Contents...5.4 Prof. Sunil G. Janiyani, Department of Mechanical Engineering Mechanical Measurement and Metrology (3141901) | Unit-5 Force, Torque, Pressure, Strain & Temperature Measurement

Contents

5.1 Force Measurement .......................................................................................................................... 5.2

5.2 Measurement of Torque and Shaft Power .................................................................................... 5.10

5.3 Measurement of Strain ................................................................................................................... 5.17

5.4 Types of Strain Gauges ................................................................................................................... 5.17

5.5 Resistance Strain Gauge ................................................................................................................. 5.19

5.6 Metallic Strain Gauge Materials ..................................................................................................... 5.23

5.7 Wheatstone Bridge Circuit .............................................................................................................. 5.24

5.8 Temperature Compensation in Strain Gauge ................................................................................ 5.25

5.9 Temperature Measurement ............................................................................................................ 5.27

5.10 International Temperature Scale (ITC) .......................................................................................... 5.28

5.11 Temperature Measuring Instruments ............................................................................................ 5.29

5.12 Thermocouple ................................................................................................................................. 5.36

5.13 Total Radiation Pyrometer .............................................................................................................. 5.38

5.14 Optical Pyrometers.......................................................................................................................... 5.41

5.15 Resistance Thermometers and Thermistors ................................................................................ 5.43

5.16 Introduction to Pressure Measurements ....................................................................................... 5.46

5.17 Pitot Tube......................................................................................................................................... 5.48

5.18 Elastic Transducers ........................................................................................................................ 5.49

5.19 Bourdon tube ................................................................................................................................... 5.52

5.20 Measurement of Vacuum ............................................................................................................... 5.53

5.2

Prof. Sunil G. Janiyani, Department of Mechanical Engineering

Mechanical Measurement and Metrology (3141901) |

Unit-5 Force, Torque, Pressure, Strain & Temperature Measurement

5.1 Force Measurement

Force may be defined as a cause that produces resistance or obstruction to any moving body, or

changes the motion of a body, or tends to produce these effects. Force is usually measured by

applying it to a calibrated device which resists the force and indicates or records its magnitude.

The unknown force may be measured by the following methods:

i. Balancing the unknown force against known gravitational force due to standard mass.

Scales and balances work based on this principle.

ii. Applying unknown force to an Elastic member (spring, beam, cantilever, ring, etc) and

measuring the resulting deflection on a calibrated force scale or the deflection may be

measured by using a secondary transducer. i.e. Spring scale, Cantilever beam, proving ring,

Strain gauge load cell.

iii. Translating the force to fluid pressure and then measuring the resultant pressure. Hydraulic

and pneumatic load cells work on this principle.

iv. Applying force to known mass and then measuring the resulting acceleration.

v. Balancing force against a magnetic force which is developed by the interaction of a magnet

and current in the coil.

5.1.1 Scales and Balances

5.1.1.1 Equal arms beam balance scale

The equal arm beam balance scale operates on the principle of moment comparison. The moment

produced by the unknown mass or force is compared with that produced by a gravitational force

due to known standard mass. When the null balance is obtained, the two weights or forces are

equal.

For null balance W1l1 = W2l2 . For equal arms l1 = l2

W1 = W2

Fig.5.1 - Equal arms beam balance scale

5.1.2 Even or unequal arms balance scale

The main disadvantage of equal arms balance scale is requiring a set of weights at least as heavy

as the heaviest load to be measured. In the unequal arms balance scale, two arms are used one is




5.3

called load arm (which is associated with unknown load) and the other is called the power arm

(which is associated with known weights).

For null balance, W1b = W2a

2 1

bW = W

a

Fig.5.2 - Unequal arms beam balance scale

In this scale known weight can be decreased by increasing length b, hence heavier load can be

measure with the help of small known mass and large arm. Further power arm b may be calibrated

to read the unknown weight W2 directly if W1 and a are fixed.

5.1.2.1 Platform scale

When large weights are to be measured, the equal and unequal arms balance scales are not

suitable. In such a case, the platform scale is used. It consists of a multi-level system.

In this system, a large weight W is measured in terms of smaller weights WP (poise weight) and Ws

(pan weight). Before the unknown load W is placed to the platform, the poise weight WP is set at

zero of the beam scale and the counterweight is adjusted to get initial zero balance.

