Dr. Monika IvantysynovaMAHA Professor Fluid Power SystemsDesign and Modeling of Fluid Power SystemsME 597/ABE 591 - Lecture 8MAHA Fluid Power Research CenterPurdue UniversitySICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5912Content of 6th lecture 2Aim:Derivation of basic equations for gap flow and calculation ofGap flow parameters (pressure and velocity distribution, load ability,gap flow and viscous friction)Basic knowledge about the gap design and simulation modelsInstantaneous cylinder pressure – conservation of massGap flow calculationValve plate design issuesSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59130 50 100 150 200 250 300 350125130135140145150155f[] Effective discharge [l/min] Flow pulsations0 100 200 300 400020406080100120140160φ [°]Pressure[bar]measuredsimulatedInst. cylinder pressure0 50 100 150 200 250 300 350-150-100-50050100150200f[] Swash plate moment [Nm] Oscillating forcesNoise generation in piston pumpsStructure-borne noisefluid-borne noiseSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5915Instantaneous cylinderpressurePKStart of opening of precompressionPKEnd of precompression openingPKPressure port full openSuctionHigh pressureOpenings in cylinderAdditional compressionPre-expansionAdditional expansion3SICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59164Instantaneous cylinderpressuredpVKdV 1ITATHKplK 0VdtdQQQQmSGmSKmSBmr dtdVdtdVVdtddtdpKdtd(index „K“ used for piston instead of „P“)(1)Conservation of mass:(2)(3) dtdVdtdpKVVdtd(4)Qm... mass flow 0dtdVdtdpKVQQQQSGSKSBr(5)QQmSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 591723costanRyyRbbzzsPPiston displacement: cos1tan  RsPPiston stroke:tan2  RHPHPsPR … pitch radiusOuter dead point ATInner dead point ITφ=0KinematicsAxial Piston MachineSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59185Instantaneous cylinder pressureITATHKplKKKAsVV 0KKAvdtdVdtd dtdVQQQQVKdtdpSGSBSKrKKSGSBSKrKKAsVQQQQAvKddp0KKTAHVV 0 0dtdVdtdpKVQQQQSGSKSBr(5)(6)(7)(8)(9)(10)(11)3121hbxpQ SICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 5919Instantaneous cylinderpressureITATHKplKKKSGSBSKrKKAsVQQQQAvKddp0KKTAHVV 0tan2  RHK6(11) cos1tan  RsPSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59110ArInstantaneous cylinderpressureFlow from displacement chamber through valve plate openings to pressure port   rrrDrppppAQ  sgn2Turbulent flow – orifice equation: fArGap flows – laminar flow:bhvhbxpdzvbQh2121030 KKKeKKKSKvhdpplhdQ 2123Gap flow between piston and cylinder assuming parallel gap8SICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59111Instantaneous cylinder pressureGap flow through the gap between cylinder block and valve plateValve plateCylinder blocklppdldpe    where1123fldlpphQeBSBAssuming a parallel gap9SICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59112 edGGGddGSGpplhrRddhQ 3443128ln6Instantaneous cylinder pressure10ldpeGap flow through the gap between slipper and swash plate eGGGGSGpprRhQ ln63 GddSGppldQ 1284Flow through laminar throttleSICFP’05, June 1-3, 2005, Linköping © Dr. Monika IvantysynovaDesign and Modeling of Fluid PowerSystems, ME 597/ABE 59113Measurement Results – PressureProfileVi= 100 %Dp = 100 barn = 2000