optimal vehicle suspension characteristics for increased
TRANSCRIPT
Optimal vehicle suspension characteristics for increased structural fatigue life
Braham Breytenbach
Public defence
28 Mei 2010
Problem statement
� Highly competitive market for vehicles
� Reduce vehicle mass, increase payload
� Road loads on structure must be reduced!!!
Problem statement
Questions:
1. Suspension characteristics for structural life?
2. Are the optimal characteristics sensitive to payload?
Approach
Mathematical modelling
�Experimentally validated
�Computationally efficient
Suspension optimisation for life
�Dynamic-Q algorithm
�Optimal spring and damper characteristic
�Different load cases considered
Test vehicle
� Land Rover Defender 110 -> fully instrumented
� Hydro-pneumatic 4S4 suspension system
Instrumentation
� Suspension force load cell
� Strain gauges => suspension mounting
Field tests
Discrete obstacles:
Ride comfort mode Handling mode
Field tests
Rough road / Random terrain:
Ride comfort mode Handling mode
Field tests
Data repeatability:
0.5 1 1.5 2 2.5 3-10
0
10Body Vertical Accelerations
LR
Acc.[
m/s
2]
0.5 1 1.5 2 2.5 3-10
0
10
RR
Acc.
[m/s
2]
0.5 1 1.5 2 2.5 3-20
0
20
LF
Acc.
[m/s
2]
Time [s]
Run 16Run 20Run 22
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 30
2000
4000
6000
8000
Load C
ell
Forc
e [
N]
Left Rear Suspension Forces
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 30
2000
4000
6000
8000
Calc
ula
ted L
R F
orc
e [
N]
Time [s]
Run 16
Run 20
Run 22
Mathematical model
� Linear models inadequate
� 7-DOF model with non-linear force characteristics
� Stresses predicted by quasi-static approach
� Damage estimated by Miner’s rule Z
Friction characterisation
Experimental Setup
Friction characterisation
Test input
100 110 120 130 140 150 160 170 180 190 200
-0.1
-0.05
0
0.05
0.1
Displacement 1
Dis
pla
cem
ent [m
]
250 300 350 400 4500
0.05
0.1
Displacement 2
Dis
pla
cem
ent [m
]
240 260 280 300 320 340 360 380 400 4200
0.05
0.1
Displacement 3
Time [s]
Dis
pla
cem
ent [m
]
Spring
Friction
Tester
Friction characterisation
Test results
-0.1 -0.05 0 0.05 0.13500
4000
4500
5000
5500Force Displacement
Displacement [m]
Fo
rce [N
]
Measured
Model
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-500
-400
-300
-200
-100
0
100
200
Experimental Friction Characteristics
Velocity [m/s]
Frictio
n F
orc
e [N
]
500 kPa
1500 kPa
2000 kPa
2500 kPa
3000 kPa
Friction characterisation
Test results
300 320 340 360 380 400 420 440 460 480 500-500
-400
-300
-200
-100
0
100
200
300
Time [s]
Frictio
n F
orc
e [N
]
Friction Force for Displacement 3
Measured
Model
Model correlation
Discrete obstacles: body vertical accelerations
0.5 1 1.5 2 2.5 3 3.5-10
-8
-6
-4
-2
0
2
4
6
8
10
Time [s]
Re
ar
Ac
cele
ratio
n [m
/s2]
Measured
Linear Pitch Bounce Model
0.5 1 1.5 2 2.5 3 3.5-10
-8
-6
-4
-2
0
2
4
6
8
10
Time [s]
Rear
Vert
ical A
ccele
ratio
n [m
/s2]
Measured
Non-linear Full Vehicle Model
Linear model 7-DOF non-linear model
Model correlation
Discrete obstacles: suspension forces
Linear model 7-DOF non-linear model
0.5 1 1.5 2 2.5 3 3.50
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Time [s]
Rear
Suspe
nsio
n F
orc
e [N
]
Measured
Linear Pitch Bounce Model
0.5 1 1.5 2 2.5 3 3.50
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Time [s]
Re
ar
Su
sp
en
sio
n F
orc
es
[N
]
Measured
Non-linear Full Vehicle Model
Model correlation
Rough road / Random terrain:
� Low speed correlation poor -> tyre and friction models!!!
� High speed dynamic correlation excellent (error < 5%)
� Damage correlation acceptable (error < 30%)
� Better correlation in ride comfort mode
Mathematical optimisation
� Objective function: structural damage over rough terrain
� Design variables: � Static gas volume (pneumatic spring stiffness)
� Damper scale factor
� Constraint functions:� Loss of wheel contact < 10% of total time
� Bump stop contact unacceptable
� Two load cases considered:� Unladen Land Rover 2.2 ton
� Fully laden Land Rover 4.5 ton
Mathematical optimisation
Cost function visualisation:
Unladen 2.2 ton Fully laden 4.5 ton
Mathematical optimisation
Monte Carlo simulation:
Unladen 2.2 ton Fully laden 4.5 ton
Mathematical optimisation
Results:
Unladen vehicle
Static Gas Volume
DamperScale Factor
Damage as % of baseline
Fatigue damage 0.4-0.8ℓ 0.4 29%
Ride comfort 0.5ℓ 0.3 -
Handling 0.1ℓ 3 -
Fully Laden vehicle
Static Gas Volume
DamperScale Factor
Damage as % of baseline
Fatigue damage 0.5-0.8ℓ 0.7 86%
Mathematical optimisation
Robust optima:
Step into the feasible design space:
[ ]
( )
( )xg
xgu
uxx
xxxrobust
∇
∇=
⋅×
∆+
∆+=
***
1
Mathematical optimisation
Robust optima:
Spring Static Volume [l]
Dam
per
Sca
le F
acto
r
Unladen
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
1
1.5
2
2.5
3
3.5
4
Cost Function
Feasible
Bump Stop Constraint Active
Optimum X*=[0.49; 0.34], F*=22.3%, Std. Dev. =1.2536%
Spring Static Volume [l]
Dam
per
Sca
le F
acto
r
Fully Laden
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
1
1.5
2
2.5
3
3.5
4
Cost Function
Feasible
Bump Stop Constraint Active
Optimum X*=[0.38; 0.36], F*=47.7%, Std. Dev. =3.448%
Mathematical optimisation
Multi-variable optimisation:
0 0.5 1 1.5 2 2.5 3 3.5 4
-0.5
0
0.5
Strut Force Response
Displacement [m]
Velocity [m/s]
0 0.5 1 1.5 2 2.5 3 3.5 4
4000
6000
Forc
e [N
]
Spring Force
0 0.5 1 1.5 2 2.5 3 3.5 4
-2000
0
2000
Forc
e [
N]
0 0.5 1 1.5 2 2.5 3 3.5 4
2000
3000
4000
5000
6000
7000
Forc
e [
N]
Time [s]
Symmetric Damper Scale Factor
Assymmetric Damper Scale Factor
Suspension Force - Symmetric DSF
Suspension Force - Assymmetric DSF
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-3000
-2500
-2000
-1500
-1000
-500
0
500
1000Damper Characteristics
Velocity [m/s]
Dam
pe
r F
orc
e [N
]
Unladen
Fully Laden
Heavy Load
Extreme Load
Conclusions
� Minima in low damping, low stiffness region
� Cost function is insensitive to static gas volume -> load levelling pneumatic suspension
� Optima are constrained by bump stop constraint
� Damper characteristic is sensitive to payload change
Recommendations
� Variable damping suspension, rather than 4S4
� 4S4 should be considered for handling
� Improved tyre and friction model!!!