Bryan L. Programmable controllers. Theory and implementation
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Data Measurements
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Changes in temperature affect strain gauge circuits, so these circuits require
temperature compensation. A dummy gauge, added to the bridge-condition-
ing circuit, can provide this compensation (see Figure 13-25). As the tempera-
ture increases, the resistance in the measuring gauge changes as a result of
both temperature and pressure. The resistance in the dummy gauge also
changes due to temperature, since it is made of the same material as the
measuring gauge. However, it does not change due to force because stress is
measured in only one direction. Thus, the dummy gauge provides a value for
resistance change based solely on temperature change. The bridge circuit
uses the information from the dummy circuit to compensate for temperature
resistance change in the measuring gauge value, resulting in a resistance
based on force only. The resistance-equivalent signal provided by a strain
gauge is usually very small, so the signal requires amplification through a
transmitter to provide the proper voltage level to a PLC analog input.
BOURDON TUBES
A Bourdon tube is a pressure transducer that converts pressure measure-
ments into displacement. This displacement is proportional to the pressure
being measured. The different types of Bourdon tubes include spiral, helical,
twisted, and C-tube.
Figure 13-24. (a) Bonded and (b) unbonded strain gauges.
Fine Resistive Wire
Linear
Displacement
(b)
(a)
Stress/Force
Gauge Cemented
to Support
Fine Resistive
Wire (tension)
R
1
R
4
R
3
R
2
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Figure 13-26 illustrates the most commonly used type of Bourdon tube, the
C-tube. The pressure inlet end of the tube is fixed, while the other end of the
tube is free to move. Since the intermediate conversion is displacement, a
linear variable differential transformer converts the pressure in the tube
into a proportional electrical signal. Hence, the Bourdon tube and the
LVDT perform a pressure measurement–to–linear displacement–to–electri-
cal signal conversion.
Figure 13-25. Strain gauge using a dummy gauge to compensate for changes in
temperature.
Figure 13-26. Illustration of a Bourdon C-tube.
Stress/Force
Strain gauge
not active
Strain gauge
active
D
R
1
R
3
R
2
R
4
R
3
R
4
Force
Strain gauge
not active
Active strain
gauge responds
to force applied
in its direction
R
3
R
4
Core
LVDT
Mounting Block
Output
Input
Spring
Pressure Line
Bourdon C-Tube
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LOAD CELLS
Load cells are force or weight transducers based on a direct application of
bonded strain gauges. These devices measure deformations produced by
weight. Load cells are used in many applications, especially ones that require
weight measurements.
13-7 FLOW TRANSDUCERS
Flow transducers measure the flow of materials in a process. This flow of
materials can be in solid, gas, or liquid form. All flow control applications
utilize the term Q, or rate of flow, to define flow measurement in the system.
In this section, we will discuss the rate of flow for each kind of material—
solid, liquid, and gas—and the transducers used to measure them.
SOLID FLOW TRANSDUCERS
Solid flow is typically measured with a strain gauge–based load cell trans-
ducer, which measures the weight of the product. Solid flow measurement
frequently integrates the use of a conveyor or belt product transporter with a
load cell. The units generally used for this type of flow measurement are
lbs/min or kg/min. Figure 13-27 illustrates an example of how a load cell
measures the flow of solids. The equation that describes the flow (Q) is:
Q
WV
L
=
Figure 13-27. Load cell measuring the flow of solids.
Conveyor
Velocity (V)
Weight
(W)
Length
L
Load Cell Transducer and
Signal Conditioning Circuit
Hopper
W
L
V
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EXAMPLE 13-9
A conveyor transports material that is weighed on a platform 2
meters in length. A load cell, which is connected to an analog input
module through a bridge circuit and an amplifier, must weigh 50 kgs
of the material. The required flow is 1200 kgs/min. Find the speed at
which the conveyor must run to obtain the required flow. Also, suggest
how to control the conveyor so that the flow rate remains constant.
