2012 University of Cincinnati baja race team brake system
Transcript of 2012 University of Cincinnati baja race team brake system
2012 University of Cincinnati SAE Baja
Race Team Brake System
A thesis submitted to the
Faculty of the Mechanical Engineering Technology Program
of the University of Cincinnati
in partial fulfillment of the
requirements for the degree of
Bachelor of Science
in Mechanical Engineering Technology
at the College of Engineering & Applied Science
by
MARK SCHMIDT
Bachelor of Science University of Cincinnati
May 2012
Faculty Advisor: Allen Arthur
Abstract
The following report covers the brake system design of the 2012 University of Cincinnati
Baja SAE car. It covers research into similar products, design of components, budget,
timeline, proof of design and testing. This report is submitted for senior capstone project for
degree in Mechanical Engineering Technology.
Baja Braking System Mark Schmidt
Table of Contents
Introduction ..................................................................................................................................... 1
From the Manager ........................................................................................................................... 1
Problem Statement .......................................................................................................................... 3
Alternatives ..................................................................................................................................... 3
Proposal........................................................................................................................................... 3
Customer Needs .............................................................................................................................. 5
Research and Existing Products ...................................................................................................... 5
Pedal Setup .................................................................................................................................. 5
Master Cylinders ......................................................................................................................... 6
Biasing ......................................................................................................................................... 7
Product Objectives and Features ..................................................................................................... 8
Design ............................................................................................................................................. 9
Pedal Setup .................................................................................................................................. 9
Solidworks ............................................................................................................................... 9
Stress Calculations ................................................................................................................. 10
Finite Element Analysis......................................................................................................... 12
Hydraulics Calculations ............................................................................................................ 14
Purchased Components.......................................................................................................... 16
Fabrication and Assembly............................................................................................................. 16
Proof of Design ............................................................................................................................. 17
Testing Results .............................................................................................................................. 17
Project Management ..................................................................................................................... 18
Schedule .................................................................................................................................... 18
Budget ....................................................................................................................................... 18
Conclusion and Recommendations ............................................................................................... 18
References ..................................................................................................................................... 19
Appendix A- Research .................................................................................................... Appendix A
Appendix B- Part Drawings ............................................................................................ Appendix B
Bill of Material ................................................................................................................ Appendix B
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Appendix C- Calculations ................................................................................................ Appendix C
Hydraulics Calculations .............................................................................................. Appendix C
Force Calculations on Pedal ........................................................................................ Appendix C
Appendix D- Schedule ..................................................................................................... Appendix D
Appendix E- Budget ......................................................................................................... Appendix E
List of Figures
Figure 1 2011 Brake Pedal Setup.................................................................................................... 4
Figure 2 2011 Inboard Rear Brakes ................................................................................................ 4
Figure 3 Wilwood Pedal Setup ....................................................................................................... 6
Figure 4 Single Master Cylinder ..................................................................................................... 6
Figure 5 Dual Master Cylinder ....................................................................................................... 7
Figure 6 Balance Bar ...................................................................................................................... 8
Figure 7 Pedal Concept 1 ................................................................................................................ 9
Figure 8 Pedal Concept 2 .............................................................................................................. 10
Figure 9 Loading Conditions ........................................................................................................ 11
Figure 10 Shear Diagram .............................................................................................................. 11
Figure 11 Moment Diagram.......................................................................................................... 11
Figure 12 Pedal Loading Conditions ............................................................................................ 12
Figure 13 Pedal FEA Results ........................................................................................................ 13
Figure 14 Base Loading Conditions ............................................................................................. 13
Figure 15 Base FEA Results ......................................................................................................... 14
Figure 16 Hydraulic Calculations Constants ................................................................................ 15
Figure 17 Hydraulic Calculations Results .................................................................................... 15
Figure 18 Required Machined Parts ............................................................................................. 16
Figure 19 Finished Assembly ....................................................................................................... 17
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Introduction
Every year the Society of American Engineers (SAE) has an intercollegiate competition that puts
colleges against each other in a design and race competition to see who can build the best mini
baja vehicle. The colleges compete against one another in design, build, test, promotion, and a
race event. Colleges and Universities also need to raise the money needed to build the vehicles.
