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## Mechanical Sensors

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Title: Mechanical Sensors

1
Mechanical Sensors
• Chapter 6

2
Force sensors
• A class of sensors
• Includes a fairly large number of different
sensors
• Based on many principles
• Will discuss four types of general sensors
• force sensors
• accelerometers
• pressure sensors
• gyroscopes
• cover most principles involved in sensing of
mechanical quantities - directly and indirectly.

3
Force sensors
• Some of these sensors are used for applications
which initially do not seem to relate to
mechanical quantities.
• Example measure temperature through expansion of
gases in a volume (pneumatic temperature sensor
discussed in chapter 3).
• Some mechanical sensors do not involve motion or
force.
• Example the fiber optic gyroscope and will be
discussed below

4
Force sensors - Strain Gauges
• Strain gauge - The main tool in sensing force.
• Strain gauges, measure strain
• Strain can be related to stress, force, torque
and a host of other stimuli including
displacement, acceleration or position.
• At the heart of all strain gauges is the change
in resistance of materials due to change in their
length due to strain.

5
Force sensors - Strain Gauges
• Definition of strain consider a length of
metallic wire L, of conductivity??? and
cross-sectional area A.
• The resistance of the wire is

Taking the log on both sides
6
Force sensors - Strain Gauges
• Taking the differential on both sides

Change in resistance is due to two terms Due to
change in conductivity Due to the deformation of
the conductor. For small deformations (linear
deformation), both terms on the right hand side
are linear functions of strain, ?. Bundling both
effects together (that is, the change in
conductivity and deformation) we can write
7
Force sensors - Strain Gauges
• For small deformations (linear deformation), both
terms on the right hand side are linear functions
of strain, ?.
• Bundling both effects together (that is, the
change in conductivity and deformation) we can
write

Ss is the sensitivity of the strain gauge Also
known as the gauge factor
8
Strain Gauge
• For any given strain gauge the gauge factor is a
constant
• Ranges between 2 to 6 for most metallic strain
gauges
• From 40-200 for semiconductor strain gauges.
• The strain gauge relation gives a simple linear
relation between the change in resistance of the
sensor and the strain applied to it.

9
Stress and Strain
10
Strain and Stress
• Given the conductor discussed above and applying
a force along its axis, the stress is

? stress N/m2 E Youngs modulus of the
material (modulus of elasticity) N/m2 ?
dL/L strain
11
Strain and Stress
• Strain is a normalized linear deformation of the
material
• Stress is a measure of elasticity of the material.

12
Strain gauges
• Strain gauges come in many forms and types.
• Any material, combination of materials or
physical configuration that changes its
resistance due to strain constitutes a strain
gauge.
• Will restrict our discussion to two types that
account for most of the strain gauges in use
today
• wire (or metal) strain gauges - resistive
• semiconductor strain gauges.

13
metallic strain gauge
• In its simplest form
• A length of wire, held between two posts
• When a force is applied to them, will deform the
wire causing a change in the wires resistance.
• This method was used in the past and is valid
• It is not very practical (construction,
attachment to system, change in resistance is
very small).
• Sometimes, multiple lengths of wire were used.

14
Wire strain gauge
15
Metallic strain gauge common form
• A more practical strain gauge - resistive
• Built out of a thin layer of conducting material
• Deposited on an insulating substrate (plastic,
ceramic, etc.)
• Etched to form a long, meandering wire (figure)
• Constantan (60 copper, 40 nickel) is most
common material
• negligible temperature coefficient of resistance
(TCR see Table 3.1)).
• Other materials are commonly used (table)

16
The resistive strain gauge
17
Materials for resistive strain gauges
18
Metallic strain gauge common form
• Strain gauges may also be used to measure
multiple axis strains by simply using more than
one gauge or by producing them in standard
configurations.
• Some of these are shown next.

19
Two-axis strain gauge
20
120 degree rosette
21
45 degree rosette
22
45 degree stacked rosette
23
membrane rosette
24
Semiconductor strain gauges
• Operate like resistive strain gauges
• Construction and properties are different.
• The gauge factor for semiconductors is much
higher than for metals.
• The change in conductivity due to strain is much
larger than in metals.
• Are typically smaller than metal types
• Often more sensitive to temperature variations
(require temperature compensation).

