r86467 (1)
TRANSCRIPT
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Final Control Elements Characteristics
In many control systems the rate of flow of a fluid along a pipe is
controlled by a valve which uses pneumatic action to move a valve stem
and hence a plug or plugs into the flow path, so altering the size of the
gap through which the fluid can flow (Figure 6.21). The term single
seatedis used where just one plus is involved and double seatedwherethere are two. A single-seated valve has the advantage compared with
the double-seated valve of being able to close more tightly but the
disadvantages that the force on the plug is greater from the fluid and so a
larger area diaphragm may be needed.
Figure 6.22 shows the basic elements of a common form of such a
control valve. The movement of the stem, and hence the position of the
plug or plugs in the fluid flow, results from the use of a diaphragm
moving against a spring and controlled by air pressure (Figure 6.22).
The air pressure from the controller exerts a force on one side of the
diaphragm, the other side of the diaphragm being at atmospheric
pressure, which is opposed by the force due to the spring on the other
side. When the air pressure changes then the diaphragm moves until
there is equilibrium between the forces resulting from the pressiu^e andthose from the spring. Thus the pressure signals from the controller
result in the movement of the stem of the valve. There are two alternative
forms, directand reverse action forms (Figure 6.23) with the difference
being the position of the spring. The valve body is joined to the
diaphragm element by the yoke.
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6.4.1 Forms of plug
There are many forms of valve body and plug. The selection of the form
of body and plug determine the characteristic of the control valve, i.e. the
relationship between the valve stem position and the flow rate through it.
For example. Figure 6.24 shows how the selection of plug can be used to
determine whether the valve closes when the controller air pressure
increases or opens when it increases and Figure 6.24 shows how the
shape of the plug determines how the rate of flow is related to the
displacement of the valve stem:
1Linear plug
The change in flow rate is proportional to the change in valve stem
displacement, i.e.:change in flow rate = k(change in stem displacement)
where it is a constant. IfQ is the flow rate at a valve stem
displacement Sand ^max is the maximum flow rate at the maximum
stem displacement S'max, then we have:
or the percentage change in the flow rate equals the percentage
change in the stem displacement. Such valves are widely used forthe control of liquids entering cisterns when the liquid level is being
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controlled.
2 Quick-opening plug
A large change in flow rate occurs for a small movement of the
valve stem. This characteristic is used for on-oflf control systems
where the valve has to move quickly from open to closed and vice
versa.
3Equal percentage plugThe amount by which the flow rate changes is proportional to the
value of the flow rate when the change occurs. Thus, if the amount
by which the flow rate changes is Ag for a change in valve stem
position A5, then it is proportional to the value of the flow Q when
the change occurs, i.e.
where k is a constant. Generally this type of valve does not cut off
completely when at the limit of its stem travel, thus when S = 0 we
have Q = gmin. If we write this expression for small changes and
then integrate it we obtain:
And so
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Example
A valve has a stem movement at full travel of 30 mm and has a
linear plug which has a minimum flow rate of 0 and a maximum
flow rate of 20 mVs. What will be the flow rate when the stem
movement is 15 mm?
The percentage change in the stem position from the zero setting is
(15/30) X 100 = 50%. Since tlie percentage flow rate is the same asthe percentage stem displacement, then a percentage stem
displacement of 50% gives a percentage flow rate of 50%, i.e.
10 mVs.
ExampleA valve has a stem movement at full travel of 30 nun and an equal
percentage plug. This gives a flow rate of 2 mVs when the stem
position is 0. When the stem is at fiill travel there is a maximum
flow rate of 20 mVs. What will be the flow rate when the stem
movement is 15 mm?
6.4.2 Rangeability and turndown
The term rangeability R is used for tlie ratio Qnax/Qmn, i.e. the ratio of
the maximum to minimum rates of controlled flow. Thus, if theminimum controllable flow is 2.0% of the maximum controllable flow,
then the rangeability is 100/2.0 = 50. Valves are often not required to
handle the maximum possible flow and the tenn turndown is used for the
For example, a valve might be required to handle a maximum flow
which is 70% of tliat possible. With a minimum flow rate of 2.0% of the
maximum flow possible, tlien the turndown is 70/2.0 = 35.
6.4.3 Control valve sizing
The term control valve sizingis used for the procedure of determining
the correct size, i.e. diameter, of the valve body. A control valve changes
the flow rate by introducing a constriction in the flow path. But
introducing such a constriction introduces a pressure difference between
the two sides of the constriction. The basic equation (from an application
of Bernoulli's equation) relating the rate of flow and pressure drop is:
where AT is a constant which depends on the size of the constrictionproduced by the presence of the valve. The equations used for
determining valve sizes are based on this equation. For a liquid, this
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equation is written as:
where >4v is the valve flow coefficient, Ap the pressure drop in Pa across
the valve and p the density in kg/m^ of the fluid. Because the equation
was originally specified with pressure in pounds per square inch and
flow rate in American gallons per minute, another coefficient Cv based
on these units is widely quoted. With such a coefficient and the
quantities in SI units, we have:
where Vis the specific volume of tlie steam in m^/kg, the specific volume
being the volume occupied by 1 kg. Table 6.1 shows some typical values
of ^v, Cv and the related valve sizes.
