Download CHAPTER 7 Linear Actuators

CHAPTER 7
Linear Actuators
Fluid Power Circuits and Controls,
John S.Cundiff, 2001
Introduction
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Linear actuators are commonly used in modern
manufacturing plants.
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z
z
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Hydraulic cylinder to tilt a ladle of molten metal,
A pneumatic cylinder to install a rivet
Set of cylinders to close a box of frozen chicken.
Mobile industrial and agricultural machines also use
cylinders to lift, dig, dump and position loads.
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Introduction
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Concept of Linear actuators:
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Fluid at a given pressure and flow is pumped into cylinder
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Fluid pressure pushes against the piston, causing it to extend.
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Velocity is a function flow rate
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Force is a function pressure.
Analysis of Cylinders in
Parallel and Series
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If two independent cylinders in different locations extend at
the same time.
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When cylinders are connected in parallel, the cylinder
having the lowest pressure will extend first.
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Consider two cases
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z
Cylinder 1
Cylinder 2
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Analysis of Cylinders in
Parallel and Series
Analysis of Cylinders in
Parallel and Series
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Cylinder 1 (Refer Fig 7.1)
z
z
z
z
z
No load extension of cylinder 1 requires 80 psi pressure.
Back pressure is 20 psi.
Using force balance to calculate friction force,
PC1AC1 = Ff1 + Pr1Ar1
2
2
By calculation AC1 = 7.07 in , Ar1 = 5.3 in
Ff1 = 80(7.07) – 20(5.3) = 459.6 lbf
Total pressure at the cap end to extend the load is
PC1 = (Ff1 + FL1 + Pr1Ar1)/AC1
= 646 psi
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Analysis of Cylinders in
Parallel and Series
Analysis of Cylinders in
Parallel and Series
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Cylinder 2 : (Refer Fig 7.1)
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z
z
z
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No-load extension of Cylinder 2 requires 65 psi
Back pressure is 15 psi.
Using force balance to calculate friction force,
PC2AC2 = Ff2 + Pr2Ar2
2
2
By calculation Ar2 = 3.68 in and AC2= 4.91 in .
Ff2 = 65(4.91) – 15(3.58)
= 263 lbf
Total pressure to extend the load is
PC2AC2 = Ff2 + FL2+ Pr2Ar2
= 615 psi
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Analysis of Cylinders in
Parallel and Series
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Consider a fixed displacement
pump, refer figure 7.2
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Relief valve is set at 2000 psi.
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When the DCV is shifted , the pump
builds up pressure to 615 psi.
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Fluid flows to Cylinder 2, causing it
to extend fully.
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When full extension is reached,
pressure builds to 646 psi, Cylinder
1 extends and at full extension
pressure builds to 2000 psi.
Analysis of Cylinders in
Parallel and Series
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Parallel circuit supplied by a pressurecompensated pump. (Refer Figure 7.3)
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The pump is set to maintain 2000 psi;
thus 2000 psi is available when DCV is
shifted.
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Maximum pressure required is 646 psi
for Cylinder 1 and 615 psi for Cylinder
2.
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Both cylinders will start to move;
Pressure will drop to the load pressure.
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Flow will increase to Cylinder 2 and
decrease to Cylinder 1, pressure will
continue to decrease until 615 psi is
achieved.
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Analysis of Cylinders in
Parallel and Series
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Consider two cylinders connected in
series.
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Pressure required to extend Cylinder
2 (615 psi) is the back pressure (rodend pressure) on Cylinder 1.
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Total pressure to extend Cylinder 1 is
PC1AC1 = Ff1 + FL1 + Pr1Ar1
PC1 = 459.6 + 4000 + 615(5.3)
7.07
= 1092 psi.
Analysis of Cylinders in
Parallel and Series
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When pressure reaches 1092 psi, both the cylinders
move simultaneously.
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Cylinder 2 stops when the Cylinder 1 stops.
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If the cylinders are sized such that Ac2 = Ar1, both the
cylinders will extend the same distance.
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Here we neglect leakage. In actual practice, the
extension will never be exactly equal.
