2016 CU Boulder Baja Braking System & Pedal Assembly

Landis MacMillan

Bachelor of Science: Mechanical Engineering

Advisor: Peter Himpsel

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2016 CU Boulder Baja – Braking System

Landis MacMillan The University of Colorado at Boulder

Pedal System Design Lead

Abstract The purpose of this project was to design a brake system

for the CU Boulder Baja SAE vehicle that could

adequately handle the given input forces, and produce

braking forces that would stop the rotation (lock) of all

for wheels. This system would need to abide by the

competition rules and optimize weight and packaging

characteristics. This report will record and state design

intent, budget, proof of design and testing.

Contents Abstract ........................................................................... 2 Introduction .................................................................... 2 Applicable Rules .............................................................. 2 Brake System ................................................................... 2

Objective ..................................................................... 2

Design .......................................................................... 3

Purchased Components .............................................. 3

Master Cylinders ..................................................... 3

Calipers .................................................................... 4

Brake Rotors ............................................................ 5

Bias-Bar ................................................................... 5

Brake Pedal Assembly ................................................. 5

Calculations ............................................................. 5

Design Intent ........................................................... 6

Brake Pedal ............................................................. 6

Pedal Brackets ......................................................... 7

Configuration .......................................................... 8

Throttle Pedal .......................................................... 8

Assembly ................................................................. 9

Budget ......................................................................... 9

Testing and Proof of Design ...................................... 10

Conclusion ..................................................................... 10 Recommendations ........................................................ 10 Contact .......................................................................... 11 References .................................................................... 11 Definitions, Acronyms, Abbreviations .......................... 11 Appendix A .................................................................... 12

Appendix B .................................................................... 13 Appendix C .................................................................... 14

Introduction The objective of the Baja SAE competition is to design

and manufacture a four-wheel off-road vehicle that can

be operated by one person and can compete with

manufactured products in terms of safety, appearance,

performance and cost. The University of Colorado at

Boulder will be competing in the 2016 California Baja SAE

competitions.

The goal for the 2016 team was to design a vehicle that

would pass tech inspection and finish all coinciding races

and challenges. Being a first year team, this seems to be

a realistic and appropriate goal considering the team has

never had any prior experience in automotive design

competitions. To achieve the presented goal, the brake

system must be robust, but retaining a lightweight design

and create a comfortable motion for the driver.

Applicable Rules To see full wording of rules, see Appendix A.

B11.1 Foot Brake B11.2 Independent Brake Circuits B11.3 Brake(s) Location B11.4 Cutting Brakes B11.5 Brake Lines

Brake System

Objective The brake system must be able to produce more than the

required braking force designated by the SAE

competition rules. The brakes must allow the driver to

lock all for wheels at a comfortable input force. The brake

system should also be robust enough to withstand larger

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than anticipated forces and make it through all racing

events, but light enough to reduce weight in the vehicle

and weight at the wheels.

Design The braking system was designed in sync with the rules,

restrictions, and requirements provided by the SAE

organization. Being a first year team, there was no set

budget for cost or weight for the pedal system because

no team member knew what would be an adequate

budget. Recommendations for future teams and designs

will be mentioned in the section Recommendations.

Purchased Components There are certain components in the brake system that

would be too costly and time consuming to design and

manufacture. These components will be discussed in this

section, along with reasons for selection and

implementation.

Master Cylinders The master cylinders (MC’s) are the components that

directly transfer the force of the pedal to pressurize the

hydraulic braking circuit. In order to receive the proper

amount of force needed to decelerate at 0.7g, the MC’s

needed to transfer the correct pressure to the brake

caliper pistons.

There are two types of master cylinders that can be

chosen for this application. There is a single chamber

master cylinder that acts like a plunger and cylinder. One

plunger pressurizes one brake circuit. The other type of

master cylinder is a dual chamber. One push of the

plunger on this MC pressurizes two circuits at different

or the same pressure. Figure 1 shows the basic

mechanism of the dual chamber master cylinder below.

To understand the general concept of this master

cylinder, follow this reference [1].

