Optimal vehicle suspension characteristics for increased ...

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!!!