For simplification of analysis, it is assumed that load W is replaced by two arbitrary weights W1

and W2, and WP sets at zero position.

For equilibrium position,

s

1 2

T b = W a ............1

fBut T c = W ............2

d

h fif lever system is so proportional that = , then

e d

e W h

1 2 T c = h = Wh .....3W W

From the above equation, it is clear that the weight W may be placed anywhere on the platform and

its position relative to two knife edges of the platform does not affect the reading. From equations,

we get

s s

a cW= × ×W =M×W ..........4

b h

a cWhere M= × called multiplication ratio of the scale

b h

5.4




Fig.5.3 - Multi-lever platform scale

If M = 1000, means that Ws (weight put on pan) = 1 kg can be used to measure weight W = 1000

kg put on the platform. Further pan weight Ws can be reduced by changing the position of poise

weight on calibrated length in terms of weight. Hence beam is balanced by proper combination of

pan weight and adjustment of poise weight along with calibrated beam scale.

5.1.2.2 Pendulum Scale

Fig.5.4 - Pendulum scale

The pendulum scale is a deflection type instrument in which the unknown weight is converted to a

torque that is then balanced by the torque of a fixed standard mass arranged as a pendulum.

When unknown weight W is applied to the load rod, sectors tend to rotate due to tension in the

loading tubes, and consequently the counterweights we swing-out.

The system equilibrium conditions are attained when the moment due to counterweights is

becoming the same as the moment due to the applied load.




5.5

The motion of the equalizer bar is converted into an angular movement of the indicator by a rack

and pinion arrangement. The deflection of the pointer is calibrated in terms of applied force.

5.1.3 Elastic Force Meter

The elastic elements (spring, rod, cantilever, simply supported beam, ring, bellows, diaphragm, etc.)

can be used for the measurement of force directly or indirectly through the displacement of the

elastic element.

5.1.3.1 Spring scale

Fig.5.5 - Spring scale

In the spring scale, the unknown weight is suspended from a hook. The deflection of spring

concerning weight is read on the scale in terms of the weight. The scale is calibrated based on the

stiffness of the spring (F = K.x, where K is the stiffness of spring, x is deflection, F is load).

5.1.3.2 Cantilever beams load cell

Fig.5.6 - Cantilever beam

It is the simplest type of load cell of force measurement. It measures force based on principle as

'bending moment developed in the beam is proportional to applied force' to the end of the beam.

Consider a cantilever beam, one end is fixed and at another end, the force F is applied at the free

end.

Due to the application of force at the free end of the beam, the maximum deflection will occur at

the free end and maximum strains occur at the fixed end of the beam.

5.6




5.1.3.3 Proving ring

In manufacturing industries, proving rings are most commonly used for the measurement of large

forces (2 KN to 2 MN). A proving ring consists of a circular ring of precisely known diameter,

providing with projection lugs for compressive loading.

The force is determined by measuring the deflection of a steel ring. When an external compressive

or tensile load is applied to the lugs, the ring changes in its diameter. The change of ring diameter

is proportional to the applied load.

The amount of the deflection of the steel ring can be measured using a micrometer and a vibrating

reed which are attached to the internal bosses.

Fig.5.7 - Proving ring

The micrometer is adjusted with the help of a screw and the vibrating reed helps in determining

when contact is made. Before applying the load, the micrometer tip is moved up by a rotating screw

until the contact of reed and micrometer reading is noted.

Now, down the tip of micrometer and applied compressive load on the ring, again micrometer tip

is advanced by rotating the screw and micrometer reading is noted.

The difference in the micrometer reading taken before and after the application of load is the

measure of the amount of deflection of the ring.

This deflection is calibrated in terms of applied force. The deflection of proving ring can be

measured by LVDT, which senses the movement of the core that is attached to the 1ing and moves

because of the deflection of the ring.

Advantages:

i. Wide range of force measuring capacities.

ii. Good accuracy of force measurement.

iii. These instruments furnish a relatively high output signal.




5.7

5.1.3.4 Hydraulic force meter (load cell)

The hydraulic force meter operates on the principle of a force counterbalance. When force is

applied to a definite area of an enclosed fluid, the resulting fluid pressure increases.

The resulting fluid pressure is transmitted to some form of a pressure sensing device such as a

bourdon tube or manometer. The pressure gauge reading is calibrated in terms of force applied.