These vehicles all share the same 10 horsepower Briggs and Stratton four cycle motor. It is up to
each college to build off of that motor a vehicle that will endure some of the harshest tests and
courses designed to break anything that attempts them. This competition allows the students to
test what they have learned from the classroom into the real world.
The 2011 SAE Baja Racing team designed and engineered a great car that they took to
competition in the spring of 2011. They had to overcome some major obstacles along the way
but finished strong with a three member team. The competition took a toll on the vehicle and
these issues need to be addressed for the 2012 season. One of the key issues with the 2011
vehicle is weight. The vehicle is about 75-100 pounds too heavy. In order to have a chance at
the competition the cars need to be under 500 lbs. The lighter the car is, the faster it will be and
less stress on the components. Another issue is the inadequacy of the braking system. At the
competition, it took the team four or more tries and many adjustments to pass the brake test.
The following report will cover the braking system of the car. It will focus on making the
braking system more effective, more ergonomic for the driver, as well as making it easily
adjustable. The report will contain calculations for a new pedal setup, and fluids calculations for
the hydraulic braking system. In addition, FEA results will be displayed, and proof of design
showed of the system.
From the Manager
The 2012 team consists of 4 Mechanical Engineering Technology seniors that are determined to
set out and improve on last year's results at the SAE competition. In order to perform this goal
each senior chose one aspect of the old car that they will re-design, re-engineer, and build to
make it a success on the new car. The front suspension and steering of the car needs to be re-
worked to eliminate bump steer. This will be handled by Jeremy Jacobs, who is also managing
the team. A new drive line from the engine to the rear axle as well as lowering the overall center
of gravity is being engineered by Rob Faust. Mike Ratliff will design a new frame that will be
lighter and stronger than last year. Finally, Mark Schmidt will properly design a new brake set
up from the pedal to the wheels, including outboard brakes. The 2012 SAE competition will be a
nice proving ground to ensure these 4 seniors are ready for the real world and real applications.
Not only are these four seniors leading the project, but the overall team has grown to 15
members, including 3 juniors and 2 sophomores who also had projects on the car. The
contribution of everyone on the team and the leadership of the seniors fielded a car that placed
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39th
out of 103 other colleges and universities in the Baja SAE competition on April 18-21st in
Auburn, Al. This was the best finish for any UC team to date. The largest improvement was in
design and maneuverability. The placement finishes are below.
Baja Bearcats Competition Placement
Design 31st
Acceleration 59th
Maneuverability 11th
Suspension 57th
Hill Climb 40th
Endurance Race 37th
Overall 39th
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Problem Statement
The current car is setup with a hydraulic braking system to effectively stop the car. However, this
braking system was proven to be inadequate (especially in the rear wheels) as evidenced by
multiple tries and adjustments to pass the brake test at the previous competition. The system
required too large of a driver input, and too much time to make any adjustments to the system,
such as biasing.
A new braking system from the pedals to the wheels will be designed and implemented to better
perform at the 2012 SAE competition.
Alternatives
1. New easily adjustable pedal setup (top or bottom mount) with single master cylinder, inboard
brakes.
2. New easily adjustable pedal setup (top or bottom mount) with dual master cylinders, inboard
brakes.
3. New easily adjustable pedal setup (top or bottom mount) with single master cylinder,
outboard brakes.
4. New easily adjustable pedal setup (top or bottom mount) with dual master cylinders,
outboard brakes.
Proposal
Looking further into the braking system on the 2011 car, it was seen that there was not enough
mechanical advantage in the system to be effective and ergonomic for a driver during a four hour
endurance race. Mechanical advantage is created two ways in a breaking system. One is through
the pedal in something called the pedal ratio (essentially a force multiplier leverage ratio), and
the other is through the sizing of master cylinders, creating hydraulic pressure.
Another problem with the car was that it took too long, and too many tools to make any sort of
adjustments to the system, especially changing the bias from front to rear. In a race setting, time
is off the essence, and teams need to be able to make fast adjustments. Below is an image
showing the setup of the brake pedal and master cylinders on the 2011 car.
