MODELLING AND SIMULATION OF A PNEUMATIC PROPORTIONAL CONTROL VALVE

Transcription

1 MODELLING AND SIMULAION OF A NEUMAIC ROORIONAL CONROL VALVE Mihai Avram, Despina Duminică, udor Cătălin Apostolescu Department of Mechatronics and recision Mechanics, OLIEHNICA University of Bucharest 33, Splaiul Independenței, Bucharest, Romania mavram@yahoocom ; despina_duminica@yahoocom Faculty of Informatics, itu Maiorescu University 87, Calea Văcăreşti, Bucharest, Romania apostolescucatalin@yahoocom Abstract he authors present a simplified mathematical model that describes the functioning of a pneumatic proportional control valve, together with the simulation diagrams obtained after its implementation using MALAB-SIMULINK Simulation diagrams matched the available eperimental characteristics, recommending the elaborated model for the theoretical study of such equipments Keywords: neumatic proportional control valve, mathematical model, simulation Introduction Control of speed and braking in mobile machines, sandblasting and cutting operations, feed control at welding devices, adjustment of voltage in wires, at presses, in grinding, adaptive suspension control can be listed among the main applications of pneumatic proportional equipment [], the most important appliances being directional control valves and pressure regulators Accordingly, significant efforts were performed in order to master this kind of devices by theoretical modelling and simulation, as well as by eperimental research [-9] he functioning of a pneumatic proportional control valve is presented in Figures and When the system does not operate the spool pushes the magnet armature to the left hand side due to the spring If a reference voltage is generated, a corresponding current i will pass through the magnet winding; the resulting electromagnetic force pushes the spool to the right hand side, connecting the pressure nozzle to the output by a section proportional to the reference signal Simplified mathematical model of the pneumatic proportional control valve he mathematical model that describes the functioning of a proportional pneumatic control valve is a very comple one, due mainly to the equations governing the behaviour of the proportional magnet he paper presents a simplified mathematical model he model was established correlated to the principle scheme of Figure he following notations were used: i - current through the winding of the proportional magnet; - electrical time constant; R - magnet winding resistance; FEM - force developed by the proportional magnet; kem - proportional magnet constant; - spool position; ms - spool mass; Farc - force developed by the spring; Ff - friction force; Fc - aerodynamic flow force; karc - spring constant; f - compression of the string due to the tensioning; Ds spool diameter; Dn diameter of the pipe; absolute pressure; atm - atmospheric pressure; a - air temperature; - adiabatic factor; R - air constant c a b () BD A E-M A E-M BD Figure : neumatic proportional control valve a) View of the device: AE-M electro-mechanical amplifier; BD distribution unit b) Symbol c) rinciple scheme: supply; A consumer; spool; bushing; 3 helical spring A () I (3) 3 6 he Romanian Review recision Mechanics, Optics & Mechatronics, 5, Issue 48

2 (I) () () (3) l a () () (3) Due to the construction of the proportional magnet, the magnetic force is practically independent of the armature position in the usable operation range his force leads the spool to displace in a new equilibrium position, as presented in Figure he equation of movement of the spool is: m d F dt F F F Where F k f s EM arc f c arc arc (3) (4) In a first approimation, friction forces and the flow force can be neglected in (3) he theoretical relation between the flow section and the mobile unit position looks like in Figure 4 () () () (3) S -A Figure : Operation of the device S n he proposed methodology was applied to the 3/ proportional pneumatic control valve VEF 3 (SMC) he characteristic diagrams made available by the producer are presented in Figure 3 l a n n S S n S A-Atm Figure 4: heoretical relation between the flow section and the mobile unit position he following equations can be written based on this variation: Figure 3: Characteristic diagrams for the model VEF3 (SMC) According to [], the electronic system and the electromechanical signal converter can be described as a first order delay system: dit it ut dt R () In most practical cases, this linear equation is a good approimation of the nonlinear equations specific to the proportional magnet he output signal of the electric subsystem is represented by the magnetic force F his is considered approimately equal to the intensity of the current i, according to (): EM EM F t k i t () where: Sn if S D if if AAtm s n n n (5) if n S D if A s n n n S n if n (6) D (7) n n 4 Ds Remark: he overlap la was considered equal to in (5) and (6) he flow rates transported through the two flow sections can be established using the notations presented in Figure 5: he Romanian Review recision Mechanics, Optics & Mechatronics, 5, Issue 48 7

