SAE Mini Baja Proposal

Tanner Harmon & Ramon Viada III

Southeastern Louisiana University

Advisor/Instructor Dr. Ho-Hoon Lee

Abstract: SAE mini baja is an intercollegiate competition across the United States that puts

engineering students to the test on how well they’re knowledge acquired can be put into the real world.

By understanding basic automotive mechanisms and having knowledge from courses throughout the

curriculum such as: statics, dynamics, strength of materials, etc., the design and development of the

mini baja buggy can be achieved. A mini baja buggy is a scaled down dune buggy for a single driver but

functions very like its larger model. For the spring semester of ET 493 our team, Tanner Harmon & I

Ramon Viada III, are responsible for the design and development of the suspension system that will be

equipped on the mini baja buggy for the senior design project. Using knowledge gained throughout the

progression in the engineering technology curriculum, we can tackle the daunting task of completing the

suspension system.

Introduction: The SAE mini baja buggy competition has been around for over a decade. The event

used to be called “Mini Baja”. SAE competitions take place across the US and even in other countries

such as China, India, Brazil, South Africa, and Korea. Each buggy must be designed to meet specific

rules/regulations set by the SAE board. The buggy must be able to be operated by any driver regardless

of weight and height. By understanding the average weight, height, and stature/percentiles the

appropriate space can be allowed for comfortable operation. For the SAE mini baja senior design

project, it was split into 4 separate teams. Framing, suspension, drivetrain/power transmission, and

steering are the 4 separate teams designated by Dr. Lee. Our team is responsible of the suspension

system. We must design and develop a suspension system so that the buggy handles comfortably and

the driver is comfortable while operating.

Body: The first step of completing the task of

designing and developing a suspension system was

understanding how a suspension system functions and its

mechanisms. Every suspension system operates with one

characteristic in mind, providing the most comfortable

ride for the passengers in the cabin. While there are

several different styles of suspension types with different

mechanisms in each design their performance and

function are very similar. Each suspension system is setup

with a type of lever system which allows the

wheels/suspension to articulate. While the wheels/suspension is articulating, the force being

transmitted through the wheels due to the weight of the vehicle is passing through the suspension

system. The suspension’s job is to dampen the forces acting on the vehicle so that the passengers

remain comfortable while the vehicle is in operation. Each vehicle and every suspension system varies

in how it performs due to each vehicle having a different weight and spring rate/spring constant on each

dampener. The spring rate/spring constant of a dampener is responsible for taking the force being

transmitted by the wheels pushing up due to the weight of the vehicle and deflecting it in the opposite

direction allowing the vehicle to travel comfortably. The spring rate is also responsible for the vibration

frequency the vehicle’s suspension system has. Average or most desired frequency is around 1hz, being

the suspension would cycle one complete time throughout a 1 second interval. Having a vibration

frequency higher than 1hz translates to a bouncy ride quality being the suspension would be cycling

more throughout a one second interval. Vibration frequencies lower than 1hz are expected to be of a

stiff ride quality as the suspension travels less than one complete cycle each second. Our goal was to

design and develop a suspension system to function properly while achieving a vibration frequency of

1hz throughout its travel.

To begin the process of fulfilling this task we must first understand basic geometry and

trigonometric functions. Deriving an equation using no set values just variables so that later the

suspension can be fine-tuned was the first step. The first equation we were to derive had to show how

the change in length of the dampener was related to the change in displacement of the system

throughout the suspension travel. In other words, how much does the dampener change in length as

the lower arm moves up or down throughout the suspension’s travel. By not using any set values or

parameters besides having variables to

plug in later which would yield the

results of the travel it would allow us to

pick the angles which the dampener and

control arms be mounted, the lengths of

each control arm/segment, and show

the amount of suspension travel the

system has overall. Having this equation

determines the proper length

specifications that would be needed for the given angles and lengths of control arms and dampener.