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Figure 1 2011 Brake Pedal Setup
A final problem with the current brake system setup is the inboard brakes in the rear. Because of
the differential setup, the inboard brakes are not very effective during braking. The 2011 team
had the most trouble getting the rear wheels to lock up. Figure 2 shows the current inboard setup
in the rear.
Figure 2 2011 Inboard Rear Brakes
From talking to previous years’ teams, since the differential is an open differential, under
braking, the differential would torque back and forth and would actually be counterproductive
under braking. Having the brakes on the axles also creates more stress on the axles. By moving
brakes to the wheels, it puts the braking power directly to the ground, as well as allowing for axle
redesign in the form of shortening the axles and possibly making them lighter.
In order to solve the problems of the braking system, it is proposed that there is a total revamp of
the system. A new pedal setup will be designed with a larger pedal ratio. This setup will be easily
Bias adjusted by moving
spacers around
Pedal with 5:1 ratio
Brake
s
Differential
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adjustable, minimizing the time and tools needed. Also, to achieve the correct braking pressures
with minimal driver input, master cylinders will be sized correctly. Finally, the inboard brakes on
the axles of the 2011 car will be moved outboard to the wheels. This will place the braking
forces closer to the wheels, as well as taking space out of the axles, allowing the rear of the car to
be narrower in the future.
Customer Needs
Because this baja vehicle is being designed for an SAE competition, many of the needs are
defined by SAE. The major requirement of the braking system is that all four wheels need to lock
up on pavement from an acceleration run. This test needs to be passed before the car is deemed
safe to drive at the competition.
However, keeping an off-road race setting in mind, there are other requirements that the end
“customer” requires. The customer requires that the system is easily adjusted. Biasing pressure
between front and rear in order to get maximum performance and handling is important.
Especially in a race setting, the customer cannot spend a lot of time searching for tools and
taking time out of a race to adjust the bias in the system. Also, there needs to be minimal driver
input (input force) during braking. This especially applies to the four hour endurance race at the
SAE competition. If the system is designed for a high input force, then the driver can tire very
quickly, and can become a hazard to him/herself or even other drivers/competitors.
Finally, all braking components need to be robust. The braking system is an essential safety
feature of any car, and if parts in the system fail, results can be catastrophic. The customer
requires that every component is strongly built in order to ensure safety and performance.
Research and Existing Products
Pedal Setup
The pedal setup below can be floor mounted or swing mounted, depending on your application
and how much room is available in the vehicle. This specific pedal uses a dual master cylinder
setup (one for front circuit, one for rear), however similar pedals can be purchased that use a
single master cylinder for both circuits. This pedal uses a balance bar for biasing, which can be
easily adapted to be adjusted by the driver on the fly. It has a pedal ratio of 6:1 multiplying driver
input force by a factor of 6. The pedal is shown in Figure 3.
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Figure 3 Wilwood Pedal Setup
As seen, the master cylinders mount out front, which may not fit in the limited space of the baja
car.
Master Cylinders
Braking systems can use a single master cylinder for both front and rear brake circuits, or a dual
master cylinder setup using one for front and one for rear. SAE rules stipulate that front and rear
circuits must be separate from one another, making the dual master cylinder ideal. However a
single master cylinder with a separate fluid reservoir for each circuit may be used. Figure 4
shows a single master cylinder with separate fluid reservoirs.
Figure 4 Single Master Cylinder
Master cylinders mount
here
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Because of the combined reservoirs, this package is large, and will be harder to fit within the
spatial limitations of the baja car. Figure 5 shows a typical single master cylinder.
Figure 5 Dual Master Cylinder
Compared to the single master cylinder, this is much more compact, especially in the length of it.
Another advantage to using two separate master cylinders is the biasing. Different sized bore
master cylinders can be used since different braking pressures may be required between the front
and rear of the car.
The size of the master cylinders is the second way that mechanical advantage can be achieved in
a braking system. Smaller bore master cylinders produce higher line pressures, creating more
force between the pads and rotors, however there is not as much fluid displacement, requiring
longer pedal travel. Larger bore master cylinders are just the opposite creating lower pressures,
but displacing more fluid. When designing the system, it is about making a tradeoff between
pressures generated and fluid displaced.
