AEIJST June Vol 2 Issue 6 ISSN

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1 Theoretical Invetigation Performance of Proportional Directional Control Value Uing Matlab /Simulink *Sudhindra R. Kulkarni **S.H.Kulkarni ***Sudhindra R. Kulkarni *Department of Mechanical Engineering, Gogte Intitute of Technology, Belgaum, India **At.Prof. Gogate Intitute of Technology, Belgaum, India Department of Mechanical Engineering ***Gogte Intitute of Technology, Belgaum Abtract: - Thi paper propoe the performance of proportional directional control valve. A mathematical model i derived that decribe the dynamic of a valve embedded within a imple hydraulic circuit. The aim i to capture the mechanim of intability of uch valve, taking into account of bulk modulu of oil. The model i imulated uing MATLAB / SIMULINK model (R2007). Thi report contain the aumption, variable, mathematical modeling and analyi involved in modeling and imulating proportional directional control valve. Key word: - hydraulic ytem, proportional directional control valve, bulk modulu, MATLAB / SIMULINK etc.. Introduction Hydraulic ytem are widely employed in many application due to their ability to convert mechanical energy into hydraulic energy. It can be regulated and controlled to provide flow rate, force, peed and direction with the help of direction control valve. In the context of the hydraulic ervo ytem, flow control valve are broadly claified in to two type like proportional and ervo valve. Proportional valve ue direct actuation of the pool from an electrical olenoid or torque motor. Wherea ervo valve ue at leat one intermediate hydraulic amplifier tage between the electrical torque motor and the pool. When modeling complex ervo valve, it i ometime poible to ignore any inherent nonlinearitie and derive a linear modeled which approximate the phyical ytem. Such model are often baed on claical firt or econd order differential equation, it i neceary to model the ervo valve dynamic a a nonlinear model. Thi paper dicue the dynamic behavior of hydraulic ytem. It alo dicue the approach of uing a Matlab/SIMULINK to model a nonlinear proportional directional control valve. Thi nonlinear model can be ued a a valuable tool in the analyi and control of hydraulic actuation ytem. Matlab /SIMULINK package will be ued to imulate the hydraulic control ytem. 2. Mathematical Model The ytem decribe detailed mathematical modeling of HSS for hydraulic mini pre machine. The ytem conit of high-peed, electronic drive, hydraulic actuator, and poition tranducer. The mathematical model behavior of ervo valve can be developed from the relationhip between the diplacement ( ) and input voltage ( ) for

2 the proportional valve. A third order model i ufficient for HSS, which i decribed by the equation given in following ection []. Fig.. A hydraulic actuator with four-way valve configuration. In preing machine, the hydraulic actuator i typically a double-acting hydraulic cylinder. The cylinder port are connected to a proportional valve, and piton motion i obtained by modulating the oil flow into and out of the cylinder chamber. A ervo valve provide thi modulation a hown in Fig. The actuator can be preciely controlled by regulating the flow rate and. However, the relationhip between the piton poition and the flow rate depend on the dynamic propertie of the load acting on the piton []. The mathematical model ued in imulation i repreented by the following ytem of equation: Where () 2

3 Fp i the net force acting on the piton which can be computed by multiplying the area of the piton annulu Ap by the differential preure between two chamber and 2. (2) The hydraulic power upply All hydraulic ytem require a upply of preurized fluid, uually a form of mineral oil. The behavior of the hydraulic power upply may be modeled by applying the flow continuity equation to the volume of trapped oil between the pump and control valve. In thi cae, the input flow i held contant by the teady peed of the pump motor, and the volume doe not change. The equation of the model i (3) Thi equation take into account the load flow QL drawn from the upply by the control valve, and accurately model the cae of a high actuator lew rate reulting in a load flow which exceed the flow capacity of pump. The action of the preure relief valve may be modeled uing a limited integrator to clamp the ytem preure to the nominal value. Cylinder Chamber Preure The relationhip between the valve control floe and actuator chamber i important becaue the compreibility of oil create a pring effect in the cylinder chamber which interact with the piton ma to give a low frequency reonance. The effect can be modeled uing the net flow into a container to the internal fluid volume and preure The ame equation can alo be repreenting chamber 2. (4) Flow rate; The main function of directional control valve i to direct and ditribute flow between onumer ie between cylinder and pump and tank from the other ide. The way of valve i modeled by well known relationhip flow-preure for turbulent flow. (6) (5) 3

