Length and Position
Measurement
Primary standards were once based on the
length of a bar of metal at a given temperature.
The present standard is:
1 meter = distance traveled by light in a vacuum
in 3.335641 X 10-9 seconds.
Laboratory standards are usually "gauge blocks"
which are polished non corrosive metal blocks
ground to precise dimensions (± 0.000001 inch).
Micrometers can measure to ± .0001 in using a
Vernier scale.
Figure 12.3 in 2nd Edition
For more precise measurements, optical
methods are used, based on the principle of
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interferometry.
Figure 12.7 in 2nd Edition
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The interferometer works by measuring the light
and dark fringes produced by interference of two
light beams. The precision is related to the
wavelength of the light. Interferometers using
visible laser light can measure distances with a
precision of ± . 000001 in. The output can also
be converted to an electrical signal using
photodiodes.
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Displacement Measurement
The potentiometer (pot) is a coil of wire with a
sliding contact (wiper) which divides the
resistance of the coil into two parts. By placing
a voltage across the coil and measuring the
voltage from one end to the sliding contact, the
position can be calculated.
Figure 12.8 in 2nd Edition
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The LVDT (Linear Variable Differential
Transformer) uses a movable magnetic core to
induce a voltage in two secondary coils by the
principle of induction.
Figure 10.9 Construction of an LVDT
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Figure 12.9 in 2nd Edition
The LVDT has better resolution (± 0.00001 in)
than the potentiometer, but the linear range is
more limited. Both the LVDT and potentiometer
are subject to "loading" errors, which we will
discuss later.
Figure 10.10 in 2nd Edition
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LVDT Theory of Operation
An LVDT is much like any other transformer in that it consists of a primary coil, secondary coils,
and a magnetic core. An alternating current, known as the carrier signal, is produced in the primary
coil. The changing current in the primary coil produces a varying magnetic field around the core.
This magnetic field induces an alternating (AC) voltage in the secondary coils that are in proximity to
the core. As with any transformer, the voltage of the induced signal in the secondary coil is linearly
related to the number of coils. The basic transformer relation is:
(1)
where:
Vout is the voltage at the output,
Vin is the voltage at the input,
Nout is the number of windings of the output coil, and
Nin is the number of windings of the input coil.
As the core is displaced, the number of coils in the secondary coil exposed to the coil changes
linearly. Therefore the amplitude of the induced signal varies linearly with displacement.
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The LVDT indicates direction of displacement by having the two secondary coils whose outputs are
balanced against one another. The secondary coils in an LVDT are connected in the opposite sense
(one clockwise, the other counter clockwise). Thus when the same varying magnetic field is applied
to both secondary coils, their output voltages have the same amplitude but differ in sign. The
outputs from the two secondary coils are summed together, usually by simply connecting the
secondary coils together at a common center point. At an equilibrium position (generally zero
displacement) a zero output signal is produced.
The induced AC signal is then demodulated so that a DC voltage that is sensitive to the
amplitude and phase of the AC signal is produced.
Magnetostriction
A pulse is induced in a specially-designed
magnetostrictive waveguide by the momentary
interaction of two magnetic fields. One field
comes from a movable magnet which passes
along the outside of the sensor tube, the other
field comes from a current pulse or interrogation
pulse launched along the waveguide. The
interaction between the two magnetic fields
produces a strain pulse, which travels at sonic
speed along the waveguide until the pulse is
detected at the head of the sensor. The position
of the magnet is determined with high precision
by measuring the elapsed time between the
launching of the electronic interrogation pulse
and the arrival of the strain pulse. As a result,
accurate non-contact position sensing is
achieved with absolutely no wear to the sensing
components.
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