Force and displacement measurements have been performed in situ on the piston rod mechanical lead-through transmission in the direct drive of the second experimental wave energy converter (WEC) 3 km offshore at the Lysekil research site (LRS) during a 130-day continuous full-scale experiment in 2009. The direct drive consists of a buoy line and a piston rod transmission with a double-hinged link (DHL) at the lower end connecting the point absorbing surface-floating buoy to the translator of an encapsulated permanent magnet linear generator on the seabed. The buoy line is guided by a funnel in the buoy line guiding system 3.2 m above the generator capsule. The 3 m long piston rod reciprocates through a mechanical lead-through in the capsule wall, sealing off seawater from entering the generator capsule. A setup of laser triangulation sensors measures the relative lateral displacement of the piston rod. This paper introduces a method and a system of equations for calculating piston rod relative tilt angle and piston rod azimuth direction of tilting from the relative lateral displacement measurements. Correlation with piston rod axial displacement and forces enables evaluation of the three-dimensional (3D) oscillation dynamics. Results are presented from 2 weeks after launch and from 3 months after launch in altogether four cases representing two different stages of wear in two different sea states. Piston rod tilting from accumulated wear in the buoy line guiding system is separated from tilting due to elastic displacement. Structural mechanical finite element method (FEM) simulations verify the magnitude of elastic displacement and indicate negligible stress and strain at the mounting point of the laser sensor setup. The proposed theory for piston rod 3D motion is validated by the experiment. As the experiment progressed, wear in the buoy line guiding system accelerated due to splitting of the buoy line jacketing compound, thereby increasing the piston rod tilt angles. Over 94 days into the experiment, 21.8 mm of accumulated wear in the buoy line guiding system had altered the characteristics of the piston rod oscillations and increased the maximum piston rod relative tilt angle by 0.39 deg in the predominant azimuth direction of wave propagation. Further accumulated wear in the buoy line guiding system led to buoy line rupture 130 days after launch. The results presented in this paper have been used in assessments for improving the mechanical subsystems in subsequent experimental WECs based on the Uppsala concept.

References

References
1.
Kofoed
,
J. P.
,
Frigaard
,
P.
,
Friis-Madsen
,
E.
, and
Sorensen
,
H. C.
,
2006
, “
Prototype Testing of the Wave Energy Converter Wave Dragon
,”
Renewable Energy
,
31
(
2
), pp.
181
189
.
2.
Henderson
,
R.
,
2006
, “
Design, Simulation, and Testing of a Novel Hydraulic Power Take-Off System for the Pelamis Wave Energy Converter
,”
Renewable Energy
,
31
(
2
), pp.
271
283
.
3.
Agamloh
,
E. B.
,
Wallace
,
A. K.
, and
von Jouanne
,
A.
,
2008
, “
A Novel Direct-Drive Ocean Wave Energy Extraction Concept With Contact-Less Force Transmission System
,”
Renewable Energy
,
33
(
3
), pp.
520
529
.
4.
Margheritini
,
L.
,
Vicinanza
,
D.
, and
Frigaard
,
P.
,
2009
, “
SSG Wave Energy Converter: Design, Reliability and Hydraulic Performance of an Innovative Overtopping Device
,”
Renewable Energy
,
34
(
5
), pp.
1371
1380
.
5.
Elwood
,
D.
,
Yim
,
S. C.
,
Prudell
,
J.
,
Stillinger
,
C.
,
Von Jouanne
,
A.
,
Brekken
,
T.
,
Brown
,
A.
, and
Paasch
,
R.
,
2010
, “
Design, Construction, and Ocean Testing of a Taut-Moored Dual-Body Wave Energy Converter With a Linear Generator Power Take-Off
,”
Renewable Energy
,
35
(
2
), pp.
348
354
.
6.
Hodgins
,
N.
,
Keysan
,
O.
,
McDonald
,
A. S.
, and
Mueller
,
M. A.
,
2012
, “
Design and Testing of a Linear Generator for Wave-Energy Applications
,”
IEEE Trans. Ind. Electron.
,
59
(
5
), pp.
2094
2103
.
7.
