Download Strain, Force and Flow

Strain Gauges
These devices are useful in measuring not only strain but also force and pressure.
Technically speaking, this description refers to resistive strain gauges - but those are
the type used in 99.999% of applications!
Stress and strain
To recap school Physics:
Stress = Force per unit cross-sectional area (like pressure)
Strain = Extension or compression per unit length
and Stress/Strain = a constant for a particular material (Young's Modulus).
Principle of the Resistive Strain Gauge
A piece of (usually) resistive metal foil (the gauge) is attached by means of an
insulating cement (Canada Balsam is the usual one) to the material whose strain is to
be measured. The gauge deforms as the material is strained and its resistance changes
as a result.
We remember (or have forgotten) that resistance = resistivity  length / area, and if we
stretch the gauge, the length increases and the area decreases ("Poisson's Ratio"). This
"double whammy" (sorry for quoting J. Major Esq.) causes the resistance to change by
more than the strain would suggest. We define the gauge factor as the fractional
change in resistance divided by the strain. For metallic strain gauges, its value is
approximately two; it is higher for semiconductor gauges, but their relation between
resistance and strain tends to be nonlinear.
There is a problem if the coefficients of thermal expansion of the gauge and the object
to which it is attached are not equal. In that very common situation, a temperature
change will cause the gauge to "think" that there is a strain! The problem can be
overcome by attaching a dummy gauge to a piece of unstrained material near the
active gauge, or to use more than one active gauge. The following arrangements can
prove very effective.
Axial Force F
A
A
B
C
B
C
D
D
E
Axial Force F
The left-hand arrangement is a beam firmly fixed in a wall or similar object at the top
with a force assumed to be applied down into the page at E. The application of the
force will bend the beam such as to bring gauges B and C into tension and A and D
into compression. The right-hand one is a "strain tube" set up here to measure axial
force, with B and C in compression and A and D in tension if the force is applied as
shown to compress the tube axially. In either case, a voltage proportional to force can
be obtained as follows:
A
C
+
+
Vs
-
B
Differential
Vo
Amplifier
D
The lab. experiment will indicate that we still do not obtain a very large output!
Strain gauges can nevertheless be used in measuring many force-related quantities.
Other Methods of Measuring Force
1.
Use a spring and measure its compression or extension by means of a
potentiometer or LVDT.
2.
Use a semiconductor or other device device whose voltage, resistance or
leakage current is directly force-dependent (yes, there are some - e.g.
piezoelectric).
Transducing Pressure
1.
See RS/Farnell/Maplin - there are pressure-sensitive semiconductor devices
and recommendations on how to use them.
2.
Developments of the force methods.
3.
By means of a diaphragm and (for example) strain gauges.
Flow
1.
Venturi (high flow) and orifice plate (low flow).
Flow
Venturi
Orifice Plate
X
Y
X
Y
In each case, the pressure at Y will be lower than that at X. If we use a differential
pressure transducer between X and Y, we will obtain a voltage proportional to the
pressure difference and therefore dependent on the flow. We find that the flow is
approximately proportional to the square-root of the pressure drop. (Any
mechanically- or physics-minded folk can deduce this relation from Bernoulli's
Equation - see any simple Fluid Mechanics book).
2.
The impulse turbine flowmeter.
A propeller-like device is inserted in the flow path and it rotates at a speed which is
reasonably accurately proportional to the flow rate. It is possible either to attach a
small tachogenerator to the rotor to obtain a voltage proportional to the flow rate, or to
attach a magnet to it to induce an alternating signal in an adjacent coil - whose
frequency is proportional to the flow.
3.
Electromagnetic flowmeter.
A magnetic field is generated at right-angles to the flow and an e.m.f. is induced by
"electric generator" action mutually at right-angle sto flow and field ("e = Blu"). This
method has the advantage over the other methods that it does not place any
obstruction in the flow path, but it only works with conducting fluids and, if a d.c.
magnetic field is used, it suffers from electrolytic effects masking the voltage.
4.
The Pitot-static Tube
Outer Tube
Inner Tube
P1
Air Flow
P2
The pressure P2 is the static air pressure in the flowing air, whilst P1 will be higher as
the air has been brought to a stop at the end of the inner tube. The difference gives a
measure of the speed of the air flow - it is found that the speed is proportional to the
square root of the difference between P1 and P2. This device is also the basis of
airspeed measurement instruments on aircraft.
These are the common methods, though others exist.