ME 464

INSTRUMENTATION
FORCE, TORQUE PRESSURE,
LEVEL AND FLOW
MEASUREMENTS
 Mass (weight) measurement

2
 Mass (weight) measurement
Mechanical load cells-Spring balance
• Spring balances provide a method of mass
measurement that is both simple and cheap.
• The mass is hung on the end of a spring and the
deflection of the spring due to the downwards
gravitational force on the mass is measured against a
scale.
• Because the characteristics of the spring are very
susceptible to environmental changes, measurement
accuracy is usually relatively poor.
• However, if compensation is made for the changes in
spring characteristics, then a measurement
inaccuracy less than ±0.2% is achievable.
• According to the design of the instrument, masses
between 0.5kg and 10 tonnes can be measured.
3
 Mass-balance (weighing) instruments
Mechanical load cells

Beam balance (equal-arm balance).

4 Weigh beam
 Hydraulic and Pneumatic load cell
Mechanical load cells
Hydraulic load cell Pneumatic load cell

5
 Mass (weight) measurement
Electronic load cell (electronic balance)
• Electrical resistance strain gauge The most common transducer for
experimentally measuring strain in a mechanical component is the
bonded metal foil strain gauge.

• Commercially available strain gauge specifications usually report

a constant gauge factor F as
Δ𝑅/𝑅
𝐹=
𝜀𝑎𝑥𝑖𝑎𝑙
6
Mass (weight) measurement
Electronic load cell (electronic balance)
WHEATSTONE BRIDGE

Quater Bridge Half Bridge Full Bridge

Mass (weight) measurement
Electronic load cell (electronic balance)
WHEATSTONE BRIDGE

Full Bridge
• In a full Bridge there are changes in all the resistors

𝑉𝑜 𝑅1 + ∆𝑅1 𝑅4 + ∆𝑅4 − 𝑅2 + ∆𝑅2 𝑅3 + ∆𝑅3

=
𝑉𝑖 𝑅3 + ∆𝑅3 + 𝑅1 + ∆𝑅1 𝑅2 + ∆𝑅2 + 𝑅4 + ∆𝑅4

𝑅 𝑅
This can be simplified to give(if 𝑚 = 𝑅1 = 𝑅2 and neglect second order
3 4

terms)

𝑉𝑜 𝑚 ∆𝑅1 ∆𝑅2 ∆𝑅3 ∆𝑅4

= 2
− − +
𝑉𝑖 𝑚+1 𝑅1 𝑅2 𝑅3 𝑅4

𝑉𝑜 1 ∆𝑅1 ∆𝑅2 ∆𝑅3 ∆𝑅4

𝑖𝑓 𝑚 = 1; = − − +
𝑉𝑖 4 𝑅1 𝑅2 𝑅3 𝑅4
 Mass (weight) measurement
Electronic load cell (electronic balance)

• A load cell is a sensor used to measure a force.

• It contains an internal flexural element, usually with
several strain gauges mounted to its surface.
• The flexural element’s shape is designed so that the
strain gauge outputs can be related to the applied
force.
• The load cell is usually connected to a bridge circuit
to yield a voltage proportional to the load.
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 Mass (weight) measurement
Electronic load cell (electronic balance)

Different configurations of load cells

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 Mass (weight) measurement
Electronic load cell (electronic balance)

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 Torque measurement

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 Torque measurement
A dynamometer or "dyno" is a device for simultaneously
measuring the torque and rotational speed of an engine,
motor or other rotating prime mover so that its
instantaneous power may be calculated, and usually
displayed by the dynamometer itself as kW or hp.
Methods of torque measurement;
1. Gravity Balance Method
2. Mechanical Torsion Method
3. Optical Torsion Method
4. Electrical Torsion Method
5. Strain-Guage Torsion Method
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 Mechanical Torsion Method
• Any system involving torque
transmission through a shaft
contains both a power source and a
power absorber where the power is
dissipated.
• The magnitude of the transmitted
torque can be measured by cradling (a) Driving
either the power source or the
power absorber end of the shaft in
bearings, and then measuring the
reaction force, F, and the arm length
L, as shown.
• The torque is then calculated as the
1 simple product, FL.
4 (b) Absorption
 Rope brake-Gravity Balance Method
• The principle of the Prony brake is shown.
• It is used to measure the torque in a
rotating shaft and consists of a rope wound
round the shaft.
• One end of the rope is attached to a spring
balance and the other end carries a load in
the form of a standard mass, m. If the
measured force in the spring balance is Fs,
then the effective force, Fe, exerted by the
rope on the shaft is given by:
𝐹𝑒 = 𝑚𝑔 − 𝐹𝑠
1
5 𝑇 = 𝑅𝐹
 Rope brake-Gravity Balance Method