S
OLUTION
The velocity of the conveyor is expressed as:
Q
WV
L
V
QL
W
=
=
=
=
()()1200 2
50
48 m/min
To keep the flow rate constant, a PLC could control the speed of the
conveyor by either computing the flow rate and making changes to a
motor or by changing the drive reference speed of the motor. It could
also control the analog valve, varying the hopper output according to
the required flow rate and speed.
where:
Q
W
V
L
=
=
=
=
the rate of flow
the mass/weight of the solid
the velocity/speed of the moving transporter
the length of the weight transducer (load cell)
If English units are used—pounds, feet, and feet/min—then Q will be
expressed in lbs/min. Conversely, if metric units are used—kg, meters, and
meters/min—then Q will be expressed in kg/min.
FLUID FLOW TRANSDUCERS
To measure fluid flow, you must measure one of two conditions in the process
line: pressure differential or fluid motion. The two most common devices for
measuring the pressure differential in a process line are Venturi tubes and
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orifice plates. One of the most common fluid flow transducers for detecting
fluid motion is the turbine flow meter. This transducer transforms flow
directly into electrical signals.
Pressure-Based Fluid Flow Meters. Both the Venturi tube and the orifice
plate are based on the Bernoulli effect, which relates flow velocity to the
pressure differential between two points. These fluid flow meters use pressure
transducers, which transform pressure into an electrical signal to determine
the pressure differential. The strain gauge and the Bourdon C-tube (see
Section 13-5) are the two types of transducers most commonly used in
pressure-based flow meters. These transducers use the bridge circuit and
LVDT techniques, respectively, to convert measured pressure values into
electrical signals. If low pressures are to be measured, a Venturi tube or orifice
plate may incorporate a low-pressure transducer, such as a bellows, dia-
phragm, or capsule to enhance the pressure reading resolution. Figure 13-28
shows these low-pressure transducers.
Figure 13-29 illustrates a diagram of a Venturi tube, while Figure 13-30
shows an orifice plate flow transducer. The pressure differential ∆P in these
devices is equal to the difference in pressures P
1
and P
2
. The value ∆P also
relates to the velocity of the fluid through the Bernoulli effect. The velocity
at point P
2
as a function of ∆P is:
VkP=∆
where:
V
PPP
k
=
=−
=
the fluid velocity
a constant
∆
12
Figure 13-28. Low-pressure transducers.
Courtesy of Schaevitz Engineering, Pennsauken, NJ
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Figure 13-29. Venturi tube diagram and the pressure and velocity at points P
1
and P
2
.
Figure 13-30. Orifice plate flow transducer.
PressureVelocity
Pipe Pipe
P
1
P
2
P
1
P
2
V
1
V
2
Outlet
Cone
Inlet
Cone
Inlet
Throat
Pressure
P
1
P
1
P
2
P
2
Flow
Pipe
Outside
Orifice
Hole
Orifice
Plate
Orifice
Plate
Differential
Pressure
Measurement
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The constant k takes into account the density of the fluid, the ratio of pipe to
obstruction at cross-sectional points P
1
and P
2
, temperature, and other
factors. The equation to obtain the flow rate measurement is:
QVA
Ak P
KP
=
=
=
∆
∆
where:
V
A
KkA
=
=
=
the fluid velocity
the cross-sectional area of the pipe
a new constant composed of times the area
2
The flow rate value Q gives us the volume per unit time of the flow (ft/min
× ft
2
= ft
3
/min). Note that the velocity times the area at point 1 (V
1
A
1
) is equal
to the velocity times the area at point 2 (V
2
A
2
).
EXAMPLE 13-10
Illustrate the PLC connections and functions necessary to implement
the ratio control computation shown in Figure 13-31.
Figure 13-31. Ratio control computation application.
Mixer
ON/OFF
Valve
Product B = 40% Product A
Product C = 32% Product A
Product C
ON/OFF
Valve
0–10 VDC
Differential
Pressure Flow
Meter (Orifice)
–10 to +10 VDC
Product B
Product A
ON/OFF
Valve
ON/OFF
Valve
0–10 VDC
Differential
Pressure Flow
Meter (Orifice)
–10 to +10 VDC
Differential
Pressure Flow
Meter (Orifice)
–10 to +10 VDC
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SOLUTION
To implement the ratio control of products B and C at the specified
percentage of product A (wild flow), we must read the differential
pressures (
DP
) from the orifice flow meter and control the output of the
analog servo valves. Figure 13-32 illustrates this ratio control imple-
mentation using flow ratio as the process variable.
