Displacement sensors are those sensors which pick
up the variation of position of a body.
Displacement
Sensors are of various types . I have compiled
a few here .
1.
Capacitive
Displacement Sensor.
2. LVDT’s ( Linear Variable Differential Transducer)
3. RVDT’s (Rotary Variable
Differential Transducer)
Capacitive sensors can directly sense a variety of
things—motion, chemical composition, electric field—and, indirectly, sense many
other variables which can be converted into motion or dielectric constant, such
as pressure, acceleration, fluid level, and fluid composition. The technology
is low cost and stable and uses simple conditioning circuits - often, the
offset and gain adjustments needed for most sensor types are not required.
Capacitive displacement detectors can detect 10-14 m displacements with good
stability, high speed, and wide extremes of environment,
The simplest electrode configuration is two
close-spaced parallel plates.
With a plate size of 100 mm x 100 mm and a spacing
of 1mm, the capacitance in vacuum , neglecting a small
fringe effect, is 88.54 pF.
With a vacuum dielectric, the relative dielectric
constant er or K is 1. An air dielectric increases K
to 1.0006. Typical dielectric materials such as plastic or oil have dielectric
constants of 3-10, and some polar fluids such as water have dielectric
constants of 50 or more.
Some other popular configurations are
Sphere
Cylinder
Effect of fringing flux
If the plates are close compared to the plate
spacing, the calculation in done above is accurate. But as the plate spacing
increases relative to area, more flux lines connect from the edges and backs of
the plates and the measured capacitance can be much larger than calculated.
Spacing variation (d)
Spacing variation of parallel plates is often used
for motion detection if the spacing change is less than the electrode size. The
parallel plate capacitance formula shows that capacitance is inversely related
to spacing. This gives a conveniently large value of capacitance at small spacing , but it does often require signal conditioning
which can compensate for the parabolic capacitance-motion relationship. This is
easily done by measuring impedance rather than capacitance.
Several sources of nonlinearity corrupt the
performance of a simple parallel plate sensor. A simple two-plate Z-axis sensor
with same-sized plates will have unwanted sensitivity to
•
Transverse displacement in X or Y axes
•
Coupling from back of plate
• Tilt
Transverse displacement sensitivity is easily
handled by overlap or underlap
Area variation (A)
In the spacing-variation motion detectors above,
when displacement increases to the dimension of the electrodes, measurement
accuracy suffers from vanishing signal level. Area variation is then preferred.
As these plates slide transversely, capacitance changes
linearly with motion. Quite long excursions are possible with good linearity,
but the gap needs to be small and well-controlled. As with spacing variation,
overlap is needed so that unwanted sensitivities are minimized. Here, the
unwanted sensitivities are
• Tilt in any axis
• Gap change
• Coupling from back of plate
Several methods help with tilt sensitivity, such as
using a small pickup plate with a chevron shaped driven plate
Advantages :-
• Excellent linearity over
entire dynamic range when Area is changed (since stray electric fields are
small)
• The system responds to
average displacement of a large area of a moving electrode.
• Freedom of electrode
materials and geometry for demanding environments and applications.
• Fractional change in
capacitance can be made large.
• Capacitive sensors can
be made to respond to displacements in one direction only.
• The forces exerted by
the measuring apparatus are electrostatic and usually small enough so that they
can be disregarded
• Capacitors are noiseless:
excellent S/N ratio can be obtained (or their dissipation factor D is large
enough that the dominant noise sources are elsewhere).
LINEAR VARIABLE
DIFFERENTIAL TRANSDUCERS
The Linear Variable Differential Transformer
(LVDT) is the most broadly used variable-inductance transducer in
industry. It is an electro-mechanical device designed to produce an AC voltage
output proportional to the relative displacement of the transformer and the
armature, as illustrated in the figure below.
PRINCIPLE OF OPERATION:
When an AC excitation
signal is applied to the Primary Coil (P), voltages are induced in the two Secondary Coils (S). The magnetic core
inside the coil winding assembly provides the magnetic flux path linking
the Primary and secondary Coils.
Since the two voltages
are of opposite polarity, the Secondary Coils are connected series opposing in
the center, or Null Position. The output voltages are equal and opposite in
polarity and, therefore, the output voltage is zero. The Null Position of an
LVDT is extremely stable and repeatable.