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 Prony brake dynamometer
Gravity Balance Method

1
𝑇 = 𝑊𝐿
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 Eddy Current Dynamometer

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 Torque Measurement with Load Cells
Strain-Guage Torsion Method

𝛾𝑥𝑦 = 2𝜖𝑂𝐵 − 𝜖𝑥 + 𝜖𝑦

𝑇𝑟
𝜏 = 𝐺𝛾𝑥𝑦 =
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𝐽
 Electrical Torsion Method
Inductance Method

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 Optical torque measurement
• Two black-and-white striped wheels are mounted at
either end of the rotating shaft and are in alignment
when no torque is applied to the shaft.
• Light from a laser diode light source is directed by a pair
of optic-fibre cables onto the wheels.
• The rotation of the wheels causes pulses of reflected light
and these are transmitted back to a receiver by a second
pair of fibre-optic cables.
• Under zero torque conditions, the two pulse trains of
reflected light are in phase with each other.
• If torque is now applied to the shaft, the reflected light is
modulated.
• Measurement by the receiver of the phase difference
between the reflected pulse trains therefore allows the
magnitude of torque in the shaft to be calculated.
• The cost of such instru ments is relatively low, and an
additional advantage in many applications is their small
2 physical size
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 Force measurement

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 Force measurement
• If a force of magnitude, F, is applied to a body of mass, M,
the body will accelerate at a rate, A, according to the
equation: F=MA .
• The standard unit of force is the Newton, this being the force
that will produce an acceleration of one metre per second
squared in the direction of the force when it is applied to a
mass of one kilogram.
• One way of measuring an unknown force is therefore to
measure the acceleration when it is applied to a body of
known mass.
• An alternative technique is to measure the variation in the
resonant frequency of a vibrating wire as it is tensioned by
an applied force.

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 PRESSURE MEASUREMENT
Methods and Applications

CE319F - Elementary Mechanics of

Fluids - Laboratory
Copyright: UT Austin, 2000-2018 24
 Pressure measurement
• Pressure measurement is a very common requirement for most
industrial process control systems and many different types of
pressure-sensing and pressure-measurement systems are available.
• Absolute pressure: This is the difference between the pressure of
the fluid and the absolute zero of pressure.
• Gauge pressure: This describes the difference between the
pressure of a fluid and atmospheric pressure.
• Absolute and gauge pressure are therefore related by the
expression:
Absolute pressure=Gauge pressure + Atmospheric pressure
• Differential pressure: This term is used to describe the difference
between two absolute pressure values, such as the pressures at
two different points within the same fluid (often between the two
2 sides of a flow restrictor in a system measuring volume flow rate).
5
 Overview
Pressure (P ) expresses the magnitude of normal force (F-N) per
unit area (A-m2) applied on a surface
𝐹 𝛥𝐹
𝑃= 𝑜𝑟 𝑃=
𝐴 𝛥𝐴
Units: Pa(= N/m2), psi(=lbf/in2), bar (=105 Pa=100 kPa), mbar (=100
Pa=1 hPa), atm (=101.3 kPa), mmHg (or Torr), inHg, etc.
Note: For every Unit: hUnit=hector Unit=100 Unit
𝑃𝑎𝑏𝑠 = 𝑃𝑎𝑡𝑚 + 𝑃𝑔𝑎𝑔𝑒
Where Pabs : Absolute pressure
Patm : Atmospheric pressure
(standard is: 101.3 kPa =14.696 psi=760 mmHg)
Pgage : Gage pressure
 Elastic element pressure transducer.
Diaphragm pressure sensor Fibre-optic pressure sensors

Capacitive pressure sensor Bellows

A capacitive pressure sensor is simply a
diaphragm-type device in which the
diaphragm displacement is determined
by measuring the capacitance change
between the diaphragm and a metal
plate that is close to it.
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 Bourdon tube
• The Bourdon tube is also an elastic element type of pressure
transducer. It is relatively cheap and is commonly used for
measuring the gauge pressure of both gaseous and liquid fluids.
• It consists of a specially shaped piece of oval-section, flexible,
metal tube that is fixed at one end and free to move at the other
end.
• When pressure is applied at the open, fixed end of the tube, the
oval cross-section becomes more circular.
• In consequence, there is a displacement of the free end of the
tube.
• This displacement is measured by some form of displacement
transducer, which is commonly a potentiometer or LVDT.
• Capacitive and optical sensors are also sometimes used to
2
measure the displacement.
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 Bourdon tube
Principles: change in curvature of the tube is proportional to
difference of pressure inside from that outside the tube.
Applications: tire pressure, pressure at the top or along the walls of
tanks or vessels

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 Manometers
• Manometers are passive instruments that give a
visual indication of pressure values.
• Various types exist. The U-tube manometer, shown
in, is the most common form of manometer.
Manometers:
(a) U-tube;
(b) well type;
(c) inclined type
Principles:
Hydrostatic Law
∆P=ρ g h

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 Resonant-wire devices
• Wire is stretched across a chamber
containing fluid at unknown pressure
subjected to a magnetic field
• The wire resonates at its natural
frequency according to its tension, which
varies with pressure.
• Thus, pressure is calculated by measuring
the frequency of vibration of the wire.
• Such frequency measurement is normally
carried out by electronics integrated into
the cell.
• These devices are highly accurate, with a
typical inaccuracy figure being ±0.2% full-
scale reading.
• They are also particularly insensitive to
ambient condition changes and can
measure pressures between 5mbar and
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1 2bar.
 Dead-weight gauge
• The dead-weight gauge, is a null-
reading type of measuring
instrument in which weights are
added to the piston platform until
the piston is adjacent to a fixed
reference mark, at which time the
downward force of the weights on
top of the piston is balanced by
the pressure exerted by the fluid
beneath the piston.
• The fluid pressure is therefore
calculated in terms of the weight
added to the platform and the
known area of the piston.
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 Selection of pressure sensors
• Choice between the various types of instrument available for
measuring mid-range pressures (1.013–7000bar) is usually
strongly influenced by the intended application.
• Manometers are commonly used when just a visual indication of
pressure level is required, and deadweight gauges, because of
their superior accuracy, are used in calibration procedures of
other pressure-measuring devices.
• When an electrical form of output is required, the choice is
usually either one of the several types of diaphragm sensor
(strain gauge, capacitive or fibre optic) or, less commonly, a
Bourdon tube.
• Bellows-type instruments are also sometimes used for this
purpose, but much less frequently.
• If very high measurement accuracy is required, the resonant-wire
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3 device is a popular choice.
 Flow measurement

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 Flow measurement
• The rate at which fluid flows Mass Flow Rate
through a closed pipe can be Conveyor-based methods
quantified by either measuring the
mass flow rate or measuring the
volume flow rate.
• Of these alternatives, mass flow
measurement is more accurate,
since mass, unlike volume, is
invariant.
A load cell measures the mass M of
• In the case of the flow of solids, the
choice is simpler, since only mass material distributed over a length L of the
flow measurement is appropriate. conveyor. If the conveyor velocity is v, the
mass flow rate, Q, is given by:
• The method used to measure mass 𝑚𝑣
flow rate is largely determined by 𝑄=
whether the measured quantity is 𝐿
in a solid, liquid or gaseous state.

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 Volume flow rate
• Volume flow rate is an appropriate way of
quantifying the flow of all materials that are in a
gaseous, liquid or semi-liquid slurry form (where
solid particles are suspended in a liquid host),
although measurement accuracy is inferior to mass
flow measurement as noted earlier.
• Materials in these forms are carried in pipes, and
various instruments can be used to measure the
volume flow rate as described below

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 Differential pressure (obstruction-type) meters
• Differential pressure meters involve the insertion of some
device into a fluid-carrying pipe that causes an obstruction and
creates a pressure difference on either side of the device.
• Such meters are sometimes known as obstruction-type meters
or flow-restriction meters.
• Devices used to obstruct the flow are shown below

Obstruction devices:
(a) orifice plate;
(b) venturi;
(c) flow nozzle;
(d) Dall flow tube.

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 Types of orifice plate
• Concentric type of orifice plate is inadequate to cope
with difficult conditions experienced in metering dirty or
viscous fluids and gives a poor disposal rate of
condensate in flowing steam and vapors.
• Several design modifications can overcome these
problems, in the form of segmental or eccentric orifice
plates, as shown.

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 Profile of flow across orifice plate

𝐶𝐷 𝐴2 ′ 2(𝑃1 − 𝑃2 )
𝑄=
1 − 𝐴′2 /𝐴1 ′ 2 𝜌

where
𝐴1 ′ and 𝐴2 ′ are the pipe diameters
before and at the obstruction and CD is
a constant, known as the discharge
coefficient, which accounts for the
Reynolds number and the difference
between the pipe and flow diameters.
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 Orifice plate
• The orifice plate is a metal disc with a concentric hole in it, which
is inserted into the pipe carrying the flowing fluid.
• Orifice plates are simple, cheap and available in a wide range of
sizes.
• In consequence, they account for almost 50% of the instruments
used in industry for measuring volume flow rate.
• One limitation of the orifice plate is that its inaccuracy is typically
at least ±2% and may approach ±5%. Also, the permanent
pressure loss caused in the measured fluid flow is between 50%
and 90% of the magnitude of the pressure difference.

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 Turbine meters
• A turbine flowmeter consists of a multi-bladed wheel mounted in a pipe along an
axis parallel to the direction of fluid flow in the pipe, as shown.
• The flow of fluid past the wheel causes it to rotate at a rate that is proportional to
the volume flow rate of the fluid.
• This rate of rotation has traditionally been measured by constructing the
flowmeter such that it behaves as a variable reluctance tachogenerator.
• This is achieved by fabricating the turbine blades from a ferromagnetic material
and placing a permanent magnet and coil inside the meter housing.
• A voltage pulse is induced in the coil as each blade on the turbine wheel moves
past it, and if these pulses are measured by a pulse counter, the pulse frequency
and hence flow rate can be deduced.

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 Electromagnetic flowmeters
• Electromagnetic flowmeters are limited to
measuring the volume flow rate of electrically
conductive fluids.
• The instrument, consists of a stainless-steel
cylindrical tube, fitted with an insulating liner,
which carries the measured fluid.
• A magnetic field is created in the tube by placing
mains-energized field coils either side of it, and
the voltage induced in the fluid is measured by
two electrodes inserted into opposite sides of
the tube.
• The ends of these electrodes are usually flush
with the inner surface of the cylinder.
• E, induced across a length, L, of the flowing fluid The typical voltage signal
moving at velocity, v, in a magnetic field of flux measured across the
density, B, is given by: electrodes is 1mV when the
𝐸 = 𝐵𝐿𝑣 fluid flow rate is 1m/s.
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 Ultrasonic flowmeters
• The ultrasonic technique of volume flow rate measurement is, like the
magnetic flowmeter, a non-invasive method.
• It is not restricted to conductive fluids, however, and is particularly useful for
measuring the flow of corrosive fluids and slurries.
• Besides its high reliability and low maintenance requirements, a further
advantage of an ultrasonic flowmeter over a magnetic flowmeter is that the
instrument can be clamped externally onto existing pipework rather than being
inserted as an integral part of the flow line.
• As the procedure of breaking into a pipeline to insert a flowmeter can be as
expensive as the cost of the flowmeter itself, the ultrasonic flowmeter has
enormous cost advantages.

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 Barometer
• A lot of procedures and techniques have been developed for the measurement
of pressure. For example: Barometer, piezometric , pitot tube
• A barometer is an instrument that is used to measure air pressure in a certain
environment.
• A piezometer is A piezometer is a device used to measure fluid pressure in a
system by measuring the height to which a column of fluid rises against gravity,
or groundwater pressure (more precisely, a piezometric head) at a specific
point. A piezometer is designed to measure static pressure.
• The pitot tube is a simple and convenient instrument to measure the static
pressure, and total pressure its difference gives the dynamic pressure to
determine the air speed.
 Pitot static tube
• The Pitot static tube is mainly used for
making temporary measurements of
flow, although it is also used in some
instances for permanent flow
monitoring.
• It measures the local velocity of flow at
a particular point within a pipe rather
than the average flow velocity as
measured by other types of flowmeter.
• This may be very useful where there is
a requirement to measure local flow From Bernoulli's
rates across the cross-section of a pipe
in the case of non-uniform flow.
equation
• Multiple Pitot tubes are normally used 𝑣 = 𝐶 2𝑔∆𝑃
to do this.
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 Level measurement

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 Level measurement
• Dipsticks Float systems
• ordinary dipstick
• optical dipstick

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 Level measurement
Capacitive devices Ultrasonic level gauge

𝑏
𝐶 log 𝑒 𝑎 − 2𝜋𝜀𝑜
ℎ=
2𝜋𝜀𝑜 (𝜀 − 1)
where ε is the relative permittivity of the
measured substance and εo is the permittivity
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of free space.
 Translational motion measurement
s, v and a

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 Translational motion transducers
The resistive potentiometer
• The resistive potentiometer is perhaps
the best-known displacement-
measuring device. It consists of a
resistance element with a movable
contact as shown.
• A voltage Vs is applied across the two
ends A and B of the resistance element
and an output voltage Vo is measured
between the point of contact C of the
sliding element and the end of the 𝑉𝑜 𝐴𝐶
resistance element A. =
• A linear relationship exists between the 𝑉𝑠 𝐴𝐵
output voltage Vo and the distance AC,
5 which can be expressed by:
0
 Linear Variable Differential Transformer
• Linear Variable Differential Transformer (LVDT) is a transducer for
measuring linear displacement. As illustrated, it consists of primary
and secondary windings and a movable iron core
• The advantages of the LVDT are accuracy over the linear range and an
analogue output that may not require amplification. Also, it is less
sensitive to wide ranges in temperature than other position
transducers.
• The object whose translational displacement is to be measured is
physically attached to the central iron core of the transformer, so that
all motions of the body are transferred to the core.

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 Variable capacitance transducers
• Like variable inductance,
the principle of variable
capacitance is used in
displacement measuring
transducers in various ways.
• The three most common
forms of variable
capacitance transducer are
shown

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 Piezoelectric transducers
• The piezoelectric transducer is effectively a force-measuring device that is used in
many instruments measuring force, or the force-related quantities of pressure and
acceleration.
• It is included within this discussion of linear displacement transducers because its
mode of operation is to generate an e.m.f. that is proportional to the distance by
which it is compressed.
• The device is manufactured from a crystal, which can be either a natural material
such as quartz or a synthetic material such as lithium sulphate.
• The crystal is mechanically stiff (i.e. a large force is required to compress it), and
consequently piezoelectric transducers can only be used to measure the
displacement of mechanical systems that are stiff enough themselves to be
unaffected by the stiffness of the crystal.

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 Piezoelectric transducers
• When the crystal is compressed, a charge is
generated on the surface that is measured as the
output voltage.
• As is normal with any induced charge, the charge
leaks away over a period of time. Consequently,
the output voltage–time characteristic is as
shown.
• Because of this characteristic, piezoelectric
transducers are not suitable for measuring static
or slowly varying displacements, even though the
time constant of the charge–decay process can be
lengthened by adding a shunt capacitor across the
device.
• As a displacement-measuring device, the
piezoelectric transducer has a very high
sensitivity, about one thousand times better than
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4
the strain gauge.
 Nozzle flapper
• The nozzle flapper is a displacement transducer that translates
displacements into a pressure change.
• A secondary pressure-measuring device is therefore required
within the instrument.
• The general form of a nozzle flapper is shown

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 Range sensors
• Range sensors provide a well-used
technique of measuring the
translational displacement of a
body with respect to some fixed
boundary.
• The common feature of all range
sensing systems is an energy
source, an energy detector and an
electronic means of timing the
time of flight of the energy
between the source and detector.
• The form of energy used is either
ultrasonic or light.