There are pros and cons to both of these master

cylinders. The dual chamber MC allows for a simpler

design of the pedal assembly. The pedal only needs to

actuate one piston that will provided pressure to both

brake circuits. Once again with one master cylinder,

mounting becomes easier to design. However, the

assembly itself is much more complicated than a single

chamber MC. As one can see from Figure 1, there are

many more part interfaces than the single chamber

master cylinder in Figure 2. These part interfaces are

areas susceptible to wear and potential failure.

When designing separate brake circuits proportioning

the pressure in each circuit is vital in order to prevent one

set of wheels locking before the other, which causes

unwanted handling characteristics (slide 32-33) [2];

These effects are mitigated by adding a proportioning

valve to the dual chamber MC brake circuit. The valve is

simple and is easy to adjust.

A single chamber MC has the opposite benefits of a dual

chamber MC. It is a much simpler design, therefore there

is less potential for failure. However, the single chamber

only produces pressure for one circuit, which means that

there needs to be two single chamber MC’s in the final

design to abide by SAE’s rules. With two MC’s, features

need to be designed to mount and position both MC’s.

Along with added features, there needs to be a way to

proportion the pressure of each circuit. This is done with

the use of a mechanical mechanism called a bias-bar. The

bias bar works as a simple lever. Depending where you

position the pedal input (fulcrum), the proportion of the

lever dimensions directly relates to the amount of force

Figure 1: Dual Master Cylinder

Figure 2: Single Chamber MC

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distributed between the two brake circuits [3]. An image

of a bias-bar’s basic operation can be seen in Figure 3.

The bias-bar achieves what a proportioning valve would

do on a dual chamber MC, but with added parts and

features. Not only do you have to include the bias-bar in

your design, but you must design features into the pedal

to allow for a bias bar to slide. This sliding allows for the

bar to proportion the two circuits accordingly.

For the final design, two single chamber MC’s were

chosen. Reliability was the teams main concern, so the

two single chamber MC’s seemed like the better choice.

Along with reliability, it was easy to find different bore

sizes that would match the sizes produced by the brake

system calculations. The master cylinders selected for

use, were two Wilwood racing master cylinders (part

number: 260-12385 & 260-12384). These master

cylinders had a bore size of 0.625 inches (front) and 0.75

inches (rear). These bore sizes were chosen based of the

calculations performed, seen in Appendix B, and for a

more centered brake bias-bar.

In terms of pros and cons, the decision between the dual

and single chamber MC is a wash. They both have perks

that could aid in design and implementation and they

both have obstacles that make design a little difficult.

The true deciding factor is how the MC will work in the

vehicle. Analyze the packaging requirements, cost,

weight, personal understanding MC operation, and its

ability to produce enough pressure for the required

braking force. If cost and weight can be reduced, while

maintaining braking performance, by switching to a dual

chamber MC, then it could be worth the design change.

But the decision should be based on the considerations

listed above. However, please read my comments in

Testing and Proof of Design, as well as the

Recommendations section to understand some of my

difficulties.

Calipers The calipers were chosen based on packaging (ability to

fit and operate within allotted space) requirements and

other sub-teams’ decisions. They needed to be small

enough to fit within the front wheel hubs but large

enough to house the proper piston size to produce the

needed braking force. Things to consider when choosing

a caliper are cost, weight, packaging and most

importantly its functionality with the designed system.

Keep weight low to reduce the sprung weight of the

vehicle. Cost is always nice to keep low because there will

be unforeseen expenses. The shape and size of the

caliper needs to be considered in order to fit properly in

other sub-teams’ assemblies. Coordination with these

teams is crucial in order to successfully integrate parts.

Having an accurately modeled part in Solidworks will

streamline this process. Lastly, will the caliper be able to

produce the needed clamping force on the rotor? This

needs to be analyzed in the braking system calculations.

See section Calculations for more details.

The Wilwood PS1 caliper with a 1.12-inch piston bore

was chosen for the final design. This caliper was able to

produce more than the needed force on the rotors, while

still remaining small enough for packaging concerns.

Figure 3: Bias-Bar Operation

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Brake Rotors The brake rotors were chosen based on packaging

requirements as well. The front rotors are from a Yamaha

Banshee 300 because they came with the front hubs the

suspension team chose to use. These are outboard

brakes, so there needs to be individual calipers and lines

routed to each rotor.

The rear brake rotor was designated as an inboard rotor.

Because packaging was limited on the rear uprights, the

rotor was mounted to the final driveline coming from the

Spicer gearbox. This meant that only one caliper was

needed for the rear brake circuit. The rotor chosen was

a Hammerhead Sportworks 8.635” rotor sourced from

BMI Karts and supplies. These rotors were produced for

a two-person buggy, so it was assumed the design could

handle the use in a Baja SAE vehicle.

Bias-Bar The brake bias-bar allows for minor adjustment in the

force allocated to each master cylinder. Depending the

results seen in testing, the bias-bar can be adjusted to

direct more force to the corresponding master cylinder

in order to keep consistent lock-up between the front

and the rear wheels, as mentioned in the Master

Cylinders section.

Brake Pedal Assembly Given the bore sizes, rotor diameters of purchased

equipment and other assumed values, the pedal

assembly was designed to create the needed braking

force from the driver input.

Calculations The calculations to determine the pedal ratio and the

required force will be recorded in the following section.

Apart from the assumptions made, the calculations

stayed very close to the calculations found through

online research [4]. The following spreadsheet can be

found in the following server file location:

cubaja->Controls->Resources->Brake Data Sheet

There were assumptions that needed to be made in

order to make these calculations. Without a completed

Solidworks model, these values were estimated to the

most accurate degree possible. The center of gravity was

assumed to be 24 inches based on ride height of shocks

and driver position. The wheelbase was determined

through the suspension team’s design. The total weight

was assumed to be 600 pounds; with an average driver

weight of 150 pounds and an anticipated vehicle weight

of 450 pounds. From the preliminary solidworks model,

the weight distribution was 40:60 (40% front, 60% rear).

The assumed rate of deceleration was 0.7 g, based on the

advice given by the team’s advisor. With the given

assumptions and the dimensions of the purchased parts,

the calculations could be made.

First the dynamic weight shift needed to be calculated.

When the car begins to decelerate, the momentum of

the vehicle causes the weight to transfer to the front.

This weight shift applies more force to the front of the

vehicle, essentially adding more weight. Using the

equations found from the online sources [4], the amount

of weight shifted to the front of the vehicle was 158

pounds. This then calculated the amount of weight on

each axle during braking (dynamic mass). 434 pounds

would be located on the front axle and 172 would be

located on the rear.

Once the dynamic weight was calculated, the clamping

force (pressure) of the brake system could be calculated.

Using 0.7 as the coefficient of friction for rubber on

Caliper

Rotor

Figure 4: Front Hub & Brake Assembly

Figure 5:Rear Brake Location

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asphalt [5], the wheel locking force was calculated. This

value describes how much force the brake caliper needs

to exert on the rotor to lock of the wheels. By multiplying

this force by a factor of safety of 1.5, any unknown

inefficiencies are mitigated and one can assume the

brakes will lock the wheels. Once the lock-up force is

found, the torque required to produce the force on the

rotor was calculated by using the effective radius of

contact between the rotors and the calipers. Then the

clamping force could be determined by dividing the

torque by the number of friction surfaces, effective

radius and the coefficient of friction between the rotor

and brake pads (0.35) [6].

Knowing the needed clamping force, the required system

pressure could be calculated by dividing the clamping

force by the known caliper piston area. The force needed

was calculated for each brake circuit (front and rear) by

multiplying the required system pressure by the area of

the master cylinder bore. These two forces were

combined to find the total force needed from the pedal.

Once this force was calculated (700 lbf), the pedal ratio

was found by dividing the needed force by the minimum

driver input (100 lbf). All calculations can be seen in

Appendix B.

