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KEVIN T. CABANTE AUGUST 24, 2015

EE5-1

MECHANICAL SENSORS

Definition

Mechanical sensors are transducers that measure mechanical phenomena and

convert it into a signal which can be read by an observer or by an instrument. They

include pressure sensor, force and torque sensor, inertial sensor and flow sensor. In terms

of its sensing techniques, mechanical sensors use either of the following scientific

principles: piezoresistivity, piezoelectricity, capacitive techniques, inductive techniques

and resonant techniques.

1. STRAIN GAUGES

Strain gauges are sensors for measuring various mechanical quantities indirectly

by measuring the strain the quantity produces on an object. Strain can be related to

stress, force, torque and a host of other quantities 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. This change in resistance can be mathematically

expressed as

dRR

= d + d(L/A)

L/A

where R is the object’s electrical resistance, σ is the resistivity of the material, L is the length

of the material and A is the cross-sectional area of the material. As shown, the change in

resistance of a material is dependent on (1) change in conductivity and (2) change in

deformation. 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,

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dRR

= Ss

where is Ss is the sensitivity of the strain gauge, also known as the gauge factor.

For any given strain gauge the gauge factor is a constant. It ranges between 2 to

6 for most metallic strain gauges and from 40 to 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.

Strain Gauge as Force Sensor

Strain gauge can be used as a force sensor. In the diagram below, it can be shown

that deformation is proportional to stress applied to the material.

Given the conductor shown above and applying a force along its axis, the stress

is given by

= FA

= EdLL

= E

where is the stress [N/m2], E is Young’s modulus of the material (modulus of elasticity)

[N/m2 ] and is the strain (dL/L). Herein, strain is a normalized linear deformation of the

material.

Strain gauges come in many forms and types. Any material, combination of

materials or physical configuration that changes its resistance due to strain can be used

as a strain gauge. However, there are two types that account for most of the strain

gauges in use today: (1) wire (or metal) strain gauges and (2) semiconductor strain

gauges.

Metallic strain gauges in its simplest form is a length of wire held between two

posts. When a force is applied to them, the force will deform the wire causing a change

in the wire’s resistance. Sometimes, multiple lengths of wire were used. This method was

used in the past and is valid although it is not very practical.

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A more practical strain gauge is built out of a thin layer of conducting material

deposited on an insulating substrate (plastic, ceramic, etc.) and etched to form a long,

meandering wire. Constantan (60% copper, 40% nickel) is the most common material

used in this method due to its negligible temperature coefficient of resistance. Other

materials commonly used are shown in the table.

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Table 1. Materials for resistive strain gauges and their properties.

Material Gage

factor

Resistivity

[mm2/m]

Thermal

coeff. of

expansion

[10/K]

Expansion

coeff.

[10/K]

Maximum

temperatrure

[C]

Constantan (Cu60Ni40) 2.0 0.48 5 12.5 400

Nichrome (Ni80Cr20) 2.0 1.3 100 18 1000

Manganine

(Cu84Mn12Ni4)

2.2 0.43 10 17

Nickel -12 0.11 6000 12

Chromel (Ni65Fe25Cr10) 2.5 0.9 300 15 800

Platinum 5.1 0.1 2450 8.9 1300

Elinvar

(Fe55Ni36Cr8Mn0.5)

3.8 0.84 300 9

Platinum-Iridium

(Pt80Ir20)

6.0 0.36 1700 8.9 1300

Platinum Rhodium

(Pt90Rh10)

4.8 0.23 1500 8.9

Bismuth 22 1.19 300 13.4

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.

Two-axis Three-axis rosette

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Semiconductor strain gauges operate like resistive strain gauges but their

construction and properties are different. The gauge factor for semiconductors is much

higher than for metals. The change in conductivity due to strain is also much larger than

in metals. This type is typically smaller than metal types and is often more sensitive to

temperature variations that it requires temperature compensation.

Like metallic materials, all semiconductor materials exhibit changes in resistance

due to strain. The most common material used 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.

45-degrees rosette 45-degrees stacked rosette

Membrane rosette

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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, expressed as

dRR

= S1 + S12

They can also be either positive or negative temperature coefficient.

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. Special bonding agents exist

for different applications and types of materials and are 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

loading, truck weighing and many others).