25
Semiconductor strain gauges
• All semiconductor materials exhibit changes in
resistance due to strain
• The most common material is silicon because of
its inert properties and ease of production.
• The base material is doped, by diffusion of
doping materials (usually boron or arsenide for p
or n type) to obtain a base resistance as needed.
• The substrate provides the means of straining the
silicon chip and connections are provided by
deposition of metal at the ends of the device.

26
Semiconductor strain gauges
• Construction of a semiconductor strain gauge

27
Semiconductor strain gauges
• Other types of semiconductor strain gauges

28
Semiconductor strain gauges
• One of the important differences between
conductor and semiconductor strain gauges is that
semiconductor strain gauges are essentially
nonlinear devices with typically a quadratic
transfer function

Also PTC or NTC operation
29
PTC and NTC operation
30
Strain gauges - applications
• Strain gauge must be made to react to a force.
• The strain gauge is attached to the member in
which strain is sensed, usually by bonding.
Cannot be re-used!
• Special bonding agents exist for different
applications and types of materials
• Usually supplied by the manufacturers of strain
gauges or specialized producers.
• Strain gauges are often used for bending strain,
twisting (torsional and shear strain) and
longitudinal tensioning/deformation (axial
strain) of structures (engine shafts, bridge

31
Strain gauges - properties
• The properties of strain gauges vary by
application
• Most metal gauges have a nominal resistance
between 100 and 1000?, (lower and higher
resistances are available)
• Gauge factor between 2-5
• Dimensions from less than 3x3 mm to lengths in
excess of 150 mm (almost any size may be
fabricated if necessary).
• Rosettes (multiple axis strain gauges) are
available with 45, 90 and 120? axes as well as
diaphragm and other specialized configurations.

32
Strain gauges - properties
• Typical sensitivities are 5m???
• Deformation is of the order of 2-3?m/m.
• Much higher strains can be measured with
specialized gauges.
• Semiconductor strain gauges
• usually smaller than most resistive strain gauges
• can be made with higher resistances.
• their use is limited to low temperatures
• can be much less expensive than metal strain
gauges.
• often part of another device

33
Strain gauges - errors
• Strain gauges are subject to a variety of errors.
• Due to temperatures - resistance, especially in
semiconductors, is affected by temperature in the
same way as by strain.
• In metal gauges, this is usually small (materials
with low temperature coefficients of resistance).
• In semiconductors, temperature compensation is
sometimes provided on board or a separate sensor
may be used for this purpose.

34
Strain gauges - errors
• A third source of error is due to the strain
itself, which, over time, tends, to permanently
deform the gauge.
• can be eliminated by periodic re-calibration
• can be reduced by ensuring that the maximum
deformation allowed is small and below the
recommended for the device.

35
Strain gauges - errors
• Due the bonding process
• Thinning of materials due to cycling.
• Most strain gauges are rated for
• given number of cycles (i.e. 106 or 107 cycles),
• maximum strain (3 is typical for conducting
strain gauges, 1 for semiconductor strain
gauges)
• temperature characteristics specified for use
with a particular material (aluminum, stainless
steel, carbon steel) for optimal performance when
bonded
• Typical accuracies are of the order of 0.2-0.5.

36
Typical resistive strain gauges
37
Other Strain Gauges
• Other strain gauges - for specialized
applications.
• Optical fiber strain gauges.
• The change in length of the fiber due to strain
changes the phase of the light through the fiber.
• Measuring the light phase, either directly or in
an interferrometric method can produce readings
of minute strain that cannot be obtained in other
strain gauges.
• The device and the electronics necessary is far
more complicated than standard gauges.

38
Other Strain Gauges
• There are also liquid strain gauges which rely in
the resistance of an electrolytic liquid in a
flexible container which can be deformed.
• Another type of strain gauge that is used on a
limited basis is the plastic strain gauge.
graphite or carbon in a resin as a substrate and
used in a way similar to other strain gauges.
• Very high gauge factors (up to about 300), they
are otherwise difficult to use and inaccurate as
well as unstable mechanically, severely limiting
their practical use.

39
Force and tactile sensors
• Forces can be measured in many ways
• The simplest - use a strain gauge
• Calibrate the output in units of force.
• Other methods include
• measuring acceleration of a mass (Fma),
• measuring the displacement of a spring under
action of force (xkF, k is the spring constant),
• measuring the pressure produced by force and some
variations of these basic methods.
• None of these is a direct measure of force
• most are more complicated than use of a strain
gauge.

