Investigation and Phenomenological Modeling of Degraded Twin-Tube Shock Absorbers for Oil and Gas Loss
Abstract
:1. Introduction
2. Materials and Methods
3. Results
3.1. Data Analysis
3.2. Shock Absorber Model
3.3. Validation
3.4. Simulation Study
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ABS | Anti-lock braking system |
SA | Shock absorber |
F-v | Force–velocity |
F-s | Force–displacement |
PV | Piston valve |
BV | Bottom valve |
PR | Piston rod |
OS | Shock absorber seal |
IT | Inner tube wall of the shock absorber |
PSO | Particle swarm optimization |
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Shock Absorber No. | Vehicle | Axle |
---|---|---|
1 | Volkswagen Golf VI | Front |
2 | Volkswagen Golf VI | Rear |
3 | Volkswagen Passat B6 | Front |
4 | Volkswagen Passat B6 | Rear |
5 | Volkswagen Caddy III | Front |
6 | Volkswagen Caddy III | Rear |
7 | Volkswagen Passat B8 | Front |
8 | Volkswagen Passat B8 | Rear |
Shock Absorber | 1 | 2 | ||||||
Condition [%] | 100 | 60 | 40 | 0 | 100 | 60 | 40 | 0 |
Real oil volume [mL] | 321 | 161 | 112 | 0 | 264 | 166 | 106 | 0 |
Real oil proportion [%] | 100 | 50 | 35 | 0 | 100 | 63 | 40 | 0 |
Shock Absorber | 3 | 4 | ||||||
Condition [%] | 100 | 60 | 40 | 0 | 100 | 60 | 40 | 0 |
Real oil volume [mL] | 371 | 226 | 148 | 0 | 239 | 160 | 96 | 0 |
Real oil proportion [%] | 100 | 61 | 40 | 0 | 100 | 67 | 40 | 0 |
Shock Absorber | 5 | 6 | ||||||
Condition [%] | 100 | 60 | 40 | 0 | 100 | 60 | 40 | 0 |
Real oil volume [mL] | 332 | 239 | 133 | 0 | 153 | 95 | 61 | 0 |
Real oil proportion [%] | 100 | 72 | 40 | 0 | 100 | 62 | 40 | 0 |
Shock Absorber | 7 | 8 | ||||||
Condition [%] | 100 | 60 | 40 | 0 | 100 | 60 | 40 | 0 |
Real oil volume [mL] | 354 | 194 | 114 | 0 | 273 | 153 | 83 | 0 |
Real oil proportion [%] | 100 | 55 | 32 | 0 | 100 | 56 | 30 | 0 |
No. | Measurement |
---|---|
1 | Quasi-static measurements |
2 | Harmonic measurements |
3 | Speed bump crossing 8 km/h |
4 | Cleat crossings 4 km/h |
5 | Cleat crossings 20 km/h |
6 | Cleat crossings 40 km/h |
7 | Uneven road washboard 4 km/h |
8 | Uneven road braking maneuver from 30 km/h |
9 | Uneven road braking maneuver from 50 km/h |
10 | Uneven road drive 4 km/h |
11 | Uneven road drive 30 km/h |
12 | Uneven road drive 50 km/h |
Formula Symbol | Description |
---|---|
Simulation timestep | |
z | Piston rod displacement; stroke |
Piston rod velocity | |
Area of the piston valve to the rebound chamber | |
Area of the piston valve to the compression chamber | |
Volume of the rebound chamber | |
Volume of the compression chamber | |
Volume of the reserve chamber | |
Pressure in rebound chamber | |
Pressure in compression chamber | |
Total shock absorber force | |
Shock absorber gas force | |
Shock absorber friction force | |
Shock absorber fluid friction force | |
Degradation factor | |
Gas spring stiffness | |
Slope of the hysteresis loop | |
saturated quasi-static friction force | |
Exponent of the hysteresis friction gradient | |
F-v-characteristic | |
Volume flow rate | |
Relative oil volume flow | |
Relative oil volume flow change | |
Cavitation treshold velocity | |
Cavitation factor | |
Total measured shock absorber force | |
Total simulated shock absorber force | |
Total measured shock absorber work | |
Total simulated shock absorber work |
Dimensions [mm] | SA 1 | SA 2 | SA 3 | SA 4 | SA 5 | SA 6 | SA 7 | SA 8 |
---|---|---|---|---|---|---|---|---|
45.50 | 41.20 | 50.20 | 41.20 | 46.60 | 38.00 | 50.00 | 41.40 | |
