Strain Measurement (NEW).pptx

1. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 1
MANIPAL INSTITUTE OF TECHNOLOGY
STRAIN
Measurement

2. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 2
MANIPAL INSTITUTE OF TECHNOLOGY

3. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 3
MANIPAL INSTITUTE OF TECHNOLOGY
 Electrical resistance strain gauges are very widely used for strain
measurement.
 Its operation is based on the principle that the electrical
resistance of a conductor changes when it is
subjected to a mechanical deformation.
 Typically an electric conductor is bonded to the specimen with
an insulating cement under no-load conditions.
 A load is then applied, which produces a deformation in both
the specimen and the resistance element.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 4
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 This deformation is indicated through a measurement of the change in
resistance of an element as follows:
Resistance of a conductor,
Where
L = Length of the electrical conductor,
A = Cross sectional area of the conductor,
ρ = Resistivity of the conductor material.
In other words when the conductor is stretched, its length (L) will increase,
area (A) will decrease and hence the resistance (R) will increase.
Similarly, when the conductor is compressed resistance (R) will decrease.
2
..................(1)
l l
C
R
A D
 
 

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 5
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Bonded Resistance-strain Gauge
 The bonded gauge is a suitably shaped piece of resistance metal which is
bonded close to the surface whose strain is to be measured.
 The exploded view Fig. shows a thin wire shaped into a grid pattern, which
is cemented between thin sheets of insulating material such as paper or
plastic.
 The grid can also be made from thin metal foil. The assembled gauge is
bonded to the surface with a thin layer of adhesive and finally
waterproofed with a layer of wax or lacquer.
 The grid experiences the same strain as the material to which it is bonded.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 6
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 The gauge is most sensitive to the strain along its axial direction X-X while the
strain in the Y-Y direction occurs due to Poisson's ratio effect.
 This causes change of resistance, and may lead to an error of 2% in the
measured strain when using the wire bonded gauge.
 However, in the foil gauge the thickened ends reduce this cross-sensitivity effect
to virtually zero.
 If the direction of principal strain is not known then cluster of three or more
strain gauges are used, which are called rosettes.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 7
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 7
MANIPAL INSTITUTE OF TECHNOLOGY

8. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 8
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 8
MANIPAL INSTITUTE OF TECHNOLOGY

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 9
MANIPAL INSTITUTE OF TECHNOLOGY

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 10
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a) Single element
b) Two-element rosette
c) Three – element rosette
d) Special – purpose gauges (used
on pressurized diaphragms)

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 11
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 12
MANIPAL INSTITUTE OF TECHNOLOGY

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 13
MANIPAL INSTITUTE OF TECHNOLOGY

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 14
MANIPAL INSTITUTE OF TECHNOLOGY

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 15
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 16
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 16
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16

17. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 17
MANIPAL INSTITUTE OF TECHNOLOGY

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 18
MANIPAL INSTITUTE OF TECHNOLOGY

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 19
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 19
MANIPAL INSTITUTE OF TECHNOLOGY

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 20
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 20
MANIPAL INSTITUTE OF TECHNOLOGY

21. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 21
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 21
MANIPAL INSTITUTE OF TECHNOLOGY

22. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 22
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 22
MANIPAL INSTITUTE OF TECHNOLOGY

