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Types Of Transducers

Resistive Position Transducer:

The principle of the resistive position transducer

is that the physical variable under measurement

causes a resistance change in the sensing

element.

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Resistive Position Transducer(contd)

A common requirement in industrial measurementand control work is to be able to sense theposition of an object, or the distance it hasmoved.

fig.(1)Resist ive posit ive transducer, or disp lacementtransducer.

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Resistive Position Transducer(contd)

One type of displacement transducer uses aresistance element with a sliding contact or wiper

linked to the object being monitored. Thus, the

resistance between the slider and one end of the

resistance element depends on the position of theobject. Figure (1-a) shows the construction of this

type of transducer. Figure b shows a typical

method of use. The output voltage depends on

the wiper position and therefore is a function ofthe shaft position. This voltage may be applied to

a voltmeter calibrated in inches for visual display.

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Resistive Position Transducer(contd)

Typical commercial units provide a choice ofmaximum shaft strokes from an inch or less to 5

feet or more. Deviation from linearity of the

resistance versus-distance specification can be

as low as 0.1% to 1.0%.

Consider Fig. (1-b). If the circuit is unloaded, the

output voltage V0 is a certain fraction of VT,depending on the position of the wiper:

21

20

RRR

VV

T

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Resistive Position Transducer(contd)

In its application to resistive position sensors, thisequation shows that the output voltage is directly

proportional to the position of the wiper, if the

resistance of the transducer is distributed

uniformly along the length of travel of the wiper,that is, if the element is perfectly linear.

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EXAMPLE 1

A displacement transducer with a shaft stroke of3.0 in. is applied in the circuit of Fig. The total

resistance of the potentiometer is 5 k , and the

applied voltage VT=5.0V. When the wiper is 0.9

in. from B, what is the value of the output voltageV0?

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Solution

15005000.0.3

.9.02 x

in

inR

VVxVR

RV

TT

5.10.55000

150020

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EXAMPLE 2

A resistive position transducer with a resistance of5000 and a shaft stroke of 5.0 in. is used in the

arrangement of Fig. (4). Potentiometer R3R4 is

also 5000 , and VT= 5.0 V. The initial position to

be used as a reference point is such that R1=R2(i.e.. the shaft is at midstroke). At the start of the

test, potentiometer R3R4 is adjusted so that the

bridge is balanced (VE=0). Assuming that the

object being monitored will move a maximumdistance of 0.5 in. toward A, what will the new

value of VEbe?

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Solution

If the wiper moves 0.5 in. toward A frommidstroke, it will be 3.0 in. from B.

30050000.5

0.3

2 in

inR

TTERE VRR

RV

RR

RVVV

43

4

21

2

42

VVV 5.0)5(5000

2500)5(

5000

3000

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Resistive Position Transducer(contd)

This answer is a measure of the distance anddirection that the object has traveled.

F ig (2) Basic voltage divider and resistance bri dge circuits

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2-Strain Gauge Transducers

The strain gauge is an example of a passivetransducer the; uses electrical resistance

variation in wires to sense the strain produced by

a force on the wires. It is a very versatile detector

and transducer for measuring weight pressuremechanical force, or displacement.

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Strain Gauge

Transducers(contd) The construction of a bonded strain gauge Fig (3)

shows a fine-wire element looped back and forth on amounting plate, which is usually cemented to themember undergoing stress. A tensile stress tens toelongate the wire and thereby increase its length and

decrease its cross-sectional area. The combinedeffect is an increase in resistance as seen from

Eq. (1)

(1)Where

= the specific resistance of the conductor materialin ohm

L = the length of the conductor in meters

A = the area of the conductor in square meters

A

LR

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Strain Gauge

Transducers(contd)

F ig (3) Resistive strain gauges; wire construction

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Strain Gauge

Transducers(contd) As a consequence of strain two physical qualities are of

particular interest: (1) the change in gauge resistance and(2) the change in length. The relationship between thesetwo variables expressed as a ratio is called the gaugefactor.

