strain gauges
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Applications of Resistance Strain Gauges
in Measurements
Deepak Garg13209010ME 1st Year
STRAIN GAUGES
• A Strain Gauge is a device used to measure the strain of an object
• The gauge is attached to the object by a suitable adhesive
• As the object is deformed, the foil is deformed, causing its electrical resistance to
change
• The resistance change is commonly measured using a Wheatstone bridge
• The most common type of strain gauge consists of an insulating flexible backing which
supports a metallic foil pattern
What’s the Wheatstone Bridge?
• Wheatstone bridge is an electric circuit suitable for detection of minute resistance
changes., therefore used to measure resistance changes of a strain gage
• The bridge is configured by combining four resistors as shown in Fig.• Initially R1=R2=R3=R4, in this condition no
output voltage is there, e=0
• When one of the Resistances is replaced by strain
Gauge attached to the object whose strain is to be
measured and load is applied, then there is small
change in the resistance of gauge, hence some output
voltage is there which can be related to strain as
From this, strain can be easily determined using the relation
Half Bridge Configuration
To increase the sensitivity of measurement,
two strain gauges are connected in the
bridge, this type of configuration is called as
Half bridge as shown in fig. and the output
voltage and strain can be related as
When gauges are connected to adjacent
arms and
When gauges are connected to opposite
arms
Full Bridge Configuration
To further enhance the sensitivity, all 4
resistances are replaced by strain gauges.
While this system is rarely used for strain
measurement, it is frequently applied to
strain-gage transducers. When the gages at
the four sides have their resistance changed
to R1 + ΔR1, R2 + ΔR2, R3 + ΔR3 and R4
+ ΔR4, respectively, the bridge output
voltage,
e, is
Or
Where K is the Gauge Factor.
Applications of 2-gage system (Strain Cantilever)
The 2-gage system is mostly used for the
following Case
•To measure the bending Strain
•To measure the tensile strain
To measure the Bending Strain,
Configuration 1 is used as shown in fig I
because output voltage from the circuit would
become if fig II is used.
To measure the Tensile strain, Configuration
shown in Fig II is used and not fig I as output
voltage from circuit become zero in the case of
tensile loading.
Fig I
Fig II
Temperature Effects and Need for Temperature Compensation
Measurements are performed with strain gauges in mechanical stress analysis to examine
loading and fatigue. In addition to the desired measurement signal indicating mechanical
strain, each strain gauge also produces a temperature-dependent measurement signal. This
signal, called the apparent strain, is superimposed on the actual measured value.
Various effects contribute to the apparent strain:
• Thermal expansion of the measurement object (i.e. strain due entirely to temperature with
no mechanical loading as the cause)
• Temperature-dependent change in the strain gauge resistance
• Thermal contraction of the strain gauge measuring grid foil
• Temperature response of the connection wires
Methods For Temperature Compensation
•Active Dummy method
•Temperature Response matching or self compensation method
•by connecting several strain gauges together to form a half or full bridge
Active Dummy Method
•The active-dummy method uses the 2-gage system where an active gage, A, is bonded to
the measuring object and a dummy gage, D, is bonded to a dummy block which is free
from the stress of the measuring object but under the same temperature condition as that
affecting the measuring object. The dummy block should be made of the same material as
the measuring object.
•As shown in Fig, the two gages are connected to adjacent sides of the bridge. Since the
measuring object and the dummy block are under the same temperature condition,
thermally-induced elongation or contraction is the same on both of them. Thus, gages A
and B bear the same thermally-induced strain, which is compensated to let the output, e,
be zero because these gages are connected to adjacent sides.
Self-Temperature-Compensation Method
• Theoretically, the active-dummy method described above is an ideal temperature
compensation method. But the method involves problems in the form of an extra task to
bond two gages and install the dummy block. To solve these problems, the self-
temperature-compensation gage was developed as the method of compensating
temperature with a single gage.
• With the self-temperature-compensation gage, the temperature coefficient of resistance
of the sensing element is controlled based on the linear expansion coefficient of the
measuring object. Thus, the gage enables strain measurement without receiving any
thermal effect if it is matched with the measuring object.
