A strain gauge is a device used to measure strain on an object. Invented by Edward E.
Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an
insulating flexible backing which supports a metallic foil pattern. The gauge is attached
to the object by a suitable adhesive, such as cyanoacrylate. As the object is deformed,
the foil is deformed, causing its electrical resistance to change. This resistance change,
usually measured using a Wheatstone bridge, is related to the strain by the quantity known
as the gauge factor.
Physical operation A strain gauge takes advantage of the physical
property of electrical conductance and its dependence on the conductor's geometry. When
an electrical conductor is stretched within the limits of its elasticity such that it
does not break or permanently deform, it will become narrower and longer, changes that increase
its electrical resistance end-to-end. Conversely, when a conductor is compressed such that it
does not buckle, it will broaden and shorten, changes that decrease its electrical resistance
end-to-end. From the measured electrical resistance of the strain gauge, the amount of applied
stress may be inferred. A typical strain gauge arranges a long, thin conductive strip in
a zig-zag pattern of parallel lines such that a small amount of stress in the direction
of the orientation of the parallel lines results in a multiplicatively larger strain measurement
over the effective length of the conductor surfaces in the array of conductive lines—and
hence a multiplicatively larger change in resistance—than would be observed with a
single straight-line conductive wire. Gauge factor
The gauge factor is defined as:
where is the change in resistance caused by strain,
is the resistance of the undeformed gauge, and
is strain. For metallic foil gauges, the gauge factor
is usually a little over 2. For a single active gauge and three dummy resistors, the output
from the bridge is:
where is the bridge excitation voltage.
Foil gauges typically have active areas of about 2–10 mm2 in size. With careful installation,
the correct gauge, and the correct adhesive, strains up to at least 10% can be measured.
Gauges in practice
An excitation voltage is applied to input leads of the gauge network, and a voltage
reading is taken from the output leads. Typical input voltages are 5 V or 12 V and typical
output readings are in millivolts. Foil strain gauges are used in many situations.
Different applications place different requirements on the gauge. In most cases the orientation
of the strain gauge is significant. Gauges attached to a load cell would normally
be expected to remain stable over a period of years, if not decades; while those used
to measure response in a dynamic experiment may only need to remain attached to the object
for a few days, be energized for less than an hour, and operate for less than a second.
Strain gauges are attached to the substrate with a special glue. The type of glue depends
on the required lifetime of the measurement system. For short term measurements cyanoacrylic
glue is appropriate, for long lasting installation epoxy glue is required. Usually epoxy glue
requires high temperature curing. The preparation of the surface where the strain gauge is to
be glued is of the utmost importance. The surface must be smoothed, deoiled with solvents,
the solvent traces must then be removed and the strain gauge must be glued immediately
after this to avoid oxidation or pollution of the prepared area. If these steps are not
followed the strain gauge binding to the surface may be unreliable and unpredictable measurement
errors may be generated. Strain gauge based technology is utilized
commonly in the manufacture of pressure sensors. The gauges used in pressure sensors themselves
are commonly made from silicon, polysilicon, metal film, thick film, and bonded foil.
Variations in temperature Variations in temperature will cause a multitude
of effects. The object will change in size by thermal expansion, which will be detected
as a strain by the gauge. Resistance of the gauge will change, and resistance of the connecting
wires will change. Most strain gauges are made from a constantan
alloy. Various constantan alloys and Karma alloys have been designed so that the temperature
effects on the resistance of the strain gauge itself cancel out the resistance change of
the gauge due to the thermal expansion of the object under test. Because different materials
have different amounts of thermal expansion, self-temperature compensation requires selecting
a particular alloy matched to the material of the object under test.
Strain gauges that are not self-temperature-compensated can be temperature compensated by use of the
dummy gauge technique. A dummy gauge is installed on an unstrained sample of the same material
as the test specimen. The sample with the dummy gauge is placed in thermal contact with
the test specimen, adjacent to the active gauge. The dummy gauge is wired into a Wheatstone
bridge on an adjacent arm to the active gauge so that the temperature effects on the active
and dummy gauges cancel each other. Temperature effects on the lead wires can
be cancelled by using a "3-wire bridge" or a "4-wire ohm circuit".
In any case it is a good engineering practice to keep the Wheatstone bridge voltage drive
low enough to avoid the self heating of the strain gauge. The self heating of the strain
gauge depends on its mechanical characteristic. Low voltage drive levels of the bridge reduce
the sensitivity of the overall system. Errors and compensation
Zero Offset - If the impedance of the four gauge arms are not exactly the same after
bonding the gauge to the force collector, there will be a zero offset which can be compensated
by introducing a parallel resistor to one or more of the gauge arms.
