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Hydraulic Servo and Related Systems
ME4803 Motion Control
Wayne J. Book
HUSCO/Ramirez Chair in Fluid Power and Motion Control
G.W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
Hydraulics is Especially critical to the Mobile Equipment Industry
References1. Norvelle, F.D. Fluid Power Control Systems, Prentice Hall,
2000.2. Fitch, E.C. and Hong I.T. Hydraulic Component Design
and Selection, BarDyne, Stillwater, OK, 2001.3. Cundiff, J.S. Fluid Power Circuits and Controls, CRC
Press, Boca Raton, FL, 2002.4. Merritt, H.E. Hydraulic Control Systems, John Wiley and
Sons, New York, 1967.5. Fluid Power Design Engineers Handbook, Parker Hannifin
Company (various editions).6. Cetinkunt, Sabri, Mechatronics, John Wiley & Sons,
Hoboken, NJ, 2007.
The Strengths of Fluid Power(Hydraulic, to a lesser extent pneumatic)
• High force at moderate speed• High power density at point of action
– Fluid removes waste heat– Prime mover is removed from point of action– Conditioned power can be routed in flexible a fashion
• Potentially “Stiff” position control• Controllable either electrically or manually
– Resulting high bandwidth motion control at high forces
• NO SUBSTITUTE FOR MANY HEAVY APPLICATIONS
Difficulties with Fluid Power
• Possible leakage• Noise generated by pumps and transmitted by
lines• Energy loss due to fluid flows• Expensive in some applications• Susceptibility of working fluid to contamination• Lack of understanding of recently graduated
practicing engineers– Multidisciplinary– Cost of laboratories– Displaced in curriculum by more recent technologies
System Overview
• The system consists of a series of transformation of power variables• Power is either converted to another useful form or waste heat• Impedance is modified (unit force/unit flow)• Power is controlled• Function is achieved
Electric or IC prime mover
PumpTransmission line & valve
Motor or cylinder
Coupling mechanism
Load
Rpm-torque
Flow-press.
Flow-press.
Rpm-torque or force
Rpm-torque or force
Volts-amp
Simple open-loop open-center circuit
cylinder
4-way, 3 position valve
Pressure relief valve
Fixed displacement pump
filter
Fluid tank or reservoir
Actuating solenoid
Spring return
Simple open-loop closed-center circuit
Closed-loop (hydrostatic) system
Variable displacement
reversible pump
Drain or auxiliary line
Check valveMotor
Pilot operated valve
Proportional Valve
Various valve schematics
Basic Operation of the Servo Valve(single stage)
Torque motor moves spool left
Positive motor rotation
Torque motor moves spool right
Negative motor rotation
Flow enters
Flow exits
Orifice Model
xwA
C
pACQ
o
d
od
area flow orifice
coef. discharge flow orifice
2
4 Way Proportional Spool Valve Model• Spool assumptions
– No leakage, equal actuator areas
– Sharp edged, steady flow
– Opening area proportional to x
– Symmetrical
– Return pressure is zero
– Zero overlap
• Fluid assumptions
– Incompressible
– Mass density
21 qq
xppCq
CxppCq s
022
11 constant a ,
2021 ppppps
2;
2 :so
:pressure Load
21
21
ppp
ppp
ppp
ss
xpp
CxppCq ss 211
p0 p0ps
p1, q1p2, q2
x
Dynamic Equations (cont.)
s)order term(high )()(
linearize order tofirst toseriesTaylor ain Expand
1111
pp
p
qxx
x
qqq
ppxx
ppxx
xpp
C
p
qppC
x
q
sppxx
s
ppxx
22
;2
:sderivative partial Taking
11
0;2
0at which ,0;0
commonly point, operating Choose
21
11
1
Kp
qK
pC
x
q
qpx
ppxx
s
ppxx
p0 p0ps
p1, q1p2, q2
x
Dynamic Equations: the Actuator
If truly incompressible:
•Specification of flow without a response in pressure brings a causality problem
•For example, if the piston has mass, and flow can change instantaneously, infinite force is required for infinite acceleration
•Need to account for change of density and compliance of walls of cylinder and tubes
yAxKpKxKq 1211
Change in volume
Change in density
y
Net area Ap
q1
Compressibility of Fluids and Elasticity of Walls
2
:modulusBulk m
Np
dp
VMd
dp
d )/(111
For the pure definition, the volume is fixed.
