In engineering, being able to accurately measure
how objects deform under loading is fundamental for ensuring the long term integrity of structures
and mechanical systems. One essential tool for doing this is the strain
gauge, a highly accurate device used to measure the strain on the surface of an object. Strain gauges placed at strategic locations
along a bridge can detect even the slightest changes in loading, allowing engineers to
continuously monitor and manage the structural integrity of the bridge. And when attached to high-speed rotating machinery,
they provide valuable data that can be used to optimise performance and extend equipment
lifespan. They’re essential tools for testing materials
and monitoring structures. In this video we’ll dive into the fascinating
world of strain gauges, these little devices that cleverly combine elements of mechanical
engineering, electrical engineering and material science to give us a way of measuring how
an object deforms. Understanding the basic concept of strain
is crucial for appreciating how these devices work. In simple terms, strain is a measure of how
much an object deforms. It’s calculated by dividing a change in
length, Delta-L, by the original length of the object, L. Here’s an example. Imagine a steel block that's initially 200
millimetres in length. If it's subjected to a uniaxial load that
stretches it by 0.2 millimetres, the strain is 0.001, or 0.1%. The job of the strain gauge is to measure
this change in length, and different strain gauge designs do this in different ways. Some use mechanical means. Others are based on optical principles. But the most common strain gauge design and
the one that we'll focus on is the electrical resistance strain gauge. These strain gauges are carefully bonded to
the surface of the object being monitored, and work on the principle that the electrical
resistance of a conductive material changes as it deforms. As the object stretches or compresses, the
bonded strain gauge does the same. By measuring the change in electrical resistance
across the gauge, we can accurately determine the object's change in length, and so the
strain on its surface. The electrical resistance strain gauge is
made of a conductive foil grid that’s bonded to a very thin insulating plastic film. A separate film encapsulates and protects
the foil grid. Solder tabs allow the measurement wiring to
be soldered directly to the strain gauge, and markings on the foil help with alignment
of the gauge during installation. The foil grid is where all of the smart stuff
happens. It’s made from a conductive material that’s
formed into an intricate pattern using a photo etching process. The pattern is cleverly designed to maximise
the amount of material that’s stretched or compressed when loads are applied in the
axial direction, while at the same time minimising any stretching or compression of the material
when loads are applied in the transverse direction. The physical length of the grid, called the
gauge length, is selected based on the application. The shorter the gauge length is, the more
accurately it will approximate the strain at a single point, which is why most general
purpose strain gauges are very small. But in some cases, like when measuring the
strain of a composite material like reinforced concrete, a strain value averaged over a larger
distance might be more meaningful, and strain gauges with longer gauge lengths will be used. The grid is made from a carefully selected
conductive material. All conductive materials experience some kind
of change in electrical resistance as they deform. In theory you could measure the resistance
of a copper wire with an ultra sensitive multimeter, and see how it changes as you stretch it. This change in resistance as the wire is stretched
is the result of three separate mechanisms - the reduction in the cross-sectional area
of the wire, the increase in the wire length, and changes to the resistivity of the material
itself, due to the increased spacing between atoms, which affects how easily electrons
can flow through the material. Let’s look at how electrical resistance
might change as a function of strain for three strain gauges made from different materials. The graph shows the relative change in resistance,
expressed as a percentage. For material 1, a strain of 0.5% will produce
a 2% change in resistance. For materials 2 and 3 the change in resistance
will be 3% and 8%. It’s clear from this graph that strain gauges
made from different materials will behave differently. A strain gauge made from material 3 that produces
large changes in resistance for small changes in strain will be much more sensitive, and
will be much better able to measure small strains. The sensitivity of a strain gauge is defined
using a parameter called the Gauge Factor, K, which is defined as the relative change
in resistance divided by the corresponding strain - it represents the slope of the curve
in this graph. If a material has a gauge factor of 10, for
every 1% of strain the electrical resistance of the strain gauge will increase by 10%. Here are a few different gauge factors for
materials used in strain gauges. Semiconductor materials like Silicon have
really large gauge factors of around 150. These materials are only really used in specialist
strain gauges that need to measure extremely small strains. Most general purpose strain gauges are made
out of Constantan, an alloy of copper and nickel. It has a moderate gauge factor of around 2,
but has other properties that make it a really good choice for use in strain gauges. It has good resistance to corrosion, and good
fatigue properties, for example. But the main reason it’s such a good choice
is its performance over temperature. Most materials have a gauge factor that varies
significantly with temperature, which makes it difficult to get accurate measurements
when working with large temperature ranges. But Constantan is very stable - its gauge
factor varies very little from -50 to 150 degrees Celsius, and beyond. In fact, that’s where the material gets
its name. And that’s the main reason it’s the most
popular material for use in strain gauges. Strain gauges are usually used to obtain precise
measurements of small strains, typically in the order of 1 to 1000 microstrain. A standard unloaded Constantan strain gauge
has a resistance of 120 or 350 Ohms. Assuming a resistance of 350 Ohms and a gauge
factor of 2, a tensile strain of 100 microstrain will result in a 0.07 Ohm increase in the
resistance of the strain gauge. Measuring such small changes in resistance
is a challenge, but it can be done using an electrical circuit called a Wheatstone bridge. The purpose of the Wheatstone bridge is to
accurately determine the electrical resistance of the strain gauge, before and after a load
has been applied. The circuit is made up of four resistors arranged
in a diamond shape. One of these resistors is the strain gauge,
and the remaining three are resistors of known resistance. Points C and D are connected and a galvanometer
is used to precisely measure the current flowing through this segment. The circuit is connected to a voltage supply
V. Each of the two branches of the diamond acts as a simple voltage divider, which splits