Temperature coefficient of Gauge Factor - This is the change of sensitivity of the device
to strain with change in temperature. This is generally compensated for by the introduction
of a fixed resistance in the input leg, whereby the effective supplied voltage will increase
with temperature, compensating for the decrease in sensitivity with temperature.
Zero Shift with temperature - If the TCGF of each gauge is not the same, there will
be a zero shift with temperature. This is also caused by anomalies in the force collector.
This is usually compensated for with one or more resistors strategically placed in the
compensation network. Linearity - This is an error whereby the sensitivity
changes across the pressure range. This is commonly a function of the force collection
thickness selection for the intended pressure and/or the quality of the bonding.
Hysteresis - This is an error of return to zero after pressure excursion.
Repeatability - This error is sometimes tied-in with hysteresis but is across the pressure
range. EMI induced errors - As strain gauges output
voltage is in the mV range, even μV if the Wheatstone bridge voltage drive is kept low
to avoid self heating of the element, special care must be taken in output signal amplification
to avoid amplifying also the superimposed noise. A solution which is frequently adopted
is to use "carrier frequency" amplifiers which convert the voltage variation into a frequency
variation and have a narrow bandwidth thus reducing out of band EMI.
Overloading - If a strain gauge is loaded beyond its design limit its performance degrades
and can not be recovered. Normally good engineering practice suggests not to stress strain gauges
beyond +/-3000 microstrain. Humidity - If the wires connecting the strain
gauge to the signal conditioner are not protected against humidity a parasitic resistance creates
between the wires and the substrate to which the strain gauge is glued, or between the
two wires themselves. This resistance introduces an error which is proportional to the resistance
of the strain gauge. For this reason low resistance strain gauges are less prone to this type
of error. To avoid this error it is sufficient to protect the strain gauges wires with insulating
enamel. Strain gauges with unprotected wires may be used only in a dry laboratory environment
but not in an industrial one. In some applications, strain gauges add mass
and damping to the vibration profiles of the hardware they are intended to measure. In
the turbomachinery industry, one used alternative to strain gauge technology in the measurement
of vibrations on rotating hardware is the Non-Intrusive Stress Measurement System, which
allows measurement of blade vibrations without any blade or disc-mounted hardware.
Other gauge types For measurements of small strain, semiconductor
strain gauges, so called piezoresistors, are often preferred over foil gauges. A semiconductor
gauge usually has a larger gauge factor than a foil gauge. Semiconductor gauges tend to
be more expensive, more sensitive to temperature changes, and are more fragile than foil gauges.
Nanoparticle-based strain gauges emerge as a new promising technology. These resistive
sensors whose active area is made by an assembly of conductive gold nanoparticles combine a
high gauge factor, a large deformation range and a small electrical consumption due to
their high impedance. In biological measurements, especially blood
flow / tissue swelling, a variant called mercury-in-rubber strain gauge is used. This kind of strain
gauge consists of a small amount of liquid mercury enclosed in a small rubber tube, which
is applied around e.g., a toe or leg. Swelling of the body part results in stretching of
the tube, making it both longer and thinner, which increases electrical resistance.
Fiber optic sensing can be employed to measure strain along an optical fiber. Measurements
can be distributed along the fiber, or taken at predetermined points on the fiber. The
2010 America's Cup boats Alinghi 5 and USA-17 both employ embedded sensors of this type
[1]. Capacitive strain gauges use a variable capacitor
to indicate the level of mechanical deformation. Vibrating wire strain gauges are used in Geotechnical
and Civil Engineering applications. The gauge consists of a vibrating, tensioned wire. The
strain is calculated by measuring the resonant frequency of the wire.
Mechanical types
Simple mechanical types are used in civil engineering to measure movement of buildings,
foundations, and other structures. In the illustrated example, the two halves of the
device are rigidly attached to the foundation wall on opposite sides of the crack. The red
reference lines are on the transparent half and the grid is on the opaque white half.
Both vertical and horizontal movement can be monitored over time. In this picture, the
crack can be seen to have widened by approximately 0.3 mm since the gauge was installed.
More sophisticated mechanical types incorporate dial indicators and mechanisms to compensate
for temperature changes. These types can measure movements as small as 0.002 mm.
See also Resistance thermometer
References
External links British Society for Strain Measurement
Applying Finite Element Analysis Methods to Strain Gage Design
An Introduction to Measurements using Strain Gages by Karl Hoffmann
Fiber optic strain gauges - NASA patented technology