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A STUDY ON THE CONTROLLABILITY OF FLOW-PRESSURERELATIONSHIP OF THE PILOT OPERATED PRESSURE RELIEF VALVEWu Wanrong,Qiu Minxiu,Wei Jianhua,Wu GenmaoInstitute of Mechatronic Control Engineering, Zhejiang University, and Hangzhou 310027 P.R.ChinaABSTRACTThe flow-pressure relationship is an important externalcharacteristic of the pilot operated pressure relief valve.Many research efforts have been put on this topic for itssignificant impact on the overall hydraulic system.Some of the researches focused on the influences of thehydraulic bridge to the main stage, while the othersattempted to analyze the influence of difference pressuremeasurement (direct or indirect) of the system pressureusing control theories. In this project, a novel methodhas been adopted. The basic idea is to find out thecorrelation between the pilot flow and the overflow ofthe main valve, and use this relative function as acriterion to compensate for the force bore on the valvepoppet. The flow-pressure curve of the relief valve canbe bent upwards(under-compensated), flat, ordownwards(over- compensated). The above scheme hasbeen utilized in the manufacture’s product catalogs.Key words: variable hydraulic resistance, forcecompensating, relief valve, controllabilityINTRODUCTIONIn pilot operated pressure relief valve, the main valve isactually controlled by the pilot hydraulic bridge. On theother hand, the pilot hydraulic circuit and the mainvalve port hydraulic circuit form parallel hydraulicnetwork. The current researches show that the steady-state override pressure is related to the control pattern ofthe pilot valve and varied with where the pressureexerting on the pilot valve and where the pressure signcoming from[1]. This paper intends to find thecorrelationship between the pilot flow and the mainoverflow of the relief valve, and to control the flow-pressure characteristic of the pilot operated pressurerelief valve by compensating for the force bore on thepilot poppet according to the correlationship.THE CORRELATIONSHIP BETWEEN THEPILOT FLOW AND THE MAINOVERFLOW OF THE RELIEF VALVEFig.1 shows the structure and the principle of the reliefvalve with compensating for the force bore on the pilotpoppet. And the flow equations and force equilibriumequations under steady-state are described below.The related flow equations of the pilot hydraulic circuitare as follows: ppcq2111−= (1) ppybq3222−= (2) pcq333= (3)Neglecting the steady-sate hydrodymatic force, theforce equilibrium equation of the pilot poppet:apapyyk332212)( +=+ (4)The flow equation of the main valve port: pxbqx 11= (5)the force equilibrium equation of the piston: pxbApApxxk10221111)( −−=+ (6)Fig. 1 The structure and principle of the relief valve withcompensating for force bore on the pilot poppetWhere 21111ρµac= , 21333ρµac= ;µ1,µ3arethe flow coefficient of orifice r1 and r3 respectively,ρis fluid mass density, a11 and a13 are the cross-areaof r1 and r3 respectively; b1b2the coefficient of the main valve port andpilot valve port respectively; b0the coefficient of the steady-satehydrodymatic force of the main valve port; A1A2the effective area of the piston on thelower end and upper end respectively; a2a3the effective area of the different part ofthe pilot poppet; k1k2spring stiffness x1y1the precompression quantity of spring. The function between q2 and qx can be solved byformulas (1)~(6), but result is very complex. Tosimplify the result, change formulas (1)~(6) intoincrement equations. Considering q1=q2=q3, at a steady-state point(q20qx0x0y0) the increments equationsare as follows: )(22120212ppqcq∆−∆=∆ (7) )(2212020220202ppqybyyqq ∆−∆+∆=∆ (8) pqcq3202322∆=∆ (9) apapyk33222∆+∆=∆ (10) pqxbxxqxqxx 102021002∆+∆=∆ (11) xxbqbkpApxbAx∆+=∆−∆− )()(20212001221001 (12)From equations (7)~(12), the following equation can bederived. ( )( )qmqcAmmqqaybkxccqqxxxx∆++=∆320212212020230222023210222 13Where caqcaqmm2132202322204122 −+= (14) xbxbqAqmxx30210020120222 +−= (15) bykcykaqm222022302322032 −−= (16) )(2321222022321024ccbykccykm++= (17)The first part (m4) in right hand of formula (14) can beomitted when compared with the others, so do the lasttwo parts in equations (15) and (16).Therefore, formula(13) can be rewritten as follows:Fig.2 The emulation curve of pilot flow varying withthe changing of the main overflow( )[ ]qacAAcaAqqqaybkxccqxxx∆−++≈∆321122321320020230222023212)(42 (18)Generally, AA, and each of parameters in formula(18) is positive, consequently, the pilot flow increases asthe main overflow increases. The theoretical andexperimental relationship of the pilot