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Research Papers: Ocean Renewable Energy

Three-Dimensional Oscillation Dynamics of the In Situ Piston Rod Transmission Between Buoy Line and the Double Hinge-Connected Translator in an Offshore Linear Wave Energy Converter

[+] Author and Article Information
Erland Strömstedt

Division of Electricity,
Department of Engineering Sciences,
Swedish Centre for Renewable
Electric Energy Conversion,
Uppsala University,
P.O. Box 534,
Uppsala SE-751 21, Sweden
e-mail: erland.stromstedt@angstrom.uu.se

Mats Leijon

Mem. ASME
Division of Electricity,
Department of Engineering Sciences,
Swedish Centre for Renewable
Electric Energy Conversion,
Uppsala University,
P.O. Box 534,
Uppsala SE-751 21, Sweden
e-mail: mats.leijon@angstrom.uu.se

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received August 19, 2012; final manuscript received October 29, 2015; published online March 18, 2016. Assoc. Editor: Hideyuki Suzuki.

J. Offshore Mech. Arct. Eng 138(3), 031901 (Mar 18, 2016) (21 pages) Paper No: OMAE-12-1083; doi: 10.1115/1.4031972 History: Received August 19, 2012; Revised October 29, 2015

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.

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Figures

Grahic Jump Location
Fig. 1

(Left) Geographical location of the LRS. (Right) Close-up of the test site with the experimental installations in operation from May 15 to September 23 in 2009 indicated on a sea chart.

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Fig. 2

(a) L2 with buoy attached after launch; (b) L2 on cay before launch; and (c) computer-aided design (CAD) assembly of L2 with the surface-floating buoy and the foundation at 25 m depth. Distances to scale and force transducer indicated; (d) cross-sectional view displaying major subassemblies (draw-wire sensor and laser sensor setup indicated).

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Fig. 3

(Left) Translator, with track rollers and surface-mounted magnets, in longitudinal middle position 301.5 mm above and below the stator. The piston rod outside length is 1185 mm. (Right) Cross-sectional view indicating translator framework, distances to upper and lower end stop compression springs, and compression lengths to end stops.

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Fig. 4

(Left) CAD assembly views of the setup of seven laser triangulations sensors and components in the piston rod mechanical lead-through of L2. (Right) Geometrical conditions in the sensor setup.

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Fig. 5

Manufactured parts in L2. (a) Top funnel and buoy line; (b) piston rod mechanical lead-through transmission above the top plate; (c) DHL with surrounding motion restricting cylinder inside WEC; (d) seal housing; (e) seal housing and rubber gasket during assembly above the top plate; (f) seal housing and rubber gasket during assembly below the top plate; and (g) DHL with pivoting bearings.

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Fig. 6

Laser triangulation sensor setup rig during assembly of L2: (a) from the side, (b) from underneath, and (c) just before the final closing of the capsule

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Fig. 7

(a) Draw-wire sensor attached to top of upper end stop; (b) wire moving through hole in upper end stop; and (c) wire attached to top of translator

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Fig. 8

(a) Force transducer; (b) encased force transducer arrangement underneath the buoy; and (c) the cylindrical buoy of L2

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Fig. 9

Illustration of measured relative lateral displacement (Δ) by PRLSs 1–3 during piston rod tilting. Dashed circles are separated by 6 mm in axial direction and located below CR. All the circles overlap when the piston rod is in the straight reference position.

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Fig. 10

Illustration of (exaggerated) tilt angles in the transmission during (exaggerated) bending of the outer WEC structure. The axial force (FAXIAL) operates at an inclination angle creating a lateral force (FSIDE) at the buoy line/funnel interface. The piston rod tilts (θp) around CR, as the DHL (θDHL) and the Z-axis (θZ-axis) tilt in relation to the vertical axis.

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Fig. 11

Illustration of the four steps leading from the measured ΔPRLS at sensor level, via calculated Δx, Δy, and ΔU to the piston rod tilt angle (θp) with an azimuth direction of tilting in the cross-sectional plane of the final illustration. The P-axis represents the piston rod center axis.

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Fig. 12

CAD assembly of a straight DHL and a DHL with a maximum allowed tilt angle of 3.2 deg: case I—vertical (no tilt) and case II—maximum DHL tilt (90 deg rotated view)

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Fig. 13

Illustration of geometrical conditions between piston rod center axis displacement (ΔU) at the Z-axis level of PRLS 3, piston rod tilt angle (θp), and buoy line displacement in the funnel orifice (ΔBatF) during a wave cycle

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Fig. 14

(Left) Cross-sectional view of FEM simulated model, i.e., WEC outer structure and inner stator supporting framework. A lateral force of 15 kN is applied to the mounting position of the top funnel. The bottom plate is fixed in 6DOF of motion. (Middle) Results from buckling analysis. (Right) Displacement results from static FEM simulation.

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Fig. 15

Close-up of results from static FEM simulations of the WEC model displayed in the left image of Fig. 14. Images display: (a) displacement magnitude, (b) von Mises stress, and (c) max principal strain.

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Fig. 16

Case I: Measurements by PRLSs 1–3, the draw-wire sensor, and the force transducer in 2009-05-27 during time window 11:40:31–11:40:57 hrs. See Table 1 for operating conditions. Distance on Y-axis for PRLSs 1–3 refers to distance from midrange to target surface.

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Fig. 17

Case II: Measurements by PRLSs 1–3, the draw-wire sensor, and the force transducer in 2009-05-28 during time window 13:16:36–13:16:55 hrs. See Table 1 for operating conditions. Distance on Y-axis for PRLSs 1–3 refers to distance from midrange to target surface.

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Fig. 18

Case III: Measurements by PRLSs 1–3, the draw-wire sensor, and the force transducer in 2009-08-15 during time window 00:00:14–00:00:35 hrs. See Table 1 for operating conditions. Distance on Y-axis for PRLSs 1–3 refers to distance from midrange to target surface.

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Fig. 19

Case IV: Measurements by PRLSs 1–3, the draw-wire sensor, and the force transducer in 2009-08-17 during time window 14:29:15–14:29:35 hrs. See Table 1 for operating conditions. Distance on Y-axis for PRLSs 1–3 refers to distance from midrange to target surface.

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Fig. 20

(Left) Piston rod relative tilt angle (θp) for one selected wave period in cases I–IV. (Right) Corresponding piston rod azimuth directions of tilting (φp). Red curves filtered with CMA using a sliding window of 21 values.

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Fig. 21

Piston rod relative tilt angles (θp) (from Fig. 20) as a function of piston rod axial displacement (expressed as piston rod outside length). Red curves filtered with CMA using a sliding window of 21 values. X-axis scale represents maximum stroke length. Blue vertical lines indicate free stroke length and the starting points for compression of the end stop compression springs.

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Fig. 22

The funnel of the buoy line guiding system before and after the experiment in 2009. Splitting of the buoy line jacketing compound leads to accelerated wear in the predominant φ-direction of wave propagation and to a lesser degree in the opposite counter φ-direction.

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