The method of modal approximation to the distributed friction transmission line functions via frequency-domain analysis is briefly discussed. A specific form is then derived which allows time-domain analysis to be easily pursued using a digital simulation package approach. The method is applied to a highly non-linear servo-valve controlled motor system and a good comparison between experiment and theory is shown. A comparison is also made with previous work using the method of characteristics, and natural frequency predictions are also compared with some common lumped parameter approximations.
Get full access to this article
View all access options for this article.
References
1.
KibbleJ. D.Hydraulic supply systems for powered supports in minesHydraulic Pneumatic Power, July 1974, 252–257.
2.
CrookA.ThomassonP. G.The behaviour of unloading valves in long pipeline systems. BHRA report SP992, First Fluid Power Symposium, January 1969.
3.
KorobochkinB. L.Dynamic characteristics of machine tool hydraulic systems. Fluid Power International Conference, London, 1970, E1-E6.
4.
KorobochkinB. L.KomitovskiM. D.Reduction of the level of vibrations in the hydraulic drive of machinesStanki Instrum, 1968, 11, 3–6.
5.
LamontH.Dynamic analysis of an electrohydraulic servo actuator with interconnecting lines. Technical Memos 3 and 4, Grummon Aerospace Corporation, 1985.
IberallA S.Attenuation of oscillatory pressures in instrument linesJ. Res. Natn Bur. Stand, July 1950, 45 (1).
8.
RohmannC. P.GroganE. C.On the dynamics of pneumatic transmission linesTrans. ASME, May 1957, 79, 853–874.
9.
NicholsN. B.The linear properties of pneumatic transmission linesTrans. Instrum. Soc. Am, 1962, 1, 5–14.
10.
KaramJ. T.FrankeM. E.The frequency response of pneumatic linesTrans. ASME, J. Basic Engng, June 1967, 371–377.
11.
ChurchesA. E.HindE. C.BryantR. A. A.An evaluation of pneumatic transmission line propagation functionsTrans. ASME, J. Dyn. Syst. Measmnt Contr, March 1974, 77–87.
12.
BrownF. T.Transient response of fluid linesTrans. ASME, J. Basic Engng, December 1962, 84(4), 547–553.
13.
KatzS.Transient response of fluid lines by frequency response conversionTrans. ASME, J. Dyn. Syst. Measmnt Contr, December 1977, 311–313.
14.
KirshnerJ. M.KatzS.Design theory of fluidic components, 1975 (Academic Press, London).
15.
GoodsonR. E.LeonardR. G.A survey of modelling techniques for fluid line transientsTrans. ASME, J. Basic Engng, June 1972, 474–482.
16.
TadmoryM. J. A. A.Damping characteristics of transmission lines with sudden closure of an underlapped electrohydraulic servovalve. M.Sc thesis, Department of Mechanical Engineering and Energy Studies, University College, Cardiff, 1985.
17.
ZielkeW.Frequency-dependent friction in transient pipe flowTrans. ASME, J. Basic Engng, March 1968, 109–115.
18.
ManningJ. R.Computerized method of characteristic calculations for unsteady pneumatic line flows. Trans. ASME, J. Basic Engng, paper 68-FE-18, 1968.
19.
BrownF. T.A quasi method of characteristics with application to fluid lines with frequency dependent wall shear and heat transfer. Trans. ASME, J. Basic Engng, paper 68–WA/Aut7, 1969.
20.
BoucherR. F.KitsiosE. E.Simulation of fluid network dynamics by transmission line modellingProc. Instn Mech. Engrs, Part C, 1986, 200 (C1), 21–29.
21.
KitsiosE. E.BoucherR. F.Transmission line modelling of a hydraulic position control systemProc. Instn Mech. Engrs, Part B, 1986, 200 (B4), 229–235.
22.
KitsiosE. E.BoucherR. F.Stability study of vortex amplifier (VA) distributed circuitsDynamic Systems: Modelling and Control, 1985, 1, 145–153. (ASME, New York).
23.
ShearerJ. L.Digital simulation of a Coulomb-damped hydraulic servosystemTrans. ASME, J. Dyn. Syst. Measmnt Contr, December 1983, 105, 215–221.
24.
OldenburgerR.GoodsonR. E.Hydraulic line dynamics. Proceedings of Conference on Automatic and Remote Control, Basle, Switzerland, 1963.
25.
HullenderD. AHealeyA J.Rational polynomial approximation for fluid transmission line models. Fluid transmission line dynamics, 1981, H00200, 33–56 (ASME, New York).
26.
HealeyA J.HullenderD.A State variable representation of modal approximation for fluid transmission line systems. Ibid, 57–72.
27.
HsueC. Y.HallenderD.A Modal approximations for the fluid dynamics of hydraulic and pneumatic transmission lines. Fluid Transmission Line Dynamics, 1983, H00278, 51–77. (ASME, New York).
28.
HullenderD. A.WoodsR. L.HsuC. H.Time domain simulation of fluid transmission lines using minimum order state variable models. Ibid, 78–97.
29.
MargolisD. L.YangW. C.Bond graph models for fluid networks using modal approximationTrans. ASME, J. Dyn. Syst. Measmnt Contr, September 1985, 107, 169–175.
30.
WattonJ.The stability of electrohydraulic servomotor systems with transmission lines and non-linear motor friction effects. Part A: system modellingJ. Fluid Contr, 1986, 16 (2–3), 118–136.
31.
WattonJ.The stability of electrohydraulic servomotor systems with transmission lines and non-linear motor friction effects. Part B: system stability. Ibid, 137–151.
32.
WattonJ.The dynamic performance of an electrohydraulic servovalve/motor system with transmission line effectsTrans. ASME, J. Dyn. Syst. Measmnt Contr, March 1987, 109, 14–18.
33.
TakayoshiM.ToskiakiK.Resonance and transient response of pressurised complex pipe systemsBull. J.S.M.E, 1980, 23(184), 1610–1617.
34.
EdgeK. A.BrettP. N.LeahyL. C.Digital computer simulation as an aid in improving the performance of positive displacement pumps with self-acting valves. Computer aided design in high pressure hydraulic systems, 1983, 59–66. (Mechanical Engineering Publications, London).
35.
WattonJ.Modal analysis of electrohydraulic systems transmission lines in a form suitable for implementation by a digital simulation package. 1987 ASME Winter Meeting, Boston, paper 87–WA/DSC–23.