Design Intent The pedal assembly’s design was themed around stock

material thickness. The design was never intended to be

worked out of a large piece of material or billet. The parts

in the assembly were kept to common plate and tube

sizes. All of the parts were modeled to fit and be used on

both the throttle and brake pedal assemblies. Once the

material was sourced and ordered, the parts made from

the plate would be sent to be cut by a water jet, while all

the tube stock could be spun on a lathe. All the parts

were based on simple production methods.

Brake Pedal The brake pedal was designed as a second class lever,

where the load is placed between the fulcrum (bearing)

and the applied force (foot-plate). This means whichever

way the foot-plate moves, the load moves in the same

direction, like Figure 7. One can design a pedal as a first

class lever as well. This is a lever where the fulcrum is

placed between the load and the applied force. That

means when the load moves in the opposite direction of

the foot-plate. This can be seen in the Error! Reference

source not found.. Both of these pedal designs are

acceptable, and they can be used in a floor or ceiling

mounted set-up. What dictates whether one design is

used over the other is the design of the foot-box.

Depending where the steering rack is located and the

overall shape and dimensions of the foot-box, one design

will fit better than the others.

Important: Before finalizing any designs, make a

prototype of the foot box and seating position. Make

prototype parts that represent the steering rack, frame

tubes, and pedals out of foam, pvc, cardboard, etc. Set in

the mock-up and analyze how the comfort of the set-up.

Are the pedals operable? Could feet possibly get caught

in the assembly? Could a driver operate these pedals for

four hours? These are the questions that need to be

asked. Do not forget about ergonomics, they can make

or break a race, and the driver… literally.

Figure 7: Second-Class Lever Figure 7: First Class Lever

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Seen in Figure 9, the pedal was designed with two

identical ribs that were spaced by the “rib-spacer”. This

spacer was shouldered to provide proper rib spacing and

bored in order to allow the bias-bar to slide inside the

spacer. The bias bar needed approximately an inch of

travel in order to proportion the brakes properly. The

pedal could have been deigned from a billet, but that

would have taken much more time and money to

manufacture.

The fulcrum at which the pedal rotates was surrounded

by a bearing that could withstand massive radial forces.

This bearing required two different spacers to work

properly. Another alternative to this design would be a

bronze bushing. The bushing would not have as smooth

of a rotation, however, it would reduce the need for the

bearing-race spacer and bearing-spacer seen in Figure 9.

This should be considered for a future design.

The brake pedal was designed with a pedal ratio of 7:1,

calculated in Appendix B. With an assumed driver input

force of 100 lbf, a total force of 700 lbf was needed in

order lock all four wheels. However, one also needs to

consider a panic scenario, where the driver produces

forces far beyond the required force to lock the wheels.

Based on the Formula SAE safety values for acceptable

pedal strength, a pedal must be able to withstand a 2000

newton force (450 lbf) [7]. Considering that the brake

pedal was designed with two ribs that would distribute

the force evenly, the FEA was run on only one rib with a

force of 1000 newtons.

As seen in the Figure 8 above, the pedal rib only

experienced approximately 17.8 ksi while the aluminum

has the a 40 ksi yield strength. So the pedal has a factor

of safety of approximately 2.2. The fatigue analysis

produced results that stated the forces were below the

S-N curve of the material and no damaged was produced.

Concluding that the pedal can withstand the forces

produced throughout the life of the car.

Pedal Brackets The brackets were designed to be interchangeable with

the throttle pedal brackets as well. The brackets needed

to hold and position the pedal with the master cylinders,

while keeping a small profile for easy packaging. The

brackets would also need features to allow it to mount

to the frame of the vehicle.

With the given suspension and steering configuration,

the pedals were designed to be floor mounted. This

would leave sufficient room for the driver’s feet and

steering rack. These brackets needed to withstand the

same forces as the pedals, so it was run through the same

FEA scenario. With the previous input force of 450

pounds, the force on the bracket was calculated through

the use of lever proportions, equaling to 2900 pounds.

Figure 8:Brake Pedal FEA

Bearing Race

Spacer

Rib-Spacer

Pedal-Rib

Foot-Plate

Bearing

Bearing-Spacer

Figure 9: Labeled Brake Pedal

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Since the brackets act like the pedals and distribute the

force between two ribs, the force was halved and applied

to one bracket in the scenario. The resulting analysis can

be seen in the Figure 11.