40
Force and tactile sensors
• The basic method is shown in Figure 6.9.
• One measures the tensile force by measuring the
strain in the strain gauge.
• The sensor is usually provided with attachment
holes
• may also be used in compressive mode by
pre-stressing the strain gauge.
• This type of sensor is often used to measure
forces in locations such as machine tools, engine
mounts and the like.
• Often it is called a load cell, especially when
large forces are measured.

41
Force sensor
42
Force sensor
43
44
Tactile sensors
• Tactile sensors are force sensors but
• Definition of tactile action is broader, the
sensors are also more diverse.
• One view is that tactile action as simply sensing
the presence of force. Then
• A simple switch is a tactile sensor
• This approach is commonly used in keyboards
• Membrane or resistive pads are used
• The force is applied against the membrane or a
silicon rubber layer.

45
Tactile sensors
• In many tactile sensing applications it is often
important to sense a force distribution over a
specified area (such as the hand of a robot).
• Either an array of force sensors or
• A distributed sensor may be used.
• These are usually made from piezoelectric films
which respond with an electrical signal in
response to deformation (passive sensors).
• An example is shown in Figure 6.11.

46
A tactile sensor
47
Tactile sensors
• Operation
• The polyvinylidene fluoride (PVDF) film is
sensitive to deformation.
• The lower film is driven with an ac signal
• It contracts and expands mechanically and
periodically.
• When the upper film is deformed, its signal
changes from normal and the amplitude and or
phase of the output signal is now a measure of
deformation (force).

48
Tactile sensors
• Another example is shown in Figure 6.12
• Used to sense body motion due to breathing.

49
Tactile sensors
• The simplest tactile sensors are made of
conductive polymers or elastomers or with
semiconductive polymers
• Called piezoresistive sensors or force sensitive
resistive (FSR) sensors.
• In these devices, the resistance of the material
is pressure dependent and is shown schematically
in Figure 6.13.

50
FSR sensor
51
Tactile sensors
• A conducting foam (such as the foam used to ship
semiconductors) and two electrodes.
• The resistance of FSR sensors is a nonlinear
function of force (Figure 6.13)
• The change in resistance is high (large dynamic
range)
• The sensor is quite immune to noise and easily
interfaced with microprocessors.
• Either dc or ac sources may be used and the
device may be as large or as small as possible.
• An array of sensors may be built by using one
large electrode on one side of the film and
multiple electrodes on the other side.

52
Accelerometers
• By virtue of Newtons second law (F ma) a
sensor may be made to sense acceleration by
simply measuring the force on a mass.
• At rest, acceleration is zero and the force on
the mass is zero.
• At any acceleration a, the force on the mass is
directly proportional given a fixed mass.
• This force may be sensed in any method of sensing
force but, again, the strain gauge will be
representative of direct force measurement.

53
Accelerometers
• Other methods of sensing acceleration.
• Magnetic methods and electrostatic (capacitive)
methods are quite commonly used.
• The distance between the mass and a fixed
surface, which depends on acceleration can be
made into a capacitor. Capacitance increases (or
decreases) with acceleration.
• A magnetic sensor can be used by measuring the
field of a magnetic mass. The higher the
acceleration, the closer (or farther) the magnet
from a fixed surface and hence the larger or
lower the magnetic field.
• The methods used in chapter 5 to sense position
or proximity can now be used to sense
acceleration.

54
Accelerometers - principles
mechanical model of a mass ( Figure 6.14).
• The mass, moves under the influence of forces,
has a restoring force (spring) and a damping
force (which essentially prevents it from
oscillating).

55
Accelerometers - principles
• Under these conditions, and assuming the mass can
only move in one direction (along the horizontal
axis), Newtons second law may be written as

Assumes that the mass has moved a distance x
under the influence of acceleration, k is the
restoring (spring) constant and b is the damping
coefficient. Given the mass m and the constants
k and b, a measurement of x gives an indication
of the acceleration a.
56
Accelerometers - principles
• Therefore, for a useful acceleration sensor
(often called accelerometer) it is sufficient to
provide a component which can move relative to
the sensors housing and a means of sensing this
movement.
• A displacement sensor (position, proximity, etc.)
can be used to provide an appropriate output
proportional to acceleration.