Mueller
,
M. A.
, and
Baker
,
N. J.
,
2005
, “
Direct Drive Electrical Power Take-Off for Offshore Marine Energy Converters
,”
Proc. Inst. Mech. Eng., Part A
,
219
(
3
), pp.
223
234
.
8.
Leijon
,
M.
,
Bernhoff
,
H.
,
Berg
,
M.
, and
Agren
,
O.
,
2003
, “
Economical Considerations of Renewable Electric Energy Production—Especially Development of Wave Energy
,”
Renewable Energy
,
28
(
8
), pp.
1201
1209
.
9.
Leijon
,
M.
,
Danielsson
,
O.
,
Eriksson
,
M.
,
Thorburn
,
K.
,
Bernhoff
,
H.
,
Isberg
,
J.
,
Sundberg
,
J.
,
Ivanova
,
I.
,
Sjostedt
,
E.
,
Agren
,
O.
,
Karlsson
,
K. E.
, and
Wolfbrandt
,
A.
,
2006
, “
An Electrical Approach to Wave Energy Conversion
,”
Renewable Energy
,
31
(
9
), pp.
1309
1319
.
10.
Hudson
,
J. A.
,
Phillips
,
D. C.
, and
Wilkins
,
N. J. M.
,
1980
, “
Materials Aspects of Wave Energy Converters
,”
J. Mater. Sci.
,
15
(
6
), pp.
1337
1363
.
11.
Yang
,
L.
, and
Moan
,
T.
,
2011
, “
Numerical Modeling of Wear Damage in Seals of a Wave Energy Converter With Hydraulic Power Take-Off Under Random Loads
,”
Tribol. Trans.
,
54
(
1
), pp.
44
56
.
12.
Lindroth
,
S.
, and
Leijon
,
M.
,
2011
, “
Offshore Wave Power Measurements—A Review
,”
Renewable Sustainable Energy Rev.
,
15
(
9
), pp.
4274
4285
.
13.
Leijon
,
M.
,
Bostrom
,
C.
,
Danielsson
,
O.
,
Gustafsson
,
S.
,
Haikonen
,
K.
,
Langhamer
,
O.
,
Stromstedt
,
E.
,
Stalberg
,
M.
,
Sundberg
,
J.
,
Svensson
,
O.
,
Tyrberg
,
S.
, and
Waters
,
R.
,
2008
, “
Wave Energy From the North Sea: Experiences From the Lysekil Research Site
,”
Surv. Geophys.
,
29
(
3
), pp.
221
240
.
14.
Rahm
,
M.
,
Svensson
,
O.
,
Bostro
,
X. M. C.
,
Waters
,
R.
, and
Leijon
,
M.
,
2012
, “
Experimental Results From the Operation of Aggregated Wave Energy Converters
,”
Renewable Power Gener., IET
,
6
(
3
), pp.
149
160
.
15.
Svensson
,
O.
,
Strömstedt
,
E.
,
Savin
,
A.
, and
M. L.
,
2011
, “
Sensors and Measurements Inside the Second and Third Wave Energy Converter at the Lysekil Research Site
,”
9th European Wave and Tidal Energy Conference
(
EWTEC 2011
), Southampton, UK.
16.
Strömstedt
,
E.
,
Svensson
,
O.
, and
Leijon
,
M.
,
2012
, “
A Set-Up of 7 Laser Triangulation Sensors and a Draw-Wire Sensor for Measuring Relative Displacement of a Piston Rod Mechanical Lead-Through Transmission in an Offshore Wave Energy Converter on the Ocean Floor
,”
ISRN Renewable Energy
,
2012
, p.
746865
.
17.
Strömstedt
,
E.
,
Savin
,
A.
,
Svensson
,
O.
, and
Leijon
,
M.
,
2013
, “
Time Series-, Time-Frequency- and Spectral Analyses of Sensor Measurements in an Offshore Wave Energy Converter Based on Linear Generator Technology
,”
Energy Power Eng.
,
5
(
1
), pp.
70
91
.
18.
Savin
,
A.
,
Svensson
,
O.
, and
Leijon
,
M.
,
2012
, “
Azimuth-Inclination Angles and Snatch Load on a Tight Mooring System
,”
Ocean Eng.