flow and the mainoverflow are shown in Figs 2-3, from which it can beseen that they coincide very much. Figs 2-3 also showthat the changing amplitude of the pilot flow followswith the varying of the main overflow under differentsystem pressure. It can be proven that the results canmeet all pilot operated pressure relief valve withdifferent structure.Fig.3 The experimental curve of the pilot flowvarying with the overflow under different systempressureTHE COMPENSATING FOR THEFORCE BORE ON THE PILOT POPPETThe disadvantage of general relief valve is that thesystem pressure increases with the increasing of theoverflow, and the higher the system pressure, thegreater the override pressure (Fig.4 shows).Fig.4 The experimental curve of the override pressurechanging with the overflow under different systempressureAccording to the results above, the override pressure ofthe relief valve can be compensated by attachinghydraulic resistance in the pilot hydraulic circuit. Thecompensating method is to connect the pilot poppet withthe compensating piston which consists of an orifice(Fig.1), when fluid flow through the orifice, cause apressure difference in it, thus modifying the equilibrium2130252015105P1(Mpa)qx(L/min))q2(L/min))2001000 50 100 150 2000.00.20.40.60.81.01.2P1=10MPaP1=15MPaP1=20MPaq2(L/min)qx(L/min)0P1(Mpa) 30 20 10 00 100 200 qx(L/min) state of force bearing on the pilot poppet and reducingthe resistance of the variable hydraulic resistance of thepilot valve port to fluid. This results in compensatingthe unfavorable effects to system pressure causing bythe factors of the pilot valve, such as hydrodymaticforce, spring force, etc., when the main overflow varies.Compensating force Fc : apFc 33= 19According to equation (2), the hydraulic resistance ofthe pilot valve port under a steady-state point is asfollows[2]: ybppqdpdRaaaaa23222 −=∆=In order to discuss the general hydraulic resistanceproperty of the pilot valve port, the above equation canbe rewritten: ybppR2322 −= 20Transform the formula (19) and (20) into incrementequations: paFc33∆=∆ (21) yybqqppR ∆−∆−∆=∆30221020212 (22)Solve equations (7)~(10) and (22), we can get:qybkaqcaaqybkaqybybkaqR230222222023322203022222202022202222220)2()(8)2(24∆++++−−=∆ (23Where the latter part of the numerator in the firstfraction can be omitted when compared with the formerpart, the other parameters in formula (23) are positive,therefore, the hydraulic resistance of the pilot valve portdecreases with the increasing of the pilot flow. Thesecond part of the square bracket of the formula (23)results from the compensating force, which results inmore reducing the hydraulic resistance of the pilot valveport with the increasing of the pilot flow. The greaterthe parameter a3 or the smaller the parameter c3, thegreater the compensating force and the decreasingamplitude of the pilot valve port hydraulic resistance.From formulas (9) and (21), get: qcaqFc2233202∆=∆ 24Consequently, compensating force increases with theincreasing of the pilot flow. The variation of thecompensating force with the changing of the pilot flowhas something to do with the pilot flow of the steady-state point and changes with the different structuralparameters a3c3, Fig.5 shows the theoreticalrelationship of the compensating force and the pilotflow with the different structural parameter c3.Fig. 5 The emulation curve of the compensating forcevarying with the changing of the pilot flowTHE CONTROLLABILITY OF THEFLOW-PRESSURE CHARACTERISTICOF THE RELIEF VALVEBecause the changing amplitude of the compensatingforce with the varying of the pilot flow is mainlydependent on the structural parameters a3 and c3according to formula (24), it is reasonable to change thehydraulic resistance property which varies with thechanging of pilot flow. According to the formula(7)~(10) and (21): Fpc∆=∆ λ1 25 )2(22)(30202220321213220232220232130222232102ybkqaccaqcaqccybkccyk+−+++=λ 26From formula (25), it can be seen that different λ willresults in different characteristic of the controlpressure p1 varying with the compensating force:λ >0p1 increases with the increasing of thecompensating force, this is under-compensated;λ=0p1 keeps constant, and does not change withthe compensating force, right-compensated;λ <0p1 decreases with the increasing of thecompensating force, over-compensated.Meanwhile, the value of λ is only dependent on thestructural parameters and pilot flow. In formula (26),the value of denominator is positive, so, whether thevalue of λ is positive, zero or negative is decided bythe value of the numerator. The first two parts of thenumerator in the