MULTI-POLE MODELING AND INTELLIGENT SIMULATION OF CONTROL VALVES OF FLUID POWER SYSTEMS (PART 2)

Transcription

1 9th International DAAAM Baltic Conference "INDUSTRIAL ENGINEERING" April 2014, Tallinn, Estonia MULTI-POLE MODELING AND INTELLIGENT SIMULATION OF CONTROL VALVES OF FLUID POWER SYSTEMS (PART 2) Harf, M. & Grossschmidt, G. Abstract: The paper is a continuation of the Part 1. All the general aspects and a simulation tool used were considered in the Part 1. Here multi-pole mathematical models for flow regulating valves of three types are described. Mathematical models of a twodirectional flow regulating valve are presented. Examples of simulations of flow regulating valves are presented and discussed. Key words: multi-pole model, flow regulating valve, simulation. 1. INTRODUCTION In the paper, modeling and simulation of flow regulating valves used in fluid power systems are considered. Methodology, multi-pole mathematical models and simulation environment have been discussed in the Part 1 of the paper. located after pressure compensator. 2. Two-directional valve throttle is located before pressure compensator. 3. Three-directional valve throttle and pressure compensator are connected in parallel way. Functional schemes of the flow regulating valves of three types are shown in Fig.1. Fig. 1. Functional schemes of flow regulating valves 2.1 Two-directional Flow Regulating Valve (type 1) Two-directional flow regulating valve (type 1) is shown in Fig FLOW REGULATING VALVES In flow regulating valves [ 1 7 ] the flow is not related to the pressure drop between the valve input and output. This means that the fluid flow set remains constant, even with pressure deviations. Flow regulating valves are used when the working speed should remain fixed in spite of different loads at the user. Flow regulating valve contains adjustable throttle and pressure compensator ensuring constant pressure drop in the throttle. Flow regulating valves of three main types exist: 1. Two-directional valve throttle is Fig. 2. Two-directional flow regulating valve (type 1) (Mannesmann Rexroth) The valve consists of throttle pin 1 with orifice 2, normally open control spool 3 with two springs 4, bores 5, 6 to the spool surfaces and stroke limiter 7. Simulation task for dynamics on a twodirectional flow regulating valve model (type 1) is shown in Fig.2. 23

2 Fig.3. Simulation task of a two-directional flow regulating valve dynamics (type 1) Multi-pole models: RQGSR pressure compensator slots, ResYOrA regulating spool slot, VQAS21 pressure compensator spool, ResGCh, ResHCh cushioning resistors, IEH , IEH interface elements. Inputs: pressure p1, regulating slot area A, outlet pressure p3. Outputs: volumetric flows Q1 and Q3. Simulation manager: dynamic Process 3D Mathematical Models Pressure compensator slots RQGSR Inputs: pressure p1, volumetric flow Q2, displacement of the pressure compensator spool y. Outputs: pressure p2e, volumetric flow Q1, pressure drop dpe. Spool conical part length: a = (d1-d2)/2/tan(β * π /180), d1 diameter of spool sleeve, d2 diameter of the end of the cone, β half angle of the cone. Displacement of the spool corresponding to switching point from one model to another: h = a/( cos 2 (β * π /180)). If y >= h: width of the spool slot x = ((y-a) 2 +(d1-d2) 2 /4) 1/2, median diameter of the spool slot dx = (d1 + d2)/2. If y < h: x = y*sin(β * π /180), d1x = (d1-2*x*cos(β * π /180)), dx = (d1 + d1x)/2. Pressure compensator slot area: A = μ * π *dx*x, μ discharge coefficient. Output pressure: p2e = p1 - Q2 2 /A 2 *ρ /2, ρ fluid density. Output volumetric flow: Q1 = Q2. Output pressure drop: dpe = p1 - p2. Pressure compensator spool VQAS21 Inputs: pressures p1, p2, p3, pressure drop dp in poppet valve flow-through slot. Outputs: volumetric flows Q1, Q2, Q3, displacement of poppet valve y. Pressure compensator spool areas: A1 = π * d1 2 / 4, A2 = π * (d2 2 - d1 2 ) / 4, A3 = π * d2 2 / 4, d1 diameter of the spool sleeve, d2 diameter of the spool sleeve head. Force to pressure compensator spool: F = A1*p1+A2*p2-A3*p3. Coefficient of fluid jet force: B = μ*π*d1*2*dp*(cos(β *π/180))* sin(β*π/180)/c. Stiffness of springs: c1 = G * ds1 4 / (Ds1 3 * n1 * 8), c2 = G * ds2 4 / (Ds2 3 * n2 * 8), G shear modulus, ds1, ds2 diameters of spring wires, Ds1, Ds2 diameters of springs, n1, n2 numbers of turns of springs. Sum of spring stiffnesses: c = c1 + c2. Displacement of the pressure compensator spool: y1 = 1/(1-B)*(F/c-fV0), fv0 spring preliminary compressibility. Pressure compensator spool slot width: y = y0 - y1, y0 initial spool slot width. 24