Biasing
If a single master cylinder is used to combine front and rear circuits, a proportioning valve can be
used. These valves are installed inline, and can be turned to reduce or increase fluid pressure
within the brake lines. It is very easily adjustable, usually requiring no tools, however because
you have to tap into the hydraulic lines to install it, it has the potential for leaks. Adjusting bias
with a dual master cylinder setup is typically done with something called a balance bar. The
balance bar is built into the pedal itself, and is a totally mechanical way of adjusting bias. Figure
6 shows a balance bar.
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Figure 6 Balance Bar
The swivel bearing is pressed into the pedal, and the black clevises are threaded onto the master
cylinder push rods. These points are fixed. The threaded rod can then be turned to adjust the bias.
Essentially it changes the distance between the pivot thus changing the moment that the driver
applies to the master cylinders. It can be adapted to be driver adjustable using a remote cable
setup.
Biasing is important when designing a braking system. The weight of a car is not evenly
distributed, so not all wheels need the same pressure applied to them. During dynamic braking,
the weight of the car is carried forward by its momentum, generally requiring more force applied
to the front wheels.
These products can be seen in Appendix A where an overview of features will be listed.
Product Objectives and Features
The goals for this braking system are to ultimately fulfill all required SAE rules, and to pass
technical inspection at the competition so that the car is allowed to compete. In order to help the
car brake more effectively, the more specific goals are to make the system more ergonomic by
reducing the input force required by the driver. Also, a major goal is to reduce the time and tools
required to adjust bias in the system. Below is a list of itemized features that the team hopes to
achieve.
Robust system
o This needs to last through testing and the competition, including a 4 hour
endurance race.
Effective
o The system needs to be able to lock up all four wheels on pavement from an
acceleration run.
Attaches to master cylinder
pushrod
Swivel bearing inside pedal
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Ergonomic
o Reduce the required driver input
Easy Adjustability
o Reduce the time and tools required to adjust bias in the system
Design
Pedal Setup
Solidworks
To begin the design process, concept sketches were generated for brake pedal setups. In order to
have a robust design, it was decided upon to go with the pedal setup similar to the Wilwood
pedal shown in Appendix A. A similar concept was generated in Solidworks, shown in the figure
below.
Figure 7 Pedal Concept 1
This pedal setup featured a 6:1 pedal ratio, offering plenty of mechanical advantage leverage to
be ergonomic for the driver. However, after working with the team it was found that this concept
would not fit easily inside the car. By making cardboard cutouts to the dimensions of this
concept and placing it inside the concept frame it was found that in order for the pedal to be in a
comfortable position the master cylinders would be hanging outside the front of the frame. This
is definitely not an ideal scenario. Analyzing the problem, it was seen that the pivot point could
be moved and the master cylinders could be flipped around, and placed inside the car, facing the
driver. Figure 8 shows this design, which is ultimately the design that was decided upon.
Master
Cylinders
6:1 Pedal Ratio
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Figure 8 Pedal Concept 2
This pedal, like the previous has a pedal ratio of 6:1. To get a better idea of sizing inside the
prototype frame, a rapid prototype model was produced. Using this model and the prototype
frame, it was found that there was ample room to place the pedal in the car in a comfortable
position for the driver. To adjust bias, a purchased bias bar from Wilwood will be used. In order
to adjust bias quickly, a remote cable will be setup so that it will be able to be adjusted by the
driver on the fly. The master cylinders will also be purchased from Wilwood. The rest of the
pieces will be fabricated out of 6061-T6 Aluminum so that they are lightweight, keeping the total
weight of the car in mind.
Stress Calculations
In order to analyze the forces that the pedal will experience, a driver input force needed to be
assumed. To find this force, the team placed a scale against a wall and sat in a similar position as
in the car with the driver’s back against another wall. Each team member pressed the scale as
hard as they could. The maximum force that was seen was right around 200 pounds, so this was
the assumed force. Figure 9 below shows the loading conditions.
Master Cylinders
Pedal
Base
Wilwood Balance Bar
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Figure 9 Loading Conditions
Using the 200 lb measured input, the force at the master cylinder was found to be 1200 lbs and
the shearing force at the pin to be 1400 lbs. Figures 10 and 11 show the resulting shear and
moment diagrams.