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 Velocity measurement
• Translational velocity cannot be measured directly
and therefore must be calculated indirectly by other
means.
• Differentiation of position measurements obtained
from any of the translational displacement
transducers.
• Where an accelerometer is already included within
a system, integration of its output can be performed
to yield a velocity signal, using an op amp
integrator.
• The process of integration attenuates rather than
amplifies measurement noise and this is therefore
an acceptable technique.
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 Acceleration measurement
• The only class of device available for measuring
acceleration is the accelerometer.
• These are available in a wide variety of types and ranges
designed to meet particular measurement
requirements.
• They have a frequency response between zero and a
high value, and have a form of output that can be
readily integrated to give displacement and velocity
measurements.
• The frequency response of accelerometers can be
improved by altering the level of damping in the
instrument.
• Besides their use for general purpose motion
measurement, accelerometers are widely used to
measure mechanical shocks and vibrations.
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 Acceleration measurement
Seismic Accelerometer
ABSOLUTE DISPLACEMENT, X

𝑋 1 + 2ξτ 2
=𝑇=
𝑌 1 − 𝜏 2 2 + 2ξτ 2

RELATIVE DISPLACEMENT, Z=X-Y

𝑍 𝜏2
=
𝑌 1 − 𝜏 2 2 + 2ξτ 2

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 Piezoelectric Accelerometer

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MEMS(Micro Electro-Mechanical Systems)
Accelerometer; Piezo-capacitive

• It is made of components between 1-100μm

• It can be mounted on a PCB
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 Piezoresistive Accelerometer(MEMS)
Strain gauges are typically bonded to a surface and measure
deformation, while piezoresistive sensors can be integrated
directly into a material or device.

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 Hall effect and thermal accelerometers
• The Hall effect is a phenomenon that occurs
when a magnetic field is applied
perpendicular to the flow of an electric
current in a conductor.
• This interaction results in a voltage
difference, known as the Hall voltage,
developing across the conductor,
perpendicular to both the current and the
magnetic field.

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 Rotational motion measurement
θ, ω and α

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 Rotational motion transducers
• Rotational displacement transducers
measure the angular motion of a body
about some rotation axis.
• They are important not only for
measuring the rotation of bodies such
as shafts, but also as part of systems
that measure translational
displacement by converting the
translational motion to a rotary form.
• The various devices available for
measuring rotational displacements
are presented.
6
5 Multiturn Potentiometer
 Rotational differential transformer
• This is a special form of differential transformer that measures
rotational rather than translational motion.
• The method of construction and connection of the windings is
exactly the same as for the linear variable differential
transformer (LVDT), except that a specially shaped core is
used that varies the mutual inductance between the wind
ings as it rotates, as shown

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 Encoders
• Encoders are sensors that generate digital signals in response to
movement.
• Both shaft encoders, which respond to rotation, and linear
encoders, which respond to motion in a line, are available.
• When used in conjunction with mechanical conversion devices,
such as rack-and-pinions, measuring wheels, or spindles, shaft
encoders can also be used to measure linear movement, speed,
and position.
• Encoders are available with a choice of outputs.
• Incremental encoders generate a series of pulses as they move.
• These pulses can be used to measure speed, or be fed to a counter
to keep track of position.
• Absolute encoders generate multi-bit digital words that indicate
actual position directly.

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 Encoders: Sensing Technology
• Encoders can use either optical or magnetic sensing
technology.
• Optical sensing provides high resolutions, high operating
speeds, and reliable, long life operation in most industrial
environments.
• Magnetic sensing, often used in such rugged applications as
steel and paper mills, provides good resolution, high operating
speeds, and maximum resistance to dust, moisture, and
thermal and mechanical shock.

