete
Design Report.