dtqV
dpdtqdM
;
More useful here is an effective bulk modulus that includes expansion of the walls and compression of entrapped gasses
p
V
V
M
p
M
Vdp
VMd
eff2
11)/(11
Using this to solve for the change in pressure
dtqkdtMkdMV
dp eff
Choices for modeling the hydraulic actuator(simplified actuator)
Change of variables: consider q as volumetric flow rate
With no compliance or compressibility we get actuator velocity v as
q
1/Ady/dt
With compliance and/or compressibility combined into a factor k
And with moving mass m we get the following block diagram. Steady state (dy/dt)/q is the same. Transient is different. (Show with final value theorem.)
y
q Area A
m
-k dt
q pA/m
dv/dt dt
dy/dt
A
feedback load pressure may reduce q
Manufacturer’s Data: BD15 Servovalve on HAL
Manufacturer’s Data: BD15 Servovalve on HAL
Two-stage Servo Valve
Torque motor rotates flapper, obstructs left nozzle
Flow gives negative rotation
Pressure increases Spool is driven right
With flapper centered the flow and pressure is balanced
Feedback spring balances torque motor force
Details of Force Feedback Design
Shown line to line; no overlap or underlap
2 Sharp edged orifices, symmetrical opening
Another valve design with direct feedback
Position Servo Block DiagramPosition measurement
Proportional control
May be negligible
Load torque
Net flow / displacement
Flow gain / motor displacement
Design of some components(with issues pertinent to this class)
• The conduit (tubing) is subject to requirements for – flow (pressure drop)
• 2 to 4 ft/sec for suction line bulk fluid velocity
• 7 to 20 ft/sec for pressure line bulk fluid velocity
– pressure (stress)
• The piston-cylinder is the most common actuator– Must withstand pressure– Must not buckle
• Flow– Darcy’s formula– Orifice flow models
• Stress– Thin-walled tubes
(t<0.1D)– Thick-walled tubes
(t>0.1D)
• Guidelines– Fluid speed– Strengths– Factors of safety (light
service: 2.5, general: 3.15, heavy: 4-5 or more)
Darcy’s formula from Bernoulli’s Eq.
velocityfluid
areasection flow
rate flow
density mass fluid
perimeter)(section diameter)/section (flowx 4
diameter hydraulic
length tube
)Non (dependsfactor friction
tube thealong drop pressure
2
2
u
uDN
A
Q
D
L
f
p
A
Q
D
Lfp
hR
h
RD
hD
law) Poiseuille-(Hagen
viscosityabsolute
2000N ,128
or
R
4
p
L
DQ h
Friction factor for smooth pipes(empirical) from e.g. Fitch
Orifice Model
area flow orifice
coef. discharge flow orifice
2
o
d
od
A
C
pACQ
Buckling in the Piston Rod (Fitch)• Rod is constrained by cylinder at two points• Constrained by load at one point• Diameter must resist buckling• Theory of composite “swaged column” applies• Composite column fully extended is A-B-E shown below consisting of 2 segments
– A-B segment buckles as if loaded by force F on a column A-B-C– B-E segment buckles as if loaded by F on DBE– Require tangency at B
Results of Composite Column Model
r
br
bbb
aaa
b
a
D
ID
IE
FL
IE
FL
I
I
for solvethen
yiterativel solved bemay equation first The
rod ofdiameter 64
tantan
25.0
Composite column model matches manufacturer’s recommendations with factor of safety of 4
Equating the slope of the two column segments at B where they join yields:
Cylinder construction (tie-rod design)
Resulting loading on cylinder walls
Stress Formulas for Cylinders or Conduits
ratio sPoisson'
ion)concentrat stress*safety offactor strength/(
stress allowableor design
diameter inside
required thickness wall2
open) (thin, formula sBarlow'
d
i
d
i
s
D
s
PDt
12
(brittle) formula sLame'
Ps
PsDt
d
di
1)1(
)21(
2
ductile) thick,
(closed, formula sClavarino'
Ps
PsDt
d
di
1)1(
)1(
2
ductile) thick,(open, formula sBirnie'
Ps
PsDt
d
di
Pressure Specifications
• Nominal pressure = expected operating
• Design pressure = Nominal
• Proof pressure (for test) = 2x Design
• Burst pressure (expect failure) = 4x Design
Pipes versus tubesTubes are preferred over pipes since fewer joints mean
•Lower resistance
•Less leakage
•Easier construction
Fittings between tube and other components require multiple seals
Flared tube design