VALVE CONTROLLED SYSTEMS
TEP4195 TURBOMACHINERY
VALVE CONTROLLED SYSTEMS
1Load characteristics
Mechanical loads are usually considered to consist of stiffness,
friction and inertia. Mechanical stiffness requires a force that is
proportional to displacement and that required for an inertial load
is required to create acceleration. The energy associated with both
of these effects may be stored and will influence the dynamic
performance of the system.
Frictional forces affect both the dynamic and steady-state
response of the system. The force required to overcome friction is
usually expressed as a function of velocity and the energy used is
converted to heat and lost to the environment.
The forms of friction are usually classified as:
Stiction or static friction
required to initiate movement
Coulomb friction
proportional to the load force, independent of speed
Viscous friction
proportional to speed, independent of the load force
Windage
proportional to speed squared (sometimes higher)
In many applications coulomb and viscous friction
predominate.
It is convenient to plot the load characteristics in terms of
speed and force (or torque) which will provide a means for matching
them with those of the hydraulic system where flow is related to
speed and pressure related to force.
2Valve characteristicsOrifices are the principal control devices
in fluid power systems. Usually they take the form of a circular
hole or, as in the case of hydraulic control valves, an annular
ring formed between a spool valve and the valve body.
2Orifice flow
Figure 1 - Sharp edged orifice.
From elementary dynamic considerations, it can be shown for an
incompressible fluid that the fluid velocity through the vena
contracta, Figure 1 may be found using the following
relationship:
(1)whereu = Fluid velocity m s-1
g = Gravimetric constant m s-2
h = Head across orifice m
P1 = Up stream pressure N m-2
P2 = Vena contracta pressure N m-2
P3 = Down stream pressure N m-2
( = Fluid density kg m-3 (870 for hydraulic oil)
3 VelocityThe local maximum velocity in an ideal case can be
expressed in terms of the pressure drop. For example, if an orifice
has a 100 bar differential pressure and the fluid density is 870 kg
m-3, then:
(2)
4Discharge CoefficientA flow, Q, through an orifice can be
related to the area and the velocity. Generally:
(3)whereAo = orifice area m2Equations (1) and (3) can be
combined to obtain a relationship between the flow rate and the
differential pressure across the orifice. The area at the vena
contracta is reduced in relation to Ao, and a discharge coefficient
Cd is included giving:
(4)For high flow rates indicated by a high Reynolds Number, the
discharge coefficient for a sharp edged orifice has been shown to
be 0.62. For other shapes, guiding the flow path more effectively,
higher values can be obtained. For example, a Cd of 0.98 is
possible for a nozzle.
The orifice equation (4) is obtained by making the following
assumptions:
I. The velocity upstream of the orifice is very much less than
the velocity in the vena contracta.
II. The downstream pressure is measured at the vena
contracta.
5Flow CoefficientsIn the practical case of a control orifice the
conditions at the vena contracta are not easily measured. It is
usual to relate the flow through the orifice to the pressure drop
from inlet to outlet. In this case we can use a similar law with a
flow coefficient Cq instead of the discharge coefficient.
Note that if the orifice area is very much less than the
upstream area and the pressure P3 is the same as that at the vena
contracta, then:
6Variation in Flow CoefficientThe orifice flow coefficients
change with the nature of the flow through the orifice (Reynolds
Number Re effect). A convenient type of Reynolds Number, to use is
often termed the flow number, [(].
For most sections:
where( = Flow Number
Dh = Hydraulic diameter
m
( = Kinematic viscosity
m2 s-1The relationship between the flow coefficient and the flow
number can be seen in Figure 2
Figure 2 - Relationship between the flow coefficient and the
flow number.
When the coefficient reaches a steady value at high (, then the
flow equation can be considered a good representation of the actual
situation. Where ( is varying, the equation is not such an accurate
description. Indeed at low flow numbers the flow in fact becomes
directly proportional to the pressure drop across the orifice. At
intermediate flows, the situation cannot be easily described
mathematically.
7Pressure Recovery Downstream of the Vena ContractaConsidering
the expansion downstream of the vena contracta as a sudden
enlargement shows the theoretical reason for the pressure
recovery.