Figure 10 Shear Diagram
Figure 11 Moment Diagram
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As seen from the figures, the maximum shearing force seen is 1200 lbs, and the maximum
moment is 1980 in lb.
Finite Element Analysis
Knowing the maximum forces finite element analysis (FEA) could be performed in Solidworks
using Cosmos. Figures 12 and 13 show the FEA results for the pedal and figures 14 and 15 for
the base.
Figure 12 Pedal Loading Conditions
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Figure 13 Pedal FEA Results
Figure 14 Base Loading Conditions
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Figure 15 Base FEA Results
The safety factor for the pedal was found to be about 2 and 1.6 for the base. As seen from the
figures, the higher stress concentrations occurred in very small and local areas. Both components
could have been made slightly lighter by removing some material, however displacement was
also considered during the design, so as to not lose any pedal travel from the flexing of
components. When taking material out of the components (which resulted in negligible weight
loss), they became less rigid, and would have taken away from the robustness of the braking
system.
In addition to the FEA, a shear calculation was done on the pivot pin. With a factor of safety of
2, it was found that a standard alloy steel 3/8” shoulder bolt purchased from McMaster Carr
could be used.
Hydraulics Calculations
The second area to achieve mechanical advantage in a braking system is through the hydraulics
and selection of the master cylinders. This is very important to achieve the correct line pressures
in the system. Given the constants listed in Figure 16, hydraulic calculations were able to be
performed, and the results are shown in Figure 17.
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Figure 16 Hydraulic Calculations Constants
Figure 17 Hydraulic Calculations Results
Front Calpier Bore 1.19
Front Caliper Area 1.112
Front Rotor Size 7
Rear Caliper Bore 1.25
Rear Caliper Area 1.227
Rear Rotor Size 8.625
Coefficient of Friction of pads 0.4
Pedal Ratio 6
Driver force input 115
Front Bias 0.7
Rear Bias 0.3
Front Master Cylinder Size 0.625
Rear Master Cylinder Size 0.75
Pedal Travel 3
Required Torque Front Required Torque Rear
in lb in lb
4970.0 764.7
Required Front Circuit Pressure Required Rear Circuit Pressure
psi psi
1595.9 180.6
Front MC Piston Size Rear MC Piston Size
area 0.3026 1.1460
diameter 0.621 1.208
Pressure Generated Std. (Front) Pressure Generated Std. (Rear)
psi psi
1574.3 468.6
Fluid Displaced Front Fluid Displaced Rear
in3 in3
0.1534 0.2209
Caliper Piston Movement (Front) Caliper Piston Movement (Rear)
0.138 0.18
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From the calculations, it was found to be that the optimal sized master cylinders would be a 5/8”
bore for the front circuit, and a 3/4” bore for the rear. The required driver input would be 115 lbs.
Purchased Components
Items such as the calipers and rotors will be purchased parts. These will be purchased from the
team’s sponsor Polaris so that they will bolt right onto the current locations already provided on
the current Polaris hubs and uprights. Below is a list of all purchased components for the system
1. Front and rear calipers (stock Polaris parts)
2. Front and rear rotors (stock Polaris parts)
3. Front and rear master cylinders (purchased from Wilwood)
4. Balance bar (purchased from Wilwood)
5. Remote bias adjust cable (purchased from Southwest Speed)
Fabrication and Assembly
No special fixtures will be needed to fabricate the pedal assembly. There will be three parts that
will need to be machined. These are illustrated in figure 18.
Figure 18 Required Machined Parts
Only standard milling practices will be required. The middle part and the part on the right will
need to be welded together. Figure 19 shows the finished and assembled pedal assembly.
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Figure 19 Finished Assembly
Proof of Design
In order to prove the design of the braking system the car will undergo testing before the
competition. In order to prove the system is more ergonomic than the previous car, the same
hydraulics calculations will be run using the setup of the 2011 car. Ultimately the required driver
input will be looked at to see if the system is more ergonomic. The team will also compare the
time and amount of tools required to adjust bias on both cars. Finally, the car will need to stop
consistently in the SAE competition stipulated scenario (lock up all four wheels from
acceleration). Testing will be done on the car during March, before the competition.