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 Encoders: Sensing Technology
Optical encoders use a glass disk with a pattern of lines deposited on it, a
metal or plastic disk with slots (in a rotary encoder), or a glass or metal
strip (in a linear encoder). Light from an LED shines through the disk or
strip onto one or more photodetectors, which produce the encoder’s
output

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 Encoders: Sensing Technology
Magnetic sensing technology
is very resistant to dust,
grease, moisture, and other
contaminants common in
industrial environments, and
to shock and vibration. There
are several types of magnetic
sensors. Variable reluctance
sensors detect changes in the
magnetic field caused by the
presence or movement of a
ferromagnetic object.

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 ABSOLUTE VS. INCREMENTAL CODING

• Incremental Coding; Incremental encoders(relative

encoders) provide a specific number of equally spaced
pulses per revolution (PPR) or per inch or millimeter of linear
motion.
• A single channel output is used for applications where
sensing the direction of movement is not important.
• Where direction sensing is required, quadrature output is
used, with two channels 90 electrical degrees out of phase;
circuitry determines direction of movement based on the
phase relationship between them.

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 Digital Optical Encoder
• The incremental encoder is simpler in design than the
absolute encoder.
• It consists of two tracks and two sensors whose outputs are
called channels A and B.
• As the shaft rotates, pulse trains occur on these channels at
a frequency proportional to the shaft speed, and the phase
relationship between the signals yields the direction of
rotation.

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 ABSOLUTE VS. INCREMENTAL CODING
• An absolute encoder generates digital words that represent the
encoder’s actual position, as well as its speed and direction of
motion.
• If power is lost, its output will be correct whenever power is
restored. It is not necessary to move to a reference position as with
incremental type encoders.
• Electrical transients can only produce transient data errors, usually
too brief to effect the dynamics of a control system.
• An absolute encoder’s resolution is defined as the number of bits in
its output word.
• This output can be in straight binary or in gray code, which produces
only a single bit change at each step to reduce errors.

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 Digital Optical Encoder

3-bit absolute position value rotary encoder

4-bit gray code absolute encoder disk patterns.

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4
 Mechanical Gyroscopes
• Gyroscopes measure both
absolute angular
displacement and absolute
angular velocity.
• The predominance of
mechanical, spinning-wheel
gyroscopes in the market
place is now being
challenged by recently
introduced optical
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gyroscopes.
5
Coriolis Effect Vibrating Gyroscopes, MEMS
• MEMS gyroscope is an inertial sensor
which is manufactured by MEMS
technology and measures angular rate
based on Coriolis effect.
• Its application field is wide, the precision
level is gradually improved, and it has the
advantages of small size, light weight, low
cost, good reliability and so on.

𝐶𝑜𝑟𝑖𝑜𝑙𝑖𝑠 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛, 𝑎𝑐 = 2𝜔𝑉;

𝐹 = 𝑚𝑎𝑐 = 2𝑚𝜔𝑉
𝐹
𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝜔 =
2𝑚𝑉
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 Optical Gyroscope

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 Mechanical flyball
• The mechanical flyball (alternatively
known as a centrifugal tachometer) is
a velocity measuring instrument that
was invented in 1817 and so might
now be regarded as being old-
fashioned.
• However, because it can act as a
control actuator as well as a
measuring instrument, it still finds
substantial use in speed-governing
systems for engines and turbines in
which the measurement output is
connected via a system of mechanical
links to the throttle.

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 Assignment 4-1
a. Show that the gain of the full bridge shown is,
1 ∆𝑅1 ∆𝑅2 ∆𝑅3 ∆𝑅4
− − +
4 𝑅1 𝑅2 𝑅3 𝑅4

b. If the bridge shown is to have a gain of 0.5 mV/V at 500g.

Determine the change in resistance for an applied load of 20
kg. The nominal resistance is of the strain gauges is 350 Ω.
c. If the gauge factor is 2.05, determine the axial strain in the
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load cell.
9
 Assignment 4-2
•Design a circuit to output velocity and
acceleration between 0-5 V from a linear
transducer with sensitivity of 0.1mm/Ω
connected to seismic accelerometer.

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