INFLUENCE OF OPERATING AND CONSTRUCTION PARAMETERS ON THE BEHAVIOR OF HYDRAULIC CYLINDER SUBJECTED TO JERKY MOTION

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1 Proeedings of ICFDP 8: 8 th International Congress of Fluid Dynamis & Propulsion Deember 14-17, 006, Sharm El-Shiekh, Sinai, Egypt ICFDP8-EG-154 INFLUENCE OF OPERATING AND CONSTRUCTION PARAMETERS ON THE BEHAVIOR OF HYDRAULIC CYLINDER SUBJECTED TO JERKY MOTION Sadek Z. Kassab Mehanial Engineering Department Faulty of Engineering, Alexandria University Alexandria, 1544, Egypt szkassab@yahoo.om Ihab G. Adam Mehanial Engineering Department Faulty of Engineering, Alexandria University Alexandria, 1544, Egypt adam@alexeng.edu.eg Mohamed A. Swidan Mehanial Engineering Department Faulty of Engineering, Alexandria University Alexandria, 1544, Egypt maswidan@yahoo.om Mahmoud Galal Rabie Mehanial Engineering Department Modern Aademy for Engineering and Tehnology Cairo, Egypt rrabie@ids.net.eg KEYWORDS Pilot operated hek valve, Jerky motion, Modeling. ABSTRACT The present study is a step further in a planed investigation dealing with studying the dynami behavior of hydrauli ylinder subjeted to jerky motion during load lowering. It is direted to extend the use of a previously validated model to investigate theoretially the effet of some parameters, diffiult to study experimentally, on the performane of the hydrauli ylinder and onsequently on the related hydrauli system performane. These parameters inlude the pump flow rate, the spring stiffness of the pilot operated hek valve, POCV, and meter-out throttle valve. In addition, an analysis is performed using the mathematial model to study the osillation phenomena in ylinder piston side, when lowering loads. This inludes studying the behavior of poppet displaement of the POCV, pressure at ylinder piston side and the ylinder piston displaement. The results reviled that inreasing the pump flow rate results in a derease in the system pressure osillation. By dereasing the magnitude of the spring stiffness, the pressure amplitude dereases. Meanwhile, inreases the spring stiffness results in an inrease in the pressure osillation and amplitude. Using meter-out orifie with the POCV a deeleration is happened to the desending load whih overomes system pressure osillation, but the operating pressure inreases INTRODUCTION The hydrauli iruits whih is used to raise and lower heavy loads need a valve (Pilot operated hek valve, POCV, or pilot ontrol ounter balane valve, CBV) to hold the loaded ylinder when the hydrauli iruit is swithed off (neutral position). The pilot signal of the hek valve is either internally or externally. The internal pilot signal hek valve system may produe some leakage if the pressure from the loaded ylinder overomes the adjustment of the pilot signal pressure. The pilot hek valve with external pilot signal does not ause any leakage but it auses a notied unsteadiness osillation while lowering heavy loaded ylinders only. A pratial solution used for overoming this phenomena is replaing the pilot operated hek valve by a pilot ontrol ounter balane valve with external pilot signal. Although the pilot ontrol ounter balane valve solves this problem it results in leakage from the hydrauli iruit during neutral position. The present study is a ontinuation towards better understanding the previously explained problem. Bendit and Gleed [1] onsidered the pressure losses involved in measuring flow rate. These losses an be large and affet the hoie of pump or flow metering setion to be used. Solutions are developed for prediting these losses for various Copyright 006 by ASME

2 fluid meter arrangements. Several methods are desribed for reduing fluid meter loss, inluding the use of a new step diffuser and onial diffuser. Lequo et al. [] studied the frequeny response analysis of a novel eletro hydrauli servo system. A nonlineardimensional mathematial model has been derived for a onventional and new eletro hydrauli servo onfiguration. In this onfiguration the return oil instead of flowing through the servo valve is disharged through a restritor and the maximum disharge pressure is set by a relief valve. The theoretial and experimental analysis, of the proposed servo system subjeted to step inputs, led to the onlusion that the new onfiguration would offer a higher steady atuator veloity, a lower perent overshoot and a shorter settling time. Kim and Cho [3] studied the sub-optimal ontroller design method for the energy effiieny of