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 23
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 24
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 Wire type:
It consists of a very fine wire of diameter 0.025 mm
wounded into a grid shape as shown in figure and the
grid is cemented between two pieces of thin paper with
plastic or ceramic backing.
This is done in order that the grid of the wire may be
easily handled. This is securely bonded with a suitable
cement to the surface of the member in which the strain has
to be measured.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 25
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Foil type resistance strain gauge:
These gauges usually employs a foil less than 0.005 mm
thick.
The common form of foil type gauge consists of a metal foil
grid element on a thin epoxy support.
Epoxy filled with fiber glass is used for high
temperatures.
These foil type gauges are manufactured by printing on a
thin sheet of metal alloy with an acid-resistant ink, and
then the unprinted portion is etched away.
Foil gauges have the advantages of improved hysteresis,
better fatigue life and lateral strain sensitivity.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 26
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It is thinner and more flexible, thus permitting it to be applied to
fillets and sharply curved surfaces.
The common wire or foil gauges are called metallic gauges.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 27
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Semiconductor or Piezoresistive strain gauge:
Semiconductor gauges are cut from single crystals of silicon
or germanium in which are combined exact amounts of
impurities such as boron which impart certain desirable
characteristics.
The same types of backing, bonding materials, and
mounting techniques as those used for metallic gauges
can be used for semiconductor gauges.
When the gauge is bonded to a member which is strained,
causes changes of current in the semi-conductor
material.
The advantages of semiconductor gauges is their high
strain sensitivity which allows very small strains to be
measured accurately.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 28
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 A gauge whose electrical resistance increases in response
to tensile strain is known as positive or p-type
semiconductor gauge.
 On the other hand when the resistance decreases in response
to tensile strain then it is known as negative or n-type
semiconductor gauge.
The semiconductor gauge consists of a rectangular filament of about 0.05 mm thick
by 0.25 mm wide and gauge length varies from 1.5 to 12 mm as shown in Figure.

29. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 29
MANIPAL INSTITUTE OF TECHNOLOGY
Strain Gauge Metals:
 The most common metals used for the manufacture of
metallic strain gauges are:
 alloys of copper and nickel or, alloy of nickel, chromium
and iron with other elements in small percentages.
 Gauges with resistances varying from 60 Ω to 5000
Ω are available.
 The current carried by the gauges for long periods is
around 25 mA to 50 mA.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 30
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 Strain Gauge Backing Materials:
The strain-gauges are normally supported on some form of
backing material.
This provides not only the necessary electrical insulation
between the grid and the tested material, but also a
convenient carriage for handling the un-mounted gauge.
Certain types of gauges intended for high temperature
applications use a temporary backing which will be
removed when the grid is mounted.
In this case, at the time of installation the grid is
embedded in a special ceramic material that provides
the necessary electrical insulation and high-temperature
adhesion.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 31
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The desirable characteristics for backing materials
are as follows:
1. Minimum thickness consistent with other factors
2. High mechanical and dielectric strength
3. Minimum temperature restrictions
4. Good adherence to cements used, and should be non-
hygroscopic in nature.
Common backing materials include thin paper, phenolic-
impregnated paper, epoxy type plastic films, and epoxy-
impregnated fiber glass.

32. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 32
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 Bonding Materials and Methods:
Strain gauges are attached to the test item by some form of cement
or adhesive.
The adhesives commonly used are cellulose, phenolic, epoxy,
cyanoacrylate, or ceramic etc.
The desirable characteristics of strain-gauge adhesives are as
follows:
1. High mechanical and dielectric strength
2. High creep resistance
3. Minimum temperature restrictions and moisture absorption
4. Good adherence with ease of application
5. The capacity to set fast

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 33
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Treatment Regarding Preparation and Mounting of Strain
Gauges:
The following steps should be strictly followed for
proper mounting of the strain gauges:
1. The surface on which the strain gauge has to be
mounted must be properly cleaned by an emery cloth and
bare base material must be exposed.
2. Various traces of grease or oil etc must be removed by
using solvent like acetone.
3. The surface of the strain gauge coming in contact with
the test item should also be free from grease etc.

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4. Sufficient quantity of cement is applied to the cleaned
surface and the cleaned gauge is then simply placed on it. Care
should be taken to see that there should not be any air bubble in
between the gauge and the surface. The pressure applied
should not be heavy so that the cement may puncture the paper
and short the grid
5. The gauges are then allowed to set for at least eight or ten hours
before using it. If possible a slight weight may be placed by keeping
a sponge or rubber on the gauge.
6. After the cement is fully cured, the electrical, continuity of grid
must be checked by ohm meter and the electrical leads may be
welded.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 35
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 35
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Theory of strain gauges

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 36
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 36
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 37
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 37
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 38
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 38
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 39
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 39
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 40
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 40
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 41
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 41
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 46
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 47
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Resistance Strain Gauge Bridge
Unbalanced Strain Gauge Bridge