The properties of strain gauges vary by application. Most metal gauges have a

nominal resistance between 100 and 1000 ohms, gauge factor between 2 to 5 and

dimensions from less than 3x3 mm to lengths in excess of 150 mm. Rosettes (multiple axis

strain gauges) are also available with 45, 90 and 120-degree axes as well as diaphragm

and other specialized configurations.

Semiconductor strain gauges are usually smaller than most resistive strain gauges

and can be made with higher resistances. However, their use is limited to low

temperatures. They can be much less expensive than metal strain gauges and are often

part of another device.

Strain gauges are subject to a variety of errors. Resistance, especially in

semiconductors, is affected by temperature in the same way as by strain. In metal

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gauges, this is usually small through the use of 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. A third source of error is due to

the strain itself, which, over time, tends, to permanently deform the gauge. This error can

be eliminated by periodic re-calibration and can be reduced by ensuring that the

maximum deformation allowed is small and below the recommended for the device.

Specialized Strain Gauges

There are other types of strain gauges for very specialized applications. One

example is the optical fiber strain gauge. It operates on the principle that the change in

length of the fiber due to strain changes the phase of the light through the fiber. By

measuring the light phase, either directly or in an interferrometric method, it 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.

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. These are made as ribbons or threads

based on graphite or carbon in a resin as a substrate and used in a way similar to other

strain gauges. They have very high gauge factors (up to about 300) but they are

otherwise difficult to use, inaccurate and mechanically unstable, severely limiting their

practical use.

2. TACTILE SENSORS

Tactile sensors are force sensors but as the 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 where membrane or resistive pads are used.

The simplest tactile sensors are made of conductive polymers or elastomers or with

semi-conductive polymers, called piezoresistive sensors or force sensitive resistive (FSR)

sensors. In these devices, the resistance of the material is pressure dependent.

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),

such as shown in the figure below.

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In the figure, 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.

Another example of tactile sensors is shown below. It is used to detect breathing.

3. ACCELEROMETERS

Accelerometers measures the acceleration of an object indirectly by measureing

other quantities related to acceleration. It can accomplish the task using three methods:

by force, magnetic or electrostatic means.

In resistive method, a force sensor, such as a strain gauge, is used. By virtue of

Newton’s second law (F = ma) a sensor may be made to sense acceleration by simply

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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.

Magnetic methods and electrostatic (capacitive) methods are quite commonly

used. 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. On the other hand, 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.

Methods of acceleration sensing start with the mechanical model of a mass shown

below.

The mass, moves under the influence of forces, has a restoring force (spring) and a

damping force (which essentially prevents it from oscillating). Under these conditions,

and assuming the mass can only move in one direction (along the horizontal axis),

Newton’s second law may be written as

ma = kx bdxdt

which essentially tells us that the mass has moved a distance x under the influence of

acceleration a and where 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. Therefore, for a useful acceleration sensor (often called

accelerometer), it is sufficient to provide a component which can move relative to the

sensor’s 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.

In strain gauge accelerometers, the mass is suspended on a cantilever beam and

a strain gauge senses the bending of the beam, as shown in the figure below.

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Magnetic accelerometers uses variable inductance set-ups. A rod is connected

such as it is moving with the mass which in turn is linked to a coil. The inductance of the

coil is proportional to the position of the mass, as shown below.

In electrostatic accelerometers, 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. The restoring

force is then provided by springs or by a cantilever’s fixed end. Several configurations are

given below.

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In the first figure, the distance between the plates changes with acceleration. In

the second, 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 and some kind of damping mechanism

must be added to prevent the springs or the beam from oscillating. A more practical set-

up is shown below.

Other type of accelerometers also employ a moving mass in one form or another.

One particular example is the heated gas accelerometer. A gas in cavity is heated to an

equilibrium temperature. Two (or more) thermocouples are provided and are 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. Under acceleration, the gas shifts to the direction

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opposite the motion (the gas is the inertial mass) causing a temperature gradient which

is calibrated in terms of acceleration. The set-up is shown below.

Other accelerometers use optical means, for example, activating a variable

shutter by means of the moving mass. Optical fiber accelerometers use an optical fiber

position sensor. Other uses vibrating reeds whose vibration rate changes with

acceleration.