• The apparent strain that comes into play as the temperature changes can be represented
in a simplified manner as follows
Where:
εs = apparent strain of the strain gauge
∝r = temperature coefficient of the electrical resistance of the measuring grid foil
∝b = thermal expansion coefficient of the measurement object
∝m = thermal expansion coefficient of the measuring grid material
k = gauge factor (sometimes called k factor) of the strain gauge
∧ϑ = temperature difference that triggers the apparent strain
•The temperature coefficient of the electrical resistance of the measuring grid foil is
adapted by technical production measures so that the terms of the equation cancel each
other out; thus r = ( m - b) • k. ∝ ∝ ∝•Accordingly, there are different types of strain gauges that are identical in terms of
geometry and resistance values, but differ in temperature response matching for the
material on which the strain gauge is installed. Temperature response matching to a wide
range of thermal expansion coefficients is available (for example, to ferritic steel with a
thermal expansion coefficient of 10.8 • 10-6/K, or aluminum with 23 • 10-6/K).
Applications of strain Gauges
Strain gauges are basically strain transducers which converts the mechanical signals into
electrical signals and hence measure the strain produced. This strain can be utilized further
to measure the following quantities as given:
•Force
•Torque
•Pressure
•Flow Rate
•Residual Stresses
Measurement of Force•Force can be measured using strain gauge load cells
•A load cell is a transducer that is used to convert a force into electrical signal
•A load cell is made by bonding strain gauges to a spring material. To efficiently detect
the strain, strain gauges are bonded to the position on the spring material where the strain
will be the largest
•Two gauges are along the direction of
applied load and other two are at right
angle to these.
•When there is no load, all gauges have
same resistance and bridge is balanced
•When load is applied, there is change in
resistance and hence some output voltage
is there which is the measure of applied load.
e= V/2*(1+µ)*(K*P)/(A*E)
P= Load to be Measured Tension-compression resistance strain-gage load cell
Pressure Measurement • Use elastic diaphragm as primary pressure transducer
• Apply strain gage directly to a diaphragm surface and calibrate the measured strain in
terms of pressure
• Pressure is measured through force that is exerted on the diaphragm where the force will
be detected by the strain gauge and resistance change will be produced
Location of strain gages on
flat diaphragm
The central gage is subjected
to tension while the outer
gage senses compression
Flow Measurement
Torque Measurement
• Four bonded-wire strain gauges are mounted on a 450 helix with axis of rotation and
place in pairs diametrically opposite as shown in figure
• If gauges are accurately placed and have matched characteristics, the system is
temperature compensated and insensitive to bending, thrust or pulls
• Any change in resistance is purely due to torsion of shaft, hence the torque can be
determined by measuring change in voltage which can be written as
T=e/(V*K)[J*E/r(1-µ)]
Where
e= Change in Voltage
V=Applied Voltage
K=Gauge Factor
J=Polar Moment of Inertia
E=Young’s Modulus
r= Radius of Member
Amplification and Digitization of Output
Electronic Circuitry for Gain and Digitization
Measurement of Cutting Force and Torque in Drilling By Drill Tool Dynamometer
Measurement of Residual Stresses by Hole-Drilling Strain Gage Method
The most widely used modern technique for measuring residual
stress is the hole-drilling strain-gage method of stress relaxation,
Shown in fig. Briefly summarized, the measurement procedure
involves six basic steps:
•A special three element strain gage rosette is installed on the test
part at the point where residual stresses are to be determined
•The gage grids are wired and connected to a multi channel static
strain indicator
•After zero-balancing the gage circuits, a small, shallow hole is
drilled through the geometric center of the Rosette
•Readings are made of the relaxed strains, corresponding to the
initial residual stress
•Using special data-reduction relationships, the principal residual
stresses and their angular orientation are calculated from the
measured strains
Three-Element Rosettes
Through-Hole Analysis
Depicted in Figure (a) is a local area within a
thin plate which is subject to a uniform residual
stress, σx. The initial stress state at any point P
(R, α) can be expressed in polar coordinates by:
Figure (b) represents the same area of the plate
after a small hole has been drilled through it.
The stresses in the vicinity of the hole are now
quite different which can be given as:
Subtracting the initial stresses from the final (after drilling) stresses gives the change in
stress, or stress relaxation at point P (R, α) due to drilling the hole. That is:
Selection and Installation Factors for Bonded Metallic Strain Gages
•Grid material and configuration
•Backing material
•Bonding material and method
•Gage protection
•Associated electrical circuitry
Desirable Properties of Grid Material
•High gage factor, F
•High sensitivity
•Low temperature sensitivity
•High electrical stability
•High yield strength
•High endurance limit
•Good solderability or weldability
•Low hysteresis
•Low thermal emf when joined to other materials
•Good corrosion resistance
Properties of Common Grid Materials
Common Backing Materials
•Thin paper
•Phenolic-impregnated paper
•Epoxy-type plastic films
•Epoxy-impregnated fiberglass
•Most foil gages use an epoxy film backing
Bonding Procedure• Select Strain Gauge
The two primary criteria for selecting the right type of
strain gauge are sensitivity and precision. So Select
the strain gauge model and gage length which meet
the requirements of the measuring object and
purpose
• Remove Dust and Paint
Using a sand cloth polish the strain-gage bonding site
over a wider area than the strain-gage size. Wipe
off paint, rust and plating, if any, with a grinder or
sand blast before polishing
• Decide Bonding Position
Using a pencil or a marking-off pin, mark the
measuring site in the strain direction. When using a
marking off pin, take care not to deeply scratch the
strain-gage bonding surface
Bonding Procedure
• Remove grease from bonding surface and clean
Using an industrial tissue paper (SILBON paper)
dipped in acetone, clean the strain-gage bonding
site. Strongly wipe the surface in a single direction
to collect dust and then remove by wiping in the
same direction. Reciprocal wiping causes dust to
move back and forth and does not ensure cleaning
• Apply adhesive
Ascertain the back and front of the strain gage. Apply
a drop of adhesive to the back of the strain gage.
