Bond graph representations of hydraulic pipelines using normal modes with dissipative friction

Abstract

The one-dimensional (1-D) unsteady-pressure-flow equations of hydraulic pipeline can be approximated and solved numerically using a finite-mode approach. This paper deals with constructing bond graph representations for the hydraulic pipelines with laminar flow by using the previously established 1-D linear-friction bond graph structures and modal approximation techniques when 2-D frequency-dependent friction is taken into account. To model hydraulic pipelines as components in different systems using bond graphs, there are four possible input–output causalities: pressure inputs at both ends, flow rate input at both ends and the two cases of mixed inputs. In this paper, all four configurations are considered. The developed bond graph structures together with their corresponding modal parameters are presented. A comparison is made for three models, namely lossless, 1-D linear fluid friction and 2-D fluid friction. Simulation results show that the modified bond graph models studied in this work can give more satisfactory results.

Keywords

bond graphs normal mode hydraulic pipeline dissipative model

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References

Walski

Chase

Savic

Grayman

Beckwith

Koelle

. Advanced water distribution modeling and management, 1st edition. Bentley Institute Press, 2003.

Wylie

Streeter

Suo

. Fluid Transients in Systems. Prentice-Hall, 1993.

Karnopp

. Lumped parameter models of acoustic filters using normal modes and bond graphs. J Sound Vibrat 1975; 42: 437–446.

Lebrun

. Normal modes in hydraulic Lines. In Proceedings of the American Control Conference, San Diego, CA, 6–8 June 1984, pp. 458–467.

Yang

Hals

Moan

. Comparative study of bond graph models of hydraulic transmission lines with transient flow dynamics. J Dynam Syst Meas Control 2012; 134: 031005.

Karnopp

Margolis

Rosenberg

. System Dynamics: Modeling and Simulation of Mechatronic Systems, 4th edition. Hoboken, NJ: Wiley, 2006.

Margolis

Yang

. Bond graph models for fluid networks using modal approximation. J Dynam Syst Meas Control 1985; 107: 169–175.

Hullender

Healy

. Rational polynomial approximations for fluid transmission line models. In Fluid Transmission Line Dynamics (ASME Special Publication). New York: ASME, 1981.

Mäkinen

Piché

Ellman

. Fluid transmission line modeling using a variable method. J Dynam Syst Meas Control 2000; 122: 153–162.

10.

Goodson

Leonard

. A survey of modeling techniques for fluid line transients. J Basic Engng 1972; 94: 474–482.

11.

Woods

. A first-order square-root approximation for fluid transmission lines. In Franke

Drzewiecki

, Fluid Transmission Line Dynamics. New York: ASME, 1983, pp. 37–49.

12.

Piché

Ellman

. A fluid transmission line model for use with ODE simulators. In The Eighth Bath International Fluid Power Workshop, 1995.

13.

White

. Fluid Mechanics, 4th edition. New York: McGraw-Hill, 1999.

14.

Woods

. The effects of source and load impedance connected to fluid transmission lines. In Fluid Transmission Lines Dynamics (ASME special publication). New York: ASME, 1981.

15.

Zielke

. Frequency dependent friction in transient pipe flow. PhD thesis, University of Michigan, 1966.

16.

Strand

Engja

. Bond graph interpretation of one-dimensional fluid flow. J Franklin Institute 1991; 328: 781–793.

17.

Yang

. Stochastic dynamic system analysis of wave energy converter with hydraulic power take-off, with particular reference to wear damage. PhD thesis, Norwegian University of Science and Technology, 2011.

18.

20-sim, version 4.1, Controllab products B.V., The Netherlands, http://www.20sim.com.