4. VELOCITY SENSORS

Velocity sensing is more complicated than acceleration sensing. However, one

can always measure something proportional to velocity. For example, we may infer the

velocity of a car from the rotation of the wheels, 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.

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 set-up below maybe useful.

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The emf induced in the coils is governed by Faraday’s law, written mathematically

as

emf = Nddt

where N is the number of coils, Ф is the flux produced by the magnet and t is the time.

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. Practically,

constant velocity (zero acceleration) cannot be sensed by the set-up but relative

velocity of objects is easily measured.

Aside from the one illustrated, there are also fluid velocity sensors, doppler effect

sensors, time of flight devices and others to measure velocity.

5. PRESSURE SENSORS

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. 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.

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

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response to pressure. The range of methods is quite large and includes thermal, optical

as well as magnetic and electrical principles.

Mechanical Pressure Sensors

Earliest sensors were purely mechanical and involves direct transduction from

pressure to mechanical displacement. These devices are actuators that react to pressure

and are still 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, shown below.

The most common devices used for pressure sensing are the thin plate and the

diaphragm or membrane. Their behavior and response to pressure is different. In relation

to the figure below, the deflection of the center of a membrane (maximum deflection)

under radial tension S and the stress in the diaphragm are given as

dm = r2P4S

, m = St

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where P is the applied pressure difference between the top and bottom of the

membrane, r its radius and t its thickness. If the thickness is not negligible, the behavior

or response of the membrane is given as

dm = 3 1 v2 r4P

16Et2, m = 3r2P

4t2

where E is the Young’s modulus and V is the Poisson’s ratio. The displacement is linear

with pressure hence their widespread use for pressure sensing.

Pressure sensors come in four basic types. Absolute pressure sensors senses pressure

relative to absolute vacuum. Differential pressure sensors measures the difference

between two pressures on two ports of the sensor. Gage pressure sensors measures the

pressure relative to ambient pressure and is the most common. Sealed gage pressure

sensor measures the pressure relative to a sealed pressure chamber (usually 1 atm at sea

level or 14.7 psi).

Piezoresistive Pressure Sensors

Piezoresistor is a semiconductor strain gauge. Most modern pressure sensors use it

rather than the conductor type strain gauge. However, resistive (metal) strain gauges are

still used at higher temperature or for specialized applications. Piezoresistors may be

fabricated of silicon, easy to construct and allows on board temperature compensation,

amplifiers and conditioning circuitry. Its basic construction is shown below.

The change in resistance of the two piezoresistos is given as

R1

R1 =

R2

R2 = 1

2 y x

where π is an average sensitivity (gauge) coefficient and σx and σy are the stresses in

the transverse directions. 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

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pressure sensor sensing the pressure P-P0. A differential sensor is produced by placing the

diaphragm between two chambers, each vented through a port.

Another approach is to use a single strain gauge and passing a current through it.

Pressure is applied perpendicular to the current. The voltage across the element is

measured as an indication of the stress and therefore pressure.

Various pieroresistive pressure sensors are shown below.

Miniature Type

Pitran Absolute Pressure Sensors 150psi Differential Pressure Sensor

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Capacitive Pressure Sensors

The deflection of the diaphragm constitutes a capacitor in which the distance

between the plates is pressure sensitive. 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. The capacitance may be part of an oscillator, where the change in its

frequency may be quite large making for a very sensitive sensor. It has advantages of

being less temperature dependent and not sensitive to overpressures. 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.

Magnetic Pressure Sensors

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. In magnetic pressure sensors, the diaphragm is made of a ferromagnetic

material and is part of a magnetic circuit, as shown below.

100psi Pressure Sensor in TO5 Can 15 and 30 psi Differential Pressure Sensors

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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.

Optoelectronic and Thermal Pressure Sensors

Fabri-Perot optical resonator is used to measure small displacements, and

consequently, pressure. 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. It is 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.

Semiconductor-based Pressure Sensors

There are also semiconductor-based pressure sensors available. However, they

can only operate at low temperatures (-50 to +150˚C). Temperature dependent errors

can also be high unless properly compensated either externally or internally. The range

of these 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 kiloohms,

depending on device. Linearity is typically between 0.1 to 2%.