57
Accelerometers - Capacitive
• One plate of a small capacitor is fixed and
connected physically to the body of the sensor.
• A second plate serves as the inertial mass of the
sensor is free to move and connected to a
restoring spring.
• Three basic configurations are shown in Figure
6.15.
• The restoring force is provided by springs
(Figure 6.15a,c) or by a cantilevers fixed end
(Figure 6.15b).

58
Capacitive accelerometers
59
Accelerometers - Capacitive
• In Figure 6.15a and 6.15b, the distance between
the plates changes with acceleration.
• In Figure 6.15c, the effective area of the plates
changes while the distance between the plates
stays constant.
• In either case, acceleration either increases the
capacitance or decreases it, depending on the
direction of motion.
• In a practical accelerator, the plates must be
prevented from touching by stoppers
• Some kind of damping mechanism must be added to
prevent the springs or the beam from oscillating

60
Capacitive accelerometers - practical
considerations
• A more practical device

61
Capacitive accelerometers - practical
considerations
• Cantilever beam
• End of travel stops
• Capacitance proportional to vertical acceleration
• Changes in capacitance are very small
• Indirect methods such as using the capacitor in
an LC oscillator are used.
• The frequency of oscillation is a direct measure
of acceleration.
• Can be produced as semiconductor devices by
etching both the mass, fixed plate and springs
directly into silicon.

62
Capacitive accelerometers - practical
considerations
• Second structure a bridge structure
• The mass moves between two plates and forms an
upper and lower capacitor.
• A differential mode is obtained since at rest the
two capacitors are the same.

63
Strain gauge accelerometers
• The mass is suspended on a cantilever beam
• Strain gauge senses the bending of the beam

64
Variable inductance accelerometers
• A rod connected and moving with the mass links to
a coil. The inductance of the coil is
proportional to the position of the mass
• An LVDT may be used

65
Hall element magnetic accelerometers
• Acceleration changes distance to hall element
• Hall element output is calibrated as acceleration
• The magnet may be on the hall element side
(biased hall element)

66
Other types of accelerometers
• Many other types of accelerometers
• All employ a moving mass in one form or another.
• Example the heated gas accelerometer
• Gas in cavity is heated to an equilibrium temp.
• Two (or more) thermocouples are provided
equidistant from the heater.
• Under rest conditions, the two thermocouples are
at the same temperature. Their reading (one
thermocouples is the sense thermocouple, the
second the reference thermocouple) is zero.

67
Other types of accelerometers
• Under acceleration occurs, the gas shifts to the
direction opposite the motion (the gas is the
inertial mass) causing a temperature gradient
which is calibrated in terms of acceleration.

68
Other types of accelerometers
• Other accelerometers use optical means
• Example activating a variable shutter by means
of the moving mass
• Optical fiber accelerometers use an optical fiber
position sensor,
• Vibrating reeds whose vibration rate changes with
acceleration
• Many more.

69
Accelerometers - notes
• Multiple axis accelerometers can be built by
essentially using single axis accelerometers with
axes perpendicular to each other.
• These can be fabricated as two or three axes
accelerometer or two or three single axis
accelerometers may be attached appropriately.
• Proper damping must be provided to avoid
oscillations of the mass while still keeping
reasonable response times.
• The uses of accelerometers are vast and include
air bag deploying sensors, door unlocking,
weapons guidance systems, vibration and shock
measurement, satellites, intrusion alarms (by
detecting motion), and control and other similar
applications.

70
Accelerometers - notes
• Sensitivity from a few mg and up
• Noise and errors vibrations, temperature
variations, deterioration of the return spring

71
Velocity sensing
• Velocity sensing is more complicated than
acceleration sensing.
• One can always measure something proportional to
velocity. For example
• We may infer the velocity of a car from the
rotation of the wheels
• Or the transmission shaft ( a common method of
velocity measurement in cars)
• Or count the number of rotation of a shaft per
unit time in an electric motor.

72
Velocity sensing
• A free-standing sensor that measures velocity
directly is much more difficult to produce.
• One approach that may be used is the induction of
emf in a coil due to a magnet.
• This requires that the coil be stationary
• If the velocity is constant (no acceleration) the
magnet cannot move relative to the coil.
• For changing velocity (when acceleration is not
zero), the principle in Figure 6.21 may be
useful.