Fig.5.8 - Hydraulic load cell

Construction and working:

Hydraulic force meter or load cell consists of a metal diaphragm on which force to be measured is

applied. The fluid space below the diaphragm is connected to a bourdon tube pressure through the

tubing.

When the force (to be measured) acts on the loading platform, the diaphragm deflects in

downward, which increases the pressure of the fluid. This pressure is equal to the magnitude of

load applied divided by the effective area of the diaphragm.

The pressure is transmitted to a bourdon tube which calibrated in terms of load. The hydraulic load

cell may be used to measured forces in the range 0 to 2.5 MN with accuracy 0.1 %of full scale.

Advantages:

i. It has a good response against load variation.

ii. It is self-contained and requires no outside power.

iii. It is available for both compression and tensile force.

iv. It has good sensitivity.

v. It is well suited for high impact loads.

vi. It can withstand high overloads without loss of accuracy.

5.1.3.5 Pneumatic force meter (load cell)

Bourdon tube pressure gauge Pneumatic force meter also operates on the principle of a force

counter-balance. In this type of force meter variable downward force (to be measured) is balanced

by the upward force of air pressure against the effective area of the diaphragm.


A pneumatic load cell consists of a diaphragm made from flexible materials to regulate the

balancing pressure· automatically, and bleed valve which is attached to the diaphragm.

5.8




Space below the diaphragm is connected with an air supply system and a pressure measuring

device (manometer). When the force to be measured acts on the diaphragm, it moves downward

which causes to close the bleed valve and results in increased backpressure in the system.

The increased pressure acts on the diaphragm, this produces an effective upward force which

tends to return the diaphragm to its preload position.

Fig.5.9 - Pneumatic load cell

For any constant applied force, the system attains equilibrium at a specific bleed valve opening

and a corresponding pressure is indicated by the manometer.

The maximum pressure in the system is limited to air supply pressure. The pneumatic force meters

are available in ranges 0 to 250 kN with an accuracy of 0.5% of full scale.

Advantages:

i. It is suitable for use in hazardous or explosive areas.

ii. It is not required a special transmitting system.

iii. It is relatively free from temperature-related errors.

Disadvantages:

i. Poor response.

ii. The range of the instrument depends on the air supply pressure.

iii. It requires a high-pressure air source.

5.1.3.6 Strain gauge load cell

The strain gauge load cell is an electromechanical transducer that translates change in force into

a change in voltage.

Working principle:

When stress (force on unit area) is applied to a body, it gets deformed (strain) and these

deformations are related to the applied stress or force. The resistance strain gauge works on the

principle that the resistance of a wire conductor (strain gauge) changes when it is strained.

The change in the resistance has a definite relation with the strain or the applied force. This change

in resistance can be measured by the Wheatstone bridge circuit in terms of voltage.




5.9

Fig.5.10 - Strain gauge load cell


A strain gauge load cell consists of a steel cylinder that has four identical strain gauges (wire

grids). The strain gauge is bonded to a steel cylinder.

The strain gauges R1 and R4 are along the direction of applied load and the strain gauges R2 and R3

are attached circumferentially at right angles to strain gauges R1 and R4.

These four strain gauges are connected electrically to the four limbs of a Wheatstone b1idge

circuit. In the no-load condition, all the four gauges resistance are the same and hence the

Wheatstone bridge circuit in balance condition, no output on the indicator.

When a compressive load is applied, the vertical gauges R1 and R4 undergo compression (negative

strain), therefore their resistance is decreased.

The circumferential gauges R2 and R3 undergo tension (positive strain), therefore their resistance

is increased. The change in resistance of the strain gauges causes unbalance of the Wheatstone

bridge circuit and hence it produces an output that is proportional to an applied force.

Advantages:

i. It is small and compact.

ii. Fast response against load variations.

iii. It is very suitable to measure transient and non-steady forces.

iv. It can be measured compressive as well as tensile load.

5.1.3.7 Linear Variable Differential Transformer (LVDT) load cell

In this type of load cell, the load or force is converted in form of displacement by the mechanical

transducer (elastic diaphragm) called a primary transducer and then the displacement is sensed

by LVDT (called a secondary transducer) which represents voltage change concerning force on

diaphragm.

This device can be used for static as well as dynamic force measurements.

5.10




Fig.5.11 - LVDT type force transducer

5.2 Measurement of Torque and Shaft Power

Elastic diaphragm force, the measurement of torque is associated with the determination of the

power developed or consumed by the rotating part.