a loading-sensing the system. Through a series of simulation studies and experiments, the effetiveness of the design method was illustrated by omparison with non-optimal ases. They found that the sub-optimal ontrol system has muh better ontrol performane than several non-optimal ontrol systems. In addition, the setting pressure is an important parameter whih should be determined at the ontrol performane and the energy effiieny of the system. Nogi et al. [4] investigated the performane of flow rate ontrol valve using piezoeletri element. The valve has a horn and a ball whih are vibrated by the piezoeletri element. The liquid flow is ontrolled by the valve opening time. The element is effetive for dereasing the time required for the valve open in order to supply a voltage when the pulse width inreases. Tamure and Iwamoto [5] examined experimentally the fators whih ause the errors in the flow rate measured using orifie plate meter under pulsating flow onditions. In the experiment a rotary valve of the butterfly valve type is used to generate the pulsating flow in the pipeline where the orifie plate is installed, and the pulsation frequeny is hanged. The flow rate under steady flow onditions is also measured by orifie flow meter in the line onneted to the pulsating flow line via large damping tank. Kassab et al. [6] investigated experimentally a phenomenon alled jerky motion. This intermittent phenomenon is assoiated with the desending of high inertia loads arried by hydrauli equipment. Pilot operated hek valves are used to hold the load position to avoid reep due to leakage in the hydrauli iruit. In pratie, one way to eliminate the ourrene of the jerky motion, is replaing the pilot operated hek valve by a pilot ontrol ounter balane valve. Therefore, they studied the internal and external performane of a hydrauli system using both types of valves one at a time. The obtained results revealed that: for the system ontrolled by pilot operated hek valve, lowering high inertia loads result in intermittent piston motion (jerky motion) assoiated with onsiderable pressure osillations inside the ylinder. Meanwhile, using pilot ontrol ounter balane valve instead of pilot operated hek valve leads to a steady piston motion without pressure osillations even for the ase of lowering high inertia loads. For light loads, using any one of the two valves leads to a stable and steady performane, externally (no jerky motion) and internally (no pressure osillations). Moreover, operation parameters and onstrutional oeffiients, needed for theoretial alulations of the hydrauli system performane were obtained experimentally. On the other hand, as a ontinuation of Kassab et al. [6] work, Swidan et al. [7] studied theoretially the internal and external performane of the hydrauli system before, during and after the ourrene of the jerky motion. Two systems were onsidered, one using pilot operated hek valve and the other using pilot ontrol ounter balane valve. Mathematial models are dedued and omputer simulation programs are developed and used to study the behavior of these systems. For the ase of using pilot operated hek valve, the results show that for the ase of desending heavy loads piston motion is assoiated with pressure osillations inside the ylinder. While for the ase of pilot ontrol ounter balane valve the piston motion is regular and there is no pressure osillation for all load ategories, light or heavy. Comparison between the obtained theoretial results and sets of orresponding experimental results obtained by Kassab et al. [6] showed good agreement. The present study is the third step in a planed investigation dealing with studying the dynami behavior of hydrauli ylinder subjeted to jerky motion during load lowering. The first step was the experimental study [6]. The seond was the theoretial study and validation of the model through omparisons with the experimental results [7]. The third step (the present study) is direted to extend the use of the validated model to investigate theoretially the effet of some other parameters (diffiult to study experimentally) whih are not inluded in the experimental study performed by Kassab et al. [6]. These parameters inlude the effets of varying the pump flow rate, the spring stiffness of the pilot operated hek valve, POCV, and the use of meter-out throttle valve, on the system behavior. In addition, an analysis is performed using the mathematial model to study the osillation phenomena in ylinder piston side, when lowering loads. This inludes studying the behavior of poppet displaement of the POCV, pressure at ylinder piston side and the ylinder piston displaement. The need for this analysis is raised from the feed baks obtained during the disussion of the results of Swidan et al. [7] as well as a reommendation for more deep inside analysis by experts in the related field. Moreover, the analysis may explain the inside piture of the presented results in the present study. MODELING AND SIMULATION The dynami behavior of the studied system during the lowering mode is investigated in the present study. The basi Copyright 006 by ASME

