INVESTIGATION OF STATIC CHARACTERISTICS OF PILOT OPERATED PRESSURE RELIEF VALVES

Transcription

1 INVESTIGTION OF STTIC CHRCTERISTICS OF PILOT OPERTED PRESSURE RELIEF VLVES 1. TECHNICL UNIVERSITY OF SOFI, BULGRI 1. Sasko S. DIMITROV BSTRCT: Theoretical and exerimental investigation of the static characteristics of the ilot oerated ressure relief valve is resented in this article. mathematical model of ressure dro vs. flow deending for ilot oerated ressure relief valve is develoed. n exerimental test stand was created for exerimental determination of the static characteristics and comared with each other which confirm the mathematical model. The results of solving the mathematical model and exerimental investigation are resented in few diagrams. few directions for imroving the static characteristics are given, eseciall at the moment of oening of the main valve. dvantages and disadvantages of the static characteristics are discussed. KEYWORDS: Pilot oerated ressure relief valve, flow, ressure, static characteristic, mathematical model, exeriment INTRODUCTION Main feature of the static characteristic of the relief valves is its sloe. The sloe of the static characteristic is called ressure-flow coefficient. For the same setting ressure and flow, the ressure-flow coefficient is higher for direct oerated ressure relief valves comaring with ilot oerated ressure relief valves [1],[3]. dditional decrease of the ressure-flow coefficient of the conventional ilot oerated ressure relief valves can be obtain with built-in comensating control iston in front of the ilot valve. nother deficienc of the static characteristic of the ilot oerated ressure relief valve is the difference between the ressures of oening of the ilot valve and the main valve. This error can be reduced also with a comensating control iston in the ilot valve [9]. In [7] the authors have shown theoreticall and exerimentall the advantage of the ilot oerated ressure relief valves-lower ressure-flow coefficient of the static characteristic of the valve. But it cannot be clearl seen the ressure difference between oening of the ilot and the main valve. In [6] a secial attention has been taken to the influence of the hdrodnamic reaction force to the valve characteristics. lso, the author has investigated different designs of the resistance orifices in the ilot chain to imrove the characteristics of the valve. Most comrehensive theoretical mathematical model is resented in [4], in details exlained and included all the factors influencing the qualit of the static characteristics. This model was develoed for valve with ilot flow through main valve. In this stud this model has been little modified for valve with round about ilot flow. To imrove the static characteristic of the valve the built-in comensating control iston with resistance orifice in it in the ilot chain is taken into consideration. Exressions for the ressure-flow coefficient of the valve without comensating control iston and with comensating control iston are obtained numericall to determine the ressure-flow coefficient of the valve. The influence of the diameter of the comensating control iston to the static characteristics of the valve is resented, as well. This stud has exerimentall roved the validit of this model. FUNCTIONL DIGRMS OF THE VLVES On figure 1 a functional diagram of the ilot oerated ressure relief valve without comensating control iston a) and with comensating control iston b) is shown. This valve can be observed as a sstem consisted of three subsstems: main valve, ilot valve and fixed orifices (R 1 and R 3 ). In neutral osition both ilot and main valves are closed under the influence of the srings, and there is a balance of forces at the closing element of the main valve. When inlet ressure will reach higher value than the reset sring force of the ilot valve, the closing element of the ilot valve is oening and through the orifices R 1 and R 3 beginning to flow some little amount of ilot flow q. The ressure 4 in the uer art of the main valve is maintaining aroximatel constant b the ilot valve. With further increase of the inlet ressure the ressure dro,4 4 continues to increase until the main valve oens and the flow q 3 + q is flowing to the tank. coright FCULTY of ENGINEERING HUNEDOR, ROMNI 1