The different types of dynamometers are used for the measurement of torque as well as power.

The torque may be measured in terms of reaction force and arm length or angular twist.

Classification of torque and power measurement techniques:

1. Absorption dynamometer: In these types of dynamometers, the energy produced by the engine is

absorbed by frictional resistance of the brake and finally transformed into heat.

Examples:

i. Prony brake dynamometer - block type and band type.

ii. Rope brake dynamometer

iii. Hydraulic dynamometer

iv. Eddy Current dynamometer

2. Transmission dynamometers: In these types of dynamometer, the energy is not wasted in friction

but energy is conveyed to the surrounding in a useful mechanical or electrical form.

Examples:

i. Belt transmission dynamometer.

ii. Epicyclic train dynamometer.

iii. Torsion dynamometer.

iv. Strain gauge dynamometer.

3. Driving dynamometer: In this type of dynamometer, the power-producing/absorbing device (whose

power to be measured) is coupled with the electrical generator or electrical motor.

The motor or generator measure power and also supply energy to operate the tested devices. This

type of dynamometer is employed with pumps and compressors for determining their

performance.

Example: Electric cradled dynamometer




5.11

5.2.1 Torsion bar Dynamometer

The torque of the rotating element can be measured based on the rigidity of the rotating element

(elastic deflection). In this dynamometer, the torque or rotating element (shaft) can be measured

by measuring the angle of the twist of the shaft.

Consider, hollow shaft inner and outer radiuses are ri and r0 respectively, subjected to torque T the

torsion deflection or angle of twist in radian of the hollow shaft is given by

4 4

2TLθ =

( )o iG r r

Where,

G = shear modulus and

L = the length of the shaft under the case study of measuring the twisting angle.

Fig.5.12 - Torsion dynamometer

The angle of twist ϴ in the shaft due to torque T can be measured by torsion meter either optical

or an electrical arrangement and then torque T is calculated by the above equation.

An optical arrangement consists of calibrated scales is used to read the relative angular

displacement of two sections at a specified distance of the torsion bar.

The discs A and B mounted at distance L on the shaft move relative to each other through an angle

ϴ. Due to the application of torque T, the shaft is twisted with an angle ϴ. This is recorded by the

observer with the help of the optical arrangement.

5.2.2 Prony brake dynamometer

The prony brake dynamometer is an absorption-type dynamometer in which the kinetic energy of

the rotating shaft is converted into heat by friction between the brake drum or pulley and the friction

element (block or band). This dynamometer can be classified based on friction element as block

type prony brake and band type prony brake dynamometer.

The block type prony brake dynamometer consists of two wooden blocks clamped together with a

pulley between them. The pulley is fixed to the shaft of the engine or motor.

The blocks are clamped using two bolts with nuts. A helical spring is provided between the nut and

upper block to maintain the constant pressure between the blocks and pulley.

5.12




The one-block carries a lever arm to the one end of which a force can be applied using a known

weight (W) or spring balance. Another end of the arm carries a counter-weight to balance the brake

when unloaded.

Fig.5.13 - Block type prony brake dynamometer

When dynamometer in action, the friction between the blocks and the pulley tends to rotate the

blocks in the direction of the rotation of the shaft. This tendency is prevented by adding weights at

lever end so that its moment balances the moment of the friction resistance between the blocks

and pulley. The two stops are provided to limit the motion of the lever.

Torque on the shaft is given by,

T=F×R=W ×l Nm

2πNPower P=w xT, where w =

602πNT 2πN (w×l)

p= = ,kW60,000 60,000

where N =revolution of shaft per min.

w =angular velocity of shaft

F =frictional force

l =length of arm

W =applied load at end of arm

Advantages:

i. Simple in construction

ii. Less cost

iii. Suitable for measurement of small power.

Disadvantages:

i. The coefficient of friction is reduced due to wear out of the block, hence in the long run

dynamometer becomes unserviceable for measurement of large power.

ii. Due to heat generation, the temperature rises, resulting in a decrease in the coefficient of

friction. Hence the cooling system is required.

iii. When the driving torque on the shaft is not uniform, this dynamometer is subjected to

severe oscillations.




5.13

5.2.3 Rope brake dynamometer

Rope brake dynamometer is also an absorption-type dynamometer. The rope brake dynamometer

consists of two or three ropes wound around the flywheel or pulley which is fixed on engine or

motor shaft.

