Transcript Transducers

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.
Resistive Position Transducer(cont’d)
 A common requirement in industrial measurement and
control work is to be able to sense the position of an object,
or the distance it has moved.
fig.(1) Resistive positive transducer, or displacement transducer.
Resistive Position Transducer(cont’d)
 One type of displacement transducer uses a resistance
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
the object. 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 of the shaft position. This voltage may be applied
to a voltmeter calibrated in inches for visual display.
Resistive Position Transducer(cont’d)
 Typical commercial units provide a choice of maximum 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:
V0
R2

VT R1  R2
Resistive Position Transducer(cont’d)
 In its application to resistive position sensors, this equation
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.
EXAMPLE 1
 A displacement transducer with a shaft stroke of 3.0 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 voltage V0?
Solution
R2 
0.9 in.
x 5000  1500
3.0 in.
V0 
R2
1500
VT 
x 5.0 V 1.5V
RT
5000
EXAMPLE 2
 A resistive position transducer with a resistance of 5000 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 maximum distance of 0.5 in. toward A, what will the new
value ofVE be?
Solution
 If the wiper moves 0.5 in. toward A from midstroke, it will
be 3.0 in. from B.
3.0 in
R2 
 5000   300
5.0 in
VE  VR 2  VE 4 
R2
R4
VT 
VT
R1  R2
R3  R4
 3000 
 2500 

(
5
V
)



 (5V )  0.5 V
 5000 
 5000 
Resistive Position Transducer(cont’d)
 This answer is a measure of the distance and direction that
the object has traveled.
Fig (2) Basic voltage divider and resistance bridge circuits
2-Strain Gauge Transducers
 The strain gauge is an example of a passive transducer 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 pressure
mechanical force, or displacement.
Strain Gauge Transducers(cont’d)
 The construction of a bonded strain gauge Fig (3) shows a fine-
wire element looped back and forth on a mounting plate, which is
usually cemented to the member undergoing stress. A tensile
stress tens to elongate the wire and thereby increase its length and
decrease its cross-sectional area. The combined effect is an
increase in resistance as seen from
Eq. (1)
R
L
A
(1)
Where
  = the specific resistance of the conductor material in ohm
 L = the length of the conductor in meters
 A = the area of the conductor in square meters
Strain Gauge Transducers(cont’d)
Fig (3) Resistive strain gauges; wire construction
Strain Gauge Transducers(cont’d)
 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 these two variables expressed as a ratio is
called the gauge factor.
 K. Expressed mathematically as
K 
R / R
L / L
Where
 K = the gauge factor
 R = the initial resistance in ohms (without strain)
 R = the change in initial resistance in ohms

L = the initial length in meters (without strain)
 L = the change in initial length in meters
(2)
Strain Gauge Transducers(cont’d)
 Note that the term L IL in the denominator is the same as
the unit strain G.Therefore. Eq. (2) can be written as
R / R
G
(3)
Robert Hooke pointed out in the seventeenth century that for
many common materials there is a constant, ratio between
stress and strain.
K
Strain Gauge Transducers(cont’d)
 Stress is defined as the internal force per unit area. The stress
equation is
S
F
A
Where
 S
= the stress in kilograms per Square meter
 F
= the force in kilograms
 A
= the area in square meters
(4)
Strain Gauge Transducers(cont’d)
 The constant of proportionality between stress and 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
S
E
(5)
G
Where
 E
=Young's modulus in kilograms per square meter
 S
= the stress in kilograms per square meter
 G
= the strain (no units)
Strain Gauge Transducers(cont’d)
 For strain gauge applications, a' high degree of sensitivity 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.
Strain Gauge Transducers(cont’d)
 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 change in resistance.
Solution
R / R R / R
K

L / L
G
R  KGR  (2) (1x10 6 ) (130)  260
Example 4
 A round steel bar, 0.02 m in diameter and 0.40 m in length,
is subjected to a tensile force of 33.000 kg, where E=2x1010
kg/m2. Calculate the elongation, L, in meters.
 Solution:
2
2
 0.02 m 
D
A(    
  3.14 x 10  4 m 2
2
 2 
S F/A
E 
G L / L
33.000kg x 0.40m
FL
L 

0
4
2
10
2
AE (3.14 x 10 m ) (2 x 10 kg / m )
 2.1 x 10 3 m
Strain Gauge Transducers(cont’d)
 Semiconductor strain gauges are often used in high-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 often
behave 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 not sufficient to affect accuracy significantly, or in
applications for which great accuracy is not required.
Strain Gauge Transducers(cont’d)
 The strain gauge is generally used as one arm of a bridge. The
simple arrangement shown in Fig. (4-a) can be employed
when temperature variations are not sufficient to affect
accuracy significantly, or in applications for which great
accuracy is not required.
Strain Gauge Transducers(cont’d)
 However, since gauge resistance is affected by temperature,
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 variation is
significant, or when unusual accuracy is required an
arrangement such as that illustrated in Fig. (4) may be used.
Strain Gauge Transducers(cont’d)
 Here two gauges of the same type are mounted on 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 the
bridge 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.
Strain Gauge Transducers(cont’d)
 The resistance of this dummy gauge is not affected by the
deformation of the material. Therefore, it acts like a passive
resistance (such as R3 of Fig. 4-b) with regard to the strain
measurement. Since only one gauge responds to the strain, the
strain causes bridge unbalance just as in the case of the single
gauge.
Fig (4) Basic gauge bridge circuits.