Suspension system with optimized damping response
View Patent ↗An analytical methodology for the specification of progressive optimal compression damping of a suspension system to negotiate severe events, yet provides very acceptable ride quality and handling during routine events. In a broad aspect, the method provides a progressive optimal unconstrained damping response of the wheel assembly with respect to the body. In a preferred aspect, the method provides a progressive optimal constrained damping response of the wheel assembly with respect to the body, wherein below a predetermined velocity a conventional damper force is retained.
1. A method for providing a suspension system with optimized damper response, wherein a sprung mass is suspended by the suspension system, the suspension system including a wheel assembly having a wheel center and a mass, m, a nonlinear damper wherein the damper is connected between the sprung mass and the wheel assembly, and a spring having a predetermined spring force, F(x), as a function of displacement of the wheel relative to the sprung mass wherein the spring is connected between the sprung mass and the wheel assembly, said method comprising the steps of:
providing a substantially constant total force, F(L), on the wheel assembly with respect to the sprung mass during a jounce event over a travel length of the wheel center of the wheel assembly with respect to the sprung mass, wherein the travel length extends between zero and L;
wherein the wheel center of the wheel assembly has a velocity U o relative to the sprung mass responsive to the jounce event at the travel length of zero, and wherein the wheel center of the wheel assembly has a velocity of zero responsive to the jounce event at the travel length of L; and
wherein F(L) is a combination of a damper force, Φ(y), provided by the damper and of the spring force, F(x), provided by the spring, where
F
(
x
)
=
F
(
(
1
-
y
2
U
0
2
)
L
)
,
for any wheel center velocity, y, where 0≦y≦U 0 , and where the damping rate of the damper provides
Φ
(
y
)
=
F
(
L
)
-
F
(
(
1
-
y
2
U
0
2
)
L
)
,
where L is given by
m
*
U
0
2
2
=
L
*
F
(
L
)
and wherein the wheel center velocity, y, responsive to the jounce event is related to a velocity, v, of the damper by a predetermined ratio, r, where y=v/r.
2. The method of claim 1 , wherein the damper force is a smooth, continuous and monotonically increasing progressive optimal unconstrained damper force.
3. A method for providing a suspension system with optimized damper response, wherein a sprung mass is suspended by the suspension system, the suspension system including a wheel assembly having a wheel center and a mass, m, a nonlinear damper wherein the damper is connected between the sprung mass and the wheel assembly, and a spring having a predetermined spring force, F(x), as a function of displacement of the wheel relative to the sprung mass wherein the spring is connected between the sprung mass and the wheel assembly, said method comprising the steps of:
providing, if an initial velocity, U 0 , of the wheel center of the wheel assembly relative to the sprung mass in response to a jounce event at an initial position, x 0 , is less than or equal to a first predetermined wheel center velocity, u 1 :
a predetermined force, φ(y), by the damper and the spring acting in combination on the wheel assembly with respect to the sprung mass; and
providing, if the initial velocity, U 0 , of the wheel center of the wheel assembly relative to the sprung mass in response to a jounce event at the initial position, x 0 , is greater than the first predetermined wheel center velocity, u 1 :
a substantially constant total force, C 1 , by the damper and the spring acting in combination on the wheel assembly with respect to the sprung mass during a jounce event for any velocity of the wheel center of the wheel assembly greater than or equal to a second predetermined wheel center velocity, u 2 , where u 2 >u 1 ;
the predetermined force, φ(y), by the damper and the spring acting in combination on the wheel assembly with respect to the sprung mass for any velocity of the wheel center of the wheel assembly relative to the sprung mass in response to a jounce event in which the velocity of the wheel center in response thererto is less than or equal to the first predetermined wheel center velocity, u 1 ; and
a smooth, continuous and monotonically increasing transition force by the damper and the spring acting in combination on the wheel assembly with respect to the sprung mass for any wheel center velocity in response to the jounce event between velocity u 1 and velocity u 2 ; and
wherein said parameters are related by:
Ω
(
y
)
=
{
Φ
1
(
y
)
≡
C
1
-
F
(
U
0
2
-
y
2
2
C
1
m
+
x
0
)
,
y
≥
u
2
step
(
y
,
u
1
,
φ
(
y
)
,
u
2
,
Φ
1
(
y
)
)
,
u
2
≥
y
≥
u
1
φ
(
y
)
,
u
1
≥
y
≥
0
where step is the transition force acting from φ(y) at velocity u 1 to Φ 1 (y) at velocity u 2 ; and
wherein for a predetermined ratio, r, such that said y=v/r, where v is a velocity of the damper relative to the sprung mass, then a progressive optimal constrained damping function Ψ(v) as a function of the damper velocity v is given by the relation
Ψ
(
v
)
=
Ω
(
y
=
v
/
r
)
r
.
4. The method of claim 3 , wherein:
u 1 generally neighbors u 2 ; and
u 1 is substantially equal to 2.0 m/s.