The upper end of the ropes is attached to a spring balance and the lower end of ropes is kept in

position by applying weight W on it. The wooden blocks are placed at intervals around the

circumferences of the flywheel to prevent the slipping of the ropes over the flywheel.

Fig.5.14 - Rope brake dynamometer

When the engine shaft rotates at a constant speed, the frictional torque is created by means weight

placing at the end of the rope. The frictional torque due to rope and pulley is equal to torque

transmitted by engine shaft.

Let W = weight at end of the rope

S = spring balance reading

N =revolution of engine shaft per minute

D =diameter of pulley or flywheel

d =diameter of rope

eff

eff

eff

D+d R =effective radius of brake wheel =

2

Braking torque is given by

T =tangential force x radius of wheel = (W -S) x R

2πNTBrake power= kw

60,000

2πN (W -S) × Rp=

60,0

kw00

5.14




The cooling system is provided to cool the rope and flywheel.

Range and speed: Rope and band brakes dynamometers may be used for the range of 75 to 36800

W and speed up to 4000 rpm.

Advantages:

i. Simple in construction

ii. It is more suitable than a prony brake dynamometer.

iii. It can be used for a wide range of power.

iv. It can be used for the long test with little overheating and without requiring adjustment.

Disadvantages:

i. Less accuracy because of the change co-efficient of friction of rope with temperature.

ii. The cooling system is required.

5.2.4 Hydraulic (fluid friction) dynamometer

The hydraulic dynamometer operates on the water brake principle. Thus dynamometer uses fluid

friction rather than dry friction (in case of rope brake and prony brake dynamometer) to create the

braking torque.

Fig.5.15 - Hydraulic dynamometer

The hydraulic dynamometer consists of a rotor (rotating disc) and stator (stationary casing).

The rotating disc is fixed on the engine or motor shaft and it rotates with a shaft inside the

stationary casing, the casing is mounted on anti-friction bearings and has a brake arm and a

balance system attached to it.

This bearing allows the casing to rotate freely except restraint imposed by the brake arm. The

casing is in two halves, one of which is placed on either side of the rotating disc. The casing having

semi-elliptical grooves.

These semi-elliptical grooves match with corresponding grooves inside the rotating disc to form

helix chambers through which a stream of water flow is maintained.

When the dynamometer in operation, the rotor rotating with a speed of engine shaft. Due to rotation

of the rotor concerning stator, the vortex and eddy currents (turbulence of water) are set up in the

water. These tend to tum the casing (stator) in the direction of rotation of the rotor.




5.15

This tendency of the stator to rotate is opposed by an arm with a balancing weight that measures

torque. The control of braking action is carried out by changing either the quantity of water or its

pressure or changing space between the stator and rotor.

Let W = weight placed at end of the lever arm, N

N = revolution per minute of shaft

K = dynamometer constant

WNpower=

k

Range and speed: Hydraulic dynamometer may be used for the power up to 20,000 kW and for

speed up to 10,000 rpm.

Advantages:

i. It can be used for high power measurement at high speed.

ii. Water supplied to the dynamometer is served two purposes as providing braking action and

cooling.

iii. High absorption capacity in a small space and at a low cost.

5.2.5 Eddy-current dynamometer

Eddy current dynamometer utilizes the principle that the power loss produced on account of eddy

current which is generated when rotating conductor cuts across magnetic flux. These eddy

currents get dissipated in the form of heat. Therefore this dynamometer acts as an absorption-

type dynamometer.

Fig.5.16 - Eddy current dynamometer

An eddy current dynamometer consists of a toothed steel rotor fixed on the engine shaft. The rotor

rotates inside a smooth bored cast iron stator. The exiting coil is fitted into the inner surface groove

of the stator.

The exiting coil is energized by the direct current supplied from an external source. The stator is

mounted on anti-friction bearings and has a brake arm and a balance system attached to it. This

allows the stator (casing) to rotate freely.

5.16




When dynamometer is operating, the rotor rotates which causes a change in flux at all points of

the stator, voltage is induced and local current (eddy current) flow in a short circular path within

the conductor (stator) and these tend to tum the stator in the direction of rotation of the engine

shaft.

This tendency is resisted by the brake arm balance system that measures the torque.

Range and speed: Eddy current dynamometer may be used for the power up to 250 kW and for

speed up to 6,000rpm.

