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
yyycg
2/)(
21
+=
Equations of motion:
21
FFym cg
+=
Force on the car at each wheel :
111
ykyF
−−=
Equation 1
Equation 3
Equation 5
Vehicle Suspension System
Model Equations (2)
Combining Equations 1 through 6 we find
))(/2())(/2(
212121
yymyymkyy
+−+−=+
Equation 7
One scheme to solve these equations is to let
22
11
yx
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.
211
yyx
+=
111
)/2()/2(
xmxmkx
−−=
Equation 9
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:
Assume (a) even distribution of mass
(b) length of vehicle is 10% greater than wheelbase
0
Vehicle Suspension System
Model Equations (6)
Then the general solution of Equations 9 and 10 can be written as
1
12111
/
)sincos(
1
=
+
=
−
mk
tctcex
t
where
Vehicle Suspension System Dynamics:
Mode 1
Vehicle Suspension System Dynamics:
Mode 2
In mode 2 the vehicle center of gravity does not move and
the vehicle oscillates in rotation about the cg.
Vehicle Suspension System Dynamics:
Modes 1 and 2
As a function of and
(a) vehicle oscillations always damp out more quickly in the
rotational mode (mode 2) than in the translational mode (mode 1)
km,
km
=
Homework Assignment 19
Read:
In text, Sections 8.5.1.4 through 8.5.1.7
Work: