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Hydraulic Pumps Hydraulic Pumps Positive Displacement Positive Displacement Devices Devices Displacement Formulae Displacement Formulae Characteristics Characteristics
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Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Dec 22, 2015

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Page 1: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Hydraulic PumpsHydraulic Pumps

Positive Displacement DevicesPositive Displacement Devices

Displacement FormulaeDisplacement Formulae

CharacteristicsCharacteristics

Page 2: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(External Gear)(External Gear)

Pumping MechanismPumping Mechanism

Page 3: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(External Gear)(External Gear)

Displacement parameters and Displacement parameters and determinationdetermination

Displacement = Displacement = ππ/4(D/4(Doo22 – D – Dii

22)L)L

DDoo = = Outer diameter of the two gearsOuter diameter of the two gears

DDii = = Inner diameter of the two gearsInner diameter of the two gears (Actually it is the diameter of the circle defined (Actually it is the diameter of the circle defined

by the center of one gear and the outer by the center of one gear and the outer diameter of the other.)diameter of the other.)

Page 4: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.
Page 5: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(External Gear)(External Gear)

Advantages:Advantages:Cheap (easy to manufacture)Cheap (easy to manufacture)CompactCompactCheapCheap

Did I say inexpensive?Did I say inexpensive?

Page 6: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(External Gear)(External Gear)

DisadvantagesDisadvantages Limited pressure Limited pressure

capabilitycapability Unbalanced (note Unbalanced (note

where pressure is) where pressure is) Results in large Results in large bearing loadsbearing loads

Can be noisy (gear Can be noisy (gear mesh noise)mesh noise)

Volumetric efficiency?Volumetric efficiency? Fixed DisplacementFixed Displacement

Page 7: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(Internal Gear)(Internal Gear)

Pumping Pumping MechanismMechanism

Page 8: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(Internal Gear)(Internal Gear)

Displacement is a function of the number Displacement is a function of the number of teeth on the internal and external gears of teeth on the internal and external gears and the size of the crescent divider.and the size of the crescent divider.

( I don’t have a formula for the ( I don’t have a formula for the displacement. Perhaps you can derive displacement. Perhaps you can derive one.)one.)

Page 9: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(Internal Gear)(Internal Gear)

AdvantagesAdvantagesSimilar to external gear pumps in many Similar to external gear pumps in many

respectsrespectsQuieter as gear slap is reducedQuieter as gear slap is reduced

DisadvantagesDisadvantagesSomewhat more difficult to manufactureSomewhat more difficult to manufactureSame issues of volumetric efficiencySame issues of volumetric efficiencySame issues of unbalanced forcesSame issues of unbalanced forcesFixed displacementFixed displacement

Page 10: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(Internal Gear - Gerotor)(Internal Gear - Gerotor)

MechanismMechanism External (inside) External (inside)

gear is shaft drivengear is shaft driven Internal gear is Internal gear is

driven by externaldriven by external Single tooth space Single tooth space

is displacedis displaced Design keeps Design keeps

tolerance close tolerance close throughout the cyclethroughout the cycle

Page 11: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.
Page 12: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(Internal Gear - Gerotor)(Internal Gear - Gerotor)

AdvantagesAdvantagesCheapCheapSimpleSimpleCheapCheap

Page 13: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Gear PumpsGear Pumps(Internal Gear - Gerotor)(Internal Gear - Gerotor)

DisadvantagesDisadvantagesLimited pressure capabilityLimited pressure capabilityUnbalanced designUnbalanced designFixed displacementFixed displacementFrequently used as a charge pumpFrequently used as a charge pump

Page 14: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Vane PumpsVane Pumps

Pumping Pumping mechanismmechanism

Page 15: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Vane PumpsVane Pumps

DisplacementDisplacement VVDD = = ππ/2(D/2(Dcc-D-DRR)eL)eL

C = CamC = Cam R = RotorR = Rotor E = eccentricityE = eccentricity L= depthL= depth