The ultimate proof of design will be at the Baja SAE competition at the end of April, 2012.
There the car will need to be able to pass the brake test before it is deemed safe to drive. Also the
car will undergo several individual events, as well as a four hour endurance race which is
designed to break the car. If the car and brake system survives the weekend, it is safe to say that
the customer requirements were met.
Testing Results
When the car was assembled and ready for testing, the team drove the car. The brakes were
checked before the car moved, and at slow speeds. In both instances, the brakes performed their
job. It was then determined to test the brakes in a competition technical inspection scenario.
From acceleration the brakes locked up all four wheels on the pavement. The brakes also locked
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up and effectively stopped the car from a full speed run. Next, the time to adjust the bias was
recorded. To adjust the new system, only a knob needs to be turned, and the system is adjusted;
merely seconds and no tools required. The old car took in excess of five minutes to adjust, and
two wrenches; not ideal in a race/competitive setting. Finally, the driver input required to stop
the vehicles was calculated. With this new setup, a driver input of 115 lbs is required. It was
found that on the 2011 car, the driver needed to input a force in excess of 200 pounds. This is a
42% reduction, and was a major help in making the braking system more effective and
ergonomic.
At the competition, the team passed the brake test on the second try. It was seen that one front
tire would not lock up in the first run, so that line was bled quickly to remove air, and the bias
was adjusted to produce more front pressure. The car passed on the next run; a huge
improvement of the four or more tries in 2011. The car finished every event over the weekend of
the competition, including the four hour endurance race with no major complications, especially
to the braking system. It is safe to say that customer (and team) requirements were met for the
brakes.
Project Management
Schedule
The brake system design did not suffer any major setbacks. There was a delay in installation, due
to waiting on the car to get to a stage where the brakes could be installed. The schedule can be
found in the appendix.
Budget
The brake system was budgeted $1,000. The total amount spent on this project added up to
$1,154.84. The budget was exceeded by about $150. I did not anticipate that brake line fittings
would cost so much. Included in these expenses, however, are spares that were brought to the
competition, such as spare fittings, lines, brake pads, and rotors. The detailed budget can be seen
in the appendix.
Conclusion and Recommendations
It was found that the brakes on the 2011 car were ineffective. They required too large of a driver
input and too much time to adjust bias. The results of this year’s car make this even more
evident. Driver input force was reduced by over 40%, and time to adjust the bias in the system
was reduced to measly seconds compared to minutes and frustration of the 2011 car. A lot was
learned about the engineering process from research and ideation all the way up to testing and
proving the design. Also from doing a group project, a lot about working with a team of
engineers was learned. If you’re not a team player, failure is inevitable. Everybody relies on
somebody else at some point, and the more teamwork goes on, the better your results will be.
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Some notes and recommendations for next year’s team. I recommend losing weight anywhere
possible on the car. At 555 lbs, the car isn’t the heaviest one out at the competition, but it
certainly is not the lightest. To save on costs and design time, a lot of the components are
purchased parts. Many of these parts are overdesigned for our application, and thus have a lot of
weight that could be lost. Perhaps things such as hubs and uprights can be manufactured in
house, and better designed for our application. Due to the improvements in the braking system
and moving the rear brakes outboard this year, the rear axles can be shortened. Those could use a
total redesign in the shortening, as well as making them lighter, losing rotational weight in the
driveline possibly yielding better acceleration. But most of all have fun. Doing Baja for your
senior design project is a lot of work, and it WILL be hard at times. Keep your eyes on the prize.
Driving that car for the first time during testing and at the competition will make it all worth it in
the end. Seeing something come to life that you literally have blood, sweat, and tears into is the
culmination of your senior year. I wish you all good luck.
References
Ansell, Bill. The Brake Bible. 2008. November 2011
<http://www.pirate4x4.com/tech/billavista/Brakes/>.
Bicknell Racking Products. Brake Balance Bar Set-Up. 2009. January 2012
<http://www.bicknellracingproducts.com/index.php?option=com_content&view=article&id=9:br
ake-balance-bar-set-up&catid=5:brp-dirt-modifieds&Itemid=11>.