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 50
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 51
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 51
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51
2. Voltage Sensitive bridge:

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 52
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 52
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𝑖1=𝑖3 & 𝑖2=𝑖4
Assume that input impedance of the meter is infinite and therefore 𝑖𝑚=0
Output voltage 𝑒0 = 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑐𝑟𝑜𝑠𝑠 𝑡ℎ𝑒 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙𝑠 𝑏 𝑎𝑛𝑑 𝑑 = 𝑖1𝑅1 − 𝑖2𝑅2
𝑖1=
𝑒𝑖
𝑅1 + 𝑅3
𝑖2=
𝑒𝑖
𝑅2 + 𝑅4
𝑒0 =
𝑅1
𝑅1 + 𝑅3
−
𝑅2
𝑅2 + 𝑅4
𝑒𝑖
𝑅1𝑅2 + 𝑅1𝑅4 − 𝑅1𝑅2 − 𝑅3𝑅2
(𝑅1 + 𝑅3)(𝑅2 + 𝑅4)
𝑒𝑖
=
Suppose 𝑅1 changes by an amount Δ𝑅1. This causes a change in output voltage Δ𝑒0
(𝑅1+Δ𝑅1)𝑅4 − 𝑅3𝑅2
(𝑅1 + Δ𝑅1 + 𝑅3)(𝑅2 + 𝑅4)
𝑒𝑖
𝑒0 + Δ𝑒0 =
Deviding by 𝑅1𝑅4

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 53
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𝑒0 + Δ𝑒0 =
(1 +
Δ𝑅1
𝑅1
)𝑅4 −
𝑅3𝑅2
𝑅1𝑅4
(1 +
Δ𝑅1
𝑅1
+
𝑅3
𝑅1
)(1 +
𝑅2
𝑅4
)
𝑒𝑖
To simplify the relationship assume 𝑅1 = 𝑅2 = 𝑅3 = 𝑅4 = 𝑅
Under these conditions 𝑒0=0
Δ𝑅
𝑅
(4 + 2
Δ𝑅
𝑅
)
𝑒𝑖
Δ𝑒0 =
Resistance change is very small compared to initial resistance
4 >> 2
Δ𝑅
𝑅
Δ𝑒0 =
Δ𝑅
𝑅
4
𝑒𝑖 Hence Bridge sensitivity =𝑆𝐵 =
Δ𝑒0
Δ𝑅
=
𝑒𝑖
4𝑅

50. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 54
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 54
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𝑅1 = 𝑅2 = 𝑅3 = 𝑅4 = 𝑅𝑔 the strain gauge resistance and changes to ∆𝑅𝑔
Δ𝑒0 =
∆𝑅𝑔
𝑅𝑔
(4 + 2
∆𝑅𝑔
𝑅𝑔
)
𝑒𝑖
4 >> 2
∆𝑅𝑔
𝑅𝑔
Δ𝑒0 =
∆𝑅𝑔
𝑅𝑔
4
𝑒𝑖
𝐺𝑓.𝜀
4
𝑒𝑖
Δ𝑒0 =

51. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 55
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 Signal enhancement factor of the Wheatstone bridge is
defined as the maximum output due to changes in various
strain gauges of the bridge to the maximum output obtainable
with the use of only one strain gauge on the member.
 In other words, more than one active gauge (subjected to
strain), suitably arranged, can leads to increased sensitivity
or signal enhancement.
Strain gauge arrangement

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Strain gauge arrangement
 The following two factors are kept in mind while deciding the
arrangements of strain gauges on elastic members, for
measuring various physical variables:
 High sensitivity and Temperature compensation

53. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 57
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All the possible arrangement
of four strain gauges on
elastic members, for measuring
axial force with signal
enhancement factor.
Signal enhancement factor = 2(1 + ν)

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 58
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 All the possible arrangement of four strain gauges on
elastic members, for measuring bending force with
signal enhancement factor.
Signal enhancement factor = 2(1 + ν)

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 59
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 60
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 61
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 62
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 62
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 63
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 63
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 64
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 64
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 65
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 65
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 66
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 66
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 67
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 67
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 68
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 68
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 71
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 72
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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 75
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Temperature Compensation
 One of the most important and critical factors in the use of
resistance strain gauges is temperature sensitivity. Although
compensation is provided in the electrical circuitry, for a majority
of the applications, the problem is not eliminated completely.
 The following three factors are involved:
1. The gauge is unable to differentiate the strain resulting from the
differential expansion existing between the grid support and the
proper grid from the load strain.
2. The resistivity changes with the change in temperature.
3. The strong magnetic field has an influence on the gauge
performance.