Advantages:

i. It has a small size for a given capacity.

ii. It is suitable for a large speed range.

iii. It has good control at low rotating speed.

5.2.6 Servo controlled dynamometer

The servo control dynamometer is used to test the engine in the laboratory with the artificial

creation of actual torque and speed variation of the actual automobile engine.

Torque and speed are measured under actual driving conditions of an automobile engine; tape

recordings of such an exercise of an engine are obtained and then simulated under the laboratory

conditions.

Fig.5.17 - Schematic diagram of servo control dynamometer

Engine speed and torque are controlled by two feedback systems. The actual speed signal

generated by the tachometer generator from the dynamometer is compared with the preferred

speed that is set in the tape recorder (previously recorded in actual condition).

If actual and preferred speeds are not the same, the dynamometer control is automatically

adjusted until they are equal. The load cell on the dynamometer measures the actual torque from

the engine and is compared with the preferred torque that is set in the tape recorder.

If the two values differ then error signal generated actuates the engine throttle control in an

appropriate direction. Both the torque control and speed control operate simultaneously and

continually such that they conform to the desired value set in the tape recorder.




5.17

5.3 Measurement of Strain

In the design and construction of machines and structures, it is necessary to know whether the

mechanical components can carry the loads which are demanded on it without any excessive

deformation or failure. Hence, the stress and strain play a very important role.

Stress is defined as the force applied per unit area. The strain is defined as the change in length

per unit original length. The stress cannot be measured directly and hence, normally, strain (change

in dimension per unit original dimension) is measured with the help of strain gauges.

A strain gauge is a device used for measuring dimensional change on the surface of a structural

member under the test. The basic principle of operation of a strain gage is simple:

When strain is applied to a thin metallic wire, its dimension changes, thus changing the resistance

of the wire. It has got a wide range of applications. It can be used for the measurement of load,

force, thrust, pressure, torque, displacement, and flow, etc.

The effects of the above variables to be measured are first measures by primary transducer like

bellows, bourdon tube or cantilever beam, etc. and then converted into small displacement. The

displacement is then measured by the strain gauge.

5.4 Types of Strain Gauges

The strain gauge may be classified as:

1. Mechanical strain gauge

2. Optical strain gauge

3. Electrical strain gauge

The electrical strain gauges especially electrical resistance strain gauges are most popular

because of the many advantages they offer in the process of measurement.

1. Mechanical Strain gauges

In these strain gauges, the change in length of the test specimen is magnified using mechanical

devices like levers or gears. In the initial stage, an extensometer of the single mechanical lever type

was introduced. In this gauge, a lever system is employed to obtain the magnification (10 to 1) of

the movable knife-edge of an extensometer to a fixed knife-edge.

With the advancement of technology, extensometers employing compound levers (dial gauge)

having a magnification of 2000 to 1 were introduced and at the same time, these operated over

small gauge length. The most commonly used mechanical strain gauges are of Berry-type and

Huggen Berger type.

Advantage: It has a self-contained magnification system and no auxiliary equipment is needed as

required in case of an electrical strain gauge.

Disadvantages:

i. Comparatively larger and it is suitable only in cases where sufficient area is available on the

test specimen for mounting the gauge.

ii. The high inertia of the gauge makes it unsuitable for dynamic measurements and varying

strains.

iii. There is no method of recording the readings.

5.18




iv. These gauges are employed for static strain measurement only and also in cases where the

point of measurement is accessible for visual observation.

2. Optical strain gauges

Optical strain gauges are very similar to mechanical strain gauges except that the magnification is

achieved with multiple reflectors using mirrors or prisms.

The inertia of this strain gauge is reduced compared to the mechanical strain gauge. The

measurement accuracy of the optical strain gauge is high compared to the mechanical strain

gauge.

Also, it is independent of temperature variations. In Martin's mirror type extensometer, a plane

mirror is rigidly attached to a movable knife edge.

When it subjected to stress the minors rotates through an angle and the reflected light beam from

the minor subtends an angle twice that of the incident light.

The most commonly used strain gauge in this category is developed by L. B. Tuckerman. It

combines mechanical and optical levers and consists of two parts as an extensometer and as an

autocollimator.

This gauge is also satisfactory only for static measurements and suffers from the obstacles

inherent in all mechanical systems if it used for dynamic measurements.

3. Electrical strain gauges

In these strain gauges, a change in strain produces a change in some electrical characteristics.