formula (26) can be omitted whencompared with the others, so the value of λ ismainly dependent on the last two parts , i.e. caca213232− >0 λ>0 caca213232− =0 λ =0 caca213232− <0 λ<0Consequently, the value of λ is mainly dependent onthe arrangement of the parameters a2, a3, c1, c3, Whenthe parameters a2 and c1 are fixed, the value of λ isdecided by a3 and c3. Fig.6 shows the theoreticalrelationship of the control pressure varying with thecompensating force under different parameter valueof a3 (or c3), i.e. λ .0 2 4 6 8 10 120102030400 0.2 0.4 0.6 0.8 1.0 1.2c31<c32<c33c33c32c31Fc(N)q2(L/min) 0 5 10 151600000018000000200000002200000016222018p1(MPa)Fc(N)2.5233×10-20-1.9842×10-20-1.4763×10-21( a2c32-a3c12 )Fig.6 The emulation curve of the control pressurevarying with the changing of the compensating forceFrom formulas (24) and (25): qcaqp22332012∆⋅=∆ λ 27According to formulas (18) and (27), it can be seen thatthe flow-pressure relationship of the relief valve is alsodependent on the value of λ, i.e. there exists differentflow-pressure characteristic of the relief valve withthe different matching of the parameters a2, a3, c1, c3:under-compensated, λ>0, the pressure increases withthe increasing of the overflow; right-compensated,λ=0the pressurekeeps constant, and does not change with overflow;over-compensated,λ<0the pressure decreaseswith the increasing of the overflow.EXPERIMENT ON FLOW-PRESSURECHARACTERISTIC OF THE RELIEFVALVEFig.1 shows the structure of the experimental valve(NG10), the relational structural parameters are asfollows[3]: dr1=0.6mm, a2=12.566mm2, a3=164.15mm2,A1=76.2mmm2, A2=78.54mm2. Fig.7 shows theexperimental results of the pressure varying with theoverflow under dr3=1.0mm, dr3=1.1mm, dr3=1.2mm.dr3=1.0mm, the pressure reduces with the increasingof the overflow in Fig 5c; dr3=1.1mm, the pressurekeeps constant, it does not change with the increasingor decreasing of the overflow in Fig. 5b; dr3=1.2mm,the pressure increases with the increasing of theoverflow in Fig. 5a. There exists different flow -pressure characteristic of the relief valve with thedifferent of dr3 (or λ).Consequently, it is reasonable to obtain the flow-pressure characteristic required according to thedifferent parameters of the pilot hydraulic circuit.Some kinds of pressure valves have beenmanufactured by applying the above principle byRoxroth Ltd. Fig.8 shows one of the products, a pilotoperated pressure relief valve[4].Fig.8 The structure and principle of the relief valve ofRoxroth Ltd.CONCLUSIONS(1) The pilot operated pressure valve is made up ofparallel hydraulic network which formed by thehydraulic circuit of the pilot valve and that of the mainvalve port. The pilot flow increases with the increasingof the main overflow, and the greater the systempressure, the more the variation of the pilot flow varyingwith the overflow.(2) The flow-pressure characteristic of the pilotoperated pressure valve can be compensated byaltering the equilibrium state of the force bore on thepilot poppet through attaching hydraulic resistance inthe pilot poppet.(3)There exists different flow-pressure characteristicwith different compensating degree of the force bore onthe pilot poppet: under-compensated, the flow-pressure curve will be bent upwards; right-compensated, kept flat; over-compensated, bentdownwards.(4) The principle of compensating the override pressureof the relief valve by attaching a hydraulic resistance inthe pilot circuit is actually to compensate the variablehydraulic resistance of the pilot hydraulic bridge, whichis suited for other pressure valves controlled by, forexample, B half bridge.P1(MPa)20 (a) 0 50 100 150 200P1(MPa) qx (L/min)20 (b) 0 50 100 150 200P1(MPa) qx (L/min)20 (b) 0 50 100 150 200 qx (L/min)Fig.7 The experimental curves of the flow-pressure characteristic of the relief valve REFERENCES[1] Tang Quanbo, Li Zhaomin, Li Zhangyun. Theanalysis on the override pressure of relief valve,(inChinese). Machine tool and hydraulics. 1989(6):21~23[2] Backé W, Zhu Wen. Hydraulic resistance circuitsystemology, (in Chinese). Beijing: China machinery press. 1980[3] Wu GenmaoVorgesteuertesDruckbegrenzungsventil DB10 Serie 30Versuchsbericht V932Mannesmann RexrothGmbH1984[4] Rexroth. Induetrieventile und Zubehör.RD00101/09.92, ss.165 . 151600000018000000200000002200000016222018p1(MPa)Fc(N)2.5233×1 0-2 0-1 .9842×1 0-2 0-1 .4763×1 0-2 1( a2c32-a3c12 )Fig.6 The emulation curve of the control pressurevarying. on the valvepoppet. The flow-pressure curve of the relief valve canbe bent upwards(under-compensated), flat, ordownwards(over- compensated). The above scheme