Bergamo University
Italy
12th-14th June 2012
Lecture 2- Suspension Systems
Professor Mike Blundell
Phd, MSc, BSc (Hons), FIMechE, CEng
Contents
•
•
•
•
Suspension Design Process
Suspension Types
Modelling Suspension Systems
Measurements and Simulated Outputs
Suspension Design Process Activities
Wheel
Load
Variation
Body
Isolation
Handling
Load
Control
Compliant
Wheel
Plane
Control
Kinematics
Wheel
Plane
Control
Compliant
Loading
Environment
Investigation Design Strategies
Set Design Targets
Verify Proposed Designs
Wheel load variation - A classic
case of static indeterminacy
Front wheel drive hatchback
cornering pose
3
Body Isolation –Ride Model
• Proving Ground or Shaker Rig
• Isolation and Comfort
• Loss of Tyre/Ground Contact
4
Body Isolation – A Classical Quarter
Vehicle Ride Model
Vehicle Body
or
Sprung Mass
Suspension Spring
and Damper
Z
X
z
m
Body Response
k
c
zg
Ground
Input
Time (s)
• Predict Sprung Mass (Body) and Unsprung Mass
(Wheel) Natural Frequencies
• Transmissibility
5
Handling Load Control
O1
X1
GRF
Y1

M2z Izz ω
2z
 V ω )
F2y m2 ( V
2y 2x 2z
• The simplest possible representation of a vehicle
manoeuvring in the ground plane (bicycle model)
• Weight transfer
• Tyre lateral force characteristics as a function of tyre
load
6
Handling Load Control (Continued)
Front axle side force
Rear axle side force
• Side forces calculated for a 0.1 rads/s ramped input
to 0.01 rads beginning at 0.3s
7
Graphical Representation of Front
Suspension Configurations in
ADAMS/Chassis
Hotchkiss
SLA (Torsion Bar)
McPherson Strut
SLA (Perch)
Provided courtesy of MSC.Software
SLA (Coil)
Twin I-Beam
8
Graphical Representation of Rear
Suspension Configurations in
ADAMS/Chassis
Central Link
Quardalink (Strut)
4 Link Watts
Semi Trailing Arm
Provided courtesy of MSC.Software
4 Link Panhard
Twist Beam
9
Double Wishbone Suspension System
Upper Bushes (Mounts)
Upper Wishbone
(Control Arm)
Upper Ball Joint
(Bushes on Rear)
Spring Damper
Wheel Knuckle
(Stub Axle) (Kingpin)
Road Wheel
Lower Bushes (Mounts)
Lower Wishbone
(Control Arm)
Connection to Rack
(Body on Rear)
Track Rod
(Tie Rod on Rear)
Lower Ball Joint
(Bushes on Rear)
Track Rod End
10
McPherson Strut Suspension System
Upper Mount
Spring
Damper
Wheel Knuckle
(Stub Axle) (Kingpin)
Lower Bushes (Mounts)
Road Wheel
Lower Wishbone
(Control Arm)
Lower Ball Joint
Connection to Rack
Track Rod
Track Rod End
11
Double Wishbone Suspension
Modelled with Bushes
Modelled with Bushes
Modelled with Joints
Bushes
Spherical
Bushes
Revolute
Revolute
Revolute
Spherical
Spherical
Motion
In-Plane
Motion
Universal
In-Plane
Spherical
Motion
Revolute
Spherical
Motion
Universal
Spherical
Translational
Translational
12
Coventry University
Formula Student Car
Bell Crank
Push Rod Universal
Revolute
Spring Damper
Spherical
Body Mount
Modelling of push rod and bell crank
mechanism in student race car
13
Suspension Analysis
Data Requirements
Kinematic or Quasi-static vertical rebound to bump analysis
Co-ordinates of suspension linkage connections
Bush stiffnesses (If this effects the movement)
Spring stiffness ( If suspension wheel rate is to be calculated)
Static or Quasi-static durability analysis
Co-ordinates of suspension linkage connections
Bush stiffnesses
Spring stiffness
Bump and rebound stops
Component flexibility (some suspensions)
Dynamic durability or vibration analysis