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The Adjacent-Arm Compensating Gauge
The active strain gauge is installed on the
test specimen while the dummy gauge is
installed on a like piece of material and is
not subjected to any strain. The bridge is
initially balanced and therefore
If the gauges in arms 1 and 2 are alike and
mounted on similar materials and if both
gauges experience the same resistance
shift, Rt caused by temperature change,
then

71. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 77
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We see that the bridge remains in balance and the output is
unaffected by the change in temperature. When the
compensating gauge is used merely to complete the bridge and to
balance out the temperature component, it is often referred to as
the "dummy" gauge.

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Temperature compensation using more than one
active strain gauge

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 80
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Calibration of strain gauges
Normally, calibration of a measuring system means introducing an accurately
known sample of the variable that is to be measured and then observing the
system`s response.
Once a bonded strain gauge is mounted on the structure under study, it cannot be
removed or transferred.
Moreover the value of the gauge factor specified by the manufacturer of the
gauge has to be taken for granted. With these constraints, the relationship
between the strain and the output of the Wheatstone bridge has to be established.
When the gauge factor and gauge resistance are known, the shunting
method is used to calibrate strain gauge.

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In the shunting method, a small known resistance change is introduced at
the strain gauge and then an equivalent strain is calculated. This small
known resistance change is introduced at the strain gauge by shunting a
high resistance across the strain gauge as shown in diagram.

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 84
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Strain measurement on rotating shaft
The mounting of four resistance strain gauges on rotating shaft for
measuring the torque transmitted by a shaft with Wheatstone bridge
arrangement.

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During torsion of cylinder, the principal strains (tensile or compressive) exist
at 45º to the axis.
These can be measured by bonded resistance gauges, as shown in the
figure.
The output is increased by using four strain gauges so that adjacent arms of the
Wheatstone bridge have strains of opposite nature.
For taking signals in and out of the rotating shaft, slip rings and brushes are
used as shown in the figure.

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In a solid shaft of diameter d, rotating with rpm N, subjected to torque T,
Power = (2 x π x N x T) / 60
Also, Torque, T= [(fs x π x d3) / 16] ……………………..{ from DDHB }
where fs = Shear stress induced in the shaft.
Shear strain = Shear stress induced in the shaft / Shear modulus
Longitudinal strain in the shaft at 45º to the axis of the shaft, ε45 = Shear strain / 2

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The voltage output, e, is given as
Signal enhancement factor = 2
X 2
Battery Voltage E = Battery Current (R1+R4)
Sensitivity = Voltage output / Strain

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Department of Mechanical & Manufacturing Engineering, MIT, Manipal 91
MANIPAL INSTITUTE OF TECHNOLOGY

86. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 92
MANIPAL INSTITUTE OF TECHNOLOGY

87. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 93
MANIPAL INSTITUTE OF TECHNOLOGY

88. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 94
MANIPAL INSTITUTE OF TECHNOLOGY
The voltage output, e, is given as
Signal enhancement factor = 2(1 + ν)
X 2(1 + ν)
Poisson’s ratio ν = 0.3
Bridge excitation voltage E = 6V
Gauge Factor GF = 2.2
Area of the Strip A = 10 mm2

89. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 95
MANIPAL INSTITUTE OF TECHNOLOGY
= 4.785 mV
Deflection of the trace = 4.785/10 = 0.478 cm

90. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 96
MANIPAL INSTITUTE OF TECHNOLOGY

91. MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 97
MANIPAL INSTITUTE OF TECHNOLOGY
The voltage output, e, is given as
Signal enhancement factor = 4)
X 4