73
Velocity sensing
74
Velocity sensing
• The emf induced in the coils is governed by

The time derivative indicates that the magnet
must be moving to produce a nonzero change in
flux. The most common approach to velocity
sensing is to use an accelerometer and integrate
its output using an integrating amplifier
75
Velocity sensing
• constant velocity cannot be sensed (zero
acceleration)
• Relative velocity of objects is easily measured
• We shall see fluid velocity sensors
• Also doppler effect sensors, time of flight
devices - etc,

76
Pressure sensors - introduction
• Sensing of pressure is only second in importance
to sensing of strain in mechanical systems
• These sensors are used either in their own right,
(to measure pressure), or to sense secondary
quantities such as force, power, temperature and
the like.
• One of the reasons for their prominence is that
in sensing gases and fluids, force is not an
option only pressure can be measured and
related to properties of these substances.

77
Pressure sensors - introduction
• Another reason for their widespread use and of
exposure of most people to them is their use in
cars, atmospheric weather prediction, heating and
other consumer oriented devices.
• The barometer hanging on many a wall and the
use of atmospheric pressure as indication of
weather conditions has helped popularize the
concept of pressure and pressure sensing

78
Pressure sensors - Units
• The basic SI unit of pressure is the pascal
• 1 pascal Pa 1 newton per square meter N/m2
• The pascal is an exceedingly small unit
• kPa 103 Pa
• Mpa 106 Pa.
• Other often units are
• bar 1 bar 0.1 Mpa
• torr 1 torr 133Pa.
• millibar (1.333 torr100Pa)
• microbar (1 ?bar 0.1 Pa)

79
Pressure sensors - Units
• In common use - the atmosphere defined as
• the pressure exerted by a 1 meter column of
water at 4?C on one square centimeter.
• 1 atm 0.101 Mpa 760 torr
• The use of the atmosphere indicates a totally
parallel system of pressure based either on a
column of water or a column of mercury.
• The torr (named after Torricelli) is defined as
the pressure exerted by a 1mm of mercury (at 0?C
and normal atmospheric pressure)

80
Pressure sensors - Units
• In the US the common (non-metric) unit of
pressure is the psi (pounds per square inch)
• 1 psi 6.89 kPa 0.0703 atm.
• Vacuum is often used, sometimes as a separate
quantity.
• Vacuum means lack of pressure,
• Understood as indicating pressure below ambient.
• One talks about so many psi of vacuum
• This simply refers to so many psi below ambient
pressure.

81
System of units for pressurs
82
Pressure sensing
• Pressure is force per unit area
• Sensing it follows the same principle as the
sensing of force
• Measuring the displacement of an appropriate
member of the sensor in response to pressure.
• The range of methods is quite large and includes
thermal, optical as well as magnetic and
electrical principles.
• Earliest sensors were purely mechanical

83
Mechanical pressure sensors
• Mechanical pressure sensors.
• Direct transduction from pressure to mechanical
displacement
• These devices are actuators that react to
pressure
• Are as common today as ever.
• Some mechanical devices have been combined with
other sensors to provide electrical output
• Others are still being used in their original
form.
• The most common of these is the Bourdon tube.

84
The Bourdon Tube
85
Mechanical pressure sensors
• Has been used for over a century in pressure
gauges
• The dial indicator is connected directly to the
tube.
• Still the most common pressure gauge used today
• does not need additional components
• simple
• inexpensive.
• Typically used for gases but it can also be used
for sensing fluid pressure.
• Tire gauges, fuel gauges, etc.

86
Bellows and diaphragms
• Principle expansion of a diaphragm or a bellows
under the influence of pressure.
• The motion produces may be used to directly drive
an indicator or
• May be sensed by a displacement sensor (LVDT,
magnetic, capacitive etc.)
• A simple diaphragm pressure sensor used in wall
barometers is shown in Figure 6.24.

87
Diaphragm pressure sensor
88
Bellows and diaphragms
• One side is held fixed (in this case by the small
screw which also serves to adjust, or calibrate
it)
• The other moves in response to pressure.
• The device is hermetically sealed at a given
pressure
• Any pressure below the internal pressure will
force the diaphragm to expand (like a baloon)
• Any higher pressure will force it to contract.
• Very simple and trivially inexpensive, but
• Possibility of leakage
• Dependence on temperature.