3 Differences of spool velocity and spool displacement used for dynamics are calculated using the similar procedure as for difference of valve velocity and spool displacement in the direct operated pressure control valve in Part 1 of the paper. Here difference dv is calculated by formula: dv=(δt /m)*(f-(y1*(1-b)+fv0)*c- (Ff0+kfr*(p1+p2)/2)*sign(v,0.001)-hv*v). Volumetric flows: Q1 = A1*v, Q2 = A2*v, Q3 = A3*v. Regulating throttle orifice ResYOrA Inputs: pressures p1, p2, area of the regulating throttle orifice A. Outputs: volumetric flows Q1, Q2. Volumetric flows: Q1 = μ*a*(2*(p1-p2)/ ρ) 1/2, Q2=Q Simulations The following parameter values are used in the simulations. The fluid HLP46 is used. Basic parameters of the fluid have been described in the Part 1 of the paper. For RQGSR: d1=0.012 m, d2=0.01 m, μ =0.8, β=30 deg. For VQAS21: d1=0.01 m, d2=0.03 m, y0= m, μ=0.8, β=30 deg, ds1= m, Ds1=0.022 m, n1=5, ds2= m, Ds2=0.014 m, n2=4, G= 8e11 N/m, m=0.04 kg, kfr=2e-9 N/Pa, Ff0=0.3 N, hv=0 Ns/m. For ResYOrA: μ =0.8, A=1.7e-5 m 2. For ResGCh: diameters d= m, lengths l=0.02 m and 0.01 m. For ResHCh: d= m, l= 0.01 m. valve (type 1) statics simulation are shown in Fig.4. Graphs of volumetric flow (graph 1), regulated pressure (2) and displacement of the valve (3) depending on the input pressure for two different values of the area of regulating throttle orifice A = 1.7e-5 m 2 and 3e-5 m 2 are presented. As it can be seen, the valve operates normally at input pressures higher than 2e6 Pa. Output volumetric flow (1) slightly drops if input pressure increases. Fig.4. Two-directional flow regulating valve statics (type 1) valve (type 1) dynamics simulation are shown in Fig.5. Fig.5. Two-directional flow regulating valve (type 1) dynamics A step disturbance 1e6 Pa of pressure p1 during s at the left port is applied as input (4). Step change of the input pressure causes regulated pressure (2) change. Regulated pressure causes valve shift (3). Valve shift together with regulated pressure cause output volumetric flow (1) to achieve a new level. 2.2 Two-directional Flow Regulating Valve (type 2) Two-directional flow regulating valve (type 2) is shown in Fig.6. Fig. 6. Two-directional flow regulating valve (type 2) (Mannesmann Rexroth) 25

4 The flow regulating valve consists of adjustment device 1, triangle shape regulating slots 2, pressure compensator spool 3, pressure compensator round slots 4 and spring 5. Simulation task for dynamics on a two-directional flow regulating valve model (type 2) is shown in Fig.7. Fig.7. Simulation task of a two-directional flow regulating valve dynamics (type 2) Multi-pole models: ResYOrx triangle shape regulating slots, RQHSR pressure compensator round slots, VQBSx pressure compensator spool, ResGCh cushioning resistor, IEH7-1-2, IEH interface elements. Inputs: pressure p1, triangle shape regulating slot displacement x, outlet pressure p2. Outputs: volumetric flows Q1 and Q2. Simulation manager: dynamic Process 3D. The following parameter values are used in the simulations. For ResYOrx: μ=0.8, x=1.75e-6 m. For RQHSR: d=0.012 m, μ=0.8, y0= m, pressure compensator slot radius r=0.002m. For VQBSx: d=0.012m, y0=0.0022m, ds= m, Ds=0.008 m, n=6, G= 8e11 N/m, fv0= m, Ff0=0.05 N, kfr=2e-9 N/Pa, m=0.03 kg, hv=20 Ns/m. For ResGCh: diameter d= m, length l=0.003 m. valve (type 2) statics simulation are shown in Fig.8. Fig.8. Two-directional flow regulating valve (type 2) statics Graphs of volumetric flow (graphs 1), regulated pressure (2) and displacement of the valve (3) depending on the input pressure for two different values of the triangle shape regulating slot displacement x = 5e-7 m and 3e-6 m are presented. As it can be seen, the valve operates better at smaller displacements of triangle shape regulating slot. valve (type 2) dynamics simulation are shown in Fig.9. Fig.9. Two-directional flow regulating valve (type 2) dynamics A step disturbance 1e6 Pa of pressure p1 during s at the left port is applied as input (3).Step change of the input pressure causes valve shift (2). Valve shift causes regulated pressure (4) change. Regulated pressure together with input pressure cause output volumetric flow (1) to take a new level through damped oscillations. 2.3 Three-directional Flow Regulating Valve Three-directional flow regulating valve is shown in Fig

