fluid power controls laboratory (copyright – perry li ... 6_f2012.pdf · • modeling / analysis...

Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2010)

M..E., University of Minnesota (updated 12.2010)

This week:

• Lab 13: Hydraulic Power Steering

• [ Lab 14: Integrated Lab (Hydraulic test bench) ]

• 4-way directional control valve; proportional valve; servo-valve

• Modeling / Analysis of a servo-valve

• Valve sizing

• Pumps and motors (part 1)

10/19/2012:

• Hydraulic Hybrids

• Guest lecture – Mike Olson (Eaton Corporation)

Lecture 6

133



134

Directional Control Valves (DCVs)

• Controls direction of flow

• Fluidic symbol signifies function

• Manually or electrically • (solenoid or equivalent elements)

• Can also meter flow• proportional valve

• servo valve



135



136

Way-Position-Port, centering etc.• # Position = number of possible

positions for the valve shifting mechanism

• 1 = no shifting, 2={left, right}, 3={left, right, center},

• infinite

• # Way = number of flow paths (including reverse flow)

• check valve = 1 way

• 1-way, 2-way, 3-way, 4-way most common.

• # Port = number of plumbing connections.

• Center = connection while neutral• closed, open, tandem ...

3way, 3position

3port

2wayinfinite-pos

2port

4way, 3position

4port

4way, infinite-pos

4port



137

4 way valve center

• Influences rest of circuit

• Energy / pressure when this part of circuit not used

• Open center• unload pump, energy saving for

fixed displacement pump

• Can you use 2 cylinders?

• Closed center• high pressure / relief

• responsive

• Tandem center (lab)• allows 2 circuits in series



138

Modeling of directional control valve • Spool is driven by solenoid (in a

single stage valve) or by pilot stage(s) valves

• xv > 0 (spool moves downward)

Assume

• matched (i.e. supply and return orifices are the same)

• Critically lapped

• symmetric, +/- spool displacement give same orifice area

• Flow conserving load• Qin = Qout

• e.g. double ended cylinder or hydraulic motor



139

D.C. Valve modelingFlow paths: (neglect leakages)

• xv > 0: Orifices 1 and 3

• xv < 0: Orifices 2 and 4

• Area of each orifice • A1(xv), A2(xv), A3(xv), A4(xv)

• For xv > 0, [Cd = discharged coeff approx 0.6 (see notes on orifice modeling)

)(2

)( 111 PPxACQ svd −=ρ

)(2

)( 0233 PPxACQ vd −=ρ

LQQQ == 31



140

D.C. Valve Modeling

• Now the pressure across the load is:

• Area gradient = w

A1(xv) = A3(xv) = w * xv

A2(xv) = A1(-xv) = -w*xv

• Solve for QL when A1(xv) = A3(xv) =w xv (matched) to get:

21 PPPL −=

)( vv

xdx

dAw =

)(1

),( LsvdLvL PPwxCPxQ −=ρ

Rw π2=

Area gradient, w, relates orifice areato spool displacement.

For circular orifices:

Top view

Annular orifice

land

Annular

circular

Area versus xv



141

DC Valve Modeling

• Similar analysis for xv < 0:

• Normally PL < 0 when xv < 0.

• Putting formulae for +/- xv together:

• Flow increases linearly with xv

• Flow decreases with pressure load

)(1

),( LsvdLvL PPwxCPxQ +−=ρ

))sgn((1

),( LvsvdLvL PxPwxCPxQ −=ρ

Load overrun

Load overrun

Positive power

Positive power



142

Effect of lapping / centering

• For critically lapped (or sometimes called critically centered) valve• Orifice is shut when xv = 0.

• At least one orifice will open when xv !=0

• Critically lapped valves are desirable but expensive to make• flow is linear with displacement (constant gain)

• Overlapped (closed centered) valves • deadband => un-responsive

• Underlapped (open centered) valves• valve always open => power loss

• nonlinear gain => more difficult to control



143

Valve Sizing

• Valves are rated (i.e. their flow rate QR given) at 1000 Psi pressure drop across the valve.• i.e. Flow = QR is flow when the valve is fully open and with 1000 PSI

pressure drop

• There are two flow orifices (1 and 3) in flow path. It is assumed that pressure drop is 500psi across each orifice.

• Since one does not always use the valve when there is 1000 Psi pressure drop, one must translate the required flow to the equivalent flow at 1000 Psi.