3 In (8) and (9) it is assumed that a 3 Computer simulation of the model and Figure 5: he flow rates transported through the two flow sections K S A a m sign ( a ) ma a, } N min, a a (8) K S AAtm m sign ( ) ma, } N min, (9) where s K K 44 R ; m 4 [-]; R 8737 m sk ; a 38 [-] ; if 58 N a if 58 () Simulation of the pneumatic proportional control valve functioning was developed in order to validate the established mathematical model As shown in figure 6, the unit that models the functioning of the control valve has the pressures and and the control voltage u as inputs and the position of the mobile unit and the two flow rates and as outputs he schematic representation of the model is presented in figure 7 he functioning of the proportional pneumatic control valve was simulated using the software MALAB-SIMULINK he simulation diagram is presented in Figures 8 and 9 he variations of the output parameters, d/dt and, are presented in Figures and Figure illustrates the dependency between the flow section S A and the current i he obtained diagrams matched the available eperimental results Figure 6: Model equations Figure 7: Schematic representation of the model 8 he Romanian Review recision Mechanics, Optics & Mechatronics, 5, Issue 48

4 Figure 8: Simulation diagram of the whole pneumatic system, including the proportional control valve Figure 9: Simulation diagram of the block neumatic proportional control valve Figure : Variation of the parameters - spool position, d/dt spool speed he Romanian Review recision Mechanics, Optics & Mechatronics, 5, Issue 48 9

5 Figure : Variation of the pressures and Figure : Resulted characteristic diagram S A = f(i) 4 Conclusions he developed model closely reproduces the phenomena that appear during the functioning of the proportional control valve, notwithstanding its simplification It can be thus used for the theoretical study of such type of equipment 5 References [] S Anghel, G Matache, AM opescu, IC Gîrleanu, Applications of proportional equipment in industry, Hidraulica /3, ISSN , pp 9-95 [] M Avram, Hydraulic and neumatic Actuation Classical and Mechatronic Equipment and Systems (in Romanian), Editura Universitară, Bucharest, Romania, 5 [3] Dj Dihovicni, M Medenica, Mathematical Modelling and Simulation of neumatic Systems, Advances in Computer Science and Engineering, Dr Matthias Schmidt (Ed), ISBN: , Inech, available from: mathematicalmodelling-and-simulation-of-pneumatic-systems [4] G Figliolini, A Almondo, M Sorli, Modeling and eperimental validation of a pneumatic servosolenoid valve in: ower ransmission and Motion Control (MC 4), authors: C R Burrows, K A Edge, D N Johnson, John Wiley and Sons, 4 [5] M Sorli, G Figliolini, S astorelli, Dynamic model of a pneumatic proportional pressure valve, roceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Como, Italy,, pp [6] A Fernandez-Jimenez, J erez Garcia, Compressible bench flow adaptations to the eperimental characterization of pneumatic components Application to the determination of flowrate characteristics of a MYE- 5-3/8--B proportional valve, roceedings of the 3rd FNI - hd Symposium on Fluid ower, errassa, Spain, June 3 - July, 4, pp [7] A C Valdiero, CS Ritter, CF Rios, M Rafikov, Nonlinear Mathematical Modeling in neumatic Servo osition Applications, roceedings of the 9th Brazilian Conference on Dynamics Control and their Applications Serra Negra, Brasil, June 7-, pp 98-6 [8] Z Varga, Keski-Honkola, Determination of flow rate characteristics for pneumatic valves, EJ Web of Conferences, Volume 5 (), EFM Eperimental Fluid Mechanics, 96, available at: [9] R Rădoi, I Duţu, G Matache, Considerations on the dynamic testing of proportional equipment, Hidraulica 3/3, ISSN , pp 97- [] V Muraru, Research regarding the parametric synthesis of hydraulic driving systems (in Romanian), hd hesis, OLIEHNICA University of Bucharest, 3 he Romanian Review recision Mechanics, Optics & Mechatronics, 5, Issue 48