2 NNLS OF FCULTY ENGINEERING HUNEDOR International Journal Of Engineering a) b) Figure 1. Functional diagram of a ilot oerated ressure relief valve MTHEMTICL MODEL OF THE STTIC CHRCTERISTICS Static characteristic of a ressure relief valve shows changing of the control arameter (ressure dro, ) deending of the inlet arameter (inlet flow ). For theoretical determination of the static characteristics a methodolog resented in [4] is used in this stud. For this te of ressure relief valve- with ilot flow through main valve, the mathematical model in [4] is slightl modified. There is, also, an additional equation for balance forces on the comensating control iston. The static characteristics of the ilot oerated ressure relief valves are described with following equations: Flow equation across the ilot valve q μ d π x sinθ 4, (1) where: q - the flow across the ilot valve; μ - the flow coefficient of the ilot valve; d - the seat diameter of the ilot valve; x - the dislacement of the closing element of the ilot valve; θ - the angle of flowing of the oil at the ilot valve, - the densit of the oil; 4, 4 - the ressure dro in the ilot valve. Balance of forces acting on the closing element of the ilot valve c ( h + x ) 4, + 5,4 b r x 4, or 4, + 5,4 b c h x () c + r 3, where: - the area of the seat of the ilot valve; c - the sring constant of the ilot valve; h - the revious deformation of the sring of the ilot valve; r μ π d sin θ cos θ - the hdrodnamic force coefficient of the ilot valve; b - the area of the comensating control iston; d b - diameter of the comensating control iston; 5,4 - ressure dro in the comensating control iston orifice. If we solve the equations (5) and (6), the static characteristic of the ilot valve will be obtained: 4, + 5,4 b c h q μ d π sinθ 4, (3) c + r Pressure dro at the fixed orifices 1,4 R1l q + R1m q + R3l q + R3m q (4) ( R 1l + R 3l ) q + ( R 1m + R 3m ) q R l q + R m 1,4 q where:,3 3 - the ressure dro at the ilot chain, R l R 1l + R 3l - the linear hdraulic resistance in the orifices R 1 and R ; R m R 1m + R 3m - the local quadratic resistance in the orifices R 1 and R 3 ; dr - the area of the orifice R 1 and R 3 ; d dr1 - the diametar of the orifice R 1 ; l 1 - the length of 3, Tome XI (Year 13). Fascicule. ISSN

3 NNLS OF FCULTY ENGINEERING HUNEDOR International Journal Of Engineering the orifice R 1 ; d dr3 - the diameter of the orifice R 3, l 3 - the length of the orifice R 3 ; υ - the viscosit of oil. Pressure dro at the main valve, 1,4 + 4, (5) where:, - the ressure dro at the main valve Balance of forces acting on the closing element of the main valve 1,4 k 1, Δ c ( h + x ) + r x 1, or 1,4 k 1, Δ c h x (6) c + r 1, where: k - the area of the closing element of the main valve; Δ - the unbalanced area at the closing element of the main valve; φ Δ/ k - geometric arameter of the valve; h the revious deformation of the sring of the main valve; x - the dislacement of the closing element of the main valve; r μ o π D k sin θ cos θ - the hdro-dnamic force coefficient of the main valve; μ - the flow coefficient of the main valve; D k - the diameter of the closing element of the main valve; θ - the angle of flowing of the oil at the ilot valve. Flow across the main valve where: q 3 - the flow across the main valve. Flow through ilot chain q μ (7) 3 D π sinθ 1, q + (8) 1 q3 q The static characteristics of the ilot oerated ressure relief valves are full described b the equations (1) to (8). From equations (1) (8) theoreticall can be exressing the ilot flow (9) and the difference between the ressure of oening of the ilot valve and the main valve (1) if there is builtin comensating control iston [5], [9]: ( q ) 1, c h ϕ + k R 1m ( R + R ) ( q ) ccording to equation (9), the ilot flow directl deends of the geometric arameter of the valve φ and the resistance in the ilot orifices R 1 and R. Pilot oil flow is alwas higher for ilot oerated ressure relief valve without comensating control iston. 1 ( ) c + h x c r 4, b + + ( ( ) + ( ) ) 1, 1, R3l q R 3m q (1-a) 1 ϕ k For ilot oerated ressure relief valve without comensating control iston, the ressure of oening of the main valve is: 1 ( ) c + h x c r 4, + + 1, 1, (1-b) 1 ϕ k Equations (1-a) and (1-b) shows that the ressure difference between ilot and main valve is lower when there is built-in comensating control iston in the ilot valve. With increasing the diameter of comensating control iston d b, i.e. the area of the comensating iston, the last art of the equation (1-a) is getting greater and the ressure difference is getting lower. The effect of reducing the difference between the ressure of oening of the ilot and the main valve exerimentall is shown on Figure 7. With linearization of the equations (1) (8) around the stead state values of ressure and flow q, the statism can be exressed as [4]: c + r ( 1, ) k ( ) ( ) ( ) st, k st 1 + (11) R1l + R3l + R1m + R3m q, μ π D sinθ 1, k The ressure-flow coefficient of the ilot valve without comensating control iston is: c + r ( 4, ) k st, (1-a) μ π d sinθ ( 4, ) The ressure-flow coefficient of the ilot valve with comensating control iston is: + R 1l 3m 3l (9) Tome XI (Year 13). Fascicule. ISSN

