Fluid Power Controls Laboratory (Copyright – Perry Li ... · ... (Hydraulic test bench) Topics...

Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)

M..E., University of Minnesota

Systems review exercise •  To be posted this afternoon •  Due in class (10/23/15) Coming week: •  Lab 13: Hydraulic Power Steering •  Lab 14: Integrated Lab (Hydraulic test bench) Topics today: •  2 min course feedback •  Fluid Inertance •  Pumps and motors

Lecture 6 153



Write on a piece of paper, do not write your name

•  Labs: •  What works? •  What doesn’t work / can be improved.

•  Class / lecture: •  What works? •  What doesn’t work / can be improved.

•  One or two things you have learned so far that you appreciate?

Course Feedback – 2 mins 154



155

Fluid Inertance (inertia) •  F = m * a for the accelerating fluid (transients)

•  Normally, the pressure needed to accelerate the fluid is neglected. •  When is this important ? •  Momentum calculation for a hose: Length = L, Area = A

P1 P2

[ ] [ ]LQdtdLAv

dtdPA ρρ ==Δ⋅ dt

dQALP ⎥⎦

⎤⎢⎣

⎡=Δρ

inertance

Important for long, narrow pipes – water hammer effect!



How to make a big mass out of little mass?

•  Total weight of device = M •  Kinetic energy = (100 M) v2/2

•  What is in the box?

156

v v

F = (100M) dv/dt



•  Pressure drop through viscosity:

•  Equivalent stiffness:

•  Inertance:

No Free Lunch (large is better) 157

QDLP 4

128πµ

=Δ

ΔP = ρLA

"

#$%

&'dQdt

Keq =βAL

ΔF = βALΔx



158

Computer circuit analysis

0.019

SliderGain2

0.403

SliderGain

0

Pump f low

Pressure Flow rate

Pump

0

Pres s ure

Flow

turns

Pressure

Needle2

Pressure

turns

Flow

Needle1

0

Flow 1

0

Flow 2 3

Cons tant1

3

Cons tant



159

Component Modeling - Pressure Reducing Valve

•  How do we write equations for this valve?

•  Spool •  Force balance / Newton’s law

•  Spring •  Preload / Compression

•  Orifice



160

Modeling •  Function: Regulate pressure at B •  Operation: If P_B is too large (small), spool moves up (down) to

reduce (increase) orifice size

A

B

D

x

F s p r i n g

Preload x

A(x)

Possible Spring and area functions

PBAB − Fspring(x)−Fseat( )−PDAD =Mx

Fseat � 0Fseat =

(0 x > 0

contact model x = 0

Q = CdA(x)

r2

�(PA � PB)



Modeling and Analysis of Flow Divider 161

Formulate models



162

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



163

Pump - Introduction

40,000 psi



164

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



165

Non positive displacement pumps

Impeller Pump Centrifugal Pump



166

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%



167

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)



168

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



169

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.



170

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 port Outlet port



171

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



172

Pressure Compensated Vane Pump



173

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



174

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)

175



176

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



177

Piston Pump - flow ripples •  Each cylinder has a

pumping cycle •  Total flow = flow of each

cylinder •  More cylinders, less ripple •  Frequency:

Even # cylinders n*rpm Odd # cylinders (2n)*rpm

•  Can be problematic for manual operator (ergonomic issue)

•  Noise

1 piston

Filling

Pumping

2 piston Total flow

•  Displacement = # Cylinders x Stroke x Bore Area



# of Pistons Effect on Flow Ripples 178

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Angle - rad

Flow

-

n=2n=3n=4n=5



179

Pumping theory •  Create a partial vacuum (i.e. reduced pressure)

•  Atmospheric / tank pressure forces fluid into pump •  usually tank check valve opens •  outlet check valve closes

•  Power stroke expels fluid to outlet •  outlet check valve opens •  tank check valve closes

•  Power demand for prime mover (ideal calculation) •  (piston pump) Power = Force*velocity = Pressure*area*piston speed

= Pressure * Flow rate •  If power required > power available => Pumps stall or decrease speed



