Dr. Monika IvantysynovaMAHA Professor Fluid Power SystemsDesign and Modeling of Fluid Power SystemsME 597/ABE 591 Lecture 4MAHA Fluid Power Research CenterPurdue UniversitySICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5912Displacement machines – design principles & scaling lawsPower density comparison between hydrostatic and electric machinesVolumetric losses, effective flow, flow ripple, flow pulsationSteady state characteristics of an ideal and real displacement machineTorque losses, torque efficiencyContent2SICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5913Historical BackgroundWilliams und JanneyHydrostatic transmissiom15Gear pumpAxial Piston Pump2301795190501700190020001651160018001500 Archimedes Pascal Bramah Ramelli KeplerVane pumpSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5914Displacement machine2BVPumpingSuctionVmin=VTwith VT .. dead volumeAdiabatic compressionAdiabatic expansiondue to compressibility of a real fluid KA.. adiabatic bulk modulusTe , np1p2, QeSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5915Displacement machinedue to viscosity & compressibility of a real fluid 3PumpMotorPort pressurePort pressurePressure in displacementchamberPressure in displacementchamberPressure drop between displacement chamber and portSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5916sinLBIFehLpFhFbFeBhPower DensityElectric MotorHydraulic Motorwith I current [A]B … magnetic flux density [ T ] or [Vs/m2]33Torque:hbJIJ… current density [A/m2]rLBIT sinrhLpTrrbSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5917Example Power:nTTP 2For electric motor follows:assuming α=90For hydraulic motor follows:Force density:Electric MotorHydraulic MotorBbJhLLBhbJhLFewith a cross section area of conductor: 26m109Pa105 toup734phLFhnrLBIP 2nrhLpP 2Pa101.4m103mVs8.1mA106.743-2-26SICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5918Mass / Power RatioElectric MachinePositive displacement machinemasspower=1 …. 15 kg/kW0.1 … 1 kg/kW10 times lightermin. 10 times smallermuch smaller mass moment of inertia (approx. 70 times)Positive displacement machines (pumps & motors) are:much better dynamic behavior of displacement machines35SICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59110Axial Piston Pumps Te , np1p2, QeInletOutletSwash platePistonValve plate(distributor)Cylinder blockCylinder blockPitch radius RPiston stroke = f (ß,R)Variable displacement pumpRequires continous change of ß17SICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59111Bent Axis & Swash Plate Machines18Torque generation on cylinder block FRFRFRFpFpFpFNFNFNTorque generation on „swash plate“ Swash plate designBent axis machinesRadial force FR exerted on piston!Driving flange mustcover radial forceFpFNFNFNFpFRFRFRFpSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5911219Axial Piston Pumps Openings in cylinder bottomIn case of plane valve plateIn case of spherical valve plateSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5911320Axial Piston PumpsOutletInletInlet openingOutlet openingPlane valve platePlane valve plateConnection of displacement chambers with suction and pressure portSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5911421Axial Piston PumpsInletOutletKinematic reversal: pump with rotating swash plateCheck valves fulfill distributor functionSuction valvePressurevalve foreach cy-lindercan only work as pumpSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59116ideal displacement machineSteady state characteristics8Displacement volume of a variable displacement machine:maxVVconstn0Ppconstconst0Pnconstp0Tpconstconstn0Qconstpconstn0Qnconstconstp0TconstnconstpSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59118ExampleThe maximal shaft speed of a given pump is 5000 rpm. The displacementvolume of this pump is V= 40cm3/rev. The maximal working pressure isgiven with 40 MPa. Using first order scaling laws, determine:- the maximal shaft speed of a pump with 90 cm3/rev- the torque of this larger pump- the maximal volume flow rate of this larger pump- the power of this larger pumpFor the linear scaling factor follows:31.14090330VVMaximal shaft speed of the larger pump:Torque of the larger pump:Nm 25.5732m1090Pa104023-66VpTMaximal volume flow rate:l/min 343.5/min m 3435.0rpm 8.3816/revm 1090336maxmaxnVQPower of the larger pump:rpm 8.3816rpm 500031.1101nn31kW229s601m 0.3435Pa10401-36QpPSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59119Real Displacement MachineTe , np1p2, QeQSiQSeInletOutletDistributorCylinderPistonEffective Flow rate:Effective torque:SeTVpT2maxQSe… external volumetric lossesQSi… internal volumetric lossesTS …torque losses10QS… volumetric lossesSeQnVQmax12pppSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59120Volumetric LossesQSL external and internal volumetric losses = flow through laminar resistances: 11Te , np1p2, QeQSiQSeexternalinternalvolumetric losseslosses due tocompressibilitylosses due toIncompletefillingpCQSL),( pfDynamic viscosityAssuming const. gap heightSfSKmjSijniSeiSQQQQQ11123phbQSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59121Volumetric LossesEffective volume flow rate is reduced due to compressibility of the fluidBVPumpingSuctionBCAppKBBeVV11simplifiedABBKpVVBSKVnQwith n … pump speed12CBACBdpKVdV 1BCABCppKVV1lnlnSICFP’05, June 1-3, 2005, Linköping © Dr. Monika