• Basic equation:

)(2

),( 1max PPwxCPxQ sdLvL −=ρ

)(2

),( 02max PPwxCPxQ dLvL −=ρ



144

Valve Sizing• At rated condition, Ps - P1= 500Psi, P2 - P0 = 500psi

• Suppose actual operating (Ps-P1) is 700 instead, with required flow Qd, then we would like:

• So the rated flow should be at least:

• Similarly, calculate for the return orifice: pick the larger rated flow

5002

max ρwxCQ dR =

)(2

),( 1max PPwxCPxQ sdLvL −=ρ

)(2

),( 02max PPwxCPxQ dLvL −=ρ

7002

max ρwxCQ dd =

700

500dR QQ =

Pick this when picking valve

111

500

PPQQ

sdR −

=



145

Valve sizing example• Given Ps = 3000 psi; P0 = 0 psi

• Load is a 2:1 cylinder, capside Acap= 0.005 m^2.

• Required extension speed = 1 m/s

• Load F = 500 lb-f.

• Step 1: Find Qd1 = speed * Acap.; Qd2 = Qd1/2

• Step 2: find P1 and P2 during operating conditions

• Step 3:find rated flow based on each orifice

P2P1F

)(2)( 021 PPPPs −=−

FPPAcap =− )2/( 21

99

81

s

cap

P

A

FP +=

cap

s

A

FPP

9

2

9

22 −=

111

500

PPQQ

sdR −

=02

22

500

PPQQ dR −

=

21, RRR QQQ ≥

Why?



146

Other component sizing• Actuator:

• stroke: how far does it have to travel?

• Area: load/pressure or pump-flow/area

• load can be friction, gravity, brake force, acceleration load etc.

• Motor: Disp= Q/speed; Disp = Torque/Pressure

• Pump flow:• Supposed actuator area determined by load/pressure

• Qpump = actuator speed * area (beware of cap versus piston side)

• Multiple circuits:• Add required flows from all circuits

• add safety factor!

• Beware of units !!!



147

Single stage proportional valves

Solenoids

• Spool is stroked directly by solenoid actuator

• LVDT spool position feedback

• Spring (sometimes) for safety



148

Single Stage Proportional Valves• Advantages:

• Simple design• Reliable• Cost effective

• Disadvantages:• Poor dynamic performance (bandwidth)• At high flow rates and bandwidths, large stroking force is needed• Large (and expensive) solenoids / torque motors needed.• Low end market …..

Research: Using unstable flow force to improve spool agility• K. Krishnaswamy and P. Y. Li, On using unstable hydraulic valves for controlASME Journal of Dynamic Systems, Measurement and Control. Vol

124, No. 1, pp. 182-190, March, 2002. • Q.-H. Yuan and P. Y. Li,Using Steady Flow Force for Unstable Valve Design: Modeling & ExperimentsASME Journal of Dynamic Systems,

Measurement and Control. Vol 127, No. 3. pp. 451--462, 2005.• Q.-H. Yuan and P. Y. Li,Robust Optimal Design of Unstable ValvesIEEE Transactions on Control Systems Technology. Vol. 15, No. 6, pp. 1065-

1074, November, 2007



149

Multi-stage valves

• Use hydraulic force to drive the spool …..



150

Electrohydraulic servo-valve• Multi-stage valve• Typically uses a flapper-nozzle pilot stage• Built-in feedback via feedback wire• Very high dynamic performance• Bandwidth = 100-200+Hz

Pilot stage

Main stage

For a fun place to learn how a servo-valve works:R. Dolid “Electrohydraulic Valve Coloring Book”http://www.lulu.com/items/volume_67/7563000/7563085/3/print/Servovalve_Book__091207.pdf

http://tinyurl.com/8s2t3on



151

Servo-Valve



152

Servo-ValveNozzle-flapper pilot valve:1. Electromagnetic torque motor

moves flapper to left (or right)2. Nozzle and restriction at source

form two resistances in series3. Flapper differentially opens and

closes nozzle4. Pressure increases on side with

closed nozzle; decreases on side with open nozzle; creating pressure differential

Main stage:1. Four-way spool valve actuated by

differential pressure generated by pilot stage

Feedback spring:1. Regulates the position of the main-

stage by negative feedback on the flapper



153

Two spool servo valve

• Main spool consists of two spools – one for meter-in, one for meter-out

• Reduces tolerance requirement

• Pilot stage is a pressure servo valve

• Cost effective

• Bandwidth around 30 Hz

See below for a model of such a valve• R. T. Anderson and P. Y. Li, Mathematical Modeling of a

Two-spool Flow Control Servovalve Using a Pressure Control Pilot ASME Journal of Dynamic Systems, Measurement and Control Vol 124 No. 3, Sept 2002.