89
Bellows and diaphragms
• A bellows (Figure 6.25) is a similar device
• Can be used for direct reading or to activate
another sensor.
• The bellows, in various forms is also being used
as an actuator.
• One of its common uses is in vacuum motors used
in vehicles to activate valves and to move slats
and doors, particularly in heating and air
conditioning systems.

90
Membranes and plates
• The most common devices used for pressure sensing
are the thin plate and the diaphragm or membrane.
• Membrane a thin plate with negligible thickness
• Thin plate a thick membrane
• Their behavior and response to pressure is
different. In relation to Figure 6.26, the
deflection of the center of a membrane (maximum
deflection) which is under radial tension S and
the stress in the diaphragm are given as

91
Membrane and thin plate
92
Membranes and thin plates
• In relation previous figure, the deflection of
the center of a membrane (maximum deflection)
which is under radial tension S, and the stress
in the diaphragm are given as

P is the applied pressure difference between the
top and bottom of the membrane r its radius t
its thickness
93
Membranes and thin plates
• If the thickness t is not negligible, the
behavior is different and given as

E is the Youngs modulus V is the Poissons
ratio The displacement is linear with pressure
hence their widespread use for pressure sensing.
94
Pressure sensors
• Pressure sensors come in four basic types
• Absolute pressure sensors (PSIA) pressure sensed
relative to absolute vacuum.
• Differential pressure sensors (PSID) the
difference between two pressures on two ports of
the sensor is sensed.
• Gage pressure sensors (PSIG) the pressure
relative to ambient pressure is sensed. (Most
common)
• Sealed gage pressure sensor (PSIS) the pressure
relative to a sealed pressure chamber (usually 1
atm at sea level or 14.7 psi) is sensed.

95
Piezoresistive pressure sensors
• Piezoresistor is a semiconductor strain gauge
• Most modern pressure sensors use it rather than
the conductor type strain gauge.
• Resistive (metal) strain gauges are used only at
higher temperature or for specialized
applications
• May be fabricated of silicon
• simplifies construction
• allows on board temperature compensation,
amplifiers and conditioning circuitry.

96
Piezoresistive pressure sensors
• Basic structure
• two gauges are parallel to one dimension of the
diaphragm
• The two gauges can be in other directions

97
Piezoresistive pressure sensors
• The change in resistance of the two piezoresistos
is

? is an average sensitivity (gauge) coefficient
and ?x and ?y are the stresses in the transverse
directions
98
Piezoresistive pressure sensors
• Piezoresistors and the diaphragm are fabricated
of silicon.
• A vent is provided, making this a gage sensor.
• If the cavity under the diaphragm is hermetically
closed and the pressure in it is P0, the sensor
becomes a sealed gage pressure sensor sensing the
pressure P-P0.
• A differential sensor is produced by placing the
diaphragm between two chambers, each vented
through a port (figure).

99
Differential pressure sensor
100
Piezoresistive pressure sensors
• A different approach is to use a single strain
gauge
• A current passing through the strain gauge
• Pressure applied perpendicular to the current.
• The voltage across the element is measured as an
indication of the stress and therefore pressure.

101
Construction
• Many variations
• Body of sensor is particularly important
• Silicon, steel, stainless steel and titanium are
most commonly used
• Ports are made with various fittings
• The contact material is specified (gas, fluid,
corrosivity, etc.)

102
Various pressure sensors
103
Miniature pressure sensors
104
Pitran pressure sensors (absolute)
105
150 psi differential pressure sensor
106
100 psi absolute pressure sensor (TO5 can)
107
15 and 30 psi differential pressure sensors
108
Capacitive pressure sensors
• The deflection of the diaphragm constitutes a
capacitor in which the distance between the
plates is pressure sensitive.
• The basic structure shown in Figure 6.16 may be
used or a similar configuration devised.
• These sensors are very simple and are
particularly useful for sensing of very low
pressure.
• At low pressure, the deflection of the diaphragm
may be insufficient to cause large strain but can
be relatively large in terms of capacitance.

109
Capacitive pressure sensors
• The capacitance may be part of an oscillator,
• The change in its frequency may be quite large
making for a very sensitive sensor.
• less temperature dependent
• stops on motion of the plate may be incorporated,
- not sensitive to overpressure.
• Overpressures of 2-3 orders of magnitude larger
than rated pressure may be easily tolerated
without ill effects.
• The sensors are linear for small displacement but
at larger pressures the diaphragm tends to bow
causing nonlinear output

110
Magnetic pressure sensors
• A number of methods are used
• In large deflection sensors an inductive position
sensor may be used or an LVDT attached to the
diaphragm.
• For low pressures, variable reluctance pressure
sensor is more practical.
• The diaphragm is made of a ferromagnetic material
and is part of the magnetic circuit shown in
Figure 6.32.