Mini Baja - Suspension System

X is displacement of body

L3=( z+L1 )2+x2

Θ1=sin−1( xL3 )

L1=cos (sin−1( xL3 ))−z

y

z L1

L1

x

L2

L3Θ2 Θ1

1

2

11

L1z

xL3 Θ1

z=L3cos(sin−1( xL3 ))−L1z2=(L3cos (sin−1( xL3 ))−L1)

2

y2=z2+(L2+x )2

θ2=tan−1( x+L2z )

y2=(L3 cos(sin−1( xL3 ))−L1)2

+(L2+x)(L2+x )

y=√(L3cos (sin−1( xL3 ))−L1)2

+(L2+x)(L2+x )

y=√(L32−x2+L12−2 L1√L32−x2 )+(L22+x2+2L2 x)

y=√L22+L12+L32+2 L2 x−2 L1√L32−x2

This system holds true if x < L3

2

z

y

x

L2

Θ2

Our second challenge was to derive an equation that would show the net of forces acting on the

suspension system. This equation was to be derived using the understanding of vectors and statics.

Using “pz” as a force due to weight pushing up in the vertical direction, “py” as the force being exerted

by the dampener, it allows the proper spring rate/spring constant to be selected for the proper ride

frequency. To complete this equation the use of taking moment of equilibrium at the hinge on the

frame where the lower control arm mounts had to take place. Taking moment at this point allows the

only forces being exerted in the system to be pz and the forces py in the x and y directions. The force py

was to be isolated so that it equals the force pz such that py is a function of pz,”(py=()pz)”. Just like the

first equation that was to be derived this equation has no set values just variables so that the proper

spring rate could be calculated. From basic physics, the force py=k∆y. Py being the magnitude of the

force exerted by the dampener itself, k is the spring rate/spring constant of the dampener, and ∆y is the

change in length of y(y intial – y final). After calculating the spring rate of the dampener in the

suspension system the vibration frequency can then be calculated. The frequency of the system can be

calculated as, f = (1/2∏) x (√k/m). When solving for the frequency and spring rate each corner of the

buggy is solved separately as the weight in each corner is not necessarily the same although angle,

lengths can be the same. The mass being divided in the equation is ¼ the entire mass being each corner

is solved for separately. The second derivative was also calculated so that the vibration frequency

equation could be derived correctly.

m x+kx+c x

y=√L22+L12+L32+2 L2 x−2 L1√L32−x2

y=l2y+

x l1y∗√(l¿¿3¿¿2)−x2¿¿

y=( l¿¿3¿¿2)∗l1y (l3

2−x2)3 /2¿¿

The average cost to build one of these mini baja buggy’s is on the higher part of a budget. After

researching and comparing prices to suspension components mass produced for similar buggies that are

sold fully assembled and ready to go, the price of buying the components from a whole sale distributor

would be about $800 for just the suspension components. Which leaves us to either scavenge a junk

yard for parts that will fit the design criteria, have components donated to our project, or consider

purchasing the materials to build the components we need. The problem with building the components

we need is that the price of steel and other alloys fluctuate with the economy. One day a piece of steel

can be $20, the next it can be $40. Also, buying the materials and then building the components would

require a mass amount of skill in designing jigs so that each component matches if there are more than

one to be built which becomes very costly and time consuming as well. With buying the materials and

and designing the jigs the timeline for completing the project could possibly become very tight on

meeting the deadline of completion. If we were to buy the materials and bring them to a fab shop that

can fabricate the arms with our design it would also be costly as the average shop labor rate varies from

$75 an hour to $100 an hour. Throughout research if we were to buy materials and have them

fabricated, I have found information from previous SAE buggy designs stating that 1” dom tubing .065

wall is plenty strong enough as the material for the upper and lower arms. The 1” dom tubing has been

used by several teams with buggies of 500lbs and over. If we were to purchase control arms already

fabricated we could calculate and compute the stress analysis and also modify the mounts on the frame

so that the geometry of the suspension is in the correct setup.

Deliverables:

• Linearize equation(completed)

• Derive equation of y = f(x) (completed)

• Derive Dynamic equation of system (completed)

• Find the optimal K value for spring (this semester)

• Design and construct control arms and mounts for front suspension (this semester)

• Design and construct control arms and mounts for independent rear suspension (this semester)

Timeline:

1. Find the optimal K value for the spring (Late September- Early October).

2. Design and construct the suspension system using the design of the frame and given values of

weight to begin the process of solving for the correct dampener spring rate and mounting style

to be used (Early October- late October).

3. Continue to construct the suspension system while verifying that 1hz spring dampening is

achieved while assembling final project (Late October- End of November).