Engineering Inspiration. Brake Calculations. 2011. November 2011
<http://www.engineeringinspiration.co.uk/brakecalcs.html>.
Oshiro, Dean. Brake Article. 2011. November 2011
<http://www.deanoshiro.com/brakes/brakearticle.html>.
Stop Tech. Technical Support. November 2011 <http://www.stoptech.com/technical-support>.
Wilwood. November 2011 <http://wilwood.com/>.
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Appendix A| P a g e
Appendix A- Research
Pedal setup designed for off-road cars and buggies
Comments:
Uses dual master cylinders
Swing mount or floor mount
Bias adjustability
Driver bias adjustable capable
Simple design
Single, combined master cylinder for race car applications
Comments:
Separate fluid reservoir for front
and rear circuits
Large packaging
9/24/11
http://www.wilwood.com/pe
dals/PedalList.aspx
9/24/11
http://www.wilwood.com/MasterCylinders/Mas
terCylinderList.aspx?minorname=Aluminum%20
Tandem%20Master%20Cylinder
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Appendix A | P a g e
Master cylinder for race car applications
Comments:
Compact size
Lightweight
Need MC for both front and
rear
Integrated fluid reservoir
Balance Bar to adjust brake bias
Comments:
Mechanical balancing
Robust
Cheap
No tapping into brake lines
Effective
9/24/11
http://www.wilwood.com/MasterCylinders/Maste
rCylinderList.aspx?minorname=Integral%20Reserv
oir%20Compact%20Master%20Cylinder
9/24/11
http://www.wilwood.com/pedals/PedalList.aspx
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Appendix B- Part Drawings
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Bill of Material
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Appendix C | P a g e
Appendix C- Calculations
Hydraulics Calculations
Mas
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arM
ass o
f Car
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ight o
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elba
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ont T
ire D
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inin
548
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.525
Velo
city (
mph
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locit
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effic
ient
of Fr
ictio
nDe
cele
ratio
n Rat
e, (f
t/s2)
Dece
lera
tion R
ate,
(g)
Stop
ping
Dist
ance
(Fee
t)
3044
0.832
.21
112.8
Wei
ght T
rans
fer
Dyna
mic
Fron
t Axle
Wt
Dyna
mic
Rear
Axle
Wt.
lblb
lb
333.4
616.4
81.6
Baja Braking System Mark Schmidt
Appendix C | P a g e
Stopping Distance
Dynamic Weight Transfer (at 1 g deceleration rate)
Baja Braking System Mark Schmidt
Appendix C | P a g e
Using 115 lb driver input force, 6:1 pedal ratio, and 70%/30% front/rear bias forces put into
system:
Baja Braking System Mark Schmidt
Appendix C | P a g e
The closest standard sized master cylinders in the correct style are .625” and .750” in diameter.
Below are the generated pressures for these sizes.
Baja Braking System Mark Schmidt
Appendix C | P a g e
These calculations were performed using weights and heights of the center of gravity of the 2011
car. Less weight would mean that required brake torques as well as circuit pressures would
decrease. Lowering the center of gravity would increase required pressures in the rear, however
decrease in the front. Both generated pressures from a standard size master cylinder would then
exceed the required pressure.
Baja Braking System Mark Schmidt
Appendix C | P a g e
Proof of design Calculations
In order to prove the design the braking system of the 2011 car was put into the same Excel
spreadsheet that was used to design the current system on the 2012 car. Below are the inputs
of the 2011 Car, and the resulting values along with a sample calculation.