111
Variable reluctance pressure sensor
112
Magnetic pressure sensors
• The reluctance is directly proportional to the
length of the air gap between the diaphragm and
the E-core.
• Gap changes with pressure and the inductance of
the two coils changes and sensed directly.
• A very small deflection can cause a very large
change in inductance of the circuit making this a
very sensitive device.
• Magnetic sensors are almost devoid of temperature
sensitivity allowing these sensors to operate at
elevated temperatures.

113
Other pressure sensors
• Optoelectronic pressure sensors - Fabri-Perot
optical resonator to measure small displacements.
• light reflected from a resonant optical cavity is
measured by a photodiode to produce a measure of
pressure sensed.
• A very old method of sensing low pressures (often
called vacuum sensors) is the Pirani gauge.
• based on measuring the heat loss from gases which
is dependent on pressure. The temperature is
sensed and correlated to pressure, usually in an
absolute pressure sensor arrangement.

114
Pressure sensors - properties
• Semiconductor based sensors can only operate at
low temperatures (?50 to 150?C).
• Temperature dependent errors can be high unless
properly compensated (externally or internally).
• The range of sensors can exceed 50,000 psi and
can be as small as a fraction of psi.
• Impedance is anywhere between a few hundred Ohms
to about 100 k?, depending on device.
• Linearity is between 0.1 to 2 typically

115
Pressure sensors - properties
• Other speciffications include
• Maximum pressure, burst pressure and proof
pressure (overpressure)
• electrical output - either direct (no internal
circuitry) or after conditioning and
amplification.
• Digital outputs are also available.
• Materials used (silicon, stainless steel, etc.)
and compatibility with gases and liquids are
specified
• port sizes and shapes, connectors, venting ports
• cycling of the pressure sensors is also specified
• hysteresis (usually below 0.1 of full scale)
• repeatability (typically less than 0.1 of full
scale).

116
Gyroscopes
• Gyroscopes come to mind usually as stabilizing
devices in aircraft and spacecraft in such
applications as automatic pilots.
• Are much more than that and much more common than
one can imagine.
• The gyroscope is a navigational tool. Its purpose
is to keep the direction of a device or vehicle.
• Used in all satellites, in smart weapons and in
all other applications that require attitude and
position stabilization.

117
Gyroscopes
• Eventually will find their ways into consumer
products such as cars.
• They have already found their ways into toys.
• The basic principle involved is the principle of
conservation of angular momentum
• In any system of bodies or particles, the total
angular momentum relative to any point in space
is constant, provided no external forces act on
the system

118
Mechanical Gyroscopes
• Best known of the existing gyros and the easiest
to understand.
• Consists of a rotating mass (heavy wheel) on an
axis in a frame - provides the angular momentum
• If one tries to change the direction of the axis,
by applying a torque to it, a torque is developed
in directions perpendicular to the axis of
rotation
• This forces a precession motion.
• This precession is the output of the gyroscope
and is proportional to the torque applied to its
frame.

119
Mechanical (rotor) gyroscope
120
Mechanical Gyroscopes
• A torque is applied to the frame of the gyro
around the input axis,
• The output axis will rotate as shown in a motion
called precession.
• This precession now becomes a measure of the
applied torque and can be used as an output to,
for example, correct the direction of an airplane
or the position of a satellite antenna.
• Application of torque in the opposite direction
reverses the direction of precession.

121
Mechanical Gyroscopes
• The relation between applied torque and the
angular velocity of precession is

T is the applied torque ? the angular velocity
I the inertia of the rotating mass ? is the
angular velocity of precession. I? is the
angular momentum ? is a measure of the torque
applied to the frame of the device
122
Mechanical Gyroscopes
• Two or three axes gyroscope are built by
duplicating this structure with rotation axes
perpendicular to each other.
• This type of gyroscope has been used for many
• it is a fairly large, heavy and complex
• not easily adapted to small systems.
• It also has other problems, associated with the
spinning mass (bearings, friction, balancing,
etc.)
• Other devices have been developed

123
Coriolis force gyroscopes
• Coriolis acceleration has been used to devise
much smaller and more cost effective gyroscopic
sensors.
• Built in silicon by standard etching methods
• The rotating mass is replaced by a vibrating body
The coriolis acceleration is used for sensing.
• The idea is based on the fact that if a body
moves linearly in a rotating frame of reference,
an acceleration appears at right angles to both
motions as shown in Figure 6.34.