The discrete output (120 VAC) is connected to the ON/OFF valve,
which allows each of the products to flow. Each DP instrumentation
symbol represents the differential pressure measurement from the
orifice flow meter. These pressure measurements are input to the
analog input modules (–10 to +10 VDC). The flow rate for each
product, A, B, and C, is:
QK P
QK P
QK P
AAA
BBB
CCC
=
=
=
∆
∆
∆
Figure 13-32. Ratio control implementation.
Mixer
To 120 VAC
Discrete Ouput
in PLC
CB
A
DPDP
DP
120 VAC
Discrete
Output
120 VAC
Discrete
Output
–10 to +10
Analog
Output
–10 to +10
Analog
Output
–10 to +10
Analog
Input
–10 to +10 VDC
Analog
Input
0–10 VDC
Analog
Output
120 VAC
Discrete
Output
Programmable Controller
∆
P
B
∆
P
A
∆
P
C
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where
K
A
,
K
B
, and
K
C
are the given constants. The square root value
of the analog input ∆
P
should be taken after the input count value
corresponding to it has been converted to engineering units (through
linearization, etc.). As product A flows, the PLC computes the flows of
products B and C to maintain the proper ratios between A, B, and C
(B = 0.40A and C = 0.32A). The PLC must control the output control
valves for products B and C to maintain the proper ratios.
Motion Detection Fluid Flow Meters.
The turbine flow meter is one of the
most common types of motion detection flow meters. This device is used in
applications that measure liquid and gas flows, as well as in applications with
very low flow rates. Turbine meters are widely used in petrochemical and
pipeline transfers of petroleum flows. Special types of turbine flow meters are
also used in liquid oxygen and nitrogen gas-metering applications.
A turbine meter consists of a multibladed rotor, which is suspended in a liquid
flow. The fluid flow passing through the blades creates a rotary motion in
the turbine. This rotary motion creates a magnetic flux that is sensed by a
coil inside the turbine flow meter. The coil changes the flux into a small
voltage (as low as 10 to 20 mV) and then amplifies it. This design allows the
turbine meter to convert the movement of its blades into output pulses that are
proportional to the volume passing through the turbine. The output pulses
generally provide information in gallons per minute (gpm). Some turbine
meters also provide an analog output proportional to the flow rate being
measured. Figure 13-33 illustrates a simple diagram of a turbine flow meter.
Figure 13-33. Turbine flow meter.
EXAMPLE 13-11
A programmable controller system receives an analog signal from a
turbine flow meter. The flow rate is given as 60 gpm and the area of the
pipe is 2 square inches. Find the velocity of the flow to be displayed
in feet per second on a four-digit LED display.
Output Pulses/Voltage
Pipe Pipe
Flow
Signal-Conditioning
Circuit
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SOLUTION
The flow rate of the fluid is described by :
QV
A
=
where:
Q
V
A
=
=
=
the flow rate
the velocity of the flow
the cross- sectional area of the pipe
The velocity of the flow is:
V
Q
A
=
Note that the units given must be converted to obtain the velocity in
ft/sec. To convert gallons to cubic feet, we must first convert gallons
to cubic meters and then to cubic feet:
1 gal 3.785 10 m
m ft
–3 3
33
=×
=13531.
Therefore:
1 3 785 10 35 31
0 1336
3
gal ft
ft
3
3
=×
(
)
(
)
=
−
..
.
The cross-sectional area of 2 square inches is equal to 0.0139 square
feet and 60 gpm is equal to 1 gallon per second. So, the velocity in
ft/sec is:
V
=
=
()( . )
.
.
1 0 1336
0 0139
9 61 ft/sec
Hence, to obtain the velocity of a fluid in a pipe in feet/second when
the flow rate is given in gpm and the area is given in square inches, the
following equation can be used:
V
Q
A
(
.
ft/sec)
gpm
(sq in)
=
(
)
(
)
0 3208