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Analysis of Cylinders in
Parallel and Series
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Consider Fig 7.4 specified as follows
z Pump : Flow 8 GPM (at pressure
< 1200 psi, leakage is negligible)
z Cylinder 1: Stroke, x1 = 20 in.
z Cylinder 2: Stroke, x2 = 36 in.
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Rate of extension of Cylinder 1
3
3
Q1 = 8gal/min x 231 in /gal = 30.8 in /s
60 s/min
dx1/dt = Q1 = 30.8 = 4.35 in/s
Ac1 7.07
Analysis of Cylinders in
Parallel and Series
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Rate of extension of Cylinder 2
The only flow that reaches Cylinder 2 is the flow out the
rod end of Cylinder 1.
2
3
Q2 = dx1/dt* Ar1 = (4.35 in/s)(5.3 in ) = 23 in /s
dx2 /dt = Q2 = 23 = 4.68 in/s
Ac2 4.91
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Cylinder 2 extends faster than Cylinder 1, because
Ac2 < Ar1. Only when Ac2 = Ar1 are the extension rates
equal.
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Analysis of Cylinders in
Parallel and Series
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Distance the cylinder extends is a key performance
parameter.
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Total Flow from Cylinder 1 is
3
Q1= Ar1 x1 = 5.3(20) = 106 in
x2 = Q1 = 106 = 21.5 in
Ac2 4.91
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Cylinder 2 has a stroke of 40 in. but never extends
beyond 21.5 in.
Synchronization of Cylinders
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There are instances when a large mass must be
moved, and it is not feasible to move it with just one
cylinder.
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If the load to be moved is several feet in length, two
or more cylinders are used to prevent a moment, or
moments , that might distort and damage the load.
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Synchronization of Cylinders
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There are three techniques
that can be used to
synchronize two cylinders.
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Orifice-type flow divider
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Gear-type flow divider
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Mechanical coupling
Synchronization of Cylinders
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Orifice-Type Flow Divider
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Adjust the orifice on both sides of
the flow divider so ∆P across the
orifice and the load is equal on both
sides.
Flow from the pump will divide
equally
Both cylinders will extend
simultaneously.
If cylinders have same size, they
extend at same rate.
When ∆P changes, flow goes to
lower pressure side.
Cylinders have to be
resynchronized
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Synchronization of Cylinders
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Gear Type Flow Divider
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Functions like two gear motors with
shafts rigidly attached
Both motors have same
displacement. Since shafts are
attached, they turn at same speed
Same flow goes through both sides.
Excluding leakage, flow is equally
divided and cylinder extends
simultaneously
Disadvantage – Pressure
Intensification.
Synchronization of Cylinders
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Mechanical Coupling
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z
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Most reliable way to ensure two
cylinders stay synchronized is to
mechanically couple them
together.
The beam slides in a track on
both sides.
If Cylinder 1 gets ahead of
Cylinder 2, the beam will bind in
the track on that side
Pressure requirement on Cylinder
1 increases.
Bind is relieved when more flow
goes to Cylinder 2; Cylinders
adjust back and forth to stay
synchronized
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CUSHIONING
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When cylinders reach the end of their stroke,
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the pressure rises quickly
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A Shock wave in hydraulic circuit can occur.
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Cushioning is done to reduce this stock.
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The concept is shown in Fig 7.6
CUSHIONING
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Consider the case of the cylinder
retracting.
Spear closes off the large
opening where the fluid is exiting
the cap end of cylinder.
Fluid must not flow out the small
opening past the needle valve.
Valve adjusts the orifice and sets
the back pressure that develops
in the cap end.
Resultant force slows the piston
and it “coasts” to a stop.
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CUSHIONING
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Resultant pressure shock is
significantly reduced.
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Same technique is used to
cushion the cylinder when
its is extending.
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Here, a sleeve is mounted
on the rod to close the main
opening to make the flow go
through the orifice .
Rephasing of Cylinders
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When cylinders are used in series, it is necessary to rephase the
cylinders when they are fully retracted.
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Leakage will cause downstream cylinder to not fully extend.