124
Coriolis acceleration
125
Coriolis force gyroscopes
• Linear motion is supplied by the vibration of a
mass, usually a harmonic motion.
• Under normal conditions, the coriolis
acceleration is zero and the force associated
with it is zero
• If the sensor is rotated in the plane
perpendicular to the linear vibration, an
acceleration is obtained, proportional to the
angular velocity ?.
• An example of a coriolis based gyroscope is shown
next

126
Coriolis based gyroscope
127
Coriolis force gyroscopes
• Two gimbals - one is driven into oscillations by
a torque on one of the gimbals (right hand side).
• Can be done mechanically by electromagnetic or
electrostatic actuators
• The device is usually made in silicon-
electrostatic forces are sufficient
• This torque sets the gyro element (an inertial
mass) into oscillation at the drive frequency.
• If now an angular velocity exists, the flexural
element (central square piece) will oscillate at
the same frequency as the input axis.
• This motion is sensed by two pairs of electrodes
making up a capacitor one on the flexural
plate, one on the outer body.
• The differential capacitance is then a measure of
the angular velocity since the amplitude is
proportional to the angular velocity (the
frequency is fixed).
• Usually the vibration is resonant to maximize
efficiency.

128
Optical Gyroscopes
• One of the more exciting developments in
gyroscopes
• Has no moving members.
• Used extensively for guidance and control
• Based on the Segnac effect.
• The Segnac effect is based on propagation of
light in optical fibers and can be explained
using Figure 6.36.

129
The Sagnac effect
130
Sagnac effect
• The ring is at rest and two laser beams travel
the length of the ring, in opposite directions.
• The time it takes either beam to travel the
length of the ring is ?t2?R/nc where n is the
index of refraction of the optical fiber and c is
the speed of light in the fiber.
• Suppose that the ring rotates clockwise at an
angular velocity ?.
• The CW beam will travel a distance 2?R ??R?t
and the CCW beam a distance 2?R ??R?t.

131
Sagnac effect
• The difference between the two paths is

Linear relation between ? (the stimulus in this
case) and the change in length traveled. The
challenge is to measure this change in length.
This can be done in a number of ways. One method
is to build an optical resonator.
132
Resonant fiber optic gyroscope
• A resonator is any device which has a dimension
equal to multiple half wavelengths of the wave.
• A ring is built as follows

133
Resonant fiber optic ring resonator
• Light is coupled through the light coupler (beam
splitter).
• At resonance, which depends on the circumference
of the ring, maximum power is coupled into the
ring and minimum power is available at the
detector.
• The incoming beam frequency is tuned to do just
that.
• If the ring rotates at an angular velocity ?, the
light beams in the ring change in frequency
(wavelength) to compensate for the change in
apparent length of the ring.

134
Resonant fiber optic ring resonator
• The relation between frequency, wavelength and
length is

The light wavelength increases in one direction
and decreases in the other. The net effect is
that the two beams generate a frequency
difference (A is area of ring)
f is the output - linearly proportional to W
135
Coil optical fiber gyroscope
• The resonator is replaced by a coiled optical
fiber
• Fed from a polarized light source through a beam
splitter to ensure equal intensity and phase (the
phase modulator adjusts for any variations in
phase between the two beams).

136
Coil optical fiber gyroscope
• The beams propagate in opposite directions
• When returning to the detector, they are at the
same phase in the absence of rotation.
• If rotation exists, the beams will induce a phase
difference at the detector which is dependent of
the angular frequency ?.

137
Coil optical fiber gyroscope
• Optical gyroscopes are not cheap
• But they are orders of magnitude cheaper than the
spinning mass gyroscope and much smaller and
lighter.
• Have a very large dynamic range (as high as
10000) and so they can be used for sensing
angular frequency over a large span.
• Optical fiber gyroscopes are immune to
electromagnetic fields as well as to radiation
and hence can be used in very hostile
environments including space