,
40
, pp.
40
49
.
19.
Savin
,
A.
,
Svensson
,
O.
,
Strömstedt
,
E.
,
Boström
,
C.
, and
Leijon
,
M.
,
2009
, “
Determining the Service Life of a Steel Wire Under a Working Load in the Wave Energy Converter (WEC)
,”
ASME
Paper No. OMAE2009-79164.
20.
Svensson
,
O.
,
Bostrom
,
C.
,
Rahm
,
M.
, and
Leijon
,
M.
,
2009
, “
Description of the Control and Measurement System Used in the Low Voltage Marine Substation at the Lysekil Research Site
,”
8th European Wave and Tidel Energy Conference
(
EWTEC 2009
), Uppsala, Sweden, pp.
44
50
.
21.
Drew
,
B.
,
Plummer
,
A. R.
, and
Sahinkaya
,
M. N.
,
2009
, “
A Review of Wave Energy Converter Technology
,”
Proc. Inst. Mech. Eng., Part A
,
223
(
8
), pp.
887
902
.
22.
Boström
,
C.
,
Waters
,
R.
,
Lejerskog
,
E.
,
Svensson
,
O.
,
Stålberg
,
M.
,
Strömstedt
,
E.
, and
Leijon
,
M.
,
2009
, “
Study of a Wave Energy Converter Connected to a Nonlinear Load
,”
IEEE J. Oceanic Eng.
,
34
(
2
), pp.
123
127
.
23.
Danielsson
,
O.
,
Eriksson
,
M.
, and
Leijon
,
M.
,
2006
, “
Study of a Longitudinal Flux Permanent Magnet Linear Generator for Wave Energy Converters
,”
Int. J. Energy Res.
,
30
(
14
), pp.
1130
1145
.
24.
Eriksson
,
M.
,
Isberg
,
J.
, and
Leijon
,
M.
,
2005
, “
Hydrodynamic Modelling of a Direct Drive Wave Energy Converter
,”
Int. J. Eng. Sci.
,
43
(
17–18
), pp.
1377
1387
.
25.
Eriksson
,
M.
,
Waters
,
R.
,
Svensson
,
O.
,
Isberg
,
J.
, and
Leijon
,
M.
,
2007
, “
Wave Power Absorption: Experiments in Open Sea and Simulation
,”
J. Appl. Phys.
,
102
(
8
), p.
084910
.
26.
Guo
,
Y.
,
Han
,
Y.
, and
Liu
,
L.
,
2009
, “
A Measurement of Geometry Parameters in Large-Scale Pipes
,”
Symposium on Photonics and Optoelectronics
(
SOPO 2009
), Wuhan, China, Aug. 14–16, pp.
1
4
.
27.
Rana
,
N. K.
,
Sawant
,
R. R.
, and
Moon
,
A. H.
,
2006
, “
A Non-Contact Method for Rod Straightness Measurement Based on Quadrant Laser Sensor
,”
IEEE International Conference on Industrial Technology
(
ICIT 2006
), Mumbai, India, Dec. 15–17, pp.
2292
2297
.
28.
Miles
,
J. R.
,
Munro
,
L. E.
, and
Pekelsky
,
J. R.
,
2005
, “
A New Instrument for the Dimensional Characterization of Piston-Cylinder Units
,”
Metrologia
,
42
(
6
), pp.
S220
S223
.
29.
Berry
,
P. A.
,
Bridge
,
R. Q.
, and
Rotter
,
J. M.
,
1996
, “
Imperfection Measurement of Cylinders Using Automated Scanning With a Laser Displacement Meter
,”
Strain
,
32
(
1
), pp.
3
7
.
30.
Demeyere
,
M.
, and
Eugene
,
C.
,
2004
, “
Measurement of Cylindrical Objects by Laser Telemetry: A Generalization to a Randomly Tilted Cylinder
,”
IEEE Trans. Instrum. Meas.
,
53
(
2
), pp.
566
570
.
31.
Micro-Epsilon
,
2010
, “
Product Catalogue for Optoncdt Laser Sensors
,” Modifications Reserved/Y9761188-D091120DGO, http://www.micro-epsilon.com/download/products/cat–optoNCDT–en.pdf
32.