Page 16: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Vane PumpsVane Pumps(Variations)(Variations)

Vane tip pressure control optionsVane tip pressure control optionsOutlet pressure under the vanesOutlet pressure under the vanesSurface pressure under the vanesSurface pressure under the vanes Intravanes: outlet pressure is applied always Intravanes: outlet pressure is applied always

to a small area of the vane while surface to a small area of the vane while surface pressure is applied to the rest of the areapressure is applied to the rest of the area

These are probably Vickers innovations These are probably Vickers innovations and hence are highlighted in the textand hence are highlighted in the text

Page 17: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Vane PumpsVane Pumps(Variations)(Variations)

Balanced designsBalanced designs

Page 18: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Vane PumpsVane PumpsAdvantagesAdvantages

Cartridges to quickly replace rotating groupCartridges to quickly replace rotating group

Page 19: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Vane PumpsVane Pumps(Variations)(Variations)

Variable Displacement DesignVariable Displacement Design

Page 20: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Vane PumpsVane Pumps

AdvantagesAdvantagesQuieter than gear pumpsQuieter than gear pumpsHigher pressure capability than gear pumps?Higher pressure capability than gear pumps?Better volumetric efficiency than gear pumps?Better volumetric efficiency than gear pumps?Can be balanced in design for longer lifeCan be balanced in design for longer lifeVariable displacement an optionVariable displacement an option

DisadvantagesDisadvantagesMore complex and expensive than gear More complex and expensive than gear

pumpspumps

Page 21: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Piston Pump DesignsPiston Pump Designs Axial PistonAxial Piston

Page 22: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Piston Pump DesignsPiston Pump Designs

Displacement of an axial piston pumpDisplacement of an axial piston pumpVVDD = YAD = YAD tan(tan(θθ))

Y = Number of Pistons in the rotating groupY = Number of Pistons in the rotating groupA = the area of a single pistonA = the area of a single pistonD = is the diameter of the centerline circle of the D = is the diameter of the centerline circle of the

piston borespiston boresθθ is the angle of the swashplate or the bend angleis the angle of the swashplate or the bend angle

Page 23: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Piston Pump DesignsPiston Pump Designs

Radial piston designRadial piston design

Page 24: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Piston Pump DesignsPiston Pump Designs

Bent axis designBent axis design

Page 25: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Piston Pump DesignsPiston Pump Designs

Bent axis – variable displacement designBent axis – variable displacement design

Page 26: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Piston Pump DesignsPiston Pump Designs

Axial piston – variable displacement designAxial piston – variable displacement design

Page 27: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Piston Pump AdvantagesPiston Pump Advantages

Generally highest volumetric efficiencyGenerally highest volumetric efficiencyGenerally highest pressure capabilityGenerally highest pressure capabilityVariable displacement designsVariable displacement designs

Page 28: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Piston Pump DisadvantagesPiston Pump Disadvantages

Higher cost (complexity)Higher cost (complexity)

Page 29: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

General IssuesGeneral Issues

Pumps are not strictly continuous flow Pumps are not strictly continuous flow devices. Discrete chambers are involved.devices. Discrete chambers are involved.

Flow is collected for discharge through Flow is collected for discharge through valve platesvalve plates

Design of the valve plate and the pump Design of the valve plate and the pump mechanism affects pressure pulses and mechanism affects pressure pulses and variation (ripple) of torque and pressurevariation (ripple) of torque and pressure

Design of pumps is not taught hereDesign of pumps is not taught here

Page 30: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

General IssuesGeneral Issues

Our theoretical displacements can be used Our theoretical displacements can be used to determine theoretical pump flowto determine theoretical pump flow

Actual flow is a linear function of pump Actual flow is a linear function of pump displacement, speed, a units constant, and displacement, speed, a units constant, and an efficiency terman efficiency term

Two kinds of inefficienciesTwo kinds of inefficienciesVolumetric lossesVolumetric losses

Friction lossesFriction losses

Page 31: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Actual Pump Output, QActual Pump Output, Q

