Tr ansducers - I Th e pr imar y ob jec tiv e of p rocess cont ro l is to con tro l th e ph ys ica l pa ra me ters su ch as te mpe ra tu re, pr essu re , fl ow rate, fo rc e, le ve l et c . The system used to mainta in th ese param eters constant, clo se to so me de si re d sp ecific va lu e is call ed pr oce ss co ntr ol sy ste m. These param et er s may ch an ge bec aus e of in te rn al an d ex te rn al di st urb an ces hence a constant co rr ec tiv e ac tio n i s requi re d to ke ep th es e pa ra met ers constant or wit hin th e speci fied range. The Fig . 8.1 shows the genera l ar ra ngement of a pro cess lo op . It consists of fo ur elements, 1. Pro ce ss 2. Mea su re ment 3. Co ntro lle r 4. Co nt ro l el emen t. Parameter P Measurement of parameter Fo r the pr op er feed ba ck, it is ne ce ss ar y to m easu re the value of th e actual pa ra mete r P. Mos t o f th e cont ro ll ers are el ec tr on ic in nat ure an d he nc e re qu ir e el ectr ic al in pu t . Hence fe ed ba ck s ig na l requ ir ed is in el ec tr ic al fo rm in most of th e prac ti ca l process lo ops. But actual pa rame te r is tempe ratu re , pr essu re , le ve l et c . Hence a devic e is required in th e fe edback pa th whic h wil l not only measure th e output paramete r but will produc e pr opor ti on al an al og si gn al in th e el ectr ic fo rm . Many tim es th e devic e is required to measure th e physic al parameter and produce th e proporti onal sig nal whic h is als o no ne lec tri c su ch as pne um at ic pr essu re . So i n bro ad sense a tra ns du cer co nv erts on e fo rm of e nergy to anoth er fo rm. But th e el ec tr ic al transduce r pro duces an el ect ri cal sig nal
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Transducers - I
The primary objective of process control is to control the physical parameters such as
temperature, pressure, flow rate, force, level etc. The system used to maintain these
parameters constant, close to some desired specific value is called process control system.
These parameters may change because of internal and external disturbances hence a
constant corrective action is required to keep these parameters constant or within the
specified range.
The Fig. 8.1 shows the general arrangement of a process loop. It consists of four
elements,
1. Process 2. Measurement 3. Controller 4. Control element.
Parameter
P
Measurementof parameter
For the proper feedback, it is necessary to measure the value of the actual parameter P.
Most of the controllers are electronic in nature and hence require electrical input. Hence
feedback signal required is in electrical form in most of the practical process loops. But
actual parameter is temperature, pressure, level etc. Hence a device is required in the
feedback path which will not only measure the output parameter but will produce
proportional analog signal in the electric form. Many times the device is required to
measure the physical parameter and produce the proportional signal which is also
nonelectric such as pneumatic pressure. So in broad sense a transducer converts one form
of energy to another form. But the electrical transducer produces an electrical signal
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proportional to the nonelectrical quantity to be measureQ. But as we are interested in the
electrical instrumentation, a transducer can be defined as,
A device which converts a physical quantity into the proportional electrical signal is
called a transducer.
The electrical signal produced may be a voltage, current or frequency. A transduceruses many effects to produce such conversion. The process of transforming signal f rom one
f orm to other is called transduction. A transducer is also called pick up.
Actually, electrical transducer consists of two parts which are very closely related to
each other. These two parts are sensing or detecting element and transduction element.
The sensing or detecting element is commonly known as sensor.
Definition states that sensor is a device that produces a measurable response to a
change in a physical condition.
The transduction element transforms the output of the sensor to an electrical output,
as shown in the Fig. 8.2.
Non-elect
quantity
ricalSensing
SensorTransduction
Elec
element response element sig
trical
nal
The common range of an electrical signal used to represent analog signal in the
industrial environment is 0 to 5 V or 4 to 20 mA. In industrial applications, nowadays, 4
to 20 mA range is most commonly used to represent analog signal. A current of 4 m A
represents a zero output and current of 20 mA represents a full scale value i.e. 5 V in caseof voltage representation. The zero current condition represents open circuit in the signal
transmission line. Hence the standard range is offset from zero.
Many a times, the transducer is a part of a circuit and works with other elements of
that circuit to produce the required output. Such a circuit is called signal conditioning
circuit.
A transducer is a device that receives energy from one system and transmits it to
another in diff erent form. Basically there are two types of transducers; namely electrical
and mechanical. The mechanical transducers are those primary sensing elements that
respond to changes in the physical condition of a system and gives output in diff erent
f orm. For example, when a bimetallic strip is subjected to a temperature change then the
output is the mechanical displacement of the strip. The mechanical transducers are
distinguished from the electrical transducers on the basis of the output signal generated.
