07 1 Suspension Concepts
07 1 Suspension Concepts
07 1 Suspension Concepts
Overview
2.
Maintain the wheels in the proper steer and camber attitudes to the road
surface.
3.
4.
Resist roll of the chassis. Keep the tires in contact with the road with
minimal load variations. (Ex. Table with 4 legs; shopping carts, etc.)
System solution
Motional requirements are met through kinematic considerations.
Isolation is achieved by including elastic and dissipative elements.
Since the kinematic, elastic, and dissipative design will impact how
the tire interacts with the road, as well as how the body reacts, it is
essential to understand each particular vehicles dynamics in
developing a suspension system.
A balance between handling and ride is almost always necessary.
Tires obviously play a critical role.
Ks
turning
turning and
sliding
vehicle body)
rotation
turning + ball = triangular or Aarm
f=1+3=4
ball
f=3
rubber
f = 1 (3)
ball and
surface
f=5
f=1
f=2
f=4
f=2
7 steering link/gearbox
8 spring
9 damper
10 drive shaft
Wheel carrier
rigidly fixed to
vehicle (tractor)
Typical
rigid-axle
suspension
5 link
suspension
Two
wheels in
tandem
F = degrees of freedom
ME 360/390 Prof. R.G. Longoria
Vehicle System Dynamics and Control
3 links
a.
Rod link
b.
Triangular link
c.
Turning and sliding link
F = 6(k + l g ) r + fi
1
= 6(1 + 3 6) 2 + (4 3 + 1 + 2)
=1
= 4 3 + 2 = 14
g
F = 6(k + l g ) r + fi
1
= 6(1 + 3 6) 1 + 14
=1
This is a common
race car rear
suspension.
triangular link
If used with a
turning-and-sliding
joint, you form the
basic strut
suspension
k = 1, l = 4, g = 8, r = 4
= 7 3 + 1 = 22
k = 1, l = 4, g = 8, r = 3 F = 6(k + l g ) r + fi
fi = 7 3 + 1 = 22
= 6(1 + 4 8) 3 + 22
=1
F = 6(k + l g ) r + fi
1
= 6(1 + 4 8) 3 + 22
=1
f i = 10 3=30
F = 6(k + l g ) r + f i
1
= 6(1 + 5 10) 5 + 30
=1
Rigid-axle suspensions
g
F = 6(k + l g ) r + fi
1
= 6(0 + 2 3) 1 + 3 3
rod-link
=2
ball-joint
Panhard rod
F = 6(k + l g ) r + fi
1
= 6(0 + 4 7) 3 + 6 3 + 1 5
= 18 3 + 18 + 5 = 2
ball-and-surface
These bottom 3 are alternatives to controlling lateral motion using a Panhard rod.
c uses a ball/surface, d a scissors mechanism, and e a Watt linkage.
Figures from Matschinsky (2000)
l = 1 (number of links)
g = 1 (number of joints)
r = 0 (number of individual rotations of links)
= 1 2
F = 6(k + l g ) r + fi
1
= 6(0 + 1 1) 0 + 1 2
=2
Rigid-axle suspensions
From Matschinsky (2000)
= 8 3=24
g
F = 6(k + l g ) r + fi
1
= 6(0 + 5 8) 4 + 24
= 18 4 + 24 = 2
Gillespie (1992)
Gillespie summarizes both solid axle and independent suspension roll center
estimation
Steeds writes that it is hard to change roll center for a solid axle; you can change
the mounting of springs. Independent suspensions give you more options to
manipulate the roll center location. Steeds handout has good examples on finding
roll centers.
Roll center location can be useful in assessing suspension characteristics and how,
for example, lateral load transfer due to suspension influences vehicle handling.
Gillespies discussion on roll moment distribution shows how this can be done.
Blundell and Harty provide an example (using ADAMS) of finding instantaneous
roll center.
SPRUNG
MASS
AA
WC
Steeds (1960)
ME 360/390 Prof. R.G. Longoria
Vehicle System Dynamics and Control
m = (W OE + N OF ) OB
This is found by using the concept of an instantaneous center, O (refer to Steeds handout on
roll centers on VSDC clog). With m, the spring force can be found,
S = mL a
Then, in the equilibrium configuration shown, the two link
forces are found by summing forces in the y and z directions
leading to two equations in two unknowns:
sin
cos
sin P W m cos
=
cos U N + m sin
Solving gives,
Rs =
dzs
dzw
Kw =
dFw
dzw
Kw
Ks
2
s
Summary
Suspensions control the orientation of the wheel/tire relative to road
and vehicle.
We generally need to have good estimates of slip angle and camber,
vertical tire deflection, longitudinal slip in order to predict vehicle
dynamics.
We also need to be able to convey key suspension characteristics into
our ride and vibration analysis for a vehicle for other types of
analysis.
These slides review common suspension types and geometries and wheel rate determination.
A more complete discussion would also briefly review anti-squat/pitch/dive and also review
roll center analysis and roll moment distribution. Handouts will be posted that cover these
topics.
ME 360/390 Prof. R.G. Longoria
Vehicle System Dynamics and Control
References
1.
2.
3.
4.
5.
6.
7.
8.
Steeds, W., Mechanics of Road Vehicles, Iliffe and Sons, Ltd., London,
1960.
Gillespie, T.D., Fundamentals of Vehicle Dynamics, SAE, Warrendale,
PA, 1992.
Wong, J.Y., Theory of Ground Vehicles, John Wiley and Sons, Inc., New
York, 2001.
Blundell, M., and D. Harty, The Multibody Systems Approach to Vehicle
Dynamics, Elsevier Limited, 2004.
Heisler, H., Vehicle and Engine Technology, SAE, Warrendale, PA, 1996.
Matschinsky, W., Road Vehicle Suspensions, Professional Engineering
Publishing Ltd., London (Translated from German), 2000.
Milliken, W.F., and D.L. Milliken, Race car vehicle dynamics, Society of
Automotive Engineers, Warrendale, PA, 1995.
Vehicle Dynamics Terminology, SAEJ670e, Society of Automotive
Engineers, Warrendale, PA.