3 onstrution and operational parameters during this mode are shown in Fig. 1. The DCV is represented by the two restritions 3a and 3b. The following are the equations desribing this operating mode. Pump Flow Rate: Q = Q P / R (1) p t ( ) p The theoretial flow rate Q t and resistane to leakage R L were evaluated experimentally by Swidan (003). They were found to be: 4 Q = m 3 1 /s and R = 10 Pa s/m 3. t L Continuity Equation Applied To Pump Delivery Line: The pump delivery line onnets the pump to the diretional ontrol valve, during the normal operating onditions and the relief valve is losed. The ontinuity equation applied to this line is: L ( V / B)( dp dt) Q p Qvi = p p / () Flow Through Diretional Control Valve Restritions: Q vi Q vi = C A ( P P ) / ρ Or = K d1 d1 p p 1 Pp Pp (3) By negleting the down stream pressure the flow through restrition 3b is given by: Q = C A P / ρ Or d d Q = K P (4) Continuity Equation Applied To The Cylinder Piston Chamber: dy dx ( Vo + As x + A y) dp p p Qvi Ap As = (5) dt dt B dt e portion of mixture. Therefore an expression for equivalent bulk modulus of elastiity is needed to onsider the pressure of gases. The following expression for the equivalent bulk modulus of elastiity was dedued [8]. 5 n( Pp + 10 ) B for α > 0 B = 5 e (1 α) n(pp + 10 ) + αb (6) B for α 0 Equation Of Motion Of Piston: d y dy Pp A p Pr A r + F FLm = m p + f p (7) dt dt Continuity Equation Applied To The Cylinder Rod Chamber: dy ( Vor Ar y) dpr Ar Qr = (8) dt B dt Flow Rate Through The Chek Valve: Q r = C A ( P P ) / ρ (9) d r The restrition area of the hek valve (A r ) is the side area of a trunated one, Fig.. The following expressions are dedued for this area and the valve projetion area (A ) subjeted to pressure fore. Details are given in [8]. A r r = π ( R + x R r + x (R)(r) R + x R r + x R) + r ( R r ) A = h = π R + x R r + (10) π (11) x During load lowering the piston is driven by the pressure fores and onstant weight of driven mass, hene the piston speed inreases ontinuously. The pump flow rate beomes insuffiient to fill the piston hamber. The pressure in this hamber drops below the atmospheri pressure. The dissolved air in the oil is released and oil evaporates to fill the exessive hamber volume. The piston hamber is thus filled with mixture of oil and gases. The bulk modulus of mixture should be realulated to onsider the high ompressibility of gaseous Equation Of Motion Of Chek Valve Poppet: P A P A ( P P ) A + F = m p x s + K ( x + x ) + f x o r Continuity Equation Applied To The Chek Valve Inner Chamber: r C m (1) Copyright 006 by ASME

4 Q r dx Vo Ar x dp Q + Ar = (13) dt B dt The hydrauli system with POCV is desribed mathematially by equations (1 to 13). The dedued mathematial model was used to develop a omputer simulation program by using the MATLAB (SIMULINK) V. 6 pakage. The numerial values of onstrutional parameters were found by diret measurements of the real system geometry. The basi operational parameters, suh as the pump resistane to leakage, were predited experimentally [8]. The simulation program enables to alulate the transient performane of the system onsidering the different possible operating onditions, Fig. 3. RESULTS AND DISCUSSIONS Analysis Of Osillation Behavior Of System Controlled By Pilot Operated Chek Valve Figure 4 represents the behavior of valve poppet displaement, ylinder piston pressure response, ylinder piston displaement and ylinder piston veloity. Zooming is taken on two yles of osillating wave. In addition the yle is divided into different four periods to study the osillation behavior and the relation between these four parameters with respet to eah other. Period (t 1 ): At the beginning of this period the pressure reahes its minimum value 9bar, while the valve poppet is losed ompletely. During this period the pressure is inreasing, while the valve