K. Expressed mathematically as

(2)

Where

K = the gauge factor

R = the initial resistance in ohms (without strain)

= the change in initial resistance in ohms

L = the initial length in meters (without strain)

= the change in initial length in meters

LL

RRK/

/

L

R

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Strain Gauge

Transducers(contd)

Note that the term IL in the denominator is thesame as the unit strain G. Therefore. Eq. (2) can

be written as

(3)

Robert Hooke pointed out in the seventeenth

century that for many common materials there isa constant, ratio between stress and strain.

G

RRK

/

L

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Strain Gauge

Transducers(contd)

Stress is defined as the internal force per unitarea. The stress equation is

(4)

Where

S = the stress in kilograms per Square meter

F = the force in kilogramsA = the area in square meters

A

FS

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Strain Gauge

Transducers(contd)

The constant of proportionality between stressand strain for a linear stress-strain curve is known

as the modulus of elasticity of the material. E or

Young's modulus. Hooke's law is written as

(5)

Where

E =Young's modulus in kilograms per squaremeter

S = the stress in kilograms per square meter

G = the strain (no units)

GSE

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Strain Gauge

Transducers(contd)

For strain gauge applications, a' high degree ofsensitivity is very desirable. A high gauge factor

means a relatively large resistance change for a

given strain. Such a change is more easily

measured than a small resistance change.Relatively small changes in strain can be sensed.

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Strain Gauge

Transducers(contd)

EXAMPLE 3

A resistant strain gauge with a gauge factor of 2

is fastened to a steel member, which is subjected

to a strain of 1 X 10-6. If the original resistance

value of the gauge is 130 . Calculate the changein resistance.

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Example 4

A round steel bar, 0.02 m in diameter and 0.40 min length, is subjected to a tensile force of 33.000

kg, where E=2x1010kg/m2. Calculate the elonga-

tion, L, in meters.

Solution:

mx

mkgxmx

mxkg

AE

FLL

LLAF

GSE

mxmD

A

3

21024

24

22

101.2

0)/102()1014.3(

40.0000.33

//

1014.32

02.0

2(

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Strain Gauge

Transducers(contd)

Semiconductor strain gauges are often used inhigh-output transducers as load cells. These

gauges are extremely sensitive, with gauge

factors from 50 to 200. They are however,

affected by temperature fluctuations and oftenbehave in a nonlinear manner. The strain gauge

is generally used as one arm of a bridge. The

simple arrangement shown in Fig. (2-a) can be

employed when temperature variations are notsufficient to affect accuracy significantly, or in

applications for which great accuracy is not

required.

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Strain Gauge

Transducers(contd)

The strain gauge is generally used as one arm ofa bridge. The simple arrangement shown in Fig.

(4-a) can be employed when temperature varia-

tions are not sufficient to affect accuracy

significantly, or in applications for which greataccuracy is not required.

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Strain Gauge

Transducers(contd)

However, since gauge resistance is affected bytemperature, any change of temperature will

cause a change in the bridge balance conditions.

This effect can cause an error in the strain

measurement. Thus, when temperature variationis significant, or when unusual accuracy is

required an arrangement such as that illustrated

in Fig. (4)may be used.

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Strain Gauge

Transducers(contd)

Here two gauges of the same type are mountedon the item being tested close enough together

that both are subjected to the same temperature.

Consequently, the temperature will cause the

same change of resistance in the two, and thebridge balance will not be affected by the

temperature. However one of the two gauges is

mounted so that its sensitive direction is at right

Angles to the direction of the strain.

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Strain Gauge

Transducers(contd) The resistance of this dummy gauge is not affected bythe deformation of the material. Therefore, it acts like

a passive resistance (such as R3 of Fig. 4-b) withregard to the strain measurement. Since only onegauge responds to the strain, the strain causes bridgeunbalance just as in the case of the single gauge.

Fig (4) Basic g auge brid ge circu its.