Strain gauges
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 Ω to 3 kΩ
(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 strain 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 measurement error:
An example of how a pair of strain gauges may be bonded to a test
specimen so as to yield this effect is illustrated here:
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 same time:
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 systems.
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 strain gauges!).
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-bridge arrangements.
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.
Like many of the other topics addressed in this chapter, strain
gauge systems can become quite complex, and a full dissertation on
strain gauges would be beyond the scope of this book.
- REVIEW:
- A strain gauge is a thin strip of metal designed to measure
mechanical load by changing resistance when stressed (stretched or
compressed within its elastic limit).
- Strain gauge resistance changes are typically measured in a
bridge circuit, to allow for precise measurement of the small
resistance changes, and to provide compensation for resistance
variations due to temperature.
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