180

Aeration and Cavitation •  Disastrous events - cause rapid erosion

•  Aeration •  air bubbles enter pump at low pressure side •  bubbles expand in partial vacuum •  when fluid+air travel to high pressure side, bubbles collapse •  micro-jets are formed which cause rapid erosion

•  Cavitation •  fluid evaporates (boils) in partial vacuum to form bubbles •  bubbles expands then collapse •  as bubbles collapse, micro-jets formed, causing rapid erosion



181

Causes of cavitation and aeration •  For positive displacement pumps, the filling rate is determined by

pump speed; (Q-demand) = D * freq)

•  Filling pressure = tank pressure - inlet pressure •  Q-actual = f(filling pressure, viscosity, orifice size, dirt)

•  If Q-actual < Q-demand, inlet pressure decreases significantly •  This causes air to enter (via leakage) or to evaporation (cavitates)

•  To prevent cavitation/aeration •  increase tank pressure •  low viscosity, large orifice •  lower speed (hence lower Q-demand)



182

Aeration and Cavitation



183

Hydraulic Motor / Actuator •  Hydraulic motors / actuators are basically pumps run in reverse

•  Input = hydraulic power

•  Output = mechanical power

•  For motor: •  Frequency (rpm) = Q (gallons per min) / D (gallons) * efficiency •  Torque (lb-in) = Pressure (psi) * D (inch^3) * efficiency

•  efficiency about 90%

•  Note: units



• 

Models for Pumps and Motors 184



185

Non-ideal Pump/Motor Efficiencies •  Ideal torque = torque required/generated for the ideal pump/motor •  Ideal flow = flow generated/required for the ideal pump/motor •  Torque loss (friction) •  Flow loss (leakage) •  Signs different for pumping and motoring mode

Q i d e a l

Q a c t u a l

Q l o s s

Ideal pump

leakage

Friction

Functions of speed, pressure and displacements

(Reverse if motor case !! )

Pump volumetric eff:

Pump mechanical eff:

Total efficiency:

Tin/out

Tideal vol



186

Hydro-static Transmission •  A combination of a pump and a motor

•  Either pump or motor can have variable displacement

•  Replaces mechanical transmission •  By varying displacements of pump/motor, transmission ratio is changed

•  Various topologies: •  single pump / multi-motors •  multi (pump-motor) •  Open / closed circuit •  Open / closed loop control

•  Integrated package / split implementation



Hydrostatic Transmission 187



188

General Consideration - Hydrostats •  Advantages:

•  Wide range of operating speeds/torque •  Infinite gear ratios - continuous variable transmission (CVT) •  High power, low inertia (relative to mechanical transmission) •  Dynamic braking via relief valve •  Engine does not stall •  No interruption to power when shifting gear

•  Disadvantage: •  Lower energy efficiency (85% versus 92%+ for mechanical transmission) •  Leaks !



189

Closed Circuit Hydrostat Circuit

Notes: •  Charge pump circuit (pump + shuttle valve) •  Bi-directional relief •  Circuit above closed circuit because fluid re-circulates.

•  Open circuit systems draw and return flow to a reservoir



190

Hydrostatic Transmission •  Let pump and motor displacements be D1 and D2, with one or both

being variable. •  Let the torque (Nm) and speeds (rad/s) of the pump and motor be (T1,

S1) and (T2,S2) •  Assuming ideal pumps and motors:

Transmission ratio Variable by varying

D1 or D2

Infinite and negative ratios possible if pump can

go over-center

Q =S1D1

2�=

S2D2

2��P = 2�

T1

D1= 2�

T2

D2

S2

S1=

D1

D2

T2

T1=

D2

D1

Note: Pow

in

= S1T1 = S2T2 = Pow

out



191

Hydraulic Transformer •  Used to change pressure in a power conservative way •  Pressure boost or buck is accompanied by proportionate flow decrease

and increase •  Note: Hydrostatic transmission can be thought of as a mechanical

transformer (torque boost/buck)

Q 1 Q 2

�P1 �P2

D1 D2 Research opportunity!

Fluid Power Controls Laboratory (Copyright – Perry Li ... · ... (Hydraulic test bench) Topics...

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