22.00 | 13.00 | 25.00 | 13.00 | 25.00 | 14.00 | 25.00 | 13.00 | |
32.00 | 29.90 | 35.90 | 30.00 | 36.00 | 27.00 | 35.80 | 29.80 | |
34.80 | 32.00 | 38.65 | 32.00 | 38.60 | 29.00 | 38.60 | 32.10 | |
326.00 | 277.90 | 326.00 | 277.90 | 328.00 | 225.70 | 326.00 | 331.00 |
Parameter | Definition |
---|---|
Oil proportion that flows through the PV simultaneously with gas during rebound | |
Leakage factor; proportion of oil that flows through the PV without generating a damping force | |
Proportion of the oil that flows through the PV and not through the BV during the compression stroke | |
Oil proportion that flows through the PV simultaneously with gas during compression stroke | |
Oil flow proportion from through the PV in relation to the total oil outflow from in the compression stage when is completely filled with oil |
Parameter | Definition |
---|---|
Proportion of the gas volume flow through the BV, which is converted into foam during the rebound stroke | |
Oil proportion of the foam that is generated in the BV during the rebound stroke | |
Proportion of the gas volume flow through the PV, which is converted into foam during the compression stroke | |
Oil proportion of the foam that is formed in the PV during the compression stroke | |
B | Properties of the foam more like oil (B = 1) or gas (B = 0) |
E | Relationship between oil proportion of the foam and damping force |
Parameter | Definition |
---|---|
Cavitation model treshold velocity | |
Oil proportion which is transformed into gas during compression | |
Oil proportion which is transformed into gas during rebound |
Parameter | SA 1 | SA 2 | SA 3 | SA 4 | SA 5 | SA 6 | SA 7 | SA 8 |
---|---|---|---|---|---|---|---|---|
0.20 | 0.16 | 0.13 | 0.13 | 0.30 | 0.08 | 0.00 | 0.01 | |
0.59 | 0.90 | 0.01 | 0.10 | 0.90 | 0.74 | 0.00 | 0.06 | |
0.01 | 0.00 | 0.27 | 0.02 | 0.00 | 0.00 | 0.49 | 0.01 | |
0.00 | 0.14 | 0.01 | 0.04 | 0.10 | 0.07 | 0.00 | 0.15 | |
0.59 | 0.24 | 0.13 | 0.37 | 0.43 | 0.29 | 0.16 | 0.94 | |
0.07 | 1.00 | 1.00 | 0.29 | 0.10 | 0.17 | 0.00 | 0.94 | |
0.20 | 0.43 | 0.19 | 0.00 | 0.27 | 0.02 | 0.44 | 1.00 | |
1.00 | 0.00 | 0.61 | 0.93 | 0.26 | 0.28 | 0.02 | 0.72 | |
0.00 | 0.44 | 1.00 | 0.44 | 0.17 | 0.42 | 0.00 | 0.15 | |
B | 0.90 | 0.81 | 0.23 | 0.73 | 0.94 | 1.00 | 0.34 | 0.38 |
E | 48.24 | 26.01 | 13.60 | 50.00 | 92.38 | 12.58 | 0.41 | 8.68 |
1.00 | 0.90 | 1.05 | 0.00 | 0.95 | 0.00 | 0.70 | 0.90 | |
0.04 | 0.03 | 0.03 | 0.00 | 0.04 | 0.00 | 0.05 | 0.20 | |
0.04 | 0.02 | 0.03 | 0.00 | 0.04 | 0.00 | 0.05 | 0.20 |
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Schramm, T.; Zwosta, T.; Prokop, G. Investigation and Phenomenological Modeling of Degraded Twin-Tube Shock Absorbers for Oil and Gas Loss. Vehicles 2025, 7, 26. https://doi.org/10.3390/vehicles7010026
Schramm T, Zwosta T, Prokop G. Investigation and Phenomenological Modeling of Degraded Twin-Tube Shock Absorbers for Oil and Gas Loss. Vehicles. 2025; 7(1):26. https://doi.org/10.3390/vehicles7010026
Chicago/Turabian StyleSchramm, Tobias, Tobias Zwosta, and Günther Prokop. 2025. "Investigation and Phenomenological Modeling of Degraded Twin-Tube Shock Absorbers for Oil and Gas Loss" Vehicles 7, no. 1: 26. https://doi.org/10.3390/vehicles7010026
APA StyleSchramm, T., Zwosta, T., & Prokop, G. (2025). Investigation and Phenomenological Modeling of Degraded Twin-Tube Shock Absorbers for Oil and Gas Loss. Vehicles, 7(1), 26. https://doi.org/10.3390/vehicles7010026