4 k st, μ π d c NNLS OF FCULTY ENGINEERING HUNEDOR International Journal Of Engineering + r sinθ ( ) 4, ( ) 4, ( R + q R ) 3l, 3m b (1-b) From equations (1-a) and (1-b) it can be clearl seen the difference in the ressure-flow coefficient of the static characteristic of the valve without comensating iston (1-a) and with comensating iston (1-b). Decreasing of the ressure-flow coefficient can be achieved b increasing the diameter of the comensating iston d b, i.e. b increasing the area of the comensating iston b. If the second art of the equation (1-b) is equal to the first art, the ressureflow coefficient would be zero and it would be obtained ideall horizontal static characteristic. But, if the second art of the equation (13) is greater than the first art, the ressure-flow coefficient would be negative and it is ossible the valve turn to work unstable in the stead state regime. On Figure 3 a ressure-flow coefficient deendence of the diameter of the comensating iston for different ressure settings and flows across the valve is resented. It can be seen that valve with comensating control iston with diameter d b 65.5 mm and flow across the valve 3 l/min will have negative ressure-flow coefficient above 65 bar. If the setting ressure is below 65 bar, the ressure-flow coefficient is ositive and the valve is stable in stead state regime. Exerimental confirmation of this claim is shown on Figure o s i t i v e s t a t i s m n e g a t i v e s t a t i s m t h e o r e x e r i m e n t d b m m Figure 3. Pressure-flow coefficient deendence of the d b for different ressure settings and flows ( ) 4 3 ( ) x o i l o t v a l v e m a i n v a l v e x o i l o t v a l v e m a i n v a l v e x a n d x o ( m m ) x a n d x o ( m m ) x.5 x a) b) Figure 4. Stable and unstable work of the ilot oerated ressure relief valve with comensating iston 4 Tome XI (Year 13). Fascicule. ISSN

5 NNLS OF FCULTY ENGINEERING HUNEDOR International Journal Of Engineering On Figure 4-a a stable work of the ilot oerated ressure relief valve with comensating control iston with diameter d b 65.5 mm, working ressure of 6 bar and flow across the valve 3 l/min is shown. On Figure 4-b an unstable work of the same valve at the same condition but with increased working ressure of 1 bar is shown. t ever working ressure above 65 bar the valve is working unstable because the ressure-flow coefficient is negative, according to Figure 3. EXPERIMENTL ND THEORETICL CHRCTERISTICS The measurement instruments were reviousl calibrated. ressure transducer te HM17 manufactured b BoschRexroth was used for ressure measurement. For dislacement of the valve a osition sensor manufactured b BoschRexroth was used. The data are stored in the comuter through 14 bit data acquisition card manufactured b National Instruments. The subject of investigation was Denison ressure relief valve te R4V 6, shown on figure 6 [8]. The arameters of the secified ressure relief valve are: d 5 mm, c 5 N/mm, d b 5.5 mm, μ.65, υ 34 cst, 89 kg/m 3, d dr1 d dr3.8 mm, d dr.68 mm, l dr1 l dr3 1 mm, D k 8.5 mm, D 8 mm, c 7 N/mm, h 16.5 mm, μ.6. Theoretical and exerimental static characteristics are resented on figure Figure 6. The investigated ressure relief valve [7] a) without comensating iston b) d b 5.5 mm e x e r i m e n t t h e o r e x e r i m e n t t h e o r e x e r i m e n t t h e o r e x e r i m e n t t h e o r c) without comensating iston d) d b 5.5 mm Figure 7. Theoretical and exerimental static characteristics of the secified ressure relief valve On figure 7-a static characteristic of the ilot oerated ressure relief valve without comensation control iston is shown. On figure 7-b static characteristic of the ilot oerated ressure relief valve with comensation control iston d b 5.5 mm is shown. comarison between exerimental and theoretical static characteristic of the secified ressure relief valve, for two ressure settingsaround 6 bar and around 1 bar, without comensating control iston (figure7-c) and with comensation control iston d b 5.5 mm (figure7-d) is shown zoomed for lower flows across the valve. It can be noticed that the resence of the comensating control iston reduces the ilot flow and the ressure difference, according to (1). The exerimental investigation of the valve roved the Tome XI (Year 13). Fascicule. ISSN

