Research Papers: Applications

Experimental and Numerical Studies of Dynamic Behaviors of a Hydraulic Power Take-Off Cylinder Using Spectral Representation Method

[+] Author and Article Information
Moisés Brito

Instituto Superior Técnico,
Universidade de Lisboa,
Av. Rovisco Pais,
Lisboa 1049-001, Portugal
e-mail: moises.brito@tecnico.ulisboa.pt

Luis Teixeira

Facultad de Ingeniería,
Instituto de Mecánica de los Fluidos
e Ingeniería Ambiental (IMFIA),
Universidad de la República,
Montevideo 11300, Uruguay
e-mail: luistei@fing.edu.uy

Ricardo B. Canelas

Instituto Superior Técnico,
Universidade de Lisboa,
Av. Rovisco Pais,
Lisboa 1049-001, Portugal
e-mail: ricardo.canelas@tecnico.ulisboa.pt

Rui M. L. Ferreira

Instituto Superior Técnico,
Universidade de Lisboa,
Av. Rovisco Pais,
Lisboa 1049-001, Portugal
e-mail: ruimferreira@tecnico.ulisboa.pt

Maria G. Neves

Harbours and Maritime Structures Division,
Hydraulics and Environment Department,
Laboratório Nacional de Engenharia
Civil (LNEC),
Av. do Brasil 101,
Lisboa 1700-066, Portugal
e-mail: gneves@lnec.pt

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 6, 2017; final manuscript received July 18, 2017; published online September 29, 2017. Assoc. Editor: Stephen Boedo.

J. Tribol 140(2), 021102 (Sep 29, 2017) (13 pages) Paper No: TRIB-17-1072; doi: 10.1115/1.4037464 History: Received March 06, 2017; Revised July 18, 2017

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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


de O. Falcão, A. F. , 2010, “ Wave Energy Utilization: A Review of the Technologies,” Renewable Sustainable Energy Rev., 14(3), pp. 899–918.
Falnes, J. , 2002, Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction, Cambridge University Press, Cambridge, UK.
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.
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.
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.
Babarit, A. , Guglielmi, M. , and Clément, A. H. , 2009, “ Declutching Control of a Wave Energy Converter,” Ocean Eng., 36(12–13), pp. 1015–1024.
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.
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.
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.
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.
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.
Sheng, W. , Alcorn, R. , and Lewis, T. , 2014, “ Physical Modelling of Wave Energy Converters,” Ocean Eng., 84, pp. 29–36.
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.
Yanada, H. , and Sekikawa, Y. , 2008, “ Modeling of Dynamic Behaviors of Friction,” Mechatronics, 18(7), pp. 330–339.
Tran, X. B. , Hafizah, N. , and Yanada, H. , 2012, “ Modeling of Dynamic Friction Behaviors of Hydraulic Cylinders,” Mechatronics, 22(1), pp. 65–75.
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.
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.
Korde, U. , 1999, “ Efficient Primary Energy Conversion in Irregular Waves,” Ocean Eng., 26(7), pp. 625–651.
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.
Child, B. , and Venugopal, V. , 2010, “ Optimal Configurations of Wave Energy Device Arrays,” Ocean Eng., 37(16), pp. 1402–1417.
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.
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.
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.
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.
Tran, X. B. , and Yanada, H. , 2013, “ Dynamic Friction Behaviors of Pneumatic Cylinders,” Intell. Control Autom., 4(2), pp. 180–190.
Alonso, R. , Solari, S. , and Teixeira, L. , 2015, “ Wave Energy Resource Assessment in Uruguay,” Energy, 93(Part 1), pp. 683–696.
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.
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.
Shinozuka, M. , and Deodatis, G. , 1991, “ Simulation of Stochastic Processes by Spectral Representation,” ASME Appl. Mech. Rev., 44(4), pp. 191–204.
Hu, B. , and Schiehlen, W. , 1997, “ On the Simulation of Stochastic Processes by Spectral Representation,” Probab. Eng. Mech., 12(2), pp. 105–113.
Wiercigroch, M. , and Cheng, A.-D. , 1997, “ Chaotic and Stochastic Dynamics of Orthogonal Metal Cutting,” Chaos, Solitons Fract., 8(4), pp. 715–726.
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.
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.
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.


Grahic Jump Location
Fig. 1

Schematic representation (not to scale) of the side view of hydraulic cylinder: (a) experimental setup, illustrating the position of the experimental apparatus and the geometry of the mechanical system and (b) cylinder details

Grahic Jump Location
Fig. 2

Experimental setup used in the irregular motion applied to the OWSC: (a) schematic representation (not to scale) of the side view, illustrating the position of the experimental apparatus and (b) photograph

Grahic Jump Location
Fig. 5

Measured and fitting power spectrum density: (a) fluctuation signal of Ff and (b) fluctuation signal of Fp

Grahic Jump Location
Fig. 7

Comparison between measured and simulated time series for T = 5.1 and 7.0 s: (a) and (b) FPTO(t), (c) and (d) Ff(t), and (e) and (f) Fp(t)

Grahic Jump Location
Fig. 8

Comparison of measured and simulated results for T = 5.1 s: (a) FPTO(x˙), (b) FPTO(x), (c) Ff(x˙), (d) Ff(x), (e) Fp(x˙), and (f) Fp(x)

Grahic Jump Location
Fig. 10

Comparison between measured and simulated time series: (a) θ(t), (b) θ˙(t), (c) Fp(t), and (d) FPTO(t)

Grahic Jump Location
Fig. 4

Dynamic behavior measured during regular x˙ variation for T = 5.1 and 7.0 s: (a) and (b) FPTO(x˙), (c) and (d) Ff(x˙), and (e) and (f) Fp(x˙)

Grahic Jump Location
Fig. 3

Time series measured for T = 5.1 and 7.0 s: (a) and (b) x(t), (c) and (d) x˙(t), (e) and (f) Fexc(t), and (g) and (h) Fp(t)

Grahic Jump Location
Fig. 6

Comparison between measured versus simulated scatter diagrams obtained with and without stochastic components for T = 5.1 and 7.0 s: (a) and (b) Ff and (c) and (d) Fp

Grahic Jump Location
Fig. 9

Comparison of measured and simulated results for T = 7.0 s: (a) FPTO(x˙), (b) FPTO(x), (c) Ff(x˙), (d) Ff(x), (e) Fp(x˙), and (f) Fp(x)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In