QQpp = (V = (Vpp n npp ηηVpp) /1000 where:) /1000 where: Q: L/minQ: L/min VVpp : cm : cm33/rev/rev ηVpp: Volumetric efficiency (decimal): Volumetric efficiency (decimal)

OR… OR… QQpp = (V = (Vpp n npp ηηVpp) /231 where:) /231 where: Q: GPMQ: GPM VVpp: in: in33/rev/rev ηηVpp: same as above (no units): same as above (no units)

Page 32: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Torque to Drive a PumpTorque to Drive a Pump

TTpp = ( = (ΔΔP VP Vpp)/(2)/(2ππ ηηtptp) where:) where:TTpp : Newton meters torque required : Newton meters torque requiredΔΔP : pressure rise across the pump in MPaP : pressure rise across the pump in MPaVVp p : Pump displacement in cm: Pump displacement in cm33/rev/rev

ηηtp tp : Pump torque efficiency – a decimal: Pump torque efficiency – a decimal

OR…OR…

Page 33: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Torque to Drive a PumpTorque to Drive a PumpEnglish UnitsEnglish Units

TTpp = ( = (ΔΔP VP Vpp)/(2)/(2ππ ηηtptp) where:) where:TTpp : inch lbs torque required : inch lbs torque requiredΔΔP : pressure rise across the pump in PSIP : pressure rise across the pump in PSIVVp p : Pump displacement in inches: Pump displacement in inches33/rev/rev

ηηtp tp : Pump torque efficiency – a decimal: Pump torque efficiency – a decimal

Page 34: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Power to Drive the PumpPower to Drive the Pump

The hydraulic power is QThe hydraulic power is QppΔΔP/60 or P/60 or

QQppΔΔP/1714 for SI and English unitsP/1714 for SI and English units (note this is (note this is actualactual pump flow, not theoretical) pump flow, not theoretical)

Shaft power to drive the pump is given by Shaft power to drive the pump is given by PPspsp = P = Phydrhydr / / ηηpppp where: where:ηηpppp = = ηηvpvp ηηtptp which is total pump efficiency which is total pump efficiency

Page 35: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

What Determines What Determines ηηvpvp & & ηηtptp ? ?

ηηvpvp is a function of clearance spaces, system is a function of clearance spaces, system

pressure, and pump speedpressure, and pump speed Leakage Leakage flowflow at a given pressure is relatively at a given pressure is relatively

fixed regardless of pump speedfixed regardless of pump speed It is also affected by fluid viscosity as lower It is also affected by fluid viscosity as lower

viscosity fluid will result in higher leakage viscosity fluid will result in higher leakage flow and lower volumetric efficiencyflow and lower volumetric efficiency

Page 36: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

What about Torque Efficiency?What about Torque Efficiency?

Torque efficiency is a function of speed Torque efficiency is a function of speed and fluid viscosityand fluid viscosity

Higher pump speeds will result in lower Higher pump speeds will result in lower efficiency as viscous friction is speed efficiency as viscous friction is speed dependentdependent

Lower viscosity fluid can reduce viscous Lower viscosity fluid can reduce viscous losses but acts negatively on volumetric losses but acts negatively on volumetric efficiencyefficiency

Page 37: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

(μ n)/(ΔP x 1000)

Eff

icie

ncie

s

Page 38: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Sizing PumpsSizing Pumps

Component sizing begins with the LOADComponent sizing begins with the LOADLoad and actuator will determineLoad and actuator will determine

Flow requirement for this circuitFlow requirement for this circuitPressure range required by the circuitPressure range required by the circuit(We’ll do this with cylinders and motors… soon)(We’ll do this with cylinders and motors… soon)

Total the simultaneous flow requirementsTotal the simultaneous flow requirementsSelect for the maximum load pressureSelect for the maximum load pressureAdd pressure drops that will occur in valves, Add pressure drops that will occur in valves,

lines and fittings ( another topic to come…)lines and fittings ( another topic to come…)