The basic principle of an electrical strain gauge is based upon the measurement of the changes in

resistance, capacitance or inductance that are proportional to the strain transferred from the

specimen to the gauge element. The output can be magnified by some auxiliary electronic

equipment.

The electrical strain gauge can be classified as (i) Resistance gauge, (ii) Capacitance gauge, (iii)

Inductance gauge, and (iv) Piezoelectric or semiconductor gauge. Out of these, resistance strain

gauge most commonly used. Capacitance and inductance type are only employed for special

applications. Piezoelectric gauge for measurement of strain has limited application.

However, now a day, the semiconductor type strain gauge has got increasing attention due to its

high sensitivity, small size, and adaptability for both static and dynamic measurements.

The basic concept of resistance strain gauge is that the resistance of a copper or iron wire changes

when subjected to tension. The resistance of the wire changes as a function of strain, increasing

with tension and reducing with compression.

Advantages:

i. It is simple in construction.

ii. Less inertia effect and very sensitive.

iii. It is small size and hence can be installed at a place that is not easily accessible.

iv. Linear measurement is accomplished.

v. The output of the gauge can be utilized for recording and indicating purpose.

vi. The strain gauge can be calibrated in terms of force, displacement, pressure, and acceleration.

vii. It is reliable and inexpensive.




5.19

5.4.1 Gauge Factor or Strain Sensitivity Factor

Gauge factor is the important parameter of strain gauge. It measures the amount of resistance

change for a given strain and therefore serves as an index of the strain sensitivity of the gauge.

It is also called the strain sensitivity factor. In another word, gauge factor (F) is the fractional

change in resistance divided by the unit strain.

ΔR/R F =

Δl/l

Where, ΔR =change in resistance,

Δl =change in length,

R =initial resistance,

l =initial length.

The resistance and length are changed due to the straining of the gauge along the surface to which

it is bonded by the application of force. The higher gauge factor represents the higher sensitivity

of gauge. A higher gauge factor gives higher electrical output for recording and indication.

The gauge factor is normally supplied by the manufacturer and may range from 1.7 to 4 depending

on the length of the gauge. The metallic gauge has a lower gauge factor due to low resistivity. The

semiconductor has a very high gauge factor.

5.5 Resistance Strain Gauge

When a metallic conductor is stretched or compressed, its resistance changes since both the

length and diameter of conductor change. This principle is utilized to measure the displacement in

terms of resistance change of strain gauge.

Fig.5.18 - Resistance wire strain gauge

When strain gauge is mounted to surface whose displacement to be measured, it contracts or

expands with that surfaces.

This deformation of the strain gauge wire causes a change in resistance to it. This change in

resistance can be measured in terms of voltage by the Wheatstone bridge circuit.

Consider a strain gauge wire diameter D and length is subjected to a simple tensile loading. The

change in the physical dimension of wire (conductor) will cause a change in its resistance.

ln other words, wire changes its resistance when mechanically strained within the elastic limit due

to physical effects (change in its length and cross-sectional area).

5.20




5.5.1 Types of Resistance Strain Gauge

5.5.1.1 Bounded strain gauge

In this type of gauges, a grid of fine wire is cemented or bonded to a thin Bakelite sheet or thin

paper sheet and covered with a protective sheet of paper or thin Bakelite.

Bonding the gauge to the strained material (structure understudy) makes it works for compressive

strains or tensile strain.

The tensile strain makes its resistance increase and compressive strain makes it decreases. These

types of strain gauges are useful only for the measurement of small strain or displacement.

a) Flat grid type:

Fig.5.19 - Flat grid type bounded strain gauge

In this type, a wire is wound back and forth as a grid.

The grid structure is bonded to a backing material such as paper or epoxy with a bonding agent

(adhesive) that can hold wire element to the base firmly, permitting a good transference of strain

from base to the wires.

Since the ends of each section of wire are looped around, the transverse strain also causes

changes in resistance in such sections of the wire.

b) Wrap around type:

Fig.5.20 - Wrap around type bounded strain gauge

This type of gauge is wound on a flattened tube of paper, or alternately on a thin strip of card. In

this gauge, the gauge length is smaller than that of the flat grid type.

This gauge achieved the same resistance value for smaller length compared to flat grid gauge,

however, it has higher surface thickness since the grid wire is in two planes and higher hysteresis

and higher creep.




