Comparison of different gas models to calculate the spring force of a hydropneumatic suspension

2013/12/20

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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]

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Thank you

Questions?