Page 39: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Pump SizingPump Sizing

With pump outlet pressure and flow known With pump outlet pressure and flow known we will consider speed.we will consider speed. Industrial apps will use synchonous speed of Industrial apps will use synchonous speed of

electric motors. Generally 1750 rpm, or electric motors. Generally 1750 rpm, or possibly 1100. ($ decides)possibly 1100. ($ decides)

Small diesel apps such as skid loaders can Small diesel apps such as skid loaders can operate directly from engine crankshaft and operate directly from engine crankshaft and will have engine speed. (2000-3000 rpm).will have engine speed. (2000-3000 rpm).

Larger diesel apps – pump splitter with gear Larger diesel apps – pump splitter with gear reductions possible to optimize speedreductions possible to optimize speed

Page 40: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Pump SizingPump Sizing

Determine appropriate speed for your appDetermine appropriate speed for your appUse the equation for pump flow, solved for Use the equation for pump flow, solved for

displacementdisplacementVVpp = 1000Q/ = 1000Q/p p (n(npp ηηVpp))

What shall we use for What shall we use for ηηVpp????This is a function of speed, pressure, and fluid This is a function of speed, pressure, and fluid

viscosityviscosityLook for vendor data or curves and adjust…Look for vendor data or curves and adjust…

Page 41: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Example Pump ProblemExample Pump ProblemCar CrusherCar Crusher

Need 125,000 lbs of forceNeed 125,000 lbs of force8 foot stroke8 foot stroke10 seconds to extend?10 seconds to extend?Target system max pressure of 1500 psiTarget system max pressure of 1500 psiWhat is the cylinder size needed?What is the cylinder size needed?

125,000 lbs/ A 125,000 lbs/ A (area)(area) = 1500 psi = 1500 psiArea = 83.33 inArea = 83.33 in22

ππrr22 = 83.33 in = 83.33 in2 2 r = 5.15 inches (let’s use 5”)r = 5.15 inches (let’s use 5”)

Page 42: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Car Crusher Pump cont’dCar Crusher Pump cont’d

What will the system pressure be?What will the system pressure be?Cylinder area = 5Cylinder area = 522 ππ = 78.53 in = 78.53 in22

125,000 lbs / 78.53 in125,000 lbs / 78.53 in22 = 1592 psi = 1592 psi We study our plumbing and valves and allow We study our plumbing and valves and allow

for 300 psi drops in our systemfor 300 psi drops in our systemSet PRV to 1900?Set PRV to 1900?

Page 43: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Car Crusher Pump cont’dCar Crusher Pump cont’d

What is flow is required of the pump?What is flow is required of the pump?Q = cyl stroke x area /timeQ = cyl stroke x area /timeQ = 96 in x 78.53 inQ = 96 in x 78.53 in22/ 10 sec = 754 in/ 10 sec = 754 in33/sec/sec754 in754 in33/sec x 1 gal/231 in/sec x 1 gal/231 in33 x 60 sec/min x 60 sec/minQ = 195.8 GPMQ = 195.8 GPM

Note that we have sized for one cylinder. We Note that we have sized for one cylinder. We might have others (a cylinder to kick your crushed might have others (a cylinder to kick your crushed Hummer bale out of the machine). Size for those Hummer bale out of the machine). Size for those that will be used simultaneouslythat will be used simultaneously..

Page 44: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Car Crusher Pump cont’dCar Crusher Pump cont’d

Pump speed:Pump speed:Electric power available? - 1750 rpmElectric power available? - 1750 rpmRemote from grid? Diesel at 2200 rpmRemote from grid? Diesel at 2200 rpm

Determine approximate sizeDetermine approximate sizeVVpp = 1000Q/ = 1000Q/p p (n(npp ηηVpp) or 231) or 231Q/Q/p p (n(npp ηηVpp))

VVpp = 231*196/(1750*.95) = 231*196/(1750*.95)

