2013/12/20

1

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

2

4S4 Hydropneumatic suspension

2013/12/20

3

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

2013/12/20

4

Gas models

Ideal Gas

(Isothermal)

Ideal Gas (Adiabatic)

BWR (Isothermal)

Ideal Gas with energy

equation

BWR with energy

equation

Real gas corrective terms

2013/12/20

5

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

2013/12/20

6

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

2013/12/20

7

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

2013/12/20

8

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

2013/12/20

9

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)

2013/12/20

10

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.

2013/12/20

11

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

2013/12/20

12

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)

2013/12/20

13

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

14

Thank you

Questions?