When the MAGNETIC CORE is displaced
from the Null Position, an
electromagnetic imbalance occurs. This imbalance generates a differential AC
output voltage across the Secondary Coils which is linearly proportional to the
direction and magnitude of the displacement.
As shown in the figure,
when the MAGNETIC CORE is moved from the Null Position, the induced voltage in
the Secondary Coil, toward which the Core is moved, increases while the induced
voltage in the opposite Secondary Coil decreases.
Construction:
The physical construction
of a typical LVDT consists of a movable core of magnetic material and three
coils comprising the static transformer. One of the three coils is the primary
coil and the other two are secondary coils.
The basic transformer formula, which states that
the voltage is proportional to the number of coil windings, is the backbone of
the LVDT. The formula is,
where N is the
number of coil windings and V is the voltage read out.
When the iron core slides through the transformer, a certain number of coil windings are
affected by the proximity of the sliding core and thus generate a unique
voltage output.
Open
Wiring LVDT:
Most LVDT's are wired as
shown in the schematic above. This wiring arrangement is known as open
wiring. Since the number of coil windings is uniformly distributed along
the transformer, the voltage output is proportional to the iron core
displacement when the core slides through the transformer. This equation is,
where D is
displacement of the iron core with respect to the transformer, and M is
the sensitivity of the transformer (slope of the displacement-voltage curve).
Ratiometric Wiring LVDT:
Another commonly used LVDT wiring is known as ratiometric wiring, as shown schematically
below.
The displacement for ratiometric
LVDT's is given by the relation,
Advantages :
-
Relative low cost due to
its popularity.
-
Solid and robust, capable of working in a wide
variety of environments.
-
No friction resistance, since the iron core does
not contact the transformer coils, resulting in an infinite (very long) service
life.
-
High signal to noise ratio and low output
impedance.
-
Negligible hysteresis.
-
Infinitesimal resolution (theoretically). In reality,
displacement resolution is limited by the resolution of the amplifiers and
voltage meters used to process the output signal.
-
Short response time, only limited by the inertia of
the iron core and the rise time of the amplifiers.
-
No permanent damage to the LVDT if measurements
exceed the designed range.
ROTARY VARIABLE DIFFERENTIAL TRANSDUCERS
The Rotational Variable
Differential Transformer (RVDT) is used to measure
rotational angles and operates under the same principles as the LVDT sensor. Whereas the LVDT uses a cylindrical
iron core, the RVDT uses a rotary ferromagnetic core. A schematic is shown
below.
Typical RVDT Sensor
The Eddy Current
Transducer uses the effect of eddy (circular) currents to sense the proximity of
non-magnetic but conductive materials. A typical eddy current transducer
contains two coils: an active coil (main coil) and a balance coil. The active
coil senses the presence of a nearby conductive object, and balance coil is
used to balance the output bridge circuit and for temperature compensation.
Common
Specifications
Common
specifications for commercially available eddy current transducers are listed
below:
Size : about 2 to 75 mm (0.079
to 3 in) in diameter, 20 to 40 mm (0.79
to 1.58 in) long
Range
: 0.25 to 30 mm (0.0098 to 1.2 in)
Resolution : Up to 0.1 µm (3.9 µin)
Nonlinearity :0.5%
Bridge Circuit Frequency
: 50 kHz to 10 MHz
Effective
Depth
An eddy current is a
local electric current induced in a conductive material by the magnetic field
produced by the active coil. This local electric current in turn induces a
magnetic field opposite in sense to the one from the active coil and reduces
the inductance in the coil. When the distance between the
target and the probe changes, the impedance of the coil changes correspondingly.
This change in impedance can be detected by a carefully arranged bridge
circuit.
The eddy currents are
confined to shallow depths near the conductive target surface. Their effective
depth is given by,
where f is the excitation frequency of the circuit,
µ is the magnetic permeability of the target material, and sigma is the conductivity
of the target material. The target material must be at least three times
thicker than the effective depth of the eddy currents to make the transducer
successful. This is because the transducer assumes that the eddy currents are
localized near the surface of a semi-infinite solid, and the actual eddy
current amplitude decreases quadratically with
distance.
