SAE Update - December 2022 - 11

A farm boy in control
TECH FOCUS:
VEHiClE DyNAMiCS
This work is intended for readers from at least
two categories. First are those generally familiar
with the well-developed body of vehicle dynamics
knowledge. This body of knowledge was generated,
with good reason, largely for passenger cars and
then extended to other vehicles. This work will
present vehicle dynamic models - recast with
changes in long-held vehicle dynamics conventions
- thay allow generalized vehicle dynamic models
that are more applicable to complex vehicles.
Second are those who come from a general bacground
in control theory and dynamic systems and
who want to see how the general techniques they
have learned can be applied to the dynamics of
ground vehicles. A practitioner with a background in
When vehicle dynamic models are
constructed in a general form - not
assuming the familiar passenger car
configuration as a starting point - the
answer can be found. In a three-axle
vehicle, a mathematical function of axle
positions and cornering stiffnesses of each
axle's tires can be found that satisfies the
Ackermann relationship between steer
input, yaw rate, and low vehicle speeds. In
the two-axle application at low speeds, the
ratio of yaw rate to steering input equals
the ratio of forward speed to wheelbase.
This expression for equivalent wheelbase
is found from the steady-state solution of
the generalized equations of motion for a
multi-axle vehicle.
It is a pleasing result that this kinematic
result can be found from the steady-state
UPDATE
control systems and artificial
intelligence would find this study
helpful when working on
autonomous vehicles. To the
extent the reader has both
knowledge of control systems
and vehicle dynamics, the
convention changes leading to
new vehicle dynamic models will
be appreciated as more
intuitive. " n
Note: SAE members receive a
discount of up to 20% on
purchase of Williams' book. Click
here for more information.
solution. It is fascinating that this same
function of axle locations and tire
stiffnesses plays the same role as the twoaxle
intuitive stiffness in the dynamic
equations that determine stability. So, in
fact, there is a precise answer to the
question of the " wheelbase " of a threeaxle
vehicle.
An interested reader can find out more
in a book I authored, Generalized Vehicle
Dynamics. n
ABOUT THE AUTHOR
Daniel Williams, Ph.D., an industry
professional with more than 30 years'
experience in chassis control systems
from concept to launch, wrote this
article for Update. Co-organizing the
COMVEC conference is one of the ways
in which this SAE Fellow is involved
with SAE international.
December 2022
11
https://www.sae.org/publications/books/content/r-498/ https://www.sae.org/publications/books/content/r-498/ https://www.sae.org/publications/books/content/r-498/
SAE Update - December 2022

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