Co-ordinates of suspension linkage connections
Mass and inertial properties
Bush stiffnesses
Bush damping coefficients
Spring stiffness
Damper properties
Bump and rebound stops
Component flexibility (some suspensions)
Use of Virtual Test Rig to Analyse a
Half Vehicle Suspension Model
Provided courtesy of MSC.Software
Superimposed animation frames giving
visual indication of wheel envelope
15
Input of Vertical Motion
at the Wheel Centre
I

In-Plane
J

Motion
100
Bump
Movement
(mm)
-100
Bump
0.25
0.5
0.75
1.0 Time (s)
Rebound
16
Geometric and Instant Steer Axes of
a Suspension System
Geometric Steer Axis
Instant Steer Axis
17
Bump Movement, Wheel Recession
and Half Track Change
Wheel Change
Marker (WC)
BM
Fixed Ground
Marker (FG)
HTC
z
y
BM = DZ(WC,FG)
HTC = DY(WC,FG)
WR = DX(WC,FG)
WC
FG
z
WR
x
18
Half Track Change (HTC)
A measure of how much the
contact patch moves in and out
relative to the vehicle body at
bump movement
Influence in Vehicle Dynamics
•Full Track Change effect
•Beneficial on the outside wheel
•Limits of bodywork
Double Wishbone
BM = DZ(WC,FG)
HTC = DY(WC,FG)
Mc Pherson
Wheel Recession (WR)
A measure of fore-aft movement as
the wheel moves between Bump and
Rebound
Influence in Vehicle Dynamics
•Ride Comfort
•Increased component durability
Double Wishbone
WR= DX (WC, FG)
Mc Pherson
Calculation of Camber Angle and
Steer Angle
g
g
SA
z
g = (180/p) ATAN (DZ(WC,SA)/DY(SA,WC))
d
x
WC
y
d
d =(180/p) ATAN (DX(WC,SA)/DY(SA,WC))
21
SA
Camber angle (g)
As the vehicle rolls it’s needed to attempt and keep the tyre flat on the road and
avoid opposite camber thrust the tyres running on their edges
0% Camber Rollover compensation
γ = (180/π) ATAN (DY(WC,SA)/DZ(SA,WC))
Double Wishbone
Mc Pherson
100% Camber Rollover compensation
Bump (Roll) Steer (δ)
As the suspension moves between bump and rebound small amounts of steer (toe)
change may be introduced due to suspension geometry.
It can be desirable to add to an understeer characteristic
δ = (180/π) ATAN (DY(WC,WB)/DX(WC,WB))
Gradient
Shopping cars
Sport cars
4-5o/m
>10o/m
Double Wishbone
Mc Pherson
Calculation of Castor Angle and
Suspension Trail
f = (180/p) ATAN (DX(UB,LB)/DZ(UB,LB))
TR = DX(WB,LB) + DZ(LB,WB) * DX(UB,LB) / DZ(UB,LB)
f
Upper Ball Joint
Marker (UB)
Lower Ball Joint
Marker (LB)
z
x
Wheel Base
Marker (WB)
TR
Intersection of
Steering Axis
with Ground
24
Castor Angle (φ) and
Suspension Trail (TR)
Castor angle adds to the self-centering
with the Pneumatic Trail
Suspension (Mechanical) Trail
Typical Value 35-50mm
Castor Angle change
Double Wishbone
Mc Pherson
φ = (180/π) ATAN(DX(UB,LB)/DZ(UB,LB))
TR = DX (WB, LB) +DZ (LB, WB)*DX (UB, LB)/DZ (UB, LB)
Calculation of Steering Axis
Inclination and Ground Level Offset
q = (180/p) ATAN (DY(LB,UB)/DZ(UB,LB))
GO = DY(WB,LB) - DZ(LB,WB) * (DY(LB,UB) / DZ(UB,LB))
q
UB
z
y
GO
Wheel Base
Marker (WB)
Intersection of
Steering Axis
with Ground
26
Steering Axis Inclination (θ) and
Ground level Offset (GO)
GO offset minimises scrubbing
of the tyre during steering
when stationary.
Alternative method of tweaking
GO is by using rims with offset.
Steering Axis Inclination (θ) and Ground
level Offset (GO) (continued)
When braking on split mu surface vehicle tends to
yaw due to higher braking forces on the high mu side.
Using negative ground level offset can compensate
the effect.
