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1
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 1
Chapter 1
Introduction
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 2
Course Objectives
• What do you need to know to understand vehicle
dynamics?– Important vehicle and system properties
– Mechanics by which each system functions
• Why do you need to know it?– How will a system’s properties affect performance?
– What are the design conflicts for achieving good performance in
different modes?
2
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 3
Chapter 1 Objectives
• Establish background information for understanding
vehicle dynamics
• I.e., how do we model vehicle dynamics?– Coordinate systems
– The role of equations
– Newton’s Second Law
• Dynamic loads on axles
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 4
Cugnot Vehicle (1769)
• The first motorized vehicle
• Also, the first accident!
P. 2
3
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 5
Sunbeam Mabley (1901)
• Development took some peculiar turns!
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 6
Speed Increase in Early Autos
• As speed increases, so do the dynamics
193019201910190018901880
0
20
40
60
80
100
Year
Sp
ee
d (
mp
h)
Mercer Raceabout
Olds Limited
30/98 Vauxhall
Panhard Levassor
Peugeot
Victoria
Winton
Daimler
Fiat
Peugeot
Fir
st c
oncr
ete
road
Fir
st t
raff
ic s
ignal
Pav
ed r
oad
New
York
to S
an F
ranci
sco
Sp
ee
d (
km
/h)
0
20
40
60
80
100
120
140
160
4
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 7
Forces on a Car
• To understand dynamics we need to know the forces
on the vehicle
• Gravity
• Aerodynamics
• Primary forces come from the tires
DLC Tire Forces.exeDLC Truck Tire Forces.exe
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 8
SAE Vehicle-fixed Coordinate System
• For many analyses the vehicle can be treated as a lumped
mass
• Need to define a coordinate system (directions relative to
the vehicle)
P. 8
Roll
Vertical
Yaw
Pitch
Z
Y
X
pq
r
CG
5
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 9
ISO Vehicle-fixed Coordinate System
• Some use a system from the International Standards
Organization (ISO)
• Both systems will be in the new SAE J670
Roll
Vertical
Yaw
Pitch
Z
Y
X
pq
r
CG
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 10
Earth-fixed Coordinate System
X
Y
Vehicle PathCourse Angle (Positive)
Heading Anglex Projected
Projection of Instantaneous Velocity
Sideslip Angle, β (Neg. angle shown)
Steer Angle
y Projected
ψ
ν
• Need to define motions relative to an inertial frame
P. 9
6
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 11
Engineering Models
• Objective is to model automotive vehicles and
systems
• Engineers use equations to define models
• Equations are only approximations of nature
• Consider the Perfect Gas Model
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 12
Perfect Gas Model
nRTPV =• The model expresses:
– What variables are important
• (P, V, n, R, and T)
– How they relate
• Suppose I am interested in pressure
• Pressure is:
– Proportional to n and T
– Inversely proportional to VV
nRTP =
7
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 13
Engineering Models
• Models that are simple, explicit equations teach us
how something works– The textbook focuses on these
• More comprehensive models (tires, suspension
systems) require other solutions– When needed we integrate them into simulation models like
• CarSim
• TruckSim
• BikeSim
• SuspensionSim
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 14
Newton’s Second Law
• All dynamics start with NSL
• Translational systems
xx MaF =∑ Fx = Force in the x-direction
M = Mass of the body
ax = Acceleration in x-direction
• Rotational system
xxxx IT α=∑Tx = Torque around the x-axis
Ixx = Moment of inertia about x-axis
αx = Acceleration about the x-axis
8
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 15
02
f x c A hx h hz h c
LW L Ma h Mg h sin L PM R h R d Mg c cosθ θ+ + + + + + − =
cos sin / 2c x c A hx h hz hf
Mg c Ma h Mg h L L PM R h R dW
L
θ θ− − − ⋅ − − −=
cos sin / 2 ( )c x c A hx h hz h
r
Mg b Ma h Mg h L L PM R h R L dW
L
θ θ+ + − ⋅ + + + +=
• Summing moments about point A
M g
Θ
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 16
Static Loads
• Sitting statically on a level surface:
L
cWW fs =
L
bWWrs = AB
M gc
Wf Wr L
b c
P. 13
9
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 17
Acceleration at Low Speed
• Acceleration on a level surface with no aerodynamic reactions
c
xfs
c
xf
g
a
L
hWW
g
a
L
h
L
cWW −=−= )(
c
xrs
c
xr
g
a
L
hWW
g
a
L
h
L
bWW +=+= )(
P. 13
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 18
Climbing a Grade
• No aerodynamic or acceleration effects
)sincos
( θθ
L
h
L
cWW f −
⋅=
• For small angles: cosθ = 1, sinθ = θ
θL
hWWW fsf −=
)sincos
( θθ
L
h
L
bWWr +
⋅=
θL
hWWW rsr +=
• θ = Grade angle (in radians)
P. 14
10
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 19
Road Grades
• Road grade is usually
expressed in % Run
RiseGrade 100(%) =
RunRise
θ1tan ( )Rise
Runθ −=
• Example – 5% grade 0.05RiseRun
=
1tan (0.05) 2.86deg 0.0499 rad 0.05 radθ −= = = ≅
(2.862 ) 0.999 1Cos = ≅� (2.862 ) 0.0499 0.05Sin = ≅�
• Good to about 20% (<2% error)
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 20
Composite Mass
• Longitudinal • Vertical
1
1
n
i i
icomposite n
i
i
m x
X
m
=
=
=∑
∑
1
1
n
i i
icomposite n
i
i
m z
Z
m
=
=
=∑
∑
Car
Passenger
Cargo
Z
Xx1 x2 x3
z1
z2
z3Composite
Finding the
Composite
CG Locationm1
m2
m3
11
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 21
Car-trailer Combinations
• Analyze trailer first to determine hitch forces
1.85 m
550 kg90 kg 3.0 m 1.1 m
908 kg 964 kg
0.35 m
1.85 m
550 kg90 kg
)( θ+==∑ xtrhxx aMFF
ctrtrhzz gMWFF =+=∑
Fundamentals of Vehicle Dynamics, T. D. Gillespie, ©2013 22
The End