In practice, the
effective range of an eddy current transducer is given by the vendor suggested
range offset from the target surface by 20%. For example, a 2.5 mm (0.1 in)
range eddy current transducer is
generally considered effective from 0.5 to 3 mm (0.2 to 1.2 in) from the target
surface.
The targeted flat surface
area should not be smaller that the probe tip diameter. If the target surface
is smaller than 50% of the probe diameter, output signals decrease
substantially.
Pros:
- Non-contacting measurement.
-
High resolution.
-
High frequency response.
Cons:
-
Effective distance is
limited to close range.
-
The relationship between
the distance and the impedance of the coil is nonlinear and temperature
dependent. Fortunately, a balance coil can compensate for the temperature
effect. As for the nonlinearity, careful calibrations can ease its drawback.
-
Only works on conductive
materials with sufficient thickness. It can not be used for detecting the
displacement of non-conductive materials or thin metalized
films. However, a piece of conductive material with sufficient thickness can be
mounted on non-conductive targets to overcome this drawback. A self-adhesive
aluminum-foil tape is commercially available for this purpose. However, this
practice is not always possible.
-
Calibration is generally
required, since the shape and conductivity of the target material can affect
the sen temperature dependent. Fortunately, a balance
coil can compensate for the temperature
FOTONIC
SENSORS
A popular fiber optic sensor, the fotonic sensor is a displacement sensor
containing two groups of fiber optics, one set connected to a light source and
termed the transmitting fibers,
and the other set connected to a photo detector (photodiode) and known as the receiving fibers. These two groups of
fibers are bundled into a common probe.
Referring to the schematic below, the light
generated from the source is channeled
through the transmitting fibers to the probe tip. The light then travels to the
target surface and part of it is reflected back to the probe. A portion of the
reflected light is caught by the receiving fibers and transmitted to the photo
detector where its intensity is measured. The intensity of the reflected light
is a function of distance (gap) between the probe tip and the target surface.
Typical Fotonic
Sensors
The Fotonic (a popular fiber optic) sensor output function (i.e. light
intensity versus distance to target surface) can be divided into three regions:
the front slope, the transition,
and the back slope.
These three regions are shown in the schematic below.
Response of Typical Fotonic Sensors
Light Intensity (Voltage Output) vs. Distance
Interpretation
of Sensor Response:
Interpreting the Fotonic sensor output function
shown above, we can draw the following conclusions:
1.
When the gap between the probe tip and the target
surface is zero, no light can escape from the transmitting fibers to reach the
receiving fibers, so the measured intensity of the reflected light is zero.
2.
As the gap opens up, reflected light can begin to
reach the receiving fibers. However, in this region the actual intensity of the
reflected light does not change with increasing gap distance, since most of the
light is still confined to the surface directly under the probe tip (or more
precisely, directly under the transmitting fibers). The measured intensity
increases because as the gap opens up, a larger fraction of the reflected light
can reach the receiving fibers. In other words, the receiving fibers become
more and more "illuminated". As a result, the measured intensity of
the reflected light increases almost linearly with gap distance in this front
slope region.
3.
The measured intensity keeps increasing until the
gap distance is about the same order as the probe diameter. In this transition
region, the receiving fibers are now fully illuminated and the maximum measured
reflection is reached.
4.
As the gap increases past the transition region,
the measured intensity drops off following roughly an inverse-square law. This
results from the fact that, even though the receiving fibers are fully
illuminated, the actual intensity of the reflected light as seen by the probe
diminishes.
FABRICATION:
Commonly-Used Fiber Patterns
(Cross section of probe)
Pros:
- Non-contacting
measurement..
-
No moving parts, less likely to break..
Cons:
- Re-calibration is
generally required often, since the reflection index of target surfaces may
vary.
-
Works well on highly reflective surfaces, less
effective on duller surfaces.
-
May be affected by surrounding lighting conditions.
-
The characteristic length of the target surface's
roughness should be at least an order smaller than the spacing of the
transmitting and receiving fibers. In other words, a fotonic
sensor can measure the roughness of the target surface up to the order of the
spacing of the transmitting and receiving fibers.
MAGNETOSTRICTIVE DISPLACEMENT SENSORS Magnetostriction is a property of ferromagnetic materials such as iron, nickel, and cobalt. When placed in a magnetic field, these materials change size and/or shape
.
