Hydraulic cylinders are generally used as power take-off (PTO) mechanisms in wave energy converters (WECs). The dynamic behavior of its PTO force, which integrates friction and pressure forces, is a difficult constraint to include in an analytical or in a numerical model. In this paper, the PTO force characteristics of a hydraulic cylinder are experimentally and numerically investigated under different magnitudes of controlled excitation force. In order to characterize the dynamic behaviors of PTO force, the displacement, acceleration, and pressure in the cylinder chamber for given excitation forces are measured. The pressure force is calculated using the measured value of the pressure, and the friction force is calculated based on the equation of motion using measured values of the pressure, excitation force, and acceleration of the piston. Experimental results show clearly a strong nonlinear force–velocity characteristics, including stochastic and hysteretic behaviors. To model the hysteretic behavior, the modified LuGre model is used for the friction force and a new approach is proposed for the pressure force. To model the stochastic behavior of the friction and pressure forces, the spectral representation method is used. The systematically comparison between measured and simulated results shows that the numerical model captures most of dynamic behaviors of PTO force.

References

1.
de O. Falcão
,
A. F.
,
2010
, “
Wave Energy Utilization: A Review of the Technologies
,”
Renewable Sustainable Energy Rev.
,
14
(
3
), pp.
899
918
.
2.
Falnes
,
J.
,
2002
,
Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction
,
Cambridge University Press
,
Cambridge, UK
.
3.
Babarit
,
A.
,
Duclos
,
G.
, and
Clément
,
A.
,
2004
, “
Comparison of Latching Control Strategies for a Heaving Wave Energy Device in Random Sea
,”
Appl. Ocean Res.
,
26
(
5
), pp.
227
238
.
4.
de O. Falcão
,
A. F.
,
2007
, “
Modelling and Control of Oscillating-Body Wave Energy Converters With Hydraulic Power Take-Off and Gas Accumulator
,”
Ocean Eng.
,
34
(
14–15
), pp.
2021
2032
.
5.
de O. Falcão
,
A. F.
,
2008
, “
Phase Control Through Load Control of Oscillating-Body Wave Energy Converters With Hydraulic PTO System
,”
Ocean Eng.
,
35
(
3–4
), pp.
358
366
.
6.
Babarit
,
A.
,
Guglielmi
,
M.
, and
Clément
,
A. H.
,
2009
, “
Declutching Control of a Wave Energy Converter
,”
Ocean Eng.
,
36
(
12–13
), pp.
1015
1024
.
7.
Wojewoda
,
J.
,
Stefanski
,
A.
,
Wiercigroch
,
M.
, and
Kapitaniak
,
T.
,
2008
, “
Hysteretic Effects of Dry Friction: Modelling and Experimental Studies
,”
Philos. Trans. R. Soc. A
,
366
(
1866
), pp.
747
765
.
8.
Armstrong-Hélouvry
,
B.
,
Dupont
,
P.
, and
Wit
,
C. C. D.
,
1994
, “
A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction
,”
Automatica
,
30
(
7
), pp.
1083
1138
.
9.
Andersson
,
S.
,
Söderberg
,
A.
, and
Björklund
,
S.
,
2007
, “
Friction Models for Sliding Dry, Boundary and Mixed Lubricated Contacts
,”
Tribol. Int.
,
40
(
4
), pp.
580
587
.
10.
de Wit
,
C. C.
,
Olsson
,
H.
,
Astrom
,
K.
, and
Lischinsky
,
P.
,
1995
, “
A New Model for Control of Systems With Friction
,”
IEEE Trans. Autom. Control
,
40
(
3
), pp.
419
425
.
11.
Babarit
,
A.
,
Hals
,
J.
,
Muliawan
,
M.
,
Kurniawan
,
A.
,
Moan
,
T.
, and
Krokstad
,
J.
,
2012
, “
Numerical Benchmarking Study of a Selection of Wave Energy Converters
,”
Renewable Energy
,
41
, pp.
44
63
.
12.
Sheng
,
W.
,
Alcorn
,
R.
, and
Lewis
,
T.
,
2014
, “
Physical Modelling of Wave Energy Converters
,”
Ocean Eng.
,
84
, pp.
29
36
.
13.
Swevers
,
J.
,
Al-Bender
,
F.
,
Ganseman
,
C.
, and
Projogo
,
T.
,
2000
, “
An Integrated Friction Model Structure With Improved Presliding Behavior for Accurate Friction Compensation
,”
IEEE Trans. Autom. Control
,
45
(
4
), pp.
675
686
.
14.
Yanada
,
H.
, and
Sekikawa
,
Y.
,
2008
, “
Modeling of Dynamic Behaviors of Friction
,”
Mechatronics
,
18
(
7
), pp.
330
339
.
15.
Tran
,
X. B.
,
Hafizah
,
N.
, and
Yanada
,
H.
,
2012
, “
Modeling of Dynamic Friction Behaviors of Hydraulic Cylinders
,”
Mechatronics
,
22
(
1
), pp.
65
75
.
16.
Olsson
,
H.
,
Åström
,
K.
