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The Tale of Two Cars


Multibody, Dynamic Model of Modified 'Lowrider' Automobile Suspension. Setting up the Problem ... To model the dynamics and forces of a lowrider car ... – PowerPoint PPT presentation

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Title: The Tale of Two Cars

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.

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

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
  • 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
  • Fbds Force from back driver suspension system
  • Fbps Force from back passenger suspension
  • 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

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

  • To model the dynamics and forces of a lowrider
  • 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

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
  • My first method of solving the problem is a basic
    approach of the Rieman sum method of integration
    over a constant time step.

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.

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