Figure: A magnetising force, H, causes a dimensional change due to the alignment of magnetic domains
The physical response of a ferromagnetic material is due to the presence of magnetic moments, and can be understood by considering the material as a collection of tiny permanent magnets, or domains. Each domain consists of many atoms. When a material is not magnetized, the domains are randomly arranged. When the material is magnetized, the domains are oriented with their axes approximately parallel to one another. Interaction of an external magnetic field with the domains causes the magnetostrictive effect. This effect can be optimized by controlling the ordering of the domains through alloy selection, thermal annealing, cold working, and magnetic field strength.
The ferromagnetic materials used in magnetostrictive position sensors are transition metals such as iron, nickel, and cobalt. In these metals, the 3d electron shell is not completely filled, which allows the formation of a magnetic moment. (i.e., the shells closer to the nucleus than the 3d shell are complete, and they do not contribute to the magnetic moment). As electron spins are rotated by a magnetic field, coupling between the electron spin and electron orbit causes electron energies to change. The crystal then strains so that electrons at the surface can relax to states of lower energy. When a material has positive magnetostriction, It enlarges when placed in a magnetic field; with negative magnetostriction, the material shrinks. The amount of magnetostriction in base elements and simple alloys is small, on the order of 10-6 m/m.
Since applying a magnetic field causes stress that changes the physical properties of a magnetostrictive material, it is interesting to note that the reverse is also true: applying stress to a magnetostrictive material changes its magnetic properties (e.g., magnetic permeability). This is called the Villari effect. Normal magnetostriction and the Villari effect are both used in producing a magnetostrictive position sensor. 
Figure : The Wiedemann
effect describes the twisting due to an axial magnetic field applied to a
ferromagnetic wire or tube that is carrying an electric current.
An important characteristic of a wire made of a magnetostrictive material is the Wiedemann effect (see Figure 2). When an axial magnetic field is applied to a magnetostrictive wire, and a current is passed through the wire, a twisting occurs at the location of the axial magnetic field. The twisting is caused by interaction of the axial magnetic field, usually from a permanent magnet, with the magnetic field along the magnetostrictive wire, which is present due to the current in the wire. The current is applied as a
short-duration pulse, -1 or 2 µs; the minimum current density is along the center of the wire and the maximum at the wire surface. This is due to the skin effect.
The magnetic field intensity is also greatest at the wire surface. This aids in developing the waveguide twist. Since the current is applied as a pulse, the mechanical twisting travels in the wire asan ultrasonic wave. The magnetostrictive wire is therefore called the waveguide. The wave travels at the speed of sound in the waveguide material, ~ 3O00 m/s.
The operation of a magnetostrictive position sensor is shown here
Figure : Principle of Magnetostrictive Sensors 
The axial magnetic field is provided by a position magnet. The position magnet is attached to the machine tool, hydraulic cylinder, or whatever is being measured. The waveguide wire is enclosed within a protective cover and is attached to the stationary part of the machine, hydraulic cylinder, etc.
The location of the position magnet is determined by first applying a current pulse to the waveguide. At the same time, a timer is started. The current pulse causes a sonic wave to be generated at the location of the position magnet Wiedemann effect. The sonic wave travels along the waveguide until it is detected by the pickup.This stops the timer. The elapsed time indicated by the timer then represents the distance between the position magnet and the pickup. The sonic wave also travels in the direction away from the pickup. In order to avoid an interfering signal from waves travelling in this direction, their energy is absorbed by a damping device (called the damp). The pickup makes use of the Villari effect. A small piece of magnetostrictive material, called the tape, is welded to the waveguide near one end of the waveguide. This tape passes through a coil and is magnetized by a small permanent magnet called the bias magnet. When a sonic wave propagates down the waveguide and then down the tape, the stress induced by the wave causes a wave of changed permeability (Villari effect) in the tape. This in turn causes a change in the tape magnetic flux density, and thus a voltage output pulse is produced from the coil (Faraday effect). The voltage pulse is detected by the electronic circuitry and conditioned into the desired output.