an input voltage across two resistors. The output voltage of the voltage divider
depends on the input voltage and the ratio of the resistances of the two resistors. Something interesting happens with the Wheatstone
bridge when the ratios of the resistances on both branches are equal - the voltages
at points C and D are the same, so there is no current flowing through the segment. When this happens the bridge is said to be
“balanced”. If resistor R4 is replaced by an adjustable
resistor, its resistance can be adjusted so that no current flows through segment CD,
and the bridge is balanced. When the strain gauge is subjected to a load,
its resistance changes, causing a voltage imbalance in the bridge and current to flow
through segment CD. By re-balancing the bridge using the adjustable
resistor, the change in the electrical resistance of the strain gauge can be determined. And from there the gauge factor can be used
to calculate the strain seen by the strain gauge. It’s a really clever circuit that allows
very small changes in resistance to be measured accurately. In some cases instead of using an adjustable
resistor and a galvanometer, the voltage across segment CD is measured, and the resistance
of the strain gauge is calculated using the voltage, instead of having to balance the
bridge. The arrangement shown here is called a quarter
bridge circuit - the strain gauge occupies one of the four resistors. A half bridge arrangement uses two strain
gauges, and a full bridge arrangement uses four. Configurations with multiple strain gauges
are often used in load cells, which we’ll talk about later, or for temperature compensation. Temperature compensation is an important topic
because strain gauges don’t cope well with large temperature ranges. Constantan has good temperature stability,
but it can’t escape the issue of thermal expansion. When materials experience temperature changes,
they expand and contract. The amount a specific material expands by
depends on a material property called the coefficient of thermal expansion, or CTE. The foil grid of the strain gauge and the
material of the test item have different CTEs, so they’ll try to expand by different amounts. But since the two parts are physically bonded
together, the grid is forced to expand by the same amount as the test item. This means that any changes in temperature
will induce a strain in the foil grid due to differential thermal expansion, that gets
added to the strain we’re actually trying to measure. This introduces an error into the measurement,
but it can be avoided by applying temperature compensation. There are two main compensation methods. Active compensation uses a second “dummy”
strain gauge to compensate for thermal expansion. It’s placed either in an unstressed region
of the object being measured, or on a reference part that will experience the same level of
thermal expansion but without any applied loads. Both strain gauges are used in a half bridge
circuit, which cancels out the effects of thermal expansion. A simpler approach is self-compensation, where
the strain gauge material is selected to have a CTE similar to that of the test item material. Manufacturers make slight adjustments to the
composition of the Constantan alloy so that they can supply strain gauges with different
CTEs, and all you need to do is select the strain gauge with a CTE that matches the test
item. Strain gauges have a significant limitation
that we haven't discussed yet, which is that they only measure normal strain in a single
direction. This is a problem because the strain at a
single point within a body isn’t one value, it’s actually a tensor quantity. The strain tensor at a point can be represented
using a strain element. It has components acting in the normal and
shear directions, and these components change in magnitude depending on the angle at which
they’re measured. A strain gauge can only give us the normal
strain for one particular angle, the angle it’s been installed at, so a single strain
gauge can’t provide all the information needed to fully describe the strain state
at a particular point. For this reason strain gauges are often used
in sets of three, separated by angles of 45 or 60 degrees. This arrangement is called a strain gauge
rosette. The rosette provides the normal strain at
three different angles, which is enough information to fully define the strain state at a single
point. We can demonstrate this by constructing Mohr's
circle, a method used to represent the strain state at a specific point in a material on
a graph. Here's how it works. First, draw the axes. Mohr's circle for strain has normal strain
on the horizontal axis, and shear strain over two on the vertical axis, with positive shear
strains drawn, by convention, in the downward direction. Next the normal strains obtained from the
three strain gauges are drawn on the horizontal axis. Then the shear strain at gauge A is determined. For a rectangular rosette where the three
gauges are separated by 45 degrees it's given by this simple equation, derived from the
strain transformation equations. This defines the points on Mohr's circle corresponding
to Strain Gauges A and C, because the two gauges are separated by 90 degrees and so
have equal but opposite shear strains. With these two points we can draw Mohr's circle. Remember that angles on Mohr’s circle are
always doubled - strain gauges A and C are separated by 90 degrees, so there’s a 180
degree angle between points A and C on Mohr’s circle. And there’s a 45 degree angle between strain
gauge B and the other two strain gauges, so on Mohr’s circle the location of Point B
is obtained by drawing a line at 90 degrees to the line between Points A and C. Once Mohr's
circle has been constructed, useful information like the principal strains or the strains
in a particular direction can easily be determined. And Hooke’s law can be used to calculate
the stress in the material. Strain gauge rosettes come in many different
shapes and sizes. This two gauge rosette for example is used
to measure shear strain. If two strain gauges are separated by a 90
degree angle, the shear strain along the axis running between them is equal to the difference
in the normal strains measured by the two gauges. Rosettes like this one are often used to measure
the shear strain on rotating shafts, from which the torque acting on the shaft can be
determined. Here’s another interesting rosette design,
used to determine residual stresses. It’s fixed to the test item and a small
blind hole is drilled into the material at the centre of the rosette. The strain gauges measure the changes in strain
that occur due to relaxation of the residual stresses in the vicinity of the hole, and
these measurements can be used to calculate the magnitude of the residual stresses. Strain gauges have so many fascinating applications. One very important one is in load cells, sensors
that use strain gauges to measure forces extremely accurately. Load cells are used everywhere in engineering,
from weighing product on an assembly line, to measuring the thrust of rocket engines. If you’d like to learn more about load cells,
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