,
de Wit
,
C. C.
,
Gäfvert
,
M.
, and
Lischinsky
,
P.
,
1998
, “
Friction Models and Friction Compensation
,”
Eur. J. Control
,
4
(
3
), pp.
176
195
.
17.
Ismaila
,
T.
,
Akmeliawati
,
R.
, and
Salami
,
M. J. E.
,
2011
, “
Artificial Intelligent Based Friction Modelling and Compensation in Motion Control System
,”
Advances in Mechatronics
,
InTech
,
Rijeka, Croatia
.
18.
Korde
,
U.
,
1999
, “
Efficient Primary Energy Conversion in Irregular Waves
,”
Ocean Eng.
,
26
(
7
), pp.
625
651
.
19.
Yavuz
,
H.
,
McCabe
,
A.
,
Aggidis
,
G.
, and
Widden
,
M. B.
,
2006
, “
Calculation of the Performance of Resonant Wave Energy Converters in Real Seas
,”
Proc. Inst. Mech. Eng., Part M
,
220
(
3
), pp.
117
128
.
20.
Child
,
B.
, and
Venugopal
,
V.
,
2010
, “
Optimal Configurations of Wave Energy Device Arrays
,”
Ocean Eng.
,
37
(
16
), pp.
1402
1417
.
21.
Folley
,
M.
, and
Whittaker
,
T.
,
2009
, “
The Control of Wave Energy Converters Using Active Bipolar Damping
,”
Proc. Inst. Mech. Eng., Part M
,
223
(
4
), pp.
479
487
.
22.
Yavuz
,
H.
,
Mistikoğlu
,
S.
, and
Stallard
,
T.
,
2011
, “
Processing Irregular Wave Measurements to Enhance Point Absorber Power Capture Performance
,”
Ocean Eng.
,
38
(
4
), pp.
684
698
.
23.
Salter
,
S. H.
,
Taylor
,
J. R. M.
, and
Caldwell
,
N. J.
,
2002
, “
Power Conversion Mechanisms for Wave Energy
,”
Proc. Inst. Mech. Eng., Part M
,
216
(
1
), pp.
1
27
.
24.
Whittaker
,
T.
, and
Folley
,
M.
,
2012
, “
Nearshore Oscillating Wave Surge Converters and the Development of Oyster
,”
Philos. Trans. R. Soc. A
,
370
(
1959
), pp.
345
364
.
25.
Tran
,
X. B.
, and
Yanada
,
H.
,
2013
, “
Dynamic Friction Behaviors of Pneumatic Cylinders
,”
Intell. Control Autom.
,
4
(
2
), pp.
180
190
.
26.
Alonso
,
R.
,
Solari
,
S.
, and
Teixeira
,
L.
,
2015
, “
Wave Energy Resource Assessment in Uruguay
,”
Energy
,
93
(Part 1), pp.
683
696
.
27.
Stribeck
,
R.
,
1902
, “
Die wesentlichen eigenschaften der gleitund rollenlager (The Key Qualities of Sliding and Roller Bearings)
,”
Z. Ver. Dtsch. Ing.
,
46
(
38–39
), pp.
1342
1348
, 1432–1437.
28.
Patir
,
N.
, and
Cheng
,
H. S.
,
1978
, “
An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication
,”
ASME J. Lubr. Technol.
,
100
(
1
), pp.
12
17
.
29.
Shinozuka
,
M.
, and
Deodatis
,
G.
,
1991
, “
Simulation of Stochastic Processes by Spectral Representation
,”
ASME Appl. Mech. Rev.
,
44
(
4
), pp.
191
204
.
30.
Hu
,
B.
, and
Schiehlen
,
W.
,
1997
, “
On the Simulation of Stochastic Processes by Spectral Representation
,”
Probab. Eng. Mech.
,
12
(
2
), pp.
105
113
.
31.
Wiercigroch
,
M.
, and
Cheng
,
A.-D.
,
1997
, “
Chaotic and Stochastic Dynamics of Orthogonal Metal Cutting
,”
Chaos, Solitons Fract.
,
8
(
4
), pp.
715
726
.
32.
Yanada
,
H.
,
Takahashi
,
K.
, and
Matsui
,
A.
,
2009
, “
Identification of Dynamic Parameters of Modified LuGre Model and Application to Hydraulic Actuator
,”
Trans. Jpn. Fluid Power Syst. Soc.
,
40
(
4
), pp.
57
64
.
33.
Do
,
N. B.
,
Ferri
,
A. A.
, and
Bauchau
,
O. A.
,
2007
, “
Efficient Simulation of a Dynamic System With LuGre Friction
,”
ASME J. Comput. Nonlinear Dyn.
,
2
(
4
), pp.
281
289
.
34.
Wiercigroch
,
M.
,
Sin
,
V. W. T.
, and
Liew
,
Z. F. K.
,
1999
, “
Non-Reversible Dry Friction Oscillator: Design and Measurements
,”
Proc. Inst. Mech. Eng., Part C
,
213
(
5
), pp.
527
534
.
You do not currently have access to this content.