6. GYROSCOPES

Gyroscopes come to mind usually as stabilizing devices in aircraft and spacecraft

in such applications as automatic pilots. However, they 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. It is used in all satellites, in smart

weapons and in all other applications that require attitude and position stabilization.

Eventually will find their ways into consumer products such as cars although 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”.

Mechanical Gyroscopes

Mechanical gyroscopes are the best known of the existing gyros and the easiest

to understand. It consists of a rotating mass (heavy wheel) on an axis in a frame which

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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.

The relation between applied torque and the angular velocity of precession is

T = I

where T is the applied torque, the angular velocity, I the inertia of the rotating mass,

is the angular velocity of precession and I is the angular momentum.

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

decades in aircraft but it is a fairly large, heavy and complex which could not be easily

adapted to small systems. It also has other problems, associated with the spinning mass

(bearings, friction, balancing, etc.)

Coriolis Force Gyroscopes

Coriolis acceleration has been used to devise much smaller and more cost

effective gyroscopic sensors. It is built in silicon by standard etching methods. The

rotating mass of mechanical gyroscopes is replaced by a vibrating body where 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 the figure below.

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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 Ω.

An example of a coriolis based gyroscope is shown below.

Optical Gyroscopes

One of the more exciting developments in gyroscopes is the optical gyroscope.

It has no moving members and can be used extensively for guidance and control. It is

based on the Segnac effect. The Segnac effect is based on propagation of light in

optical fibers and can be explained using the figure below.

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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 Δt=2πR/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 Ω. The CW beam

will travel a distance 2πR +ΩRΔt and the CCW beam a distance 2πR - ΩRΔt. The

difference between the two paths is then given by

l = 4R2

nc

Thus, there is linear relation between Ω (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.

A resonator is any device which has a dimension equal to multiple half

wavelengths of the wave. A ring is built as shown in the following figure.

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 Ω, the light beams in the ring change

in frequency (wavelength) to compensate for the change in apparent length of the ring.

The relation between frequency, wavelength and length can then be calculated as

dff

= d

= dll

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The light wavelength increases in one direction and decreases in the other. The net effect

is that the two beams generate a frequency difference which is given as

f' = 4Anl

where f’ is the output linearly proportional to Ω.

In coil optical fiber gyroscopes, 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).

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 Ω.

Although very practical, optical gyroscopes are not cheap. But they are orders of

magnitude cheaper than the spinning mass gyroscope and much smaller and lighter.

They also 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 also

immune to electromagnetic fields as well as to radiation and hence can be used in very

hostile environments including space.

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LEVEL SENSORS

Definition

Level sensors detect the level of liquids and other fluids and fluidized solids,

including slurries, granular materials, and powders that exhibit an upper free surface. The

level measurement can either be continuous or point values. Continuous level sensors

measure level within a specified range and determine the exact amount of substance in

a certain place, while point-level sensors only indicate whether the substance is above

or below the sensing point.

Introduction

The simplest and oldest industrial level measuring device is, of course, the sight

glass. A manual approach to measurement, sight glasses have always had a number of

limitations. The material used for its transparency can suffer catastrophic failure, with

ensuing environmental insult, hazardous conditions for personnel, and/or fire and

explosion. Seals are prone to leak, and buildup, if present, obscures the visible level. It

can be stated without reservation that conventional sight glasses are the weakest link of

any installation. They are therefore being rapidly replaced by more advanced

technologies.

Other level-detection devices include those based on specific gravity, the

physical property most commonly used to sense the level surface. A simple float having

a specific gravity between those of the process fluid and the headspace vapor will float

at the surface, accurately following its rises and falls. Hydrostatic head measurements

have also been widely used to infer level.

When more complex physical principles are involved, emerging technologies

often use computers to perform the calculations. This requires sending data in a machine-

readable format from the sensor to the control or monitoring system. Useful transducer

output signal formats for computer automation are current loops, analog voltages, and

digital signals. Analog voltages are simple to set up and deal with, but may have serious

noise and interference issues. 4-20 mA current loops (where the loop current varies with

the level measurement) are the most common output mechanism today. Current loops

can carry signals over longer distances with less degradation. Digital signals coded in any

of a number of protocols (e.g., Foundation Fieldbus, Hart, Honeywell DE, Profibus, and RS-

232) are the most robust, but the older technologies such as RS-232 can handle only

limited distances. New wireless capabilities can be found in the latest transmitters' signals,

allowing them to be sent over tremendous distances with virtually no degradation.