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An agricultural implement (planter, cultivator, disk harrow) that
must be folded to an 8-ft width for road travel and unfolded to 24ft width for field operation, will after several cycles, become out of
phase so that downstream cylinders might not fully extend so
the outer sections will not make proper ground contact.
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Rephasing of Cylinders
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In one technique,
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Cylinder is designed with small
passageway for oil to flow from
the cap end to the rod end when
the piston reaches full extension.
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Passageway is small since it is
not expected to pass a large flow.
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It passes the flow required to
make up leakage from the cap
end of the cylinder immediately
downstream so this cylinder will
then extend completely.
PRESSES
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Presses are used for
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molding,
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shaping,
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shearing and other operations.
Some manufacturing plants have
lines of presses connected in
parallel
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PRESSES
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Assume that the press cylinder has a 30-in. bore and
10-in stroke.
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It needs to close in 30 s to achieve the desired cycle
time.
Q = Acx
t
2
= π(30) (10)
4(30)
3
= 236 in = 61 GPM
s
PRESSES
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Flow rate required to close an individual press is 61 GPM; a high capacity line
is required.
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Presses along the line are closed simultaneously.
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Flow dynamics in the main supply and return lines are complex.
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When two or more presses close simultaneously, flow takes the path of least
resistance.
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Flow goes to the press with smallest pressure drop first.
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After the first press is closed, other presses are closed in a similar manner.
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Disadvantage of parallel circuit design – Volume of fluid that must be moved
from the reservoir to the individual presses require high pump capacity and
high energy input.
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PRESSES
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Design shown in Fig 7.10 avoids the pumping
of fluid back and forth from the reservoir
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Typically press is controlled by solenoidactuated DCV.
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Main press cylinder is the large cylinder.
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Two outer cylinders will be referred to as side
cylinders or kicker cylinders.
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Primary function – Raise and lower the platen.
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Main press cylinder supplies most of the force
needed once platen contacts the whole piece.
PRESSES
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When operator shifts the DCV, flow
extends the two side cylinders.
Flow does not go to the press
cylinder because sequence-valve
remains closed.
When the platen contacts the work
piece, the pressure builds and
sequence valve opens.
System pressure is applied to the
press cylinder (side cylinders +
press cylinder) and full force is
applied to the work piece.
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PRESSES
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When DCV is shifted for retraction, the line to the
sequence valve is connected to the reservoir.
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No pressure to hold the sequence valve open;
consequently , it closes.
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Flow from the press cylinder cannot go back through the
sequence valve; it must go through the pilot operated
check valve into the reservoir.
PRESSES
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Pilot-Operated Check
Valve
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For flow in the forward
direction, this valve
operates just like a
normal check valve.
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Pilot line pressure holds
the valve open for flow in
the reverse direction.
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PRESSES
Load-Locking Circuit
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Cylinder is prevented from moving
in either direction until pressure is
applied from the pump.
Pump supplies pilot line pressure
to open the check valve.
Load force (FL) in either direction
will not cause the cylinder to move,
except for some small leakage
past the piston seals.
Load Analysis
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Two general classification for loads
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Resistive Load (opposite to the direction of motion)
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Overrunning Load (in the same direction as the
motion)
Both types of load can be applied to the circuit in
one cylinder cycle.
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Load Analysis
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A cylinder is lifting a weight during
retraction and lowering this weight
during extension.
The extension load is overrunning,
and the retraction load is resistive.
The DCV opening can be
continuously adjusted to create the
pressure needed to dump a
variable amount of fluid across the
relief valve.
Cylinder speed is controlleed by
varying the position of the DCV
handle.
Load Analysis
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The force versus time function required to move a load
can be divided into several categories.
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Breakaway: If load is resting on a surface, the cylinder
must develop the force required to overcome the static
friction.
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Inertial: Force must be developed to accelerate the load.
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Constant velocity: If the load slides along a surface, the
cylinder must supply the force required to overcome the
dynamic friction.
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Load Analysis
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Analysis of Acceleration of a
load using a Cylinder
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The cylinder has a 3-in. bore,
1.5-in. rod diameter and 24-in.
stroke.