The brackets saw a maximum stress of 15 ksi and the

yield strength is 40 ksi. This gives a factor of safety of 2.7,

which is plenty sufficient for the vehicle.

Configuration With the pedals and brackets designed, they needed a

way to mount to the frame. This was done by creating

0.25” tabs that were welded to the steering rack support

and the front foot-box tube. These had holes to allow the

corresponding hardware to fasten the brackets and

pedals. The tabs were made from 4130 steel plate and

had sufficient strength to handle the forces produced by

the driver. The configuration can be seen in Figure

13,Figure 10, and Figure 14.

Throttle Pedal The throttle pedal was design much like the brake pedal.

It used the exact same parts, besides the pedal-ribs. The

pedal rib geometry was altered from the brake pedal

because the throttle had no use for a bias-bar, but it still

used the rib-spacer for proper spacing. The other

difference with the throttle pedal was the cable linkage

holes. Since the throttle needs to have a mechanical

linkage (cable) to the pedal, there needs to be a feature

that allows for the cable to fasten to the pedal. In the

final design, the cable connects to the pedal via a 3/8”

bolt. This bolt extends through and out the side of the

pedal where the eyelet of the cable fastens.

The throttle cable needs to actuate the throttle

mechanism on the engine. This mechanism has a certain

amount of length in which it can travel before it is limited

by the design. If this mechanism extends past its max

travel, it can become permanently damaged, possible

limiting throttle control and endangering the driver. The

throttle assembly mitigates the chance of this

occurrence by having two features: multiple throttle

attachment holes, and an adjustable throttle stop. The

throttle mechanism on the engine has approximately

Figure 11: Bracket FEA

Figure 12: Pedal Configuration

Figure 10: In-Car Location

Figure 13: In-Car Location (Side)

Figure 14: Throttle Linkage

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1.25” of travel. This needs to be translated into pedal

travel. Through basic tests conducted on each team

member, comfortable foot travel for the driver was

about three inches. Foot travel can then be converted

into degrees of rotation by the arc length equation. Once

the degree of rotation is calculated, this can help find

what hole would be closest to the desired travel of 1.25”

by using the arc length equation again. Once the proper

hole is found, the adjustable throttle stop can be

adjusted to allow for more or less travel depending on

the situation.

The throttle pedal also needs to have a feature that

returns the throttle to idle. One of the simplest ways to

do this is through and extension spring. It can be done

with a torsional spring as well as a compression spring.

When considering a return mechanism, make sure that it

is clear from the driver’s feet to mitigate any chance of

snagging. Considering the driver’s feet, a torsion spring

might be the best option for the design. However, this

was not chosen because the brackets had to be

redesigned and manufactured within two weeks. With

such a large time-crunch, an extension spring was still

use.

The throttle assembly had a few extra features. An

aluminum tab was welded to the back of the brackets to

allow for an adjustable throttle stop to be installed. In

order to bias the throttle in its return position, another

adjustable stop was created to position the pedal in a

comfortable orientation for the driver. This return stop

also prevents the engine from hitting its kill-switch. If the

throttle returns completely on the engine, it hits a switch

that automatically shuts down the engine. This feature

along with a redundant feature on the engine bracket

prevents this from happening. The two throttle stops can

be seen in Figure 16 below.

Assembly Both the throttle and brake pedals were very similarly

designed. They used the same number of parts and were

assembled in the same fashion. The pedals were

assembled by press fitting the bearings and rib-spacers.

The foot plate was then welded on the two ribs after all

the bearings and spacers were press fit. An exploded

view of the brake pedal assembly can be seen below in

Figure 15.

Once the pedals were assembled, they were positioned

in the correct orientation and then a bolt fastened them

to the brackets. Once the adjustments were made to the

throttle cable and bias bar, the pedals were ready for

use.

Budget Without a past team to compare budgets, the brake

system had no gauge on how much it should cost or

weigh. By the end of design, the whole system, including:

brake pedals, throttle pedals, brackets, all the related

hardware, calipers, rotors, lines, and fittings weighed

approximately 21 pounds. The entire system including

pieces for the throttle cost approximately 930 dollars.