5 Fig. 10. Three-directional flow regulating valve (Mannesmann Rexroth) The valve consists of the throttle pin 1 with orifice 2, normally closed control spool 3 with two springs 4, bores 5 and 6 to the spool surfaces. Simulation task for dynamics on a threedirectional flow regulating valve model is shown in Fig.11. Fig.11. Simulation task of a threedirectional flow regulating valve dynamics Multi-pole models: ResHOrA regulating orifice, VQAS22 pressure compensator spool, RQYSR pressure compensator slots, ResGCh, ResHCh cushioning resistors, IEH , IEH interface elements. Inputs: outlet pressure p3, volumetric flow Q1, regulating orifice area A, outlet pressure p2. Outputs: inlet pressure p1, volumetric flows Q2 and Q3. Simulation manager: dynamic Process 3D. The following parameter values are used in the simulations. For ResHOrA: μ=0.8, A=2e-6 m 2. For VQAS22: d1=0.008 m, d2=0.02 m, μ=0.8, β=30 deg, ds1= m, Ds1=0.014 m, n1=5, ds2= m, Ds2=0.01 m, n2=4, G=8e11 N/m, m=0.04 kg, kfr=2e-9 N/Pa, Ff0=0.3 N, hv=5 Ns/m. For RQYSR: d1=0.008 m, d2=0.006 m, μ=0.8, β=30 deg. For ResGCh: d= m, l=0.02 m. For ResHCh: d=0.001 m, l= 0.02 m. Results of three-directional flow regulating valve statics simulation are shown in Fig.12. Fig.12. Three-directional flow regulating valve statics Graphs of output pressure of the right port (graphs 1), regulating orifice volumetric flow (2) and valve volumetric flow (3) depending on the input pressure for two different values of the area of regulating orifice A = 1e-6 m 2 and 2e-6 m 2 are presented. Output pressure linearly depends on input pressure. Sum of valve volumetric flow and regulating orifice volumetric flow equals to input volumetric flow Q1 = 1e-4 m 3 /s. If A=1e-6 m 2 the output pressure is constantly 4e6 Pa higher of the input pressure. If A=2e-6 m 2 the output pressure is constantly 2e6 Pa higher of the input pressure. Results of three-directional flow regulating valve dynamics simulation are shown in Fig.13. Fig.13. Three-directional flow regulating valve dynamics 27

6 A step disturbance of pressure p3 1e6 Pa at the right port during s is applied as input (graph 1). Step change of the input pressure causes valve shift. Valve shift causes valve volumetric flow (4) change. Difference of input volumetric flow Q1 and valve volumetric flow equals to regulating orifice volumetric flow (3). Output pressure (2) is defined by input pressure, area of regulating orifice and orifice volumetric flow. Transient responses take s. 3. CONCLUSION In the paper modeling and simulation of hydraulic flow regulating valves of fluid power systems was considered. The results of static simulations of both hydraulic pressure and flow regulating valves considered in Part 1 and Part 2 are in accordance with Mannesmann Rexroth and Eaton-Vickers catalogue performance characteristics. Dynamic simulations for valves of both types are performed and results are shown. Models and results of dynamics simulation could be useful for describing dynamic behaviour of control valves and representing their dynamic performance characteristics in catalogues. Proposed pressure and flow regulating valve models can be used as subsystems when simulating complex fluid power systems. 4. ACKNOWLEDGEMENTS This research has been partially supported by The European Regional Development Fund (ERDF) through: Estonian Centre of Excellence in Computer Science (EXCS). The project no Model-based Java software development technology. The project no Smart composites - design and manufacturing. 5. REFERENCES 1. Industrieventile und Zubehör, Mannesmann Rexroth, RD , Rexroth GmbH, Lohr am Main. 2. Eaton-Vickers. Industrial Hydraulics Manual. 5th Ed., 2nd Printing, Eaton Hydraulics Training, Murrenhoff, H. Grundlagen der Fluidtechnik, Teil 1: Hydraulik, 4. neu überarbeitete Auflage. Institut für fluidtechnische Antriebe und Steuerungen, Aachen, Schmitt, A. The Hydraulic Trainer, Vol. 1, Instruction and Information on Oil Hydraulics, RE , Rexroth GmbH, Lohr am Main. 5. Parr, A. Hydraulics and Pneumatics. A technicians and Engineer s Guide, Third Edition, Elsevier Ltd, Watton, J. Fundamentals of Fluid Power Control. Cambridge University Press, New York, Gebhardt, N., Will, D. and Nollau, R. Hydraulik: Grundlagen, Komponenten, Schaltungen, 5. Neubearb. Auflage, Springer Verlag Berlin Heidelberg,