THE STRAIN GAUGE
The strain gauge has been in use for many years and is the fundamental
sensing element for many types of sensors, including pressure sensors,
load cells, torque sensors, position sensors, etc.
The majority of strain gauges are foil types, available in a wide choice
of shapes and sizes to suit a variety of applications. They consist of a
pattern of resistive foil which is mounted on a backing material. They
operate on the principle that as the foil is subjected to stress, the
resistance of the foil changes in a defined way.
The strain gauge is connected into a Wheatstone Bridge circuit with a combination of four active gauges (full bridge), two gauges (half bridge),
or, less commonly, a single gauge (quarter bridge). In the half and
quarter circuits, the bridge is completed with precision resistors.
The complete Wheatstone Bridge is excited with a stabilised DC supply
and with additional conditioning electronics, can be zeroed at the null
point of measurement. As stress is applied to the bonded strain gauge,
a resistive changes takes place and unbalances the Wheatstone Bridge.
This results in a signal output, related to the stress value. As the signal
value is small, (typically a few millivolts) the signal conditioning
electronics provides amplification to increase the signal level to 5 to 10
volts, a suitable level for application to external data collection systems
such as recorders or PC Data Acquistion and Analysis Systems.
Some of the many Gauge Patterns available
Most manufacturers of strain gauges offer extensive ranges of differing
patterns to suit a wide variety of applications in research and industrial
They also supply all the necessary accessories including preparation
materials, bonding adhesives, connections tags, cable, etc. The bonding
of strain gauges is a skill and training courses are offered by some suppliers.
There are also companies which offer bonding and calibration services,
either as an in-house or on-site service.
More about the Strain Gauge...
If a strip of conductive metal is stretched, it will become skinnier and
longer, both changes resulting in an increase of electrical resistance
end-to-end. Conversely, if a strip of conductive metal is placed under
compressive force (without buckling), it will broaden and shorten. If
these stresses are kept within the elastic limit of the metal strip (so
that the strip does not permanently deform), the strip can be used as
a measuring element for physical force, the amount of applied force
inferred from measuring its resistance.
Such a device is called a strain gauge. Strain gauges are frequently used
in mechanical engineering research and development to measure the
stresses generated by machinery. Aircraft component testing is one area
of application, tiny strain-gauge strips glued to structural members,
linkages, and any other critical component of an airframe to measure
stress. Most strain gauges are smaller than a postage stamp, and they
look something like this:
A strain gauge's conductors are very thin: if made of round wire, about
1/1000 inch in diameter. Alternatively, strain gauge conductors may be
thin strips of metallic film deposited on a nonconducting substrate
material called the carrier. The latter form of strain gauge is represented
in the previous illustration. The name "bonded gauge" is given to strain gauges that are glued to a larger structure under stress (called the test specimen) The task of bonding strain gauges to test specimens may
appear to be very simple, but it is not. "Gauging" is a craft in its own
right, absolutely essential for obtaining accurate, stable strain measurements. It is also possible to use an unmounted gauge wire
stretched between two mechanical points to measure tension, but this technique has its limitations.
Typical strain gauge resistances range from 30 Ohms to 3 kOhms (unstressed). This resistance may change only a fraction of a percent
for the full force range of the gauge, given the limitations imposed by
the elastic limits of the gauge material and of the test specimen. Forces
great enough to induce greater resistance changes would permanently
deform the test specimen and/or the gauge conductors themselves, thus
ruining the gauge as a measurement device. Thus, in order to use the
train gauge as a practical instrument, we must measure extremely small
changes in resistance with high accuracy.
Such demanding precision calls for a bridge measurement circuit. Unlike
the Wheatstone bridge shown in the last chapter using a null-balance
detector and a human operator to maintain a state of balance, a strain
gauge bridge circuit indicates measured strain by the degree of
imbalance, and uses a precision voltmeter in the center of the bridge
to provide an accurate measurement of that imbalance:
Typically, the rheostat arm of the bridge (R2 in the diagram) is set
at a value equal to the strain gauge resistance with no force applied.
The two ratio arms of the bridge (R1 and R3) are set equal to each
other. Thus, with no force applied to the strain gauge, the bridge
will be symmetrically balanced and the voltmeter will indicate zero
volts, representing zero force on the strain gauge. As the strain
gauge is either compressed or tensed, its resistance will decrease
or increase, respectively, thus unbalancing the bridge and producing
an indication at the voltmeter. This arrangement, with a single element
of the bridge changing resistance in response to the measured variable (mechanical force), is known as a quarter-bridge circuit.
As the distance between the strain gauge and the three other
resistances in the bridge circuit may be substantial, wire resistance
has a significant impact on the operation of the circuit. To illustrate
the effects of wire resistance, I'll show the same schematic diagram,
but add two resistor symbols in series with the strain gauge to
represent the wires:
The strain gauge's resistance (Rgauge) is not the only resistance being
measured: the wire resistances Rwire1 and Rwire2, being in series with
Rgauge, also contribute to the resistance of the lower half of the
rheostat arm of the bridge, and consequently contribute to the
voltmeter's indication. This, of course, will be falsely interpreted by
the meter as physical strain on the gauge.