Figure 15: Brake Pedal Exploded View

Figure 16: Throttle Assembly

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The prices for individual components were calculated

based on SAE Baja material cost tables. The tables along

with the breakdown of weight and cost can be seen in

Appendix C.

Testing and Proof of Design Testing, as with any project, proved to be a vital learning

experience. With the initial configuration of the brake

pedal assembly, the bias-bar became bent from the

massive force produced by the pedal ratio. When the

bias-bar is bent, the brakes cannot be adjusted or

proportioned properly. The points that the clevis pins

connected to the bias-bar were too far from the center,

which produced a bend in the rod stock, seen in Figure

17.

This meant that the MC’s needed to moved closer to the

center of the bias-bar to prevent bending. The brackets

were kept, but they were moved to the center of the

pedal as opposed to having the brackets on either side of

the pedal. This can be seen in Figure 18.

Conclusion The brake system was designed and implemented to

withstand extreme driver input and allow the driver to

safely control the vehicle. Through some design

alterations, the pedal system did exactly what they were

supposed to do. They can withstand loads much higher

than SAE requires, and they effectively lock all four

wheels and control the throttle.

Recommendations After experiencing the design process and implementing

a design into a vehicle, there are some recommendations

and tips that I would make to the proceeding teams.

First, I highly recommend understanding the geometry of

the footbox. To understand how comfortable a driver will

be with a certain design, one must create a prototype

that resembles the final product. If the prototype can

rotate, has the same general shape and dimensions as

the proposed design, the team will be able to see how

well the design works with the driver.

Second, a bias-bar is not as simple of a feature to account

for. As mentioned previously in the Testing and Proof of

Design section, the balance bar was bent with the initial

pedal configuration. Because the MC’s were so far apart,

the moment on the bias-bar bent it very easily. Knowing

this, one could design a system that keeps the MC’s much

closer than they originally positioned on the first

configuration. I cannot say that a proportioning valve

would be simpler to implement, but I think it would be

worth researching.

Third, position the throttle cable so that it experiences

the most linear travel possible. The throttle cable was

mounted near the bottom of the pedal, near the fulcrum,

to limit chances of driver entanglement. However, when

the cable was mounted there, most of the pedal travel

simply rotated the cable about the fulcrum; there was

barely any throttle actuation when this happened. An

additional bracket was made in order to provide a more

linear route, which fixed the issue.

Fourth, when designing for the rear brakes, account for

the force produced by the engine. The engine does not

immediately cut the torque to the rear axle, the CVT

must slowdown in order to allow the belt to slip. Since

there is a delay in power transfer, this puts more torque

Figure 17: Balance Bar Failure

Figure 18: Brackets Moved to the Center

11

on the rear brakes than what was calculated in the

spreadsheet. Luckily multiplying by a factor of safety

allowed the system to lock the rear wheels. I am not sure

how to measure the extra torque produced by the

delayed power transfer but it should definitely be

acknowledged in future designs.

Lastly, use human resources. Do not try to do everything

yourself, you have a good advisor who knows a lot about

vehicle design, and your professors and peers know

more than you think. Heck, feel free to contact me if you

have any questions.

PS, remember to have fun with this project as well. It was

one of the best things I have ever done.

Contact Landis MacMillan, Pedal System Lead Roma9589@colorado.edu

References

[1

]

"The Brake Master Cylinder," [Online]. Available:

http://www.tegger.com/hondafaq/mastercylinderreplace/howworks.ht

ml. [Accessed 22 3 2016].

[2

]

S. International, "Brake Systems 101," [Online]. Available:

www.sae.org/students/presentations/brakes.ppt. [Accessed 22 3 2016].

[3

]

J. James Walker, "Brake Proportioning Valves," [Online]. Available:

http://stoptech.com/technical-support/technical-white-

papers/proportioning-valves. [Accessed 22 3 2016].

[4

]

" Engineering Inspiration - Brake System Design Calculations," 2016.

