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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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!
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
• 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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
159
Component Modeling - Pressure Reducing Valve
• How do we write equations for this valve?
• Spool • Force balance / Newton’s law
• Spring • Preload / Compression
• Orifice
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
Modeling and Analysis of Flow Divider 161
Formulate models
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
163
Pump - Introduction
40,000 psi
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
165
Non positive displacement pumps
Impeller Pump Centrifugal Pump
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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%
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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.
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
172
Pressure Compensated Vane Pump
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
# 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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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)
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
182
Aeration and Cavitation
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
•
Models for Pumps and Motors 184
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
Hydrostatic Transmission 187
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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 !
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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
Fluid Power Controls Laboratory (Copyright – Perry Li, 2004-2015)
M..E., University of Minnesota
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!