Figure 3 - Pressure characteristics through a sharp edge
orifice.
By considering the momentum force at 3, assuming that the
pressure at the vena contracta, P2 is constant across the pipe
diameter:
The pressure P3 is determined by the resistance or load in the
system down stream of the orifice. If this pressure is very low, it
follows that the pressure at the vena contracta will be very low.
In some cases it will be so low that air is released from the oil
(saturation pressure). Below this at the vapour pressure air and
vapour will be released into the fluid causing cavitation damage to
occur. In addition to cavitation, the vapour bubbles will condense
when the fluid enters a higher pressure region and the air will
remain as bubbles. Whilst some of these will be released to the
atmosphere in the reservoir, many will remain within the system.
This may cause a spongy system operation and in extreme cases
reduce the pump discharge.
8Control Valve Characteristics
Using the orifice equation the valve flow is given:
Thus the flow variation through a valve, for a given opening
area, varies as the square root of , the magnitude of which will be
limited by the supply pressure, Ps. In practice, the system
designer is more concerned with the pressure difference, Pm, that
is available across the actuator or motor and, consequently, it is
more convenient to relate the flow to the actuator load pressure
difference. The supply pressure, PS, is assumed to be constant.
Figure 4 Spool Type Control Valve
For the spool type valve of Figure 4, movement of the spool in
the direction shown will connect the B port to the outlet and the A
port to the return line to the reservoir, or tank. This type of
valve has three positions and is used as a directional control
valve DCV. Various configurations are available for the centre
position, which are discussed later. For partial openings of the
valve there will be a restriction in the flow created by the lands
of the valve as shown in Figure 5.
EMBED CDraw4
Figure 5 Orifice Restriction in Spool Valves
In spool valves, there is a peripheral flow of fluid through the
annulus formed by the valve land and the port as shown in Figure
5.
Figure 6 Spool valve
The flow from the high pressure inlet to the spool valve in
Figure 6 creates a high velocity in the outlet metering annulus so
that there is a resulting force on the spool tending to close the
valve. This arises from the difference between the pressure force
on the spool land on the left side, which is due to the inlet
pressure, PS, and that on the right hand spool land, which is less
because the pressure is reducing radially outwards due to the
increasing fluid velocity. This pressure force is equal to the
axial component of the momentum change so for a velocity U, the
momentum force is given by:
The flow angle ( depends on the valve opening and the clearance
between the spool and the valve bore but it is often given the
value of 690 attributed to the original work by Von Mises.
Four way valves can be used to control the velocity of actuators
by introducing both meter-in and meter-out restrictions into the
flow path as shown in Figure 7.
The valve position is fully variable and can be controlled
by:
Direct lever manual input.
Hydraulic pilot operated from an input lever or joystick.
Proportional solenoid
Figure 7 Four Way Valve Velocity Control
For proper design of the circuit and appropriate component
selection it is necessary to analyse the system in order to
determine the actuator pressures as a function of the actuator load
force. In this system the pressure drop across each valve land
needs to be considered as a function of the flow and the valve
position or opening.
9Analysis of the valve/actuator system9.1Actuator extending
Valve flow characteristics
For the parameters shown in Figure 6 the valve flows are given
by:
whereR1 = effective metering shape parameter (e.g. for annular
ports).
For zero pressure in the return line:
whereR2 = effective metering area
Also,
These equations give:
For a valve spool that has symmetrical metering, RS= 1Then
(1)
Equation 1 relates the pressures P1 and P2 for the valve
connected to the unequal area actuator
as represented Figure 8. The flow from the annulus is lower than
that to the piston because of its smaller area which results in a
lower pressure drop in the valve.
Actuator force
(2)
Figure 9 Interaction between the flow and the force
characteristics during extension
Equation 2 relates the actuator pressures for a given actuator
force with a positive force that acts in the opposing direction to
the extending movement of the actuator. This relationship is shown
on Figure 9 and the pressures for the valve controlling the
actuator are determined by the intersection of the lines for the
actuator and the valve at point A.