Front Calpier Bore 1.188
Front Caliper Area 1.108
Front Rotor Size 7
Rear Caliper Bore 1.375
Rear Caliper Area 1.485
Rear Rotor Size 7.125
Coefficient of Friction of pads 0.4
Pedal Ratio 6
Driver force input 115
Front Bias 0.6
Rear Bias 0.4
Front Master Cylinder Size 0.875
Rear Master Cylinder Size 0.875
Pedal Travel 3
Baja Braking System Mark Schmidt
Appendix C | P a g e
Mas
s of C
arM
ass o
f Car+
Drive
rHe
ight o
f CG
Whe
elbas
eFro
nt Ti
re Dia
meter
Rear
Tire D
iamet
er
lblb
inin
inin
548
698
31.05
6521
.525
Veloc
ity (m
ph)
Veloc
ity (fp
s)Co
effici
ent o
f Fric
tion
Dece
lerati
on Ra
te, (f
t/s2)
Dece
lerati
on Ra
te, (g
)Sto
pping
Dista
nce (
Feet
)
3044
0.832
.21
37.6
Weig
ht Tr
ansfe
rDy
nami
c Fro
nt Ax
le W
tDy
nami
c Rea
r Axle
Wt.
lblb
lb
333.4
616.4
81.6
Baja Braking System Mark Schmidt
Appendix C | P a g e
(Force using 115 lb driver input)
Value does not exceed the needed 1600 psi.
Force using 230 driver input produces 1606.5 psi of circuit pressure, a value meeting the
required line pressure in the front circuit. The 2012 car requires 115 lb input to stop the car—a
50% reduction in the required driver input.
Required Torque Front Required Torque Rear
in lb in lb
4970.0 764.7
Required Front Circuit Pressure Required Rear Circuit Pressure
psi psi
1601.3 180.7
Front MC Piston Size Rear MC Piston Size
area 0.2585 1.5274
diameter 0.574 1.395
Pressure Generated Std. (Front) Pressure Generated Std. (Rear)
psi psi
688.5 459.0
Fluid Displaced Front Fluid Displaced Rear
in3 in3
0.3007 0.3007
Caliper Piston Movement (Front) Caliper Piston Movement (Rear)
0.271 0.202
Baja Braking System Mark Schmidt
Appendix C | P a g e
Force Calculations on Pedal
1.65”
9.9”
Baja Braking System Mark Schmidt
Appendix C | P a g e
Shear Diagram
Moment Diagram
Baja Braking System Mark Schmidt
Appendix C | P a g e
Shear Stress of Shoulder Bolt
Alloy steel shoulder bolt from McMaster Carr has shear strength of 84,000 psi. Using factor
safety of 2, 3/8” shoulder bolt satisfies requirements.
Baja Braking System Mark Schmidt
Appendix D | P a g e
Appendix D- Schedule
Week Num
ber1
35
79
112
46
810
122
13
57
911
13
57
9
Build Point
7/4/2011
7/18/2011
8/1/2011
8/15/2011
8/29/2011
9/12/2011
9/26/2011
10/10/2011
10/24/2011
11/7/2011
11/21/2011
12/5/2011
12/19/2011
1/2/2012
1/16/2012
1/30/2012
2/13/2012
2/27/2012
3/12/2012
3/26/2012
4/9/2012
4/23/2012
5/7/2012
5/21/2012
Sponsor Money Due
Frame Design
Suspension Design
Transmission Design
Brake Design
Prototype Frame Work
Frame Construction
Suspension Construction
Transmission Construction
Brake Construction
Purchase Components
Receive Components
Suspension Installation
Transmission Installation
Brake Installation
Component Installation
Testing
Modifications
Body Fabrication
Final Preperations
Competition
Summ
er Quarter / BreakSpring Quarter
Winter Quarter
Baja Braking System Mark Schmidt
Appendix E | P a g e
Appendix E- Budget
Company Project Part DescriptionPolaris order $553.60 brakes
Sand Parts $56.79 turning brake cylinder
LPI Racing $61.45 Balance Bar
Kratter (ebay) $39.98 Balance adjuster cable
Wilwood $97.26 Master Cylinders
McMaster Carr2 $19.12 Hardware/Tube Caps
Allstar Performance (amazon) $15.99 3/16" Steel Brake Line
Pep Boys $2.65 Fittings
Summit Racing $199.66 Fittings/Brake Lines
Orielly Auto $7.97 fitting/brake fluid
Pep Boys $2.65 tube nuts
Autozone $3.18 tube nuts
Bridgetown Hardware $27.25 Hardware
Summit Racing $67.29 Banjo Fitting/Spare Lines
expense total $1,154.84
expense grand total $1,154.84
amount left to spend -$154.84