While this effect cannot be completely eliminated in this configuration,
it can be minimized with the addition of a third wire, connecting the right
side of the voltmeter directly to the upper wire of the strain gauge:
Because the third wire carries practically no current (due to the
voltmeter's extremely high internal resistance), its resistance will not
drop any substantial amount of voltage. Notice how the resistance
of the top wire (Rwire1) has been "bypassed" now that the voltmeter
connects directly to the top terminal of the strain gauge, leaving only
the lower wire's resistance (Rwire2) to contribute any stray resistance
in series with the gauge. Not a perfect solution, of course, but twice
as good as the last circuit!
There is a way, however, to reduce wire resistance error far beyond
the method just described, and also help mitigate another kind of
measurement error due to temperature. An unfortunate characteristic
of strain gauges is that of resistance change with changes in
temperature. This is a property common to all conductors, some more
than others. Thus, our quarter-bridge circuit as shown (either with
two or with three wires connecting the gauge to the bridge) works
as a thermometer just as well as it does a strain indicator.
If all we want to do is measure strain, this is not good. We can
transcend this problem, however, by using a "dummy" strain gauge
in place of R2, so that both elements of the rheostat arm will change
resistance in the same proportion when temperature changes, thus
canceling the effects of temperature change:
Resistors R1 and R3 are of equal resistance value, and the strain
gauges are identical to one another. With no applied force, the bridge
should be in a perfectly balanced condition and the voltmeter should
register 0 volts. Both gauges are bonded to the same test specimen,
but only one is placed in a position and orientation so as to be exposed
to physical strain (the active gauge). The other gauge is isolated
from all mechanical stress, and acts merely as a temperature
compensation device (the "dummy" gauge). If the temperature
changes, both gauge resistances will change by the same percentage,
and the bridge's state of balance will remain unaffected. Only a
differential resistance (difference of resistance between the two strain
gauges) produced by physical force on the test specimen can alter the
balance of the bridge.
Wire resistance doesn't impact the accuracy of the circuit as much as
before, because the wires connecting both strain gauges to the bridge
are approximately equal length. Therefore, the upper and lower sections
of the bridge's rheostat arm contain approximately the same amount of
stray resistance, and their effects tend to cancel:
Even though there are now two strain gauges in the bridge circuit, only
one is responsive to mechanical strain, and thus we would still refer to
this arrangement as a quarter-bridge. However, if we were to take the
upper strain gauge and position it so that it is exposed to the opposite
force as the lower gauge (i.e. when the upper gauge is compressed, the
lower gauge will be stretched, and visa-versa), we will have both gauges
responding to strain, and the bridge will be more responsive to applied
force. This utilization is known as a half-bridge. Since both strain gauges
will either increase or decrease resistance by the same proportion in
response to changes in temperature, the effects of temperature change
remain canceled and the circuit will suffer minimal temperature-induced
With no force applied to the test specimen, both strain gauges have
equal resistance and the bridge circuit is balanced. However, when a
downward force is applied to the free end of the specimen, it will bend
downward, stretching gauge #1 and compressing gauge #2 at the
In applications where such complementary pairs of strain gauges can
be bonded to the test specimen, it may be advantageous to make
all four elements of the bridge "active" for even greater sensitivity.
This is called a full-bridge circuit:
Both half-bridge and full-bridge configurations grant greater sensitivity
over the quarter-bridge circuit, but often it is not possible to bond
complementary pairs of strain gauges to the test specimen. Thus,
the quarter-bridge circuit is frequently used in strain measurement
When possible, the full-bridge configuration is the best to use. This
is true not only because it is more sensitive than the others, but
because it is linear while the others are not. Quarter-bridge and
half-bridge circuits provide an output (imbalance) signal that is
only approximately proportional to applied strain gauge force.
Linearity, or proportionality, of these bridge circuits is best when
the amount of resistance change due to applied force is very
small compared to the nominal resistance of the gauge(s). With
a full-bridge, however, the output voltage is directly proportional
to applied force, with no approximation (provided that the change
in resistance caused by the applied force is equal for all four
Unlike the Wheatstone and Kelvin bridges, which provide measurement
at a condition of perfect balance and therefore function irrespective
of source voltage, the amount of source (or "excitation") voltage
matters in an unbalanced bridge like this. Therefore, strain gauge
bridges are rated in millivolts of imbalance produced per volt of
excitation, per unit measure of force. A typical example for a
strain gauge of the type used for measuring force in industrial
environments is 15 mV/V at 1000 pounds. That is, at exactly
1000 pounds applied force (either compressive or tensile), the
bridge will be unbalanced by 15 millivolts for every volt of
excitation voltage. Again, such a figure is precise if the bridge
circuit is full-active (four active strain gauges, one in each arm
of the bridge), but only approximate for half-bridge and quarter
Strain gauges may be purchased as complete units, with both strain
gauge elements and bridge resistors in one housing, sealed and
encapsulated for protection from the elements, and equipped with
mechanical fastening points for attachment to a machine or structure.
Such a package is typically called a load cell.
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