[Online]. Available:

http://www.engineeringinspiration.co.uk/brakecalcs.html.

[5

]

"Friction and Coefficients of Friction," 2016. [Online]. Available: Friction

and Coefficients of Friction.

[6

]

"The Brake Bible," Pirate 4x4, [Online]. Available:

http://www.pirate4x4.com/tech/billavista/Brakes/. [Accessed 22 3

2016].

[7

]

SAE International, "2016 FSAE Rules," [Online]. Available:

http://www.fsaeonline.com/content/2015-

16%20FSAE%20Rules%20revision%2091714%20kz.pdf. [Accessed 22 3

2016].

[8

]

"2016 Baja Rules Final," 2016. [Online]. Available:

https://www.bajasae.net/content/2016_BAJA_Rules_Final-9.8.15.pdf.

Definitions, Acronyms, Abbreviations “: inch MC: Master Cylinder FEA: Finite element analysis ft: feet in: inches kgs: kilograms ksi: kilopound per square inch lbf: pound force N: newton Psi: pound per square inch

12

Appendix A B11.1 Foot Brake The vehicle must have hydraulic braking system that acts on all wheels and is operated by a single foot pedal. The pedal must directly actuate the master cylinder through a rigid link (i.e., cables are not allowed). The brake system must be capable of locking ALL FOUR wheels, both in a static condition as well as from speed on pavement AND on unpaved surfaces. B11.2 Independent Brake Circuits The braking system must be segregated into at least two (2) independent hydraulic circuits such that in case of a leak or failure at any point in the system, effective braking power shall be maintained on at least two wheels. Each hydraulic circuit must have its own fluid reserve either through separate reservoirs or by the use of a dammed, OEM-style reservoir. B11.3 Brake(s) Location The brake(s) on the driven axle must operate through the final drive. Inboard braking through universal joints is permitted. Braking on a jackshaft through an intermediate reduction stage is prohibited B11.4 Cutting Brakes Hand or feet operated “cutting brakes” are permitted provided the section (B11.1) on “foot brakes” is also satisfied. A primary brake must be able to lock all four wheels with a single foot. If using two separate pedals to lock 2 wheels apiece; the pedals must be close enough to use one foot to lock all four wheels. No brake, including cutting brakes, may operate without lighting the brake light B11.5 Brake Lines All brake lines must be securely mounted and not fall below any portion of the vehicle (frame, swing arm, A-arms, etc.) Ensure they do not rub on any sharp edges. Plastic brake lines are prohibited

13

Appendix B

21 in 1.12 in 21 in 1.12 in

0.5334 m 0.028448 m 0.5334 m 0.028448 m

24 64 in

6 in 0.985203456 in^2 0.61 1.6256 m 8 in 0.985203456 in^2

0.1524 m 0.000635614 m^2 0.2032 m 0.000635614 m^2

5 in 0.625 in 5 in 0.750 in

0.127 m 0.015875 m 0.127 m 0.01905 m

0.306796158 in^2 125 150 kg 0.441786467 in^2

0.000197933 m^2 275.6 330.6934 lbm 0.000285023 m^2

197.2 77.8125 kg

1354.086563 N 534.3384375 N

677.0432813 N 534.3384375 N

1354.086563 N 534.3384375 N

2031.129844 N 801.5076563 N

270.8511647 N-m 213.7620919 N-m

2.75 in 3.75 in

0.06985 m 0.09525 m

5539.445028 N 3206.030625 N

8715110.481 Pa 5043991.042 Pa

1264.019908 psi 731.5690499 psi

1725.004555 N 1437.653242 N

387.7964509 lbf 323.1973058 lbf

N

lbf

Assumed Values and Inputs

45.45% 54.55%

Master Cylinder Area

Rear Caliper Bore

Pad-Rotor Outer Contact

Diameter Rear Caliper Area

Pad-Rotor Inner Contact

Diameter Master Cylinder Bore (D)

Rear

606.271221

kg

lbm

Master Cylinder Bore (D)