The values of these pressures can be obtained from equations 1
and 2 for the valve and actuator. The force acting on the actuator
can be in either direction.
Using a force ratio defined by:
we get:
(3)and
(4)Variations of the force will change the position of the line
on Figure 9 that represents the actuator and, hence, change the
position of the point of intersection, A, that will change the
pressure levels according to Equations 3 and 4.
For a value of R = 1, the force will be the maximum available
and is the stall force for the system. For a given application the
actuator area is chosen to provide the desired stall force at the
chosen supply pressure. This will then determine the actuator
pressures that are obtained for any other value of the force.
9.2Actuator retracting
For retraction of the actuator the valve position is reversed,
the annulus now being connected to the supply and the piston to the
return line. Following the same method for a symmetrical valve (K1
= K2 ) as for the actuator extension we get:
and
and as
Then
(5)
Figure 10 Actuator retracting
This relationship between P1 and P2 for the retracting actuator
is shown in Figure 10 where point B is the operating condition for
retraction of the actuator. It can be seen that when the valve is
reversed there is a pressure change between points A and B.
The equations for the pressures for actuator retraction are:
(5)
(6)The actuator velocity is determined from the flow equation
for the valve using the appropriate values for the pressures P1 and
P2. The selection of a valve having the necessary capacity is
determined from the maximum required velocity condition.
It should be noted that neither of the pressures can be less
than zero so, for example, during extension, the maximum value of
the force ratio, R, that is permissible in order to avoid
cavitation of the flow to the piston is given by:
For which condition:
EMBED Equation.3 9.3Valve sizingThe valve size needs to be
selected such as to provide the flow required for the specified
velocity and force conditions. In general, it is desirable to
operate the system close to its condition of maximum efficiency,
which can be obtained by considering the power transfer
process.
For simplicity consider an equal area actuator for which the
power transmitted to the load is given by;
1Here, PV is the valve pressure drop which, from the orifice
equation, can be expressed as:
2where A = the valve orifice area.
Hence:
3For maximum power at the load:
4and giving
Based on this analysis an approximation is often applied from
the maximum power condition to give the best combination of valve
and actuator sizes for a given supply pressure such that the thrust
at maximum power is equal to two-thirds the stall force.The
actuator size and the supply pressure can be selected to provide
this stall thrust and the valve size is then determined on the
basis of the maximum required value of .
Valves are rated by determining the flow at a total fixed
pressure drop across both ports and for a given valve position.
Thus the flow at any other pressure drop is given by:
Where QR = rated flow and (PR = rated pressure drop. (PR is
sometimes given as the pressure drop through only one of the
metering lands.
9.4Valves with non-symmetrical metering
The use of valves in which the metering is non-symmetrical,
normally by machining metering notches of different shapes,
provides two major advantages over symmetrical valves which
are:
The possibility to increase the maximum negative, or overrunning
force during extension (meter - out control)
The avoidance of the pressure change during reversal of the
valve as seen from Figure 11 the valve characteristic is a single
line for both directions of movement.
Figure 11 Non-symmetrical valve metering
The dotted line on Figure 11 shows the characteristics where the
valve metering ratio, RS, has the same value as the actuator area
ratio, (.
Figure 12 shows the output velocity U plotted against the force
ratio R in comparison with the particular case of an equal area
ratio actuator for which ( =1. The equal area actuator has a
symmetrical characteristic and is often used in servo systems for
this reason. The dotted line shows the effect of asymmetrical
metering where the valve-metering ratio is the same as the area
ratio of the actuator.
Figure 12 Load locus of velocity ratio against force ratio
This type of valve is used extensively for the operation of
linear actuators in mobile systems but its major disadvantages
are:
The sensitivity of the velocity to changes in the load force
demonstrated in Figure 12 where variations in the load force have
resulted in variations in the valve flow.
The control is effected by creating a pressure loss in the valve
that leads to inefficiency of operation and heat generation in the
fluid which, in some circumstances, has to be removed by a
cooler.
