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Comparison of different gas models to calculate the spring
force of a hydropneumatic suspension
Name: S.F. van der Westhuizen
Date: 05 November 2013
2013/12/20
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4S4 Hydropneumatic suspension
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Suspension Model
Damper Force
ADAMS
Simulink
MatlabM-file
Velocity andDisplacement
Dis
pla
cem
ent
DisplacementVelocity
Fric
tio
n F
orc
e
Spring Force
Bumpstop Force
(Polynomial)
Spring Force(Gas Model)
Damper Force(Lookup Table)
Friction Force(Lookup Table)
Bu
mp
sto
p F
orc
e
Vel
oci
ty
Suspension Force
Velocity andDisplacement
Suspension Force
Oil Compression
Spring force
calculated with
gas models
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Gas models
Ideal Gas
(Isothermal)
Ideal Gas (Adiabatic)
BWR (Isothermal)
Ideal Gas with energy
equation
BWR with energy
equation
Real gas corrective terms
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Gas models
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
1.2
1.4x 10
-4
Vo
lum
e [m
3]
Time [s]
Volume vs. Time
0 5 10 15 20 250
0.5
1
1.5
2
2.5x 10
7
Time [s]
Pre
ssu
re [P
a]
Pressure vs. Time
BWR
BWR with EE
IG
IG with EE
IG Adiabatic
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Laboratory testing
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.080
0.5
1
1.5
2
2.5x 10
7
Displacement [m]
Pre
ssu
re[P
a]
Pressure vs. Displacement at 0.001Hz
Experimental
IG
IG with EE
IG Adiabatic
-0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.080
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
7
Displacement [m]
Pre
ssu
re[P
a]
Pressure vs. Displacement at 0.1Hz
Experimental
IG
IG with EE
IG Adiabatic
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Laboratory testing
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.080
2
4
6
8
10
12
14
16
18
x 106
Displacement [m]
Pre
ssu
re[P
a]
Pressure vs. Displacement at 0.001Hz
Experimental
BWR
BWR with EE
-0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.080
0.5
1
1.5
2
2.5x 10
7
Displacement [m]
Pre
ssu
re[P
a]
Pressure vs. Displacement at 0.1Hz
Experimental
BWR
BWR with EE
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Laboratory testing
m%REm values for the predicted gas pressure compared to measured gas
pressure (soft suspension) IG with EE BWR with EE IG Isothermal BWR IG Adiabatic
Avg(m%REm)
Avg(P(%)) 2.44 P(46.63) 2.06 P(46.85) 6.33 P(51.14) 6.23 P(47.22) 5.97 P(57.42)
Avg(m%RE) P(%) 4.02 P(95) 3.26 P(95) 12.11 P(95) 11.57 P(95) 15.47 P(95)
m%REm values for the predicted gas pressure compared to measured gas
pressure (stiff suspension) IG with EE BWR with EE IG Isothermal BWR IG Adiabatic
Avg(m%REm)
Avg(P(%)) 6.36 P(60.36) 5.90 P(56.14) 11.82 P(56.57) 11.74 P(56.21) 11.09 P(55.05)
Avg(m%RE) P(%) 16.99 P(95) 14.42 P(95) 29.15 P(95) 28.81 P(95) 23.65 P(95)
Stiff suspension setting is used for experimental testing since:
• Major gas model deviations take place at higher pressures
• Vehicle model errors are smaller at small roll angles
• Best and worst models are used in full vehicle model
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DLC at 75 km/h
0 1 2 3 4 5 6 7 8 9-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Time [s]
Dis
pla
cem
ent
[m]
Suspension Left Front Displacement
BWR with EE
IG (Isothermal)
Experimental
0 1 2 3 4 5 6 7 8 9-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Suspension Right Front Displacement
Dis
pla
cem
ent
[m]
Time [s]
0 1 2 3 4 5 6 7 8 9-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Suspension Left Rear Displacement
Dis
pla
cem
ent
[m]
Time [s]
0 1 2 3 4 5 6 7 8 9-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
Suspension Right Rear Displacement
Dis
pla
cem
ent
[m]
Time [s]
Left Front Right Front Left Rear Right Rear Average
m%REm m%REm m%REm m%REm m%REm
IG (Isothermal) 74.89 P(34.07) 61.23 P(48.39) 66.42 P(45.62) 83.35 P(28.75) 71.47 P(39.21)
BWR with EE 71.31 P(39.96) 64.85 P(51.72) 72.02 P(41.18) 65.57 P(46.28) 68.44 P(44.78)
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Gas amount optimisation
0 2 4 6 8 10 121.5
2
2.5
3
3.5
4
Pressure vs Time Left Rear
Pre
ssu
re [P
a]
Time [s]
Experimental (P2)
Simulated (P2)
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
x 10-4
1.5
2
2.5
3
3.5
4
Pressure vs Volume Left Rear
Pre
ssu
re [P
a]
Volume [m3]
Experimental (P2)
Simulated (P2)
Simulated (P1)
The displacement and pressure of the experimental run is used to
optimise the initial pressure, temperature and gas volume for each
suspension unit model.
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Gas amount optimisation
Suspension optimisation results
Left Front Right Front Left Rear Right Rear
Static Volume [m3] 7.37E-05 1.16E-04 9.98E-05 7.39E-05
Static Pressure [Pa] 2.28E+06 2.82E+06 3.08E+06 2.47E+06
Ambient Temperature [K] 290.4305 296.8518 294.6823 297.3961
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Pressure Correlation
Left Front Right Front Left Rear Right Rear Average
m%REm m%REm m%REm m%REm m%REm
IG (Isothermal) 27.39 P(95) 23.06 P (95) 23.54 P (95) 35.64 P (95) 27.41 P (95)
BWR with EE 29.00 P (95) 15.39 P (95) 16.64 P (95) 23.97 P (95) 21.25 P (95)
% Improvement -5.55 33.26 29.31 32.74 22.47
6 6.5 7 7.5 8 8.5 9 9.5
x 10-5
1
1.5
2
2.5
3
3.5x 10
6 Pressure vs Volume Right Rear
Pre
ssu
re [P
a]
Volume [m3]
Experimental
BWR with EE (P2)
BWR with EE (P1)
0 1 2 3 4 5 6 7 8 91
1.5
2
2.5
3
3.5x 10
6 Pressure vs Time Right Rear
Pre
ssu
re [P
a]
Time [s]
Experimental
BWR with EE (P2)
BWR with EE (P1)
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Gas amount optimisation
0 1 2 3 4 5 6 7 8 9-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Time [s]
Dis
pla
cem
ent
[m]
Suspension Left Front Displacement
BWR with EE
Ideal Gas (Isothermal)
Experimental
0 1 2 3 4 5 6 7 8 9-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
Suspension Right Front Displacement
Dis
pla
cem
ent
[m]
Time [s]
0 1 2 3 4 5 6 7 8 9-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Suspension Left Rear Displacement
Dis
pla
cem
ent
[m]
Time [s]
0 1 2 3 4 5 6 7 8 9-0.01
-0.005
0
0.005
0.01
0.015
0.02
Suspension Right Rear Displacement
Dis
pla
cem
ent
[m]
Time [s]
2013/12/20
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Thank you
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