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A STUDY OF THE INFLUENCES OF PIPE ON VALVE CONTROLHYDRAULIC SYSTEMKong XiaowuQiu Minxiu, Wei Jianhua, Wu GenmaoState Key Laboratory of Fluid Power, Zhejiang University, Hangzhou, Zhejiang, 310027,P.R.ChinaXwkong@sfp.zju.edu.cnABSTRACTThe accurate mathematical model of valve controlhydraulic system with long pipeline is constructedthrough theoretical analysis. The influences of longpipeline on valve control hydraulic system areinvestigated. A series of conclusions were obtained,which are important to the design and analysis of valvecontrol hydraulic system.INTRODUCTIONLarge-sized construction machinery usually has tens ofactuators. All of them get power from a centralhydraulic source. Some are far away from the hydraulicsource. The long pipeline between actuator andhydraulic source is essential sometimes. It causes manyproblems to electro-hydraulic system. This paper studiesthe influences of long pipeline on valve control systemand comes to some simply and valuable conclusions.TRANSFER FUNCTION OF VALVECONTROL SYSTEMIn order to analyze the characteristics of valve controlsystem with long pipeline, The transfer function ofvalve control system must be established. Fig.1 showsthe principle of valve control system with long pipelineFig.1 The principle of valve control system(1) Pipe Dynamic CharacteristicsEquation[2][4]Γ+Γ=Γ+Γ=)()()(1)()()()()()()()()(221221sshsPsZschsQsQsshsQsZschsPsPCCAssume that the hydraulic source supply constantpressure oil, the return pressure is zero and the length ofin-line and return line is equal, then we obtain0)()()()()(0)()()()()(00=Γ−Γ=Γ+ΓsshsQsZschsPsshsQsZschsPvCvsvCsv )2()1(where )(sΓ—propagation operator )(sZccharacteristic impedance(2) Four-way Slide valve Dynamic EquationIf orifice area of slide valve is matching and symmetric,then the flow-pressure equation isρρvfsvdvfsvdLPPPACPPPACQ0201−+−−−= (3) ρρvfsvdvfsvdvsvPPPACPPPACQQ02010−++−−== (4)where−≤−≥⋅+=WAXWAXXWAAVVV1010101,0,≥≤⋅−=WAXWAXXWAAVVV2020202,0,1A is the orifice area of AP → or TB →, 2A is theorifice area of BP → or TA →, 10A and 20A are theorifice area of operating point, W is the area gradient,vX is the relative motion of spool to operating point.dC is the flow coefficient. The Laplace transforms ofEq. (3) and Eq. (4) are as follows)6()()()()()()5()()()()()(0000sPKsPKsPKsXKsQsPKsPKsPKsXKsQvSsvSSfCSvQSsvvsvSfCvQL++−=++−= where=⋅≠⋅−−−++−−=∂∂=00,,)||()(20102010000AAAAPPPWCPPPPPPWCXQKvfsvdvfsvvfsvdvLQρρfLCPQK∂∂==⋅≠⋅−−+−++−−=00,,)||(2)(22010201002010020010AAAAPPPAACPPPAPPPACvfsvdvfsvvfsvdρρ=≥−−−=≥−−≠⋅−+−−−=∂∂−=00,||200,||20,)(2102002020100102010020010AAPPPACAAPPPACAAPPPAPPPACPQKvfsvdvfsvdvfsvvfsvdfSCSÇÒÇÒρρρ=≥−−−=≥−−≠⋅−+−−−=∂∂=00,||00||0)(1020020100201000AAPPPWCAAPPPWCAAPPPPPPWCXQKvfsvdvfsvdvfsvvfsvdvSQSÇÒÇÒ£¬£¬ρρρCSLCSSLSKPQKKPQK −=∂∂==∂∂=00,CSSCSSSSKPQKKPQK −=∂∂==∂∂=00,(3) The Continuity Equation and ForceBalance Equation of Cylinder)8()()7()(422EquationBalanceForceFXKdtdXBdtXdmPAEquationContinuityPCdtdPEVdtdXAQLttttttftfslfytttL+++=⋅+⋅+=where tA and tX are the area and motion of hydrauliccylinder piston respectively, YE is the equivalentvolume elastic modulus, tV is the general volume ofhydraulic cylinder, slC is the general leakagecoefficient. Eqs. (1), (2), (5), (6) together with theLaplace transforms of Eq. (7) and Eq. (8) composed aset equations, from which we can obtain the transferfunction of system as followsvtXXsG•=)()9()12()(2)12()(2'221221++++++=ssKsGsssGKKhhhChhhvpvωξωωξωwhere ))(())(()(1schsshZsGCΓΓ= tttyhVmAE24=ωtytttttytslChmEVABVmEACK4)(++=ξttyCtCShhVmEKAK2'−= ξξ tQvAKK = tCSQSCQvpAKKKKK−=THEORETICAL ANALYSIS OF THEINFLUENCES OF PIPE ON VALVECONTROL HYDRAULIC SYSTEMWhen the influence of pipe is neglectedssvPP ==constant000== PPv)(1sG=0The transfer function of system is12)(22'++==•ssKXXsGhhhvvtωξωThe influences of pipe on system can be measured bythe difference between )(sG and )('sG.While the difference in amplitude frequency and phase-frequency characteristic is expressed by|)(|||)(||)(||)('ωωωωjGjGjGeA−=and |))(())((|)('ωϕωϕωϕjGjGe −=respectively, we can reach the following conclusion.If 1|)(|)2(21<<≤− EjGKKKKCSQQSCω thenEeA≤)(ω and Ee ≤)(ωϕThe certification is neglected hereIf we define|)(|)2(2)(1ωω jGKKKKeCSQQSC−=,then )(ωe can be used to measure the influences of pipeon system approximately When slide valve is in different operating position, the influences of pipe to system