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Example
Determine the valve size for a valve that is required to control the
flow of water when the maximum flow rate required is 0.012 mVs
and the permissible pressure drop across the valve at this flow rate is
300 kPa.
Taking the density of water as 1000 kg/m^ we have
Thus, using Table 6.1, this value of coefficient indicates that the
required valve size is 960 mm.
6.4.4 Valve positioners
Frictional forces and unbalanced forces on the plug may prevent the
diaphragm from positioning the plug accurately. In order to overcome
this, valve positioners may be fitted to the control valve stem. They
position the valve stem more accurately and also provide extra power tooperate the valve and so increase the speed of valve movement. Figure
6.25 shows the basic elements of a positioner.
The output from the controller is applied to a spring-loaded bellows. A
flapper is attached to the bellows and is moved by pressure applied to the
bellows. An increase in this pressure brings the flapper closer to thenozzle and so cuts down the air escaping from it. As a consequence, the
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pressure applied to the diaphragm is increased. The resulting valve stem
displacement takes the flapper away from the nozzle until the air leakage
from the nozzle is just sufficient to maintain the correct pressure on the
diaphragm.Air
6.4.5 Other forms of flow control valves
The type of control valve described in the earlier parts of this section isbasically thesplit-body globe valve body with a plug or plugs. This is the
most commonly used form. There are, however, other forms. Figure
6.26(a) shows a 3-way globe. Other valve types are thegate (Figure
6.26(b)), the ball(Figure 6.26(c)), the butterfly (Figure 6.26(d)) and the
louvre (Figure 6.26(e)). All excise control by restricting the fluid flow.
Ball valves use a ball with a through-hole which is rotated; they have
excellent shut-oflf capability. Butterfly valves rotate a vane to restrict the
air flow and, as a consequence, suffer from the problem of requiring
significant force to move from the full-open position and so can 'stick' in
that position.
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6.4.6 Fail-safe design
Fail-safe design means that the design of a plant has to take account of
what will happen if the power or air supply fails so that a safe shut-down
occurs. Thus, in the case of a fuel valve, the valve should close if failure
occurs, while for a cooling water valve the failure should leave the valve
open. Figure 6.27 shows a direct acting valve which shuts down the fluid
flow if the air supply to the diaphragm fails.
6.5 Motors
Electric motors are frequently used as the final control element in
position or speed-control systems. The basic principle on which motors
are based is that a force is exerted on a conductor in a magnetic field
when a current passes through it. For a conductor of lengthL carrying a
current / in a magnetic field of flux densityB at right angles to the
conductor, the forceFequalsBIL.
There are many different types of motor. In the following, discussion
is restricted to those types of motor that are commonly used in control
systems, this including d.c. motors and the stepper motor. Astepper
motoris a form of motor that is used to give a fixed and consistentangular movement by rotating an object through a specified number of
revolutions or fraction of a revolution.
6.5.1 D.c. motors
In the d.c. motor, coils of wire are mounted in slots on a cylinder of
magnetic material called the armature. The armature is mounted on
bearings and is free to rotate. It is mounted in the magnetic field
produced byfield poles. This magnetic field might be produced by
permanent magnets or an electromagnet with its magnetism produced by
a current passing through the, so-termed, ^/eW coils. Whether permanent
magnet or electromagnet, these generally form the outer casing of the
motor and are termed thestator. Figure 6.28 shows the basic elements of
d.c. motor with the magnetic field of the stator being produced by acurrent through coils of wire. In practice there will be more than one
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armature coil and more than one set of stator poles. The ends of the
armature coil are connected to adjacent segments of a segmented ring
called the commutatorwhich rotates witli the armature. Brushes in fixed
positions make contact with the rotating commutator contacts. They
carry direct current to the armature coil. As the armature rotates, the
commutator reverses the current in each coil as it moves between the
field poles. This is necessary if the forces acting on the coil are to remain
acting in the same direction and so continue the rotation.
For a d.c. motor with the field provided by a permanent magnet, thespeed of rotation can be changed by changing the size of the current to
the armature coil, the direction of rotation of the motor being changed by
reversing the current in the armature coil. Figure 6.29 shows how, for a
permanent magnet motor, the torque developed varies with the rotational
speed for different applied voltages. The starting torque is proportional
to the applied voltage and the developed torque decreases with increasing
speed.
D.c. motors with field coils are classified as series, shunt, compound
and separately excited according to how the field windings and armature
windings are connected.