As for the more advanced measurement technologies (e.g., ultrasonic, radar, and

laser), the more sophisticated digital encoding formats require digital computer

intelligence to format the codes. Combining this requirement with the need for

advanced communication capabilities and digital calibration schemes explains the

trend toward embedding microprocessor-based computers in virtually all level

measurement products.

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Level measurement determines the position of the

level relative to the top or bottom of the process

fluid storage vessel. A variety of technologies can

be used, determined by the characteristics of the

fluid and its process conditions.

Floats

Floats work on the simple principle of placing a buoyant object with a specific

gravity intermediate between those of the process fluid and the headspace vapor into

the tank, then attaching a mechanical device to read out its position. The float sinks to

the bottom of the headspace vapor and floats on top of the process fluid. While the float

itself is a basic solution to the problem of locating a liquid's surface, reading a float's

position (i.e., making an actual level measurement) is still problematic. Early float systems

used mechanical components such as cables, tapes, pulleys, and gears to

communicate level. Magnet-equipped floats are popular today.

Early float level transmitters provided a simulated analog or discrete level

measurement using a network of resistors and multiple reed switches, meaning that the

transmitter's output changes in discrete steps. Unlike continuous level-measuring devices,

they cannot discriminate level values between steps.

Hydrostatic Devices

Displacers, bubblers, and differential-pressure transmitters are all hydrostatic

measurement devices. Any change in temperature will therefore cause a shift in the

liquid's specific gravity, as will changes in pressure that affect the specific gravity of the

vapor over the liquid. Both result in reduced measurement accuracy.

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Displacers work on Archimedes' principle. As shown in the figure, a column of solid

material (the displacer) is suspended in the vessel. The displacer's density is always greater

than that of the process fluid (it will sink in the process fluid), and it must extend from the

lowest level required to at least the highest level to be measured. As the process fluid

level rises, the column displaces a volume of fluid equal to the column's cross-sectional

area multiplied by the process fluid level on the displacer. A buoyant force equal to this

displaced volume multiplied by the process fluid density pushes upward on the displacer,

reducing the force needed to support it against the pull of gravity. The transducer, which

is linked to the transmitter, monitors and relates this change in force to level.

A bubbler-type level sensor is shown in the figure below. This technology is used in

vessels that operate under atmospheric pressure. A dip tube having its open end near

the vessel bottom carries a purge gas (typically air, although an inert gas such as dry

nitrogen may be used when there is danger of contamination of or an oxidative reaction

with the process fluid) into the tank. As gas flows down to the dip tube's outlet, the

pressure in the tube rises until it overcomes the hydrostatic pressure produced by the

liquid level at the outlet. That pressure equals the process fluid's density multiplied by its

depth from the end of the dip tube to the surface and is monitored by a pressure

transducer connected to the tube.

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A differential pressure (DP) level sensor is shown in the figure below. The essential

measurement is the difference between total pressure at the bottom of the tank

(hydrostatic head pressure of the fluid plus static pressure in the vessel) and the static or

head pressure in the vessel. As with the bubbler, the hydrostatic pressure difference

equals the process fluid density multiplied by the height of fluid in the vessel. The unit in

the figure uses atmospheric pressure as a reference. A vent at the top keeps the

headspace pressure equal to atmospheric pressure.

In contrast to bubblers, DP sensors can be used in unvented (pressurized) vessels.

All that is required is to connect the reference port (the low-pressure side) to a port in the

vessel above the maximum fill level. Liquid purges or bubblers may still be required,

depending on the process's physical conditions and/or the transmitter's location relative

to the process connections.

Load Cells

A load cell or strain gauge device is essentially a mechanical support member or

bracket equipped with one or more sensors that detect small distortions in the support

member. As the force on the load cell changes, the bracket flexes slightly, causing output

signal changes. Calibrated load cells have been made with force capacities ranging

from fractional ounces to tons.