TO THE LINKS
Triangulation
sensors are ideal for monitoring the distance to small, fragile parts or soft
surfaces susceptible to deformation if touched by a probe. A light source,
usually a laser, projects a beam of light onto the surface to be measured; the
light is then reflected through a lens, say to point "A." Because the
location of "A," the light source, and the lens' properties are all
known, it's possible to infer the position of the reflection surface. Engineers
can vary sensor range by selection of the lens.
Figure : The principle of
Laser Triangulation
Triangulation
sensors operate with almost any type of light source. For best performance, the
light source should be of relatively high intensity and should create a small
spot on the surface. As a result, almost all triangulation sensors use a laser
as the light source, and most standard sensor designs today use a solid-state
laser, similar to the type used in common laser pointers. The solid-state laser
diode provides a compact, efficient, long-lived light source for sensors.
Surface
effects
Triangulation
operates by reflecting the spot of light from a surface onto a position-sensing
detector. Most materials are, optically, a combination of diffuse and specular surfaces. Because triangulation operates by
imaging light reflected from the surface, a change in reflectivity changes the
level or intensity of light reaching the detector.
In
cases where the surface changes dramatically, such as components that are
different colors, the sensor must be able to respond to these changes
automatically. Applications where this is a factor require a very fast feedback
scheme that controls the laser intensity or some other exposure feature in real
time to ensure that stable and reliable data is obtained.
Detector
types
Because
triangulation requires finding the location of the center of the imaged spot,
the detector must be able to detect the spot location. There are two main types
of detectors used in triangulation sensors. The first is a position-sensing
detector (PSD), and the second is a charge-coupled device (CCD).
PSDs are available in one- and two-axis
forms, with single-axis types generally used in triangulation sensors. The PSD
is a single element detector that converts incident light into continuous
position data. The detector chip has outputs at both ends, and the amount of
current from each output is proportional to the position of the imaged spot on
the detector.
Equal
currents arrive at the two outputs if the spot centers on the detector. If the
imaged spot moves off center, the two outputs change, and the device calculates
the spot position from the relative values of the outputs. PSDs
provide the highest data rates (up to 500 kilohertz) and have the fastest rates
of gain control — an important consideration when dealing with surfaces of
varying texture, color, and reflectivity.
CCD
detectors are essentially a form of television camera and come in one- or
two-dimension forms. In most simple triangulation sensors, a single-dimension
CCD is used. The detector consists of a single row of discrete photodetectors, often referred to as pixels. This device is
essentially a one-line TV "camera." In operation, the individual
pixels electronically report their status as a train of pulses. The sensor
electronics determine the center of the imaged spot for triangulation processing.
The CCD
detector has several advantages. First, the "video" output of the
sensor can be viewed to display light levels and cleanliness of the image, as
well as show any stray light effects. Further, analysts can filter or process
the image for their unique needs. This can remove unwanted multiple spots,
reflections, or other light.
The
chief disadvantage of the CCD detector is that it's slower than a PSD. Gain
control in CCD-based sensors is not as fast as in PSD-based sensors — a
drawback in applications where surface reflectivity changes rapidly.
A
sophisticated version of the CCD sensor is available that collects data at
multiple points in a single frame, generating contour information along a line
of the part being inspected. This sensor projects a line of laser light onto
the surface rather than a single point. It uses a two-dimensional CCD as the
detector. The image of the laser line on the detector maps out the contour of
the surface. Analyzing multiple points along the laser line using the
triangulation equations generates a profile of the part. The sensor generate a
three-dimensional map of the surface if the part is moving under the sensor.
CONCLUSION
As we
have seen, displacement sensors have come a long way from the days of the LVDT’s . Nowadays, we have capacitive sensors made of
silicon wafers that are 500 micrometers thick! Among all the sensors that we
reviewed, capacitive sensors are the most sensitive instruments with almost
negligible response times. For larger distances, laser triangulation is the
preferred choice in terms of accuracy. But for applications in extreme
conditions, the LVDT is still the most preferred for its solid and robust
nature.
The ones we
discussed today are the ones that are being widely used nowadays – but with the
steady pace of scientific research, there are many new and much more accurate
devices coming up. In fact, it is highly possible, 10 years down the line, the
batch of students presenting “Displacement Sensors” won’t even mention the ones
we researched so painstakingly!