19.1.8 Other methods of measuring
small displacements
Apart from the methods outlined
above, several other techniques for measuring small translational displacements
exist, as discussed below. Some of these involve special instruments that have
a very limited sphere of application, for instance in measuring machine tool
displacements. Others are very recent developments that may potentially gain
wide use in the future but have few applications at present.
Linear inductosyn
The linear inductosyn is an extremely
accurate instrument that is widely used for axis measurement and control within
machine tools. Typical measurement resolution is 2.5 microns. The instrument
consists of two magnetically coupled parts that are separated by an air gap,
typically 0.125 mm wide, as shown in Figure 19.8. One part, the track, is
attached to the axis along which displacements are to be measured. This would generally
be the bed of a machine tool. The other part, the slider, is attached to the
body that is to be measured or positioned. This would usually be a cutting
tool.
The track, which may be several
metres long, consists of a fine metal wire formed into the pattern of a
continuous rectangular waveform and deposited onto a glass base. The typical
pitch (cycle length), s, of the pattern is 2 mm, and this extends over the full
length of the track. The slider is usually about 50 mm wide and carries two
separate wires formed into continuous rectangular waveforms that are displaced
with respect to each other by one-quarter of the cycle pitch, i.e. by 90
electrical degrees. The wire waveform on the track is excited by an applied
voltage given by:
Vs
= V sin (ωt)
This excitation causes induced
voltages in the slider windings. When the slider is positioned in the null
position such that its first winding is aligned with the winding on the track,
the output voltages on the two slider windings are given by:
V1
= 0; V2 = V sin (ωt)
For any other position, the slider
winding voltages are given by:
V1 = V sin (ωt) sin
(2µx/s); V2 = V sin (ωt) cos(2µx/s)
where x is the displacement of the
slider away from the null position.
Consideration of these equations for
the slider winding outputs shows that the pattern of output voltages repeats
every cycle pitch. Therefore, the instrument can only discriminate
displacements of the slider within one cycle pitch of the windings. This means
that the typical measurement range of an inductosyn is only 2 mm. This is of no
use in normal applications, and therefore an additional displacement transducer
with coarser resolution but larger measurement range has to be used as well.
This coarser measurement is commonly made by translating the linear
displacements by suitable gearing into rotary motion, which is then measured by
a rotational displacement transducer such as a synchro or resolver.
One slight problem with the
inductosyn is the relatively low level of coupling between the track and slider
windings. Compensation for this is made by using a high-frequency excitation
voltage (5–10 kHz is common).
Translation of linear displacements
into rotary motion
In some applications, it is
inconvenient to measure linear displacements directly, either because there is
insufficient space to mount a suitable transducer or because it is inconvenient
for other reasons. A suitable solution in such cases is to translate the
translational motion into rotational motion by suitable gearing. Any of the
rotational displacement transducers discussed in Chapter 20 can then be
applied.
Integration of output from velocity
transducers and accelerometers
If velocity transducers or
accelerometers already exist in a system, displacement measurements can be
obtained by integration of the output from these instruments. This, however,
only gives information about the relative position with respect to some
arbitrary starting point. It does not yield a measurement of the absolute
position of a body in space unless all motions away from a fixed starting point
are recorded.
Laser interferometer
This recently developed instrument is
shown in Figure 19.9. In this particular design, a dual-frequency helium–neon
(He–Ne) laser is used that gives an output pair of light waves at a nominal
frequency of 5 × 1014 Hz. The two waves differ in frequency by 2 ×
106 Hz and have opposite polarization. This dual-frequency output
waveform is split into a measurement beam and a reference beam by the first
beam splitter.
The reference beam is sensed by the
polarizer and photodetector, A, which converts both waves in the light to the
same polarization. The two waves interfere constructively and destructively
alternately, producing light–dark flicker at a frequency of 2 × 106
Hz. This excites a 2 MHz electrical signal in the photodetector.
The measurement beam is separated
into the two component frequencies by a polarizing beam splitter. Light of the
first frequency, f1, is reflected by a fixed reflecting cube into a
photodetector and polarizer, B. Light of the second frequency, f2,
is reflected by a movable reflecting cube and also enters B. The displacement
to be measured is applied to the movable cube. With the movable cube in the
null position, the light waves entering B produce an electrical signal output
at a frequency of 2 MHz, which is the same frequency as the reference signal
output from A. Any displacement of the movable cube causes a Doppler shift in
the frequency f2 and changes the output from B. The frequency of the
output signal from B varies between 0.5 MHz and 3.5 MHz according to the speed
and direction of movement of the movable cube.
The outputs from A and B are
amplified and subtracted. The resultant signal is fed to a counter whose output
indicates the magnitude of the displacement in the movable cube and whose rate
of change indicates the velocity of motion.
This technique is used in
applications requiring high-accuracy measurement, such as machine tool control.
Such systems can measure displacements over ranges of up to 2 m with an
inaccuracy of only a few parts per million. They are therefore an attractive
alternative to the inductosyn, in having both high measurement resolution and a
large measurement range within one instrument.
Fotonic sensor
The Fotonic sensor is one of many
instruments developed recently that make use of fibre-optic techniques. It
consists of a light source, a light detector, a fibre-optic light transmission
system and a plate that moves with the body whose displacement is being
measured, as shown in Figure 19.10. Light from the outward fibre-optic cable travels
across the air gap to the plate and some of it is reflected back into the
return fibre-optic
cable. The amount of light reflected
back from the plate is a function of the air gap length, x, and hence of the
plate displacement. Measurement of the intensity of the light carried back
along the return cable to the light detector allows the displacement of the
plate to be calculated. Common applications of Fotonic sensors are measuring
diaphragm displacements in pressure sensors and measuring the movement of
bimetallic temperature sensors.
Evanescent-field fibre-optic sensors
This sensor consists of a prism and a
light source/detector system, as shown in Figure 19.11. The amount of light
reflected into the detector depends on the proximity of a movable silver
surface to the prism. Reflection varies from 96% when the surface is touching
the prism to zero when it is 1 µm away. This provides a means of measuring very
tiny displacements over the range between 0 and 1 µm (1 micron).
Non-contacting optical sensor
Figure 19.12 shows an optical
technique that is used to measure small displacements. The motion to be
measured is applied to a vane, whose displacement progressively shades one of a
pair of monolithic photodiodes that are exposed to infrared radiation. A
displacement measurement is obtained by comparing the output of the reference
(unshaded) photodiode with that of the shaded one. The typical range of
measurement is ±0.5 mm with an inaccuracy of ±0.1% of full scale. Such sensors
are used in some intelligent pressure-measuring instruments based on Bourdon
tubes or diaphragms as described in Chapter 15.
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