To measure level, the load cell must be incorporated into the vessel's support

structure. As process fluid fills the vessel, the force on the load cell increases. Knowing the

vessel's geometry (specifically, its cross-sectional area) and the fluid's specific gravity, it is

a simple matter to convert the load cell's known output into the fluid level.

While load cells are advantageous in many applications because of their

noncontact nature, they are expensive and the vessel support structure and connecting

piping must be designed around the load cell's requirements of a floating substructure.

The total weight of the vessel, piping, and connecting structure supported by the vessel

will be weighed by the load cell system in addition to the desired net or product weight.

This total weight often creates a very poor turndown to the net weight, meaning that the

net weight is a very small percentage of the total weight. Finally, the supporting structure's

growth, caused by uneven heating (e.g., morning to evening sunshine) may be reflected

as level, as can side load, wind load, rigid piping, and binding from overturn-prevention

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hardware (for bottom-mounted load cells). In short, load cell weighing system

requirements must be a paramount consideration throughout initial vessel support and

piping design, or performance is quickly degraded.

Magnetic Level Gauges

These gauges are the preferred replacement for sight glasses. They are similar to

float devices, but they communicate the liquid surface location magnetically. The float,

carrying a set of strong permanent magnets, rides in an auxiliary column (float chamber)

attached to the vessel by means of two process connections. This column confines the

float laterally so that it is always close to the chamber's side wall. As the float rides up and

down with the fluid level, a magnetized shuttle or bar graph indication moves with it,

showing the position of the float and thereby providing the level indication. The system

can work only if the auxiliary column and chamber walls are made of nonmagnetic

material.

Many manufacturers provide float designs optimized for the specific gravity of the

fluid being measured, whether butane, propane, oil, acid, water, or interfaces between

two fluids, as well as a large selection of float materials. This means the gauges can

handle high temperatures, high pressures, and corrosive fluids. Oversized float chambers

and high-buoyancy floats are available for applications where buildup is anticipated.

Chambers, flanges, and process connections can be made from engineered

plastics such as Kynar or exotic alloys such as Hastelloy C-276. Special chamber

configurations can handle extreme conditions such as steam jacketing for liquid asphalt,

oversized chambers for flashing applications, and cryogenic temperature designs for

liquid nitrogen and refrigerants. Numerous metals and alloys such as titanium, Incoloy,

and Monel are available for varying combinations of high-temperature, high-pressure,

low-specific-gravity, and corrosive-fluid applications. Today's magnetic level gauges can

also be outfitted with magnetostrictive and guided-wave radar transmitters to allow the

gauge's local indication to be converted into 4-20 mA outputs that can be sent to a

controller or control system.

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Capacitance Transmitters

These devices operate on the fact that process fluids generally have dielectric

constants, , significantly different from that of air, which is very close to 1.0.

Oils have dielectric constants from 1.8 to 5. Pure glycol is 37; aqueous solutions are

between 50 and 80. This technology requires a change in capacitance that varies with

the liquid level, created by either an insulated rod attached to the transmitter and the

process fluid, or an uninsulated rod attached to the transmitter and either the vessel wall

or a reference probe. As the fluid level rises and fills more of the space between the

plates, the overall capacitance rises proportionately. An electronic circuit called a

capacitance bridge measures the overall capacitance and provides a continuous level

measurement.

Magnetostrictive Level Transmitters

The advantages of using a magnet containing a float to determine liquid level

have already been established, and magnetostriction is a proven technology for very

precisely reading the float's location. Instead of mechanical links, magnetostrictive

transmitters use the speed of a torsional wave along a wire to find the float and report its

position.

In a magnetostrictive system, the float carries a series of permanent magnets.

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A sensor wire is connected to a piezoceramic sensor at the transmitter and a

tension fixture is attached to the opposite end of the sensor tube. The tube either runs

through a hole in the center of the float or is adjacent to the float outside of a

nonmagnetic float chamber.

