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

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Automotive

Published on February 5, 2014

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S.F. van der Westhuizen, Vehicle Dynamics Group, University of Pretoria. Paper77439_0

2013/12/20 Comparison of different gas models to calculate the spring force of a hydropneumatic suspension Name: S.F. van der Westhuizen Date: 05 November 2013 1

2013/12/20 4S4 Hydropneumatic suspension 2

2013/12/20 Suspension Model ADAMS Suspension Force Velocity and Displacement Spring force calculated with gas models Simulink Suspension Force Velocity Displacement Friction Force (Lookup Table) Bumpstop Force Spring Force Displacement Friction Force Velocity Matlab M-file Damper Force Damper Force (Lookup Table) Velocity and Displacement Bumpstop Force (Polynomial) Oil Compression Spring Force (Gas Model) 3

2013/12/20 Gas models Ideal Gas (Isothermal) Ideal Gas (Adiabatic) BWR (Isothermal) Ideal Gas with energy equation Real gas corrective terms BWR with energy equation 4

2013/12/20 Gas models Volume vs. Time -4 1.4 x 10 Volume [m3] 1.2 1 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 Time [s] Pressure vs. Time 7 2.5 x 10 Pressure [Pa] 2 1.5 BWR BWR with EE IG IG with EE IG Adiabatic 1 0.5 0 0 5 10 15 20 25 Time [s] 5

2013/12/20 Laboratory testing Pressure vs. Displacement at 0.001Hz 7 2.5 x 10 Experimental IG IG with EE IG Adiabatic Pressure[Pa] 2 1.5 1 0.5 0 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Displacement [m] Pressure vs. Displacement at 0.1Hz 7 2 x 10 Experimental IG IG with EE IG Adiabatic 1.8 1.6 Pressure[Pa] 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Displacement [m] 6

2013/12/20 Laboratory testing Pressure vs. Displacement at 0.001Hz 6 x 10 18 Experimental BWR BWR with EE 16 Pressure[Pa] 14 12 10 8 6 4 2 0 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Displacement [m] Pressure vs. Displacement at 0.1Hz 7 2.5 x 10 Experimental BWR BWR with EE Pressure[Pa] 2 1.5 1 0.5 0 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Displacement [m] 7

2013/12/20 Laboratory testing m%REm values for the predicted gas pressure compared to measured gas pressure (soft suspension) IG with EE Avg(m%REm) Avg(P(%)) Avg(m%RE) P(%) BWR with EE IG Isothermal BWR IG Adiabatic 2.44 P(46.63) 4.02 P(95) 2.06 P(46.85) 3.26 P(95) 6.33 P(51.14) 12.11 P(95) 6.23 P(47.22) 11.57 P(95) 5.97 P(57.42) 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 6.36 P(60.36) 16.99 P(95) 5.90 P(56.14) 14.42 P(95) 11.82 P(56.57) 29.15 P(95) 11.74 P(56.21) 28.81 P(95) 11.09 P(55.05) 23.65 P(95) Avg(m%REm) Avg(P(%)) Avg(m%RE) P(%) 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 8

2013/12/20 DLC at 75 km/h Suspension Left Front Displacement Suspension Right Front Displacement 0.01 Displacement [m] 0.015 0.01 Displacement [m] 0.015 0.005 0 -0.005 -0.01 -0.015 0.005 0 -0.005 -0.01 0 1 2 3 4 5 Time [s] 6 7 8 9 Suspension Left Rear Displacement -0.015 0 BWR with EE IG (Isothermal) Experimental 0.015 1 2 3 4 5 Time [s] 6 7 8 9 Suspension Right Rear Displacement 0.025 0.02 0.01 Displacement [m] Displacement [m] 0.015 0.005 0 -0.005 0.01 0.005 0 -0.005 -0.01 -0.015 -0.01 0 1 2 3 4 5 Time [s] 6 7 8 9 -0.015 0 1 2 3 4 5 Time [s] 6 7 8 9 Left Front m%REm Right Front m%REm Left Rear m%REm Right Rear m%REm Average 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) 9

2013/12/20 Gas amount optimisation The displacement and pressure of the experimental run is used to optimise the initial pressure, temperature and gas volume for each suspension unit model. Pressure vs Time Left Rear 4 Experimental (P2) Simulated (P2) Pressure [Pa] 3.5 3 2.5 2 1.5 0 2 4 6 8 10 12 Time [s] Pressure vs Volume Left Rear 4 Experimental (P2) Simulated (P2) Simulated (P1) Pressure [Pa] 3.5 3 2.5 2 1.5 0.8 0.85 0.9 0.95 1 1.05 1.1 3 Volume [m ] 1.15 1.2 1.25 1.3 -4 x 10 10

2013/12/20 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 11

2013/12/20 Pressure Correlation Pressure vs Volume Right Rear 6 3.5 x 10 Experimental BWR with EE (P2) BWR with EE (P1) Pressure [Pa] 3 2.5 2 1.5 1 6 6.5 7 7.5 8 8.5 9 9.5 Volume [m3] Pressure vs Time Right Rear 6 3.5 -5 x 10 x 10 Experimental BWR with EE (P2) BWR with EE (P1) Pressure [Pa] 3 2.5 2 1.5 1 0 1 2 3 4 5 6 7 8 9 Time [s] Left Front m%REm Right Front m%REm Left Rear m%REm Right Rear m%REm Average 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 12

2013/12/20 Gas amount optimisation Suspension Left Front Displacement Suspension Right Front Displacement 0.015 Displacement [m] 0.02 0.01 Displacement [m] 0.015 0.005 0 -0.005 -0.01 -0.015 0.01 0.005 0 -0.005 -0.01 0 1 2 3 4 5 Time [s] 6 7 8 9 Suspension Left Rear Displacement -0.015 0 BWR with EE Ideal Gas (Isothermal) Experimental 2 3 4 5 Time [s] 6 7 8 9 Suspension Right Rear Displacement 0.015 Displacement [m] 0.02 0.01 Displacement [m] 0.015 1 0.005 0 -0.005 -0.01 -0.015 0.01 0.005 0 -0.005 0 1 2 3 4 5 Time [s] 6 7 8 9 -0.01 0 1 2 3 4 5 Time [s] 6 7 8 9 13

2013/12/20 Thank you Questions? 14

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