(Sauer-Danfoss)



154

Pumps

• Source of hydraulic power

• Converts mechanical energy to hydraulic energy• prime movers - engines, electrical motors, manual power

• Two main types:

• positive displacement pumps

• non-positive displacement pumps



155

Pump - Introduction



156

Positive displacement pumps

• Displacement is the volume of fluid displaced cycle of pump motion• unit = cc or in3

• Positive displacement pumps displace (nearly) a fixed amount of fluid per cycle of pump motion, (more of less) independent of pressure• leak can decrease the actual volume displaced as pressure increases

• Therefore, flow rate Q gpm = D (gallons) * frequency (rpm)

• E.g. pump displacement = 0.1 litre• Q = 10 lpm if pump speed is 100 rpm

• Q = 20 lpm if pump speed is 200 rpm



157

Non positive displacement pumps

Impeller PumpCentrifugal Pump



158

Non-positive displacement pump

• Flow does not depend on kinematics only - pressure important• Also called hydro-dynamic pump (pressure dependent)

• Smooth flow

• Examples: centrifugal (impeller) pump, axial (propeller) pump

• Does not have positive internal seal against leakage

• If outlet blocks, Q = 0 while shaft can still turn

• Volumetric efficiency = actual flow / flow estimated from shaft speed

= 0%



159

Positive vs. non-positive displacement pumps

• Positive displacement pumps• most hydraulic pumps are positive displacement

• high pressure (10,000psi+)

• high volumetric efficiency (leakage is small)

• large ranges of pressure and speed available

• can be stalled !

• Non-positive displacement pumps• many pneumatic pumps are non-positive displacement

• used for transporting fluid rather than transmitting power

• low pressure (<300psi), high volume flow

• blood pump (less mechanical damage to cells)



160

Types of positive displacement pumps

• Gear pump (fixed displacement)• internal gear (gerotor)

• external gear

• Vane pump • fixed or variable displacement

• pressure compensated

• Piston pump• axial design

• radial design



161

External gear pump

• Driving gear and driven gear

• Inlet fluid flow is trapped between the rotating gear teeth and the housing

• The fluid is carried around the outside of the gears to the outlet side of the pump

• As the fluid can not seep back along the path it came nor between the engaged gear teeth (they create a seal,) it must exit the outlet port.



162

Gerotor pump

• Inner gerotor is slightly offset from external gear• Gerotor has 1 fewer teeth than outer gear

• Gerotor rotates slightly faster than outer gear• Displacement = (roughly) volume of missing tooth

• Pockets increase and decrease in volume corresponding to filling and pumping

• Lower pressure application: < 2000psi• Displacements (determined by length): 0.1 in3 to 11.5 in3

Inlet portOutlet port



163

Vane Pump

• Vanes are in slots

• As rotor rotates, vanes are pushed out, touching cam ring

• Vane pushes fluid from one end to another

• Eccentricity of rotor from center of cam ring determines displacement

• Quiet

• Less than 4000psi



164

Pressure Compensated Vane Pump



165

PC Vane Pump (Cont’’’’d)

• Eccentricity (hence displacement) is varied by shifting the cam ring

• Cam ring is spring loaded against pump outlet pressure

• As pressure increases, eccentricity decreases, reducing flow rate

• Spring constants determines how the P-Q curve drops:

• small stiffness (sharp decrease in Q as P increases)

• large stiffness (gentle decreases in Q as P increases)

• Preload on spring determines

• pressure at which flow starts cutting off



166

Axial Piston Pump• Each piston has a pumping cycle

• Interlacing pumping cycles produce nearly uniform flow (with some ripples)

• Displacement is determined by the swash plate angle• Generally can be altered manually or via (electro-)

hydraulic actuator.

Displacement can be varied by varying swashplate angle



Bent-Axis Piston Pump• Thrust-plate rotates with shaft

• Piston-rods connected to swash plate

• Piston barrel rotates and is connected to thrust plate via a U-joint

• More efficient than axial piston pump

(less friction)

167



168

Radial Piston Pump

• Similar to axial piston pump, pistons move in and out as pump rotates.

• Displacement is determined by cam profile (i.e. eccentricity)

• Displacement variation can be achieved by moving the cam (possible, but not common though)

• High pressure capable, and efficient

• Pancake profile

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