However, this type of control is simple, employs relative few
moving parts and provides ease of control by the operator. An
example of this type of system is that used for positioning the
mobile crane jib the velocity of which responds quickly to the
valve position selected by the crane operator. When the valve is
put to the centre position its ports are blocked and the fluid
between the valve and the actuator is trapped thus locking the
actuator into its set position. Alternative valve control methods
to reduce the power loss are discussed later.
A single pump can supply several valves where, in simple systems
the pressure of a fixed displacement pump can be controlled by a
relief valve. This system will increase the total power loss and
bypass valves and/or variable displacement pumps with pressure
compensation and load sensing are used to improve the overall
efficiency. These methods are discussed in later sections.
This method of valve control can also be used to control the
speed of hydraulic motors but, wherever possible, because of the
continuous power loss in the valve it is preferable to connect the
motor directly to the pump as a hydrostatic transmission.
9Typical Control Valves
The position of spool type valves can be controlled manually as
shown in Figure 13 using a direct acting lever for its
operation.
Figure 13 Manually Operated DCV
Figure 14 DC Solenoid Operated Proportional Valve
Valve position is often controlled using electrical solenoids
for either AC or DC supplies. Proportional valves use a DC voltage
input (usually ( 10V) to provide a continuously variable valve
position, an example of this type of valve is shown in Figure
14.
10Load Holding ValvesThe radial clearance between the valve and
its housing is carefully controlled in the manufacturing process to
levels of around 2 micron. The leakage through this space, even at
high pressures, is small but for applications where it is essential
that the actuator remains in the selected position for long periods
of time (e.g. crane jibs where any movement would be unacceptable)
valves having metal-to-metal contact have to be used.
Figure 15 Pilot operated Check ValveCheck valves such as that in
Figure 15 usually employ metal-to-metal contact but they are only
open in one direction under the action of the flow into the valve.
For their use in actuator circuits it is necessary that they are
open in both directions as required by the DCV. This function can
be obtained from a Pilot Operated Check Valve that uses a control
pressure to open the valve against reverse flow
Figure 8 shows a typical pilot operated check valve (POCV)
whereby a pilot pressure is applied onto the piston to force open
the ball check valve to allow flow to pass from port 1 to port 2
when the check valve would normally be closed. The ratio of the
piston and valve seat areas has to be chosen so that the available
pilot pressure can provide sufficient force to open the valve
against the pressure on port 1.
Figure 16 Actuator Circuit using a POCV
The use of a POCV is shown in Figure 16 where the external force
on the actuator is acting in the extend direction. With the DCV in
the centre position the check valve will be closed because the
pilot is connected to the tank return line, which is at low
pressure. Opening the DCV so as to extend the actuator the piston
side pressure, now connected to the supply, will increase.
When this pressure reaches the level at which the check valve is
opened against the pressure generated on the rod side of the
actuator by the load force, the actuator will extend. The POCV acts
as a restrictor and opens just sufficiently to allow the annulus
flow to pass through at a pressure that just resists the force on
the actuator.
Speed
Force
Viscous
Coulomb
A port
Supply
P port
Return
T port
Return
T port
High
Pressure
PS
(
P T
A B
Q1 Q2
P1 P2
Velocity UE
Force F
B
port
Note that the area of the orifice or restriction is:
Area EMBED Equation.3
ISO symbol
PS
A1
A2
EMBED Designer.Drawing.6
( = A1 /A2
P2
Relationship between the
pressures for the valve
connected to the unequal
area actuator
PS /(2
P1=PS
P1
Figure 8 Valve Pressures during Extension
A
F/A1
PS /(2
P1=PS
P1
PS - P1
Pressure
relationship for
a given force F
on the actuator
P2
F/A1
B
Extend Retract
PS
A
P2
PS /(2
P1=PS
P1
F/A1
B
Extend Retract
PS
A
P2
PS /RA2
P1=PS
P1
non - symmetrical valve
retract and extend
1.4
1.0
0.8
0.4
0
-0.6
-1.2
-1.6
-1.0 -0.6 0 0.6 1.0
Force Ratio R
Velocity ratio VR
EMBED Equation.3
Non-symmetrical valve
( = 2, RS = 2
( = 2
( = 1
115P J Chapple April 2006. Valve Controlled Systems
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