Do not spread the adhesive. If spreading occurs,
curing is adversely accelerated, thereby lowering
the adhesive strength
Bonding Procedure• Bond strain gage to measuring site
After applying a drop of the adhesive, put the strain gage on
the measuring site while lining up the center marks with
the marking off lines
• Press strain gage
Cover the strain gage with the accessory polyethylene sheet
and press it over the sheet with a thumb. Once the strain
gage is placed on the bonding site, do not lift it to adjust
the position
• Complete bonding work
After pressing the strain gage with a thumb for one minute or
so, remove the polyethylene sheet and make sure the
strain gage is securely bonded. The above steps complete
the bonding work. However, good measurement results
are available after 60 minutes of complete curing of the
adhesive
Some Adhesives and Their Preferred Curing Time
Protecting the Strain Gage
• The strain gages must be protected from ambient conditions e.g. moisture, oil, dust and
dirt•Protective materials used are Petroleum waxes, silicone resins, epoxy preparations,
rubberized brushing compounds
Many materials can be used to protect strain gage installations. Perhaps
none is more versatile for short-term applications than room-temperature
vulcanizing (RTV) silicone rubber. The list of this material's capabilities
is indeed impressive:
• Available as an easy-to-apply single-component coating with uncured
consistencies ranging from a low-viscosity brush-on material for thin
coats, to a medium viscosity self-levelling form for use on level surfaces,
to a high-viscosity no-run paste for vertical and overhead applications.
• Cures at room temperature, yet is usable over a temperature range of -
75° to +550°F (-60° to +290°C).
• Has a low modulus of elasticity that is ideal for thin or flexible
structures for which coating reinforcement effects may become
significant.
• Provides good short-term protection from water; resists many
chemicals; and can be used in radiation and vacuum environments.
RTV Silicone Rubber Coatings
Some Gage Orientation and Interpretation of Results
Bar with Axial Loading
Bar with Transverse Loading
Torsion
Possible sources of error in strain gauge signals
1- Cross-sensitivity
Because a strain gauge has width as well as length, a small proportion of the resistance
element lies at right angles to the major axis of the gauge, at the points where the conductor
reverses direction at the ends of the gauge. So as well as responding to strain in the direction
of its major axis, the gauge will also be somewhat responsive to any strain there may be at
right angles to major axis.
2- Bonding faults
For perfect bonding, the suitable adhesives and procedures for bonding gauges to the strain
surface should be complied. If the bonding is unsatisfactory, creep may occur. Creep is a
gradual relaxing of the strain on the strain gauge, and it has the effect of decreasing the gauge
factor, so that the output of the bridge becomes less than it should be. Creep may also occur
where gauges have been used to measure dynamic strain, and have been subjected to many
thousands of cycles of strain.
3- Hysteresis
If a strain gauge installation is loaded to a high value of strain and then unloaded, it may be
found that the gauge element appears to have acquired a permanent set, so that resistance
values are slightly higher when unloading. The same effect continues when the direction of
loading is reversed. To manipulate this problem, repeating cycles of loading/unloading
should cause the hysteresis loop to narrow to negligible
4- Effects of moisture
The gauges or the bonding adhesive may absorb water. This can cause dimensional changes
which appear as false strain values. Another effect when moisture connections forms high
resistance connected in parallel with the gauge. To prevent this, gauges should be bonded in
dry condition or a suitable electrically insulating water repellent, such as a silicone rubber
compound.
5- Temperature change
One possible source of temperature difference is the heat produced by the current through a
strain gauge. When the bridge is first switched on, the gauges may warm up, so the bridge
should not be used for measurement until sufficient time for temperature to stabilize.
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