4 3. Simulink Model The equation () to (7)) are repreented in SIMULINK MODEL to analyze the diplacement of the poppet, Outlet flow rate and preure rate with conidering the effect of bulk modulu with the time rate. The MATLAB SIMULINK model i given below (7).8*0 ^9 Divide Contant [QA ] Product 4 From *0^-5 3 *0 ^-4 Contant Contant 2 [dxbydt ] Product 3 Subtract 2 From [PB] From 6 [PA] Product 5 From 7 Subtract *0 ^-4 Contant 4 [dxbydt ] From 8 50 Product 6 Contant Contant 6 Product 7 [X] From 9 Integrator *0 ^-6 Contant 5 [dxbydt ] From 3 Subtract Scope 5.8*0 ^8 Contant 3 Product [QB] From 2 Subtract *0 ^-6 Contant 4 /M [PA] Goto Gain Product 2 Divide Scope 4 [PB] Goto Integrator 3 Integrator PB To Workpace 0.6 [PA] [dxbydt ] Goto 5 [P] From 4 Contant 7 From 3 *0 ^-4 Contant 8 Integrator Scope Subtract Product 8 u Ab Contant 9 [X] Goto 4 Scope Divide 2 qrt Math Function Product 9 [P] From 5 Scope 3 [PB] Ab From 2 Subtract [QA] Goto 2.8*0 ^9 Contant *0 ^-.7 Contant 9 Contant Product *0 ^-4 0 Contant *0 ^-3 Contant Contant 2 B Vt QL u Contant 3 fcn P Qpump Embedded MATLAB Function 7 Divide 3 qrt Math Function Integrator 4 Product Scope 6 Scope 2 [P] Goto 6 P [QB] Goto 3 To Workpace Figure.2. SIMULINK model 4. Reult The valve model wa ready for analyi and imulation. Certain parameter like tiffne of pring, volume, inlet flow rate, bulk modulu and area were kept contant. The analyi wa conidered with time a given in Figure. 4

5 Figure 3 Spool diplacement Figure 4 Spool diplacement 5

6 Figure 5. Spool diplacement Figure 6.Flow rate in port A 6

7 Figure 7. Flow rate in port B 4. Concluion The preent work ha derived a mathematical model for a proportional directional control valve. The developed mathematical model i repreented in MATLAB SIMULINK which predict the pool diplacement, flow rate through the port by changing the parameter a hown in figure above. Reference []. W. Bolton. Pneumatic and hydraulic ytem.butterworth-heinemann, 997. [2] B. Brogliato. Impact in Mechanical Sytem Analyi and Modelling. Springer Verlag, New York, Lecture Note in Phyic, Volume 55. [3] M. di Bernardo, C. J. Budd, A. R. Champney, and P. Kowalczyk. Piecewie-mooth dynamical ytem.springer, [4] E. J. Doedel. AUTO-07P: Continuation and Bifurcation Software for Ordinary Differential Equation. Technical manual. [5] R. D. Eyre, A. R. Champney, and N. A. J. Lieven.Modelling and dynamic repone of a damper with relief valve. Nonlinear Dynamic, (40):9 47, [6] R. D. Eyre, P. T. Piiroinen, A. R. Champney, and N. A. J. Lieven. Grazing bifurcation and chao in the dynamic of a hydraulic damper with relief valve. SIAM Journal on Applied Dynamical Sytem, 4(4):076 06, [7] J. Guckenheimer and P. Holme. Nonlinear ocillation, dynamical ytem, and bifurcation of vector field. Springer, 983. [8] S. Hayahi. Intability of poppet valve circuit. JSME International Journal,38(3), 995. [9] S. Hayahi, T. Hayae, and T. Kurahahi. Chaoe in a hydraulic control valve. Journal of fluid and tructure, ():693 76, 997. [0] K. Kaai. On the tability of a poppet valve with an elatic upport. Bulletin of 7

8 JSME, (48), 968. [] F. X. Kay. Pneumatic for indutry. The Machinery Publihing Co. Ltd., 959. [2] Yuri A. Kuznetov. Element of applied bifurcation theory. Springer, 997. [3] Gábor Lickó. Nonlinear analyi of a hidraulic preure relief valve. Mater thei, Budapet Univerity of Technology and Economic, [4] H. L. Stewart. Hydraulic and pneumatic power for production. The Indutrial Pre, 963. [5] H. Thomann. Ocillation of a imple valve connected to a pipe. Journal of Applied Mathematic and Phyic, 976. [6] M. Wiercigroch and B. de Kraker. Applied Nonlinear Dynamic and Chao of Mechanical Sytem with Dicontinuitie. World Scientific Publihing,