poppet is seated along the whole period. The ylinder piston veloity is dereasing at the beginning of the period until it stops ompletely, although the poppet is losed due to load inertia. Meanwhile during the rest of this period the ylinder piston veloity starts to at in the raising diretion (opposite diretion) due to reation fore effet. Period (t ): At the beginning of this period the pressure is inreasing and reahes its maximum value 0 bar at the end of the period, and the poppet displaement inreases too due to pressure inrease. Meanwhile the veloity at the beginning of period ontinues ating in the opposite diretion and at the rest of the period it starts to inrease in the diretion of lowering. Period (t 3 ): At the beginning of this period the pressure reahes its maximum value and starts to derease all over the period, due to the inrease in ylinder piston veloity, while the valve poppet displaement is still inreasing due to valve inertia and the high flow rate through its restrition area resulting from the ylinder piston high veloity. Period (t 4 ): The pressure and the poppet displaement are still dereasing until they reah their minimum value at the end of this period. Meanwhile the ylinder piston veloity inreases until it reahes its maximum value and then starts to derease again due to the derease in poppet displaement. It was notied that the ylinder piston (displaement and veloity) are the main parameters affeting the pressure variation and hene the opening and losing of the POCV during desending stroke. Parametri Study Some parameters are studied theoretially using the mathematial model, whih is easier than studying them experimentally. Pump Flow Rate: Figure 5 represents the pressure performane of system loaded by 680 N, while using different flow rate values. Figure 5-a shows the results for the ase of inreasing pump flow rate from 9.6 lit/min, whih is the used flow rate value in both experimental [6] and theoretial [8], by 5% and 50%, to be 1 lit/min and 14.4 lit/min respetively. It is notied that by inreasing pump flow rate the pressure osillation dereases and the load starts to desend smoothly. These results onfirm the explanation given by Swidan et al. [7] for system osillation while lowering 610 and 680 N loads. As it was stated that the speed of ylinder piston inreases rapidly by inreasing the load and the pump flow rate beomes less than the rate of inrease of piston hamber volume therefore the pressure drops in the pressure line and in pilot line ausing the hek valve to lose and ylinder piston stop. Meanwhile the use of high pump flow rate, ompensate the inrease of piston hamber volume due to rapid speed while using loads 610 and 680 N. Consequently, the osillation effet is disappeared. Figure 5-b shows the results for the ase of dereasing pump flow rate from 9.6 lit/min, whih is the used flow rate, by 5% and 50%, to be 7. lit/min and 4.8 lit/min respetively. This figure shows that by dereasing pump flow rate the pressure osillation is still found, but with lower amplitude. This phenomena may be beause when the pressure reahes the raking pressure value of pilot operated hek valve (just starts to open), there is a tiny time delay until the valve is opened due to valve overlap distane between the valve piston and poppet, whih is equal to 3.5 mm in the present study. At this tiny time delay period the ylinder piston is at rest (onstant ylinder piston hamber volume). Consequently, the main fator affeting the pressure amplitude is the hange of oil volume oupying the ylinder piston hamber. By dereasing the pump flow rate the hange of oil volume oupying the ylinder piston hamber will derease too, leading to the derease of the pressure amplitude. Spring Stiffness: Figure 6 represents the pressure performane of system loaded by 680 N, while using different spring stiffness. By hanging the spring stiffness, 110 kn, whih is the value of Copyright 006 by ASME