Master Cylinder Area

FrontFront Caliper Bore

Front Caliper Area

Loaded Tire Diameter

Pad-Rotor Outer

Contact Diameter

Pad-Rotor Inner

Contact Diameter

Mass Front

kg

Loaded Tire Diameter

Total Mass (Car&Driver)

-

Friction Between Tire & Road

0.7

Number of Friction Surfaces

2

Frinction Between Calipers&Pads

-

72.1875 kg

lbm

71.70% 28.30%

Dynamic Mass Shift

Dynamic Weight Distribution

Dynamic Mass Front Dynamic Mass Rear

kg

Braking Force Per Caliper

Total Needed Input Force

Front Input Force + Rear Input Force

3163

Required System Pressure

Needed Input Force into Master Cylinder

F_i = P_s*A_mc

Braking Force

F_b = g*a*m_df

F_bc=F_b/2

After Factor of Safety

Wheel Lock Force For Front Axel

F_wl=m_df*9.81*friction

F_bfos = fos*F_wl

Braking Torque per Front Wheel

T_b = F_bfos*R_tr

Effective Radius

R_e = (Do_r+Di_r)/4

Clamping Force

F_c = T_b/(R_e*friction*surfaces)

P_s = F_c/A_cal

711

Needed Input Force into Master Cylinder

F_i = P_s*A_mc

Effective Radius

R_e = (Do_r+Di_r)/4

Clamping Force

F_c = T_b/(R_e*friction*surfaces)

Required System Pressure

F_wl=m_dr*9.81*friction

After Factor of Safety

F_bfos = fos*F_wl

Braking Torque per Rear Axel

T_b = 2*F_bfos*R_tr

-

P_s = F_c/A_cal

0.35 -

Factor of Safety

1.5

F_bc=F_b

Wheel Lock Force For Rear Axel

Braking Force

F_b = g*a*m_dr

Braking Force Per Caliper

StaticWeight Distribution

Mass Rear

275

Deceleration

G0.7

Height of CG Wheelbase

in

m

14

Appendix C

Cost Breakdown

Cost Quantity Total

Pedal Plate 0.73125 2 1.4625

Brake Pedal Ribs 2.3205 2 4.641

Throttle Pedal Ribs 2 0

Pedal Spacers 0.468 4 1.872

Bearing Spacers 0.039 2 0.078

Bracket Spacers 0.073125 4 0.2925

Bearing Spacers 2 0.004875 4 0.0195

Pedal Brackets 2.613 4 10.452

Front Tabs 0.17608 4 0.70432

Rear Tabs 0.52256 4 2.09024

Throttle stop 10.71 1 10.71

Thrtottle stop tab 0.5265 1 0.5265 Front Throttle Stop tab 0.44872 1 0.44872

Bias Bar 57.78 1 57.78

Master Cylinders 85.95 2 171.9

Calipers 91.74 3 275.22

Rotor 29.95 1 29.95

Hardline 21.99 1 21.99

Flexline 26.07 2 52.14

Fittings 100 1 100

Switches 19.99 2 39.98

rod stock 7 2 14

MC nut 0.2792 4 1.1168

Fulcrum Bolt 2.298 2 4.596

Fulcrum Nut 0.2644 2 0.5288

Brake Pads 47.5 2 95 Throttle cable 28.5 1 28.5

Total $926.00

Weight Breakdown

Part/Assembly Weight Quantity Total

Brake Pedal Assem 3.07 1 3.07

Throttle Pedal Assem 3.42 1 3.42

Master Cylinders 0.9 2 1.8

Calipers 1.19 3 3.57

Rotors 1.5 3 4.5

Misc 4 1 4

20.36 lbs

Material Cost Table Density

Mild Steel, e.g. 1010, 1025 $ 1.00 /lb 0.284 lb/in³

Alloy Steel, e.g. 4130, ChroMoly $ 2.00 /lb 0.284 lb/in³

Aluminum $ 5.00 /lb 0.0975 lb/in³

Mag $ 9.00 /lb 0.0648 lb/in³

Titanium $ 20.00 /lb 0.160 lb/in³

Non-graphite composites $ 40.00 /lb -

Graphite-based composites $ 100.00 /lb -