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The fixed displacement pump
has a theoretical output of 12
GPM and relief valve is set on
1500 psi.
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Load is 4,000 lbf.
Load Analysis
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During no-load extension, pressure drop between the
relief valve and cap end of the cylinder was 40 psi.
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The rod end pressure was 15 psi.
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A force balance was done and the friction force was
found to be Ff = 330 lbf.
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Load Analysis
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Pressure during extension
Pc = (Ff + FL + PrAr) / Ac
= 330 + 4000 + 15(5.3)
7.07
= 624 psi.
Prve = pressure at relief valve during
extension
= Pc + 40 = 624 + 40 = 664 psi
Load Analysis
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Cylinder velocity during extension (assuming volumetric
efficiency is 92%)
dxa = Q = 12(0.92)(231)/60 = 6.0 in/s
dt
Ac
7.07
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Velocity of the load was carefully measured and it was
determined that it took 0.0628 s from the time the DCV
was activated for the load to reach a constant velocity
of 6.0 in/s.
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Load Analysis
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Maximum force that can be exerted is the force when the
pressure equals the relief valve setting.
Pc max = 1500 – 40 = 1460 psi
Fmax = Pc maxAc – Ff – PrAr
= 1460(7.07) – 330 – 15(5.3)
= 9912 lbf
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Theoretical acceleration of the load is given by
dx2/dt2 = Fmax / m
2
where m = mass = 124.2 lbf-s /ft
Load Analysis
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Theoretical acceleration
2
dx2/dt2 = 9912 / 124.2 = 79.8 ft/s
2
= 957.6 in/s
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Using the measured ∆t, the actual acceleration is
dx2/dt2 = ∆x• a = 6.0 – 0 = 95.5 in/s2
∆t
0.0628
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Expected acceleration was 957.6 in/s and the
2
achieved acceleration was 95.5 in/s , or 10% of
expected.
2
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Load Analysis
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Factors that influence the acceleration of a mass with fluid power
circuit.
z Time for valve to open .
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Compressibility of oil.
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Compliance of lines (volume change due to pressure increase)
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Characteristics of relief valve.
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Characteristics of pump.
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Leakage in DCV.
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Leakage in cylinder.
Load Analysis
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Further discussion of these interactions are
given in the text.
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The study of the complexities of hydraulic circuit
analysis has been the topic of studies in flow
dynamics, and control systems modeling.
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Types of Cylinders
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The types of cylinders are :
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Double-acting
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Single-acting
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Double-rod
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Tandem
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Telescoping
Types of Cylinders
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The double-rod cylinder has the same annular area on
both sides, so it develops the same maximum force in
both directions for a given relief valve pressure.
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The tandem cylinder provides a means for increasing
the force that can be generated with a given pressure.
For extension, the total force is
F = (Ac + Ar) P
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Telescoping cylinders are used when a long stroke is
needed and the space available to mount cylinder is
limited.
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Types of Cylinders
Cylinder Selection
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Cylinder manufacturers typically classify their products as
heavy duty, medium-duty and light-duty.
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Pressure ratings up to 6000 psi are available.
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Some manufacturers build agricultural-grade cylinders.
These are satisfactory where annual use are limited.
Types of Cylinders
Cylinder mounting methods
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Types of Cylinders
Cylinder mounting
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Designers use one of the mounting methods shown on precious slide
to prevent binding.
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Guides are provided to ensure that the load follows the prescribed
pathway, and minimizes side loading.
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Plan for a disturbance from an atypical direction, particularly for
cylinders mounted on mobile machines.
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It is generally less expensive to protect from a side load than to
replace a damaged cylinder.
Cylinder Construction
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The seals are a key feature, as is the rod wiper.
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Dirt from the environment settles on the rod and will ingress into the
hydraulic system if it is not removed.
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Some small particles escape the wiper and these must be removed
by the filtration system.
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Industrial cylinders typically have multiple o-ring seals, because they
are designed for a large number of cycles during their design life.
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They also have a rod bearing to support the rod when the load is not
a pure axial load.
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Cylinder Construction
END OF CHAPTER 7
THANK YOU
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