VVpp = 27.2 inches = 27.2 inches33/revolution/revolution

Page 45: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Car Crusher Pump cont’dCar Crusher Pump cont’d

Large pump (27.2 inLarge pump (27.2 in33/rev)/rev)Now we would look at vendorsNow we would look at vendorsFor this large, a piston design is likelyFor this large, a piston design is likelyCould also select two or more smaller pumps Could also select two or more smaller pumps

operating in tandem with outlets coupledoperating in tandem with outlets coupledSelection will be based upon costs of Selection will be based upon costs of

installation, costs of operation, and required installation, costs of operation, and required lifelifeContinuous use favors efficiencyContinuous use favors efficiencyIntermittent use may favor low initial costIntermittent use may favor low initial cost

Page 46: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Pumps SelectionPumps Selection

Fixed or variable displacement?Fixed or variable displacement?So far our circuit is simple and we would likely So far our circuit is simple and we would likely

use a fixed displacement pumpuse a fixed displacement pumpLater we will look at more efficient circuits and Later we will look at more efficient circuits and

may wish to select a variable displacement may wish to select a variable displacement pump with appropriate controlspump with appropriate controls

Page 47: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Reciprocating piston

External gear pump

Double screw pump

Sliding vane

Three-lobe pump (left)Double circumferential piston (centre)

Flexible tube squeegee(peristaltic)

Positive displacement pumps:

Page 48: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Pumps in series and parallelPumps in series and parallel

Series

Parallel

Equivalent pump

Equivalent pump

Page 49: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Pumps in Series

Add the heads (H) at each flow rate (Q)

For example, for two identical pumps the head will be double that of a single pump.

Page 50: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Pumps in Parallel

Add the flow rates (Q) at each head (H)

For example, for two identical pumps the flow rate will be double that of a single pump.

Page 51: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Pump-system operationPump-system operationSystem resistance (losses) curves

(typically H Q2)

C = operating point

Page 52: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Positive Displacement Positive Displacement PumpsPumps

Typical Characteristics Typical Characteristics Constant Flow at Various PressuresConstant Flow at Various PressuresPulse Flow is possiblePulse Flow is possibleMost can pump solids suspended in liquidsMost can pump solids suspended in liquidsSelf-primingSelf-priming

Page 53: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Types of PD PumpsTypes of PD Pumps

Rotary PumpsRotary Pumps Gear – Internal, ExternalGear – Internal, External LobeLobe VaneVane ScrewScrew

Reciprocating PumpsReciprocating Pumps PistonPiston PlungerPlunger DiaphragmDiaphragm

Page 54: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Rotary vs. Reciprocating Rotary vs. Reciprocating PumpsPumps

Rotary pumps transfer liquid through the Rotary pumps transfer liquid through the action of a rotating mechanism (gear, lobe action of a rotating mechanism (gear, lobe or vane) operating inside a rigid containeror vane) operating inside a rigid container

Pumping rates varied by changing speed Pumping rates varied by changing speed of rotorof rotor

Page 55: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Rotary vs. Reciprocating Rotary vs. Reciprocating Pumps Pumps

Reciprocating pumps Reciprocating pumps move liquids by move liquids by changing the internal changing the internal volume of the pumpvolume of the pump

Require valves on the Require valves on the suction and discharge suction and discharge sidessides

Pumping rates varied Pumping rates varied by changing the by changing the frequency or the stroke frequency or the stroke lengthlength

Source: http://www.watson-marlow.com/wna-se/p-fmi.htm

Page 56: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

Internal Gear PumpsInternal Gear Pumps

•Smaller gear rotating within a bigger gear

•Partial vacuum created by meshing and unmeshing of internal teeth with external teeth

•Crescent divides liquid flow between rotor and idler gears

Source: http://www.pumpschool.com/principles/internal.htm

Page 57: Hydraulic Pumps Positive Displacement Devices Displacement Formulae Characteristics.

PD Pump CurvePD Pump Curve

Source: http://www.driedger.ca/ce2_pdp/CE2_PDP.html