θ = (180/π) ATAN(DY(LB,UB)/DZ(UB,LB))
GO =DY (WB, LB)-DZ (LB, WB)*(DY (LB, UB)/DZ (UB, LB))
GO typical Value 10mm
Double Wishbone
Mc Pherson
Front right wheel
Instant Centre and Roll Centre Positions
Double Wishbone Suspension
Double Wishbone Suspension
Centre Line
A
Instant Centre
B
D
C
Roll Centre
z
y
Roll Centre Height
Wheel Base (WB)
McPherson Strut Suspension
Centre
A
Line
Instant Centre
C
B
Wheel Base (WB)
D
Roll Centre
y
z
Roll Centre Height
29
Position of Instant Centre Construction
Points on Wheel Centre YZ Plane
B
A
WC
D
Z
C
X
Y
30
Height of Roll Centre (RC)
RC is the corresponding point of lateral force application
on the vehicle sprung mass and relative to its distance
from the Vehicle’s CM is the applied roll torque.
Double Wishbone
Mc Pherson
Calculation of Wheel Rate (Equivalent
Spring Acting at the Wheel Centre)
Fw
VEHICLE BODY
kw
Fs
kw
dw
ks
Equivalent spring
acting at the
wheel centre
A
ds
dw
Fw
ls
lw
32
Wheel Rate
The “equivalent” spring acting
between wheel centre and the
vehicle body
Wheel rate can be set so as to be softer
during initial bump and stiffer during
increased bump travel for better ride
comfort and roll control
Double Wishbone
Mc Pherson
Case Study – Suspension Kinematics
34
Modelling Bushes
35
Modelling Bushes
36
Data Input – Joint, Linear Bush, Non-Linear Bush
37
Comparison of Suspension Outputs
38
Suspension Durability
•
•
•
Static Analysis
Single Suspension System Model, Range of Load Cases
(3G Bump, 2G Rebound, 1G Braking, ….)
Dynamic Analysis using Road Load Data
Single Suspension System Model, Quarter or Full Vehicle Model
Full Virtual Modelling and Analysis for Durability
Full Vehicle Model with Transient Dynamics
Physical Tyre Model Required
Road/ Terrain model (Laser scanned)
39
Suspension Durability Analysis
LOADCASE
Fx (N)
Fy (N)
3G Bump
11180
2G Rebound
Fx
Longitudina
l
loads
Fz
Vertical
loads
Fy
Lateral
loads
Garrett, T. K., (1953) Automobile dynamic loads
some factors applicable to design, Automobile
Engineer, February.
Fz (N)
-7460
0.75G Cornering
(Outer Wheel)
4290
5880
0.75G Cornering
(Inner Wheel)
-1180
1620
1G Braking
5530
5530
0.35G Reverse
Braking
-2150
3330
Kerb Impact
Pothole Braking
9270
15900
4120
12360
Weight Transfer-Braking
Hand calculations can be performed
To establish loads for braking or cornering
cm
mAx
Z
h
mg
X
FRx
FFx
FRz = FSRz – FB
FFz = FSFz + FB
a
b
L
FFz = FSFz + FB =
FRz = FRFz – FB =
+m g b
2L
-m g a
2L
m Ax h
2L
m Ax h
2L
FFx = m FFz
FFx = m FFz
41
Case Study - Pothole Braking Case
•
•
•
•
Ramping loads on over 1 second (Quasi-static)
Allows animation (visual check)
UNI
Load path through damper not modelled
Unless static equivalent force included
REV
SPH
BUSH
SPH
CYL
BUSH
BUSH
REV
MOTION
I marker
at
wheelbase
12360
N
SPH
FIX
BUSH
ZP for
marker 3
15900 N
Z
ZP for
marker 1
X
Y
ZP for
marker 2
GRF
Typical Results
Animation
Quarter Vehicle Model
Simple starting point
Dynamic Analysis
Road Bump Strike
Tyre stiffness and damping
Tyre can lift off
Quarter
Vehicle Body
Part
Body
connects to
Ground by
Translational
Joint
Jack
Part
45
Road Profile
10 m/s
Z
X
GRF
1000
y
.
1
x
200
200
200
200
200
200
10000
.
.
.
.
. .
.
2
5
4
3
6
7
Point
1
Distance x (mm)
Time x (s)
Height y (mm)
0
0
0
2
3
4
5
.
8
150
6
1000 1200 1400 1600 1800
0.10 0.12 0.14 0.16 0.18
0
75
150
150
150
9
7
2000
0.20
75
8
9
2200 12200
0.22 1.22
0
0
46
Animation
Quarter Model Results
Time = 0 sec
Time = 0.14 sec
Time = 0.18 sec
48