To locate the float, the transmitter sends a short current pulse down the sensor

wire, setting up a magnetic field along its entire length. Simultaneously, a timing circuit is

triggered ON. The field interacts immediately with the field generated by the magnets in

the float. The overall effect is that during the brief time the current flows, a torsional force

is produced in the wire, much like an ultrasonic vibration or wave. This force travels back

to the piezoceramic sensor at a characteristic speed. When the sensor detects the

torsional wave, it produces an electrical signal that notifies the timing circuit that the

wave has arrived and stops the timing circuit. The timing circuit measures the time interval

(TOF) between the start of the current pulse and the wave's arrival. From this information,

the float's location is very precisely determined and presented as a level signal by the

transmitter. Key advantages of this technology are that the signal speed is known and

constant with process variables such as temperature and pressure, and the signal is not

affected by foam, beam divergence, or false echoes. Another benefit is that the only

moving part is the float that rides up and down with the fluid's surface.

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Ultrasonic Level Transmitters

Ultrasonic level sensors measure the distance between the transducer and the

surface using the time required for an ultrasound pulse to travel from a transducer to the

fluid surface and back (TOF). These sensors use frequencies in the tens of kilohertz range;

transit times are ~6 ms/m. The speed of sound (340 m/s in air at 15°C (1115 fps at 60°F)

depends on the mixture of gases in the headspace and their temperature. While the

sensor temperature is compensated for (assuming that the sensor is at the same

temperature as the air in the headspace), this technology is limited to atmospheric

pressure measurements in air or nitrogen.

Laser Level Transmitters

Designed for bulk solids, slurries, and opaque liquids such as dirty sumps, milk, and

liquid styrene, lasers operate on a principle very similar to that of ultrasonic level sensors.

Instead of using the speed of sound to find the level, however, they use the speed of

light.

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A laser transmitter at the top of a vessel fires a short pulse of light down to the

process liquid surface, which reflects it back to the detector. A timing circuit measures

the elapsed time (TOF) and calculates the distance. The key is that lasers have virtually

no beam spread (0.2° beam divergence) and no false echoes, and can be directed

through spaces as small as 2 in.2 Lasers are precise, even in vapor and foam. They are

ideal for use in vessels with numerous obstructions and can measure distances up to 1500

ft. For high-temperature or high-pressure applications, such as in reactor vessels, lasers

must be used in conjunction with specialized sight windows to isolate the transmitter from

the process. These glass windows must pass the laser beam with minimal diffusion and

attenuation and must contain the process conditions.

Radar Level Transmitters

Through-air radar systems beam microwaves downward from either a horn or a

rod antenna at the top of a vessel. The signal reflects off the fluid surface back to the

antenna, and a timing circuit calculates the distance to the fluid level by measuring the

round-trip time (TOF). The fluid's dielectric constant, if low, can present measurement

problems. The reason is that the amount of reflected energy at microwave (radar)

frequencies is dependent on the dielectric constant of the fluid, and if r is low, most of

the radar's energy enters or passes through. Water ( r = 80) produces an excellent

reflection at the change or discontinuity in r.

In through-air radar systems, the radar waves suffer from the same beam divergence that

afflicts ultrasonic transmitters. Internal piping, deposits on the antenna, and multiple

reflections from tank buildup and obstructions can cause erroneous readings. To

overcome these problems, complex algorithms using fuzzy logic must be incorporated

into the transmitter. Transmitter setup can be tedious and changes in the process

environment (buildup, etc.) can be problematic.

Guided wave radar (GWR) systems can be the answer. A rigid probe or flexible

cable antenna system guides the microwave down from the top of the tank to the liquid

level and back to the transmitter. As with through-air radar, a change from a lower to a

higher r causes the reflection. Guided wave radar is 20 × more efficient than through-air

radar because the guide provides a more focused energy path. Different antenna

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configurations allow measurement down to r = 1.4 and lower. Moreover, these sytems

can be installed either vertically, or in some cases horizontally with the guide being bent

up to 90° or angled, and provide a clear measurement signal.

GWR exhibits most of the advantages and few of the liabilities of ultrasound, laser,

and open-air radar systems. Radar's wave speed is largely unaffected by vapor space

gas composition, temperature, or pressure. It works in a vacuum with no recalibration

needed, and can measure through most foam layers. Confining the wave to follow a

probe or cable eliminates beam-spread problems and false echoes from tank walls and

structures.

References:

www.sensorsmag.com/sensors/leak-level/a-dozen-ways-measure-fluid-level-and-how-

they-work-1067. Accessed August 25, 2015.

www. ee.ascs3.uakron.edu/ida/sensors/chapter6.ppt. Accessed August 24, 2015.