are discussed as follows(i) Zero positionWhen slide valve is in zero position, 0==CSCKK,0)( =e. Pipe has a little influence on the dynamiccharacteristics of system. The actual value of cK andcsK arent zero but very small. So, the influence of pipeto system is minimal under the condition(2) Nonzero positionWhen slide valve is in nonzero position, QSQKK = ,CSCKK = ,|)(|2)(1 jGKeC=It will be seen that if CK is small enough, the influencesof pipe on system can be neglected. According to thetheory of fluid transmission lines, |)(|1jG reachesmaximal point at resonance frequency and fluctuatesperiodically as frequency ascends. Accordingly, )( jGfluctuates periodically relating to )('jG. Thefluctuation frequency is proportional to the length ofpipe. The fluctuation amplitude descends as frequencyascends.SIMULATION STUDYIt will be seen that the influences of pipe on hydraulicsystem are related to the steady-state point of slidevalve. Slide valve is in zero position in positioncontrol system and in nonzero position in velocitycontrol system. The following is the simulation studyof them.(1) Position Control SystemThe simulation parameters are as follows:2.137=h1s11102.4ì=CK12102.3ì=CSK5.0==QSQKK5.0=h495.0'=h250=vK9107.9ì=vpKFig.2 presents the frequency response characteristics ofvalve control hydraulic system under different pipelength. The simulation result shows: the frequency response curve of system existsperiodic fluctuation the fluctuation frequency is proportional to the lengthof pipe. the fluctuation amplitude reaches maximum near thenatural frequency of system and is smaller in low-frequency and high-frequency stage The frequency response is generally approximate tosecond-order system. Fig.2 The frequency response characteristic of systemwhen slide valve is in zero PositionFig.3 The frequency response characteristic of systemwhen slide valve is in nonzero position50 100 150 200 250 300 350 400 450 500-180-160-140-120-100-80-60-40-200Phase-frequency characteristicsƯỉÊă1/sÊâƯếÊăƯỉÊâL=25m L=50m L=0m 50 100 150 200 250 300 350 400 450 500-40-30-20-1001020304050Amplitude frequency characteristicƯỉÊă1/sÊâAÊăƯỉÊâÊădBÊâL=0m L=50m L=25m 50 100 150 200 250 300 350 400 450 500-250-200-150-100-50050100Phase-frequency characteristicƯỉÊă1/sÊâƯếÊăƯỉÊâL=25m L=50m L=0m 50 100 150 200 250 300 350 400 450 50025303540455055Amplitude frequency characteristicƯỉÊă1/sÊâAÊăƯỉÊâÊădBÊâL=25m L=50m L=0m (2) Velocity Control SystemThe simulation parameters are as follows2.137=hω1−s11102.4−×=CK12102.4−×=CSK5.0==QSQKK5.0=hξ495.0'=hξ250=vK0=vpKFig.3 presents the frequency response characteristics ofvalve control hydraulic system under different pipelength.The simulation result shows:the frequency response of system fluctuatesperiodically. the fluctuation amplitude descends when thefrequency ascends the fluctuation frequency is proportional to the lengthof pipe. If the length of pipe or the value of CK isn’t smallenough, the system can’t be considered as second-orde system.CONCLUSIONThis paper has presented an accurate mathematicalmodel for valve control hydraulic system with longpipeline. On the basis of the analysis to it, someconclusions are reached.1. The influences of pipe on system can be measuredapproximately with the frequency domain criterion|)(|)2(2)(1ωω jGKKKKeCSQQSC−=2. For given pipe parameters, cK decides the influencesof pipe on system in terms of ideal zero lap slidevalve.3. Pipe makes the frequency response of systemfluctuating periodically. The fluctuation frequency isproportional to the length of pipe. The fluctuationamplitude is decided by valve coefficient, pipe elasticmodulo and pipe inner diameter.4. The influences of pipe are greater to velocity controlsystem than to position control system.REFERENCES[1] T.J.Viersma, A.A.Ham, “Hydraulic LineDynamics”,1979.[2] 1986[3] H.E.1976[4] “”1987[5] .“”CAD[6] .“”CAD[7] “”94[8] Chen, Jine, “Theoretic solution of the transient flowof liquid in the pipe with fluid Machinery”, Journalof Hydrodynamics, v 4 n 4 Oct 1992. p 119-126 . 50 0-1 8 0-1 6 0-1 4 0-1 2 0-1 0 0-8 0-6 0-4 0-2 00Phase-frequency characteristicsƯỉÊă1/sÊâƯếÊăƯỉÊâL=25m L=50m L=0m 50 100 150 200 250 300 350 400 450 50 0-4 0-3 0-2 0-1 001020304050Amplitude. characteristicƯỉÊă1/sÊâAÊăƯỉÊâÊădBÊâL=0m L=50m L=25m 50 100 150 200 250 300 350 400 450 50 0-2 5 0-2 0 0-1 5 0-1 0 0-5 0050100Phase-frequency characteristicƯỉÊă1/sÊâƯếÊăƯỉÊâL=25m L=50m L=0m 50