Micro-Epsilon
,
2010
, “
Instruction Manual, Optoncdt 1700
,” Version X9751139-C151100HDR.
33.
Feng
,
J.
,
Feng
,
Q.
, and
Kuang
,
C.
,
2003
, “
Status of Laser Displacement Measurement Techniques Based on Triangulation
,”
International Symposium on Test and Measurement
, pp.
3658
3661
.
34.
Micro-Epsilon
,
2010
, “
Product Catalogue for Draw-Wire Sensors
,” Modifications Reserved Y9761111-F021110DGO.
35.
Micro-Epsilon
,
2010
, “
Instruction Manual, Wiresensor Wds
,” Version X975X034-D031090HDR.
36.
HBM
,
2010
, “
Datasheet for U2b Force Transducer
,” Modifications Reserved/B0482-2.5 en.
37.
Tyrberg
,
S.
,
Svensson
,
O.
,
Kurupath
,
V.
,
Engstrom
,
J.
,
Strömstedt
,
E.
, and
Leijon
,
M.
,
2011
, “
Wave Buoy and Translator Motions—On-Site Measurements and Simulations
,”
IEEE J. Oceanic Eng.
,
36
(
3
), pp.
377
385
.
38.
Beder
,
C.
, and
Förstner
,
W.
,
2006
, “
Direct Solutions for Computing Cylinders From Minimal Sets of 3D Points
,”
Lecture Notes in Computer Science
(Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer, Berlin, Heidelberg, pp.
135
146
.
39.
Zeng
,
L.
,
Yuan
,
F.
,
Song
,
D.
, and
Zhang
,
R.
,
1999
, “
A Two-Beam Laser Triangulation for Measuring the Position of a Moving Object
,”
Opt. Lasers Eng.
,
31
(
6
), pp.
445
453
.
40.
Goriely
,
A.
,
Neukirch
,
S.
, and
Hausrath
,
A.
,
2011
, “
Helices Through 3 or 4 Points?
Note di Matematica 00 (2011)
,
Oxford Centre for Collaborative Applied Mathematics (OCCAM)
,
Oxford, UK
, pp.
1
17
.
41.
Ahn
,
S. J.
,
Rauh
,
W.
,
Cho
,
H. S.
, and
Warnecke
,
H. J.
,
2002
, “
Orthogonal Distance Fitting of Implicit Curves and Surfaces
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
40
, pp.
40
49
.
42.
Bolles
,
R. C.
, and
Fischler
,
M. A.
,
1981
, “
RANSAC-Based Approach to Model Fitting and Its Application to Finding Cylinders in Range Data
,”
7th International Joint Conference on Artificial Intelligence
, Vol.
2
, pp.
637
643
.
43.
Harman
,
T. L.
,
Dabney
,
J.
, and
Richert
,
N.
,
2000
,
Advanced Engineering Mathematics With Matlab
,
Brooks/Cole Publication
.
44.
Nilsson
,
K.
,
Danielsson
,
O.
, and
Leijon
,
M.
,
2006
, “
Electromagnetic Forces in the Air Gap of a Permanent Magnet Linear Generator at No Load
,”
J. Appl. Phys.
,
99
(
3
), p.
034505
.
45.
Waters
,
R.
,
Stalberg
,
M.
,
Danielsson
,
O.
,
Svensson
,
O.
,
Gustafsson
,
S.
,
Stromstedt
,
E.
,
Eriksson
,
M.
,
Sundberg
,
J.
, and
Leijon
,
M.
,
2007
, “
Experimental Results From Sea Trials of an Offshore Wave Energy System
,”
Appl. Phys. Lett.
,
90
(
3
), p.
034105
.
46.
Smith
,
S. W.
,
1999
,
The Scientist and Engineer's Guide to Digital Signal Processing
,
California Technical Publishing
,
San Diego, CA
.
47.
Savin
,
A.
,
Svensson
,
O.
, and
Leijon
,
M.
,
2012
, “
Estimation of Stress in the Inner Framework Structure of a Single Heaving Buoy Wave Energy Converter
,”
IEEE J. Oceanic Eng.
,
37
(
2
), pp.
309
317
.
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