6 NNLS OF FCULTY ENGINEERING HUNEDOR International Journal Of Engineering roosed mathematical model for theoretical determination of the static characteristics of the ilot oerated ressure relief valves with and without comensating control iston. t the diagrams on figure 7 can be seen that ressure difference between oening of the ilot and the main valve is higher for the valve without comensating iston and it is decrease with the increasing of the comensating control iston diameter d b. lso, the ilot oil flow and the ressureflow coefficient of the valve are decreasing with increasing of the comensating control iston diameter d b and higher without comensating control iston. CONCLUSIONS Exerimental investigation roved the theoretical examination (eq. 1-a and eq. 1-b) that inserting a comensating control iston in front of the ilot valve can reduce the ilot flow and the ressure difference between oening of the ilot valve and the main valve. The error at the beginning of oening of the valve can be reduced if the relative ratio of the areas of the comensating iston and the seat of the ilot valve is increased. Figure 7 shows that a valve without comensating control iston has ressure error of around 1 bar at 6 bar ressure setting and around 15 bar at 1 bar ressure setting (Figure 7-a and Figure 7 c). Inserting the comensating control iston with d b 5.5 mm, the ressure error is around 4 bar at 6 bar ressure setting and 8 bar at 1 bar ressure setting (Figure 7-b and Figure 7 d). Theoretical investigation sas that higher diameter of the comensating control iston d b can much more reduce the ressure error (1), but it is ossible the ressure-flow coefficient of the static characteristic of the valve to be negative (1) in that case. Grahicall it is resented the values of the ressure-flow coefficient deending of the diameter of the comensating control iston d b, Figure 3, and the limit values of d b when valve is working unstable. This claim is also exerimentall confirmed and resented on Figure 4. ccording to eq. (9) and eq. (1) additional imrovement decreasing of the ilot oil flow and ressure difference between oening of the ilot and the main valve can be achieved b minimizing the geometric arameter φ of the main valve. REFERENCES [1.] Backé W., Murrenhoff H. Grundlagen der Ölhdraulik. Institut für fluidtechnische ntriebe und Steuerungen. Technische Hochschule achen [.] Will D., Ströhl H., Gebhardt N. Hdraulik. Sringer-Verlag Berlin [3.] Brodowski W. Beitrag zur Klärung des stationären und dnamischen Verhaltens direktwirkender Druckbegrenzungsventile. Dissertation [4.] Komitovski М. Elements of hdro- and neumo-drives (in Bulgarian). Technika, Sofia, [5.] Komitovski M. Pressure controlling in hdraulic sstems with ressure-unloading valves (in Bulgarian). Scientific Conference EMF99, Sozool, Bulgaria, 1999 [6.] Wobben, G. D. Statisches und dnamisches Verhalten vorgesteuerter Druckbegrenzungsventile unter besonderer Berücksichtigung der Strömungskräfte, Dissertation, RWTH achen, 1978; [7.] Takenaka, T.,Urata, E. Static and Dnamic Characteristics of Oil-Hdraulic Control Valves, Fluid Power International Conference, Toko, 1968 [8.] DENISON HYDRULICS GmbH, Pressure relief valve R4V, Catalogue sheet 3-EN 4-; [9.] Dimitrov, S. Static characteristics of ilot oerated ressure relief valves with comensating control iston. Scientific Conference EMF11, Sozool, Bulgaria, 11 NNLS of Facult Engineering Hunedoara International Journal of Engineering coright UNIVERSITY POLITEHNIC TIMISOR, FCULTY OF ENGINEERING HUNEDOR, 5, REVOLUTIEI, 33118, HUNEDOR, ROMNI htt://annals.fih.ut.ro 6 Tome XI (Year 13). Fascicule. ISSN