Vehicle Suspension System
Model Definitions
Position of vehicle centerline at right wheel relative
to equilibrium position
=
1
y
=
2
y
Position of vehicle centerline at left wheel relative to
equilibrium position
=
cg
y
Position of vehicle center of gravity relative to
equilibrium position
Geometry:
Vehicle Suspension System
Model Equations
Equations of motion:
Force on the car at each wheel :
Vehicle Suspension System
Model Equations (2)
Combining Equations 1 through 6 we find
One scheme to solve these equations is to let
11
yx
=
Vehicle Suspension System
Model Equations (3)
However, from Equations 7 and 8 we see that a better choice is to let
Then Equations 7 and 8 become
Equations 9 and 10 are uncoupled and easy to solve.
Vehicle Suspension System
Model Equations (4)
Before we solve Equations 9 and 10 it is useful to
(a) compute the moment of inertia
I
Vehicle Suspension System
Model Equations (5)
z
2/b
2/l
2/l−
2/b−
Computing the moment of inertia:
0
Vehicle Suspension System
Model Equations (6)
Then the general solution of Equations 9 and 10 can be written as
1
24232
/
=
mk
where
Vehicle Suspension System Dynamics:
Mode 1
In mode 1 the vehicle center of gravity oscillates up and
down and there is no rotation
Vehicle Suspension System Dynamics:
Mode 2
Vehicle Suspension System Dynamics:
Modes 1 and 2
As a function of and
(a) vehicle oscillations always damp out more quickly in the
km,
km
=
Homework Assignment 19
Read:
In text, Sections 8.5.1.4 through 8.5.1.7