The mechanical transducers generate output signal which is mechanical by nature. The
electrical transducers respond to non-electrical quantities but generate output signal which
is electrical by nature. It is practically always possible to use either mechanical or electrical
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iii) Resistance of corrosion,
iv) Accessibility of the transducer for later repairs.
4. Measuring System Compatibility : The transducer selected and the electrical
system used for measurement should be compatible. The output impedance of the
transducer and the impedance imposed by the measuring system must be such
that one does not adversely affect the other.
5. Cost and Availability: General factors involved in selection are cost, availability,
basic simplicity, reliability, and low maintenance.
While selecting transducers of comparatively equal merits f or a given application, the
one that is most simple in operation and contains minimum number of moving parts
would usually be selected.
Transducers are selected which do not require excessive repair or continuous
calibration checking.
The selection of a transducer for a given application is normally a compromise
beh'een a number of factors discussed above.
In electrical circuits, there are combinations of three passive elements : resistor,
inductor and capacitor. These three passive elements are described with the help of the
primary parameters such as resistance, self or mutual inductance and capacitance
respectively. Any change in these parameters can be observed only if they are externally
powered. We have studied that the passive transducers do not generate any electrical
signal by themselves and they require some external power to generate an electrical signal.
The transducers based on variation of parameters such as resistance, self or mutualinductance capacitance, due to an external power are known as passive transducers. Hence
resistive transducer, inductive transducer and capacitive transducer are the basic passive
transducers.
In general, the resistance of a metal conductor is given by,
pL
A
Resistivity of conductor (D m)
Length of conductor (m)
Area of cross-section of conductor (m 2)
The electrical resistive transducers are designed on the basis of the methods of
"arintioll o f anyone of the qnantities in above equation; such as change in length, change
in iueil of cross-section and change in resistivity.
where p --
L
A
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The sensing element which is resistive in nature, may be in different forms depending
u p o n the mechanical arrangement. The change in pressure can be sensed by Llsing
~nsitive resistive elements. The resistance pressure transducers may use Bellow,
Diaphragm or Bourdon tube.
Resistance
lead
Resistance
leads.
Resistancecontact.
Fig. 8.17 Resistance pressure transducer
8 .9 Resistance Position Transducer
In many industrial measurements and control applications, it is necessary to sense
position of the ob ject or the distance that object travels. For such applications, simple
resi~tanceposition transducer is very useful.
It works on the principle that resistance of the sensing element changes due to the
wiations in physical quantity being measured.
A simple resistance position transducer is as shown in the Fig. 8.18 (a).
Shaft ~: : : = = = = = = Wiper- R 1
W
V in+
R2
W Vout
B
(b) Equivalent circuit
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The transducer consists a sliding contact or wiper. A resistive element is mounted with
the sliding contact which is linked with the ob ject whose position is to be monitored.
Depending upon the position of the object, the resistance between slider and the one end
of resistive element varies. The equivalent circuit is as shown in the Fig. 8.18 (b). T h e
output voltage Vout depends on the position of the wiper. Thus depending upon positionof the wiper, the output voltage is given by,
Thus Y o u I is proportional to R2 i.e. wiper position. The output voltage is measured
using voltmeter which is calibrated in centimeters and allows direct readout of the object
position.
)1). Example 8.1 : A r esistance posit ion transducer uses a sha f t with a stro ke of 50 CI11.T h e
tot al resistance of t he po t ent iomet er is 5ill. Calculat e out put voltage when w iper is 1 0 e m
f rol11 e xtreme end if a p plie d v oltage is 5 V.
Solution: The equivalent circuit is as shown in the Fig. 8.19.
R2
= 10 cm x 5 K = 1 kn50cm
VOUl
~
The strain gauge is a passive resistive transducer which is based on the principle of
conversion of mechanical displacement in to the resistance change.
A knowledge of strength of the material is essential in the design and construction of
machines and structures. The strength of the material is normally characterized in terms of
stress, which is defined as the force experienced per unit area, and is expressed in pressure
units. Stress as such cannot be directly measured. It is normally deduced f rom the changes
in mechanical dimensions and the applied load. The mechanical def ormation is measured
with strain-gauge elements. The strain is defined as the change, ( t d ), in length, (I), per unit
length and is expressed as t : . ; { in microstrains.
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Breaking
stress
It is observed that the curve is linear as long as the stress is k ept below the elasticmits.Strain measurements are usually carried out on the free surface of a body. Normally
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The most common materials used for wire strain gauges are constantan alloys
containing 45% Nickel and 55% Copper, as they exhibit high specific resistance, constant
gauge factor over a wide strain range, and good stability over a reasonably large
temperature range (from O°C to 300°C). For dynamic strain measurements, Nichrome
alloys, containing 80% Nickel and 20% Chromium are used. They can be compensated for
temperature with platinum.