5 spring stiffness used in the mathematial model, one inreasing it by 100% to be 0 kn and the other by dereasing it by 50% to be 55 kn. It was notied that by inreasing the spring stiffness the osillation amplitude inreases due to the inrease of fore needed to open the valve. Meanwhile by dereasing the spring stiffness the load desends smoothly with small transient period. On the other hand, dereasing the spring stiffness results in a derease in the operating pressure amplitude. This derease leads to failitate the probability of leakage from the valve restrition area. This leakage may results in desending the load while the system is swithed off. Using Meter-Out Throttle Orifie: Figure 7 represents the pressure performane at 680 N load while using the same system with POCV, but after adding meter-out orifie of diameter, d =.5 mm. It was notied that by using the orifie no pressure osillation is notied in the system, but the operating pressure inreases. The obtained results an be explained, as follows: By using the meter-out orifie it auses a deeleration to the desending load so the pump flow rate an overome the inrease in ylinder piston hamber due to the piston displaement. One the other hand, the obtained results due to the presene of meter-out orifie, an help in understanding and explain the reason for the differene in response for system using POCV and system using CBV. It was notied from the measured values of poppet onstrution [8], that the magnitude of the variation in restrition area due to poppet displaement is greater in ase of POCV than that of CBV, Fig. 8. Meanwhile it an be noted that this throttling effet in ase of CBV leads to stability of operating pressure due to the slow inrease of the piston hamber volume. This effet is orresponding to the effet of using meter-out throttle orifie as shown in Fig. 7. CONCLUSION In the present study, a parametri study is performed for the hydrauli system ontrolled by pilot operated hek valve, POCV, using a mathematial model. From the parametri study it was dedued that: - By inreasing pump flow rate the system pressure osillation dereases. - By dereasing the magnitude of the spring stiffness, the pressure amplitude dereases, but may lead to failitate the probability of leakage from the valve restrition area. - By inreasing the spring stiffness the pressure osillation and amplitude inreases. - By using meter-out orifie with the POCV a deeleration is happened to the desending load whih overomes system pressure osillation, but the operating pressure inreases. Engineering Transations of the ASME, De. 1976, pp [] Lequo, S., Cheng, R.M.H. and Leung, K Frequeny Response Analysis of a Novel Eletro hydrauli servo system, ASME paper 88-WA/DSC-5, Nov [3] Kim, S. and Cho, C.1991 A Sub optimal ontroller Design Method for the Energy effiieny of a Load sensing Hydrauli servo system Journal of dynami systems Measurement and ontrol, Vol.113, pp [4] Nogi, T., Yamauhi, T. and Ohyama, Y. 199 A flow rate ontrol valve using a piezoeletri element, JSME International journal, Vol.35, No. 3, pp [5] Tamura, E. and Iwamoto, J Errors in the measurement of flow rate with orifie flow meter in pulsating flow, ASME Fluids Engineering division summer meeting, pp.1-6. [6] Kassab, S.Z., Swidan, M.A., Adam, I.G., and Rabie, M.G. 004, Dynami Behavior of Hydrauli Cylinder Subjeted to Jerky Motion During Load Lowering Part 1: Experimental Work, 11 th International Conferene on Applied Mehanis and Mehanial Engineering, Military Tehnial College, Cairo, Egypt, 3-5 Nov. 004, Paper DV01, pp [7] Swidan, M.A., Adam, I.G., Rabie, M.G., and Kassab, S.Z. 004, Dynami Behavior of Hydrauli Cylinder Subjeted to Jerky Motion During Load Lowering Part : Modeling and Simulation, 11 th International Conferene on Applied Mehanis and Mehanial Mehanial Engineering, Military Tehnial College, Cairo, Egypt, 3-5 Nov. 004, Paper DV0, pp [8] Swidan, M.A Response of hydrauli system ontrolled by Pilot-operated hek valve and ounterbalane valve. M.S. Thesis, Alexandria University, Egypt.. REFERENCES [1] Bendit, R. and Gleed, A Methods of reduing losses aross fluid metering nozzles Journal of Fluid Copyright 006 by ASME

6 1. Gear pump. Eletri motor 3. 4/3 DCV 4. Single ating ylinder 5. Load, 6. Relief valve 7. Pressure gauge 8. Tank 9. POCV 10. Pressure transduer Fig. Sheme of the hek valve (a 1 = A, a = A r ) Fig. 1. Funtional sheme of the system during lowering mode Fig. 3 First page of the SIMULINK program developed for the system with POCV. Copyright 006 by ASME

7 Fig.4 The relation ship between poppet displaement, ylinder piston pressure response, ylinder piston displaement and ylinder piston veloity during lowering with a load of 680 N. Copyright 006 by ASME

8 Fig. 6. Pressure response aording to spring stiffness Fig. 5. Pressure transient response with respet to pump flow rate Fig. 7. Pressure response using meter out throttle orifie 80 restrition area mm^ POCV CBV poppet displaement mm Fig, 8. Response of restrition areas of POCV & CBV aording to the poppet displaement Copyright 006 by ASME