The Tale of Two Cars

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The Tale of Two Cars

• A summer project should benefit both the student
  and the greater good of science. Both of my
  projects are appealing to those who are
  underrepresented in the fields to which these
  projects belong, mathematics and computing. My
  projects are a benefit to science as a motivation
  tool for these youths. Both show the power and
  magic of mathematics amidst a creative framework
  that these youths can relate to and appreciate.

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Multibody, Dynamic Model of Modified Lowrider
Automobile Suspension
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Setting up the Problem
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(No Transcript)
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Uniqueness of my model

• Though there exists a wide variety of suspension
  models, my approach is unique in that I do not
  make the standard assumption that the tires do
  not leave the ground
• This means that I am not allowed to say all
  forces are zero when the car is equilibrium, but
  rather that all forces are opposite and equal.
  That is gravity and contact is considered. This
  is actually always the case, but unnecessary if
  the tires are always in contact with the ground.

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ms zcg - Ws Ffds Ffps Fbds Fbps ?Mx -
We re rfs ( Ffds Ffps ) - rb Wb rt Wt
rbs (Fbds Fbps) ?My rx/2 ( Ffds Fbds)
rx/2 ( Ffps Ffps ) Ffds Kfs ( ?s
zfdw zfds ) B (zfdw zfds) Fh Ffps
Kfs ( ?s zfpw zfps ) B (zfpw zfps) Fh
Fbds Kbs ( ?s zbdw zbds ) B (zbdw
zbds) Fh Fbps Kbs ( ?s zbpw zbps )
B (zbpw zbps) Fh mus zfdw Kfw (
?w rw zfdw ) Ffds mus g mus zfpw
Kfw ( ?w rw zfpw ) Ffps mus g mus
zbdw Kbw ( ?w rw zbdw ) Fbds mus g
mus zbpw Kbw ( ?w rw zbpw ) Fbps mus
g ?x I-1 ?Mx ?y ?My
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• ms sprung mass
• mus unsprung mass
•  
• Ws sprung weight
• We engine weight
• Wb body/chassis weight
• Wt trunk weight
•  
• Ffds Force from front driver suspension system
• Ffps Force from front passenger suspension
  system
• Fbds Force from back driver suspension system
• Fbps Force from back passenger suspension
  system
• Fh - Hydraulic impulse force
• ?s - suspension spring free length
• ?w - tire spring free length
• Kfs front suspension spring constant
• Kbs - back suspension spring constant
• B - Damping ratio

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Specifics and Assumptions

• The car body/chassis is represented by a
  rectangular box with a given mass density.
• The engine and trunk(which carries a heavy load
  due to the hydraulic system and extra batteries)
  are represented by point masses.
• The wheel/suspension system is given an
  independent degree of freedom in the z direction.
• The suspension link is also given a degree of
  freedom in the x, y and z directions, however
  only the z direction affects the outcome of the
  differential equations.
• The center of gravity is given a degree of
  freedom in the x, y, and z directions, and a
  moment about the x and y, but not the z.A
• All force evaluations are enforced at the center
  of gravity about the car. However the
  Differential equations are focused on the
  position of each suspension link. Therefore the
  car is repositioned after every time step of
  solving

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Applications

• To model the dynamics and forces of a lowrider
  car
• The same model can be used for off road vehicles
  (Rice mini-baja, for example) in that the tires
  of an off road vehicle is likely to leave the
  ground given extreme conditions
• To capture the imaginations of underrepresented
  youths to what math can do. The end idea of the
  project is to put together a visual output of the
  simulation with some interface and deliver this
  over the internet to those targeted youths

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Solving the Problem

• The main benefit that I receive out of this
  project is a study of numerical methods and their
  approach to solving different kinds of problems.
  My second benefit is an increased ability and
  confidence of using computer codes to solve my
  problems
• My first method of solving the problem is a basic
  approach of the Rieman sum method of integration
  over a constant time step.

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Future Research and Direction

• Once my Rieman sum method and given equations
  return agreeable results, my focus of research
  will be focused on optimizing my code,
  specifically my numerical method
• I will study other methods of solving
  differential equations (Eulers method and
  variations, Runge-Kutta, etc.)
• I will also focus on finding an optimal time step
  variation function.

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Acknowledgements

• Matthias Heinkenschloss Faculty Advisor
• Victor Udoewa Graduate Mentor
• Edward Gonzalez Graduate Mentor
• AGEP