Bonding cements are adhesives used to fix the strain gauge onto the test specimen.
This cement serves the important function of transmitting the strain from the specimen to
the gauge-sensing element. Improper bonding of the gauge can cause many errors.
Basically, the cement can be classified under two categories, viz, solvent-setting cement
and chemically-reacting cement. Duco cement is an example of solvent-setting cements
which is cured by solvent evaporation. Epoxies and phenolic bakelite cement are
chemically-reacting cements which are cured by polymerization. Acrylic cements are
contact cements that get cured almost instantaneously.
The proper functioning of a strain gauge is wholly dependent on the quality of
bonding which holds the gauge to the surface of the structure undergoing the test.
8.10.2 Derivation of Gauge Factor
The gauge factor is defined as the unit change in resistance per unit change in length.
It is denoted as K or S. It is also called sensitivity of the strain gauge.
S = ~RjR
~l/l
Length of the gauge wire in unstressed condition
~l = Change in length in stlessed condition.
Derivation: Consider that the resistance wire is under tensile stress and it is deformed
by ~I as shown in the Fig. 8.14.
= Length of the wire in m
A = Cross-section of the wire in m2
When uniform stress (J is applied to th.is wire along the length, the resistance R
changes to R + ~R because of change in length and cross-sectional area.
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I I
: d :~I I
J - l - J
rR changes
1to
R+LiR
F
Fig. 8.21 Deformed resistance wire
f ' . . 1
a = Stress = -I
f ' . . I I I =Per unit change in length
f ' ..A / A =Per unit change in area
f ' ..p/p =Per unit change in resistivity
(specific resistance)
Now R =p i
A
d( ~ IdR A ) P 0 1 pi oA I op
.. - --=-----+--da da A o a A20 a A o a
Note thato~( ~ )
1 oA=---A20 a
Multiply both sides by i,1 dR p 01 1 pi o A I op
--------+--Rd a RA oa R A 2 o a RA ca
Using R ~ on right hand side,
1 dR 1 al 1 oA 1 (lp=--- _ ._+--
Rda l oa A O G P o a
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dl dA a p---+-
I A p
/ ' ) . 1 / ').A / '). p---+-
I A p
Key Point : ThliS fo r finit e str ess, total change in resistance is dl le t o fractional cha nge in
len gth , area 17nd resi stivity.
For a circular wire, A = ~d24
a A~(2d) ad=
as 4 . as
1 a A~~(2d)ad=
A as A 4 as
1 a A 1 (2d) ad=A as (d2) a s
Cancelling as,a A
~ad i.e. / ').A 2 / ').d
... ( 2)----
A d A d
Now the Poisson/s ratio 1 1 for the wire is defined as the ratio of strain In lateral
direction to strain in the axial direction.
/ ').d/d1 1 = - / ' ) . I j I = Poisson' s ratio
/ ' ) . d d = -11 ( ~/ )
Using (2) and (3) in (1)/
t.R .t .l_ nd + t.p = t .1_2[ _ 1 1 t .l]+ t.p
Rid p I I P
t.R / ' ) . 1 t.pR = [[1 +21 l]+p-
Neglecting piezoelectric effect, / ') .p can be neglected.p
))). Example 8.2 : A res istance strain gau ge with a ga ug e f ac to r o f 4 is cemented to a steel
member which is subjec t ed t o a s tr ai n o f 1x 10-6. If t he or iginal gauge resist a nce i s 15 0 n,calculat e the change in r es istance .
Solution : The gauge factor is given by,
S = t :.RjR
t : . l /l
t : . l
SRi
8.10.3 Types of Strain Gauges
Depending upon the principle of operation and their constructional features, strain
gauges are classified as mechanical, optical, or electrical. Of these, the electrical strain
gauges are most commonly used.
1. Mechanical Gauges : In these gauges, the change in length, t :.l , is magnified
mechanically using levers or gears. These gauges are comparatively larger in size,
and as such can be used in applications where sufficient area is available on the
specimen for fixing the gauge. These gauges are employed for static strain
measurements only.
2. Optical Gauges: These gauges are similar to mechanical strain gauges except that
the magnification is achieved with multiple reflectors using mirrors or prisms. In
one type a plain mirror is rigidly fixed to a movable knife-edge. When stress is
applied, the mirror rotates through an angle, and the reflected light beam from the
mirror subtends an angle twice that of the incident light. The measurement
accuracy is high and independent of temperature variations.
3. Electrical Strain Gauges : The electrical strain gauges measure the changes that
occur in resistance, capacitance, or inductance due to the strain transf erred fromthe specimen to the basic gauge element. The most commonly used strain gauge is
the bonded resistance type of strain gauge. The other two, viz., capacitance and
inductance type are used only in special types of applications.