5.21

c) Etched foil type:

Fig.5.21 - Etched foil type bounded strain gauge

The metal foil type strain gauge is manufactured by the photo-etching technique. Here the thin

strips of the foil are the active elements of the strain gauge, while the thick ones are for providing

electrical connections.

Because of the large area of the thick portion, their resistance is small and they do not contribute

to any change in resistance due to strain but increase the heat dissipation area and hence higher

thermal stability and better bonding properties.

Also, it is easier to connect the lead wires with the strain gauge.

In this gauge, there is no stress concentration at the terminals due to the absence of joints, thereby

extending the life of the gauge

d) Woven grid type:

Fig.5.22 – Woven grid type bounded strain gauge

In this type of gauge, Eureka wire is wound as weft on a rayon wrap to form a woven type gauge.

This gauge is useful for tests on fabrics and leather. This gauge can be measured large strain.e.

e) Semiconductor type:

These gauges are produced in wafers from silicon or germanium crystal in which the exact amount

of special impurities such as boron has been added to impart certain desirable characteristics.

They can be of two types: p-type and n-type. In the former, the resistance increases with positive

strain while in the later the resistance decreases with temperature.

The semiconductor gauges are usually provided with plastic or stainless steel backing and are

bonded to the test surface by the same methods as wire and foil gauges.

5.22




The main advantages of semiconductor gauge are high gauge factor (about 100 to 200) and

sensitivity (no need for amplification of output), which can be used for dynamic strain and low

hysteresis.

(a) Single film (b) Combination of n and p-type

Fig.5.23 - Semiconductor type bounded strain gauge

However, it is suitable only for small strain measurement because of the brittle characteristic of

gauge material.

f) Rosette gauge:

The single element strain gage can measure strain in one direction only. But if we want to measure

the strain in two or more directions at the same point, multiple strain gauges are used.

Multiple strain gages configuration is manufactured by stacking multiple strain gages in different

directions.

(a) Two elements rosette (b) Three elements' rosette (c) Three elements rosette

Fig.5.24 - Rosette gauge

This multiple strain gauges configuration in which more than one strain gauges bonded to the

same supporting material in definite relative positions, this configuration of gauges called a

rosette. There are three types of rosettes as rectangular, delta or T -delta rosettes.

5.5.2 Unbounded strain gauge

It consists of a stationary frame and moving armature which connected with a body (whose

displacement to be measured).

A four-strain sensitive wire fitted on or inside the armature. The one end of the wire is fixed at the

frame and another on the armature.

The movement of the armature is limited by strain gauge wires. When external force or

displacement applied to the armature, the strain gauge wire stretched.




5.23

The strain gauges and in compression and are in tensile. The resistance change of four strain

gauges is proportional to their change in length, and this change can be measured with a

Wheatstone bridge circuit.

Fig.5.25 - Unbounded strain gauge

5.6 Metallic Strain Gauge Materials

All electrical conductors exhibit a strain gauge effect, but only a few fulfill the requirements to be

useful as strain gauges.

The major properties of concern are (1) Gauge factor, (2) resistance, (3) temperature coefficient

of gauge factor, (4) thermal coefficient of resistivity, and (5) stability.

High gauge factor materials tend to be more sensitive to temperature and less stable than the

lower gauge factor materials. Strain gauge materials that have been commonly used are given as

follow:

1. Constantan (45%Ni/55%Cu): Constantan or advance (copper-nickel alloy) is most commonly used

for wire strain gauge for static strain measurement because of its low and controllable temperature

coefficient.

They exhibit high specific resistance, constant gauge factor over a wide strain range and good

stability over a reasonably large temperature range. For static measurements, under ideal

compensation conditions, or for dynamic measurements, the alloy may be used from 73.3 to

283°C.

2. Karma (74 % Ni 20% Cr/ 3% Fe): Karma (nickel-chrome alloy with precipitation forming additives)

provides a wider temperature compensation range than constantan.

Special treatment of this alloy gives minimum drift to 316°C and excellent self-temperature

compensation characteristics to 4270C.

3. Nichrome (80% Ni/20% Cr): Nichrome V (nickel-chrome alloy) is commonly used for high-

temperature static and dynamic strain measurements. Under ideal conditions, this alloy may be

used for static measurements to 649°C and dynamic measurements to 982°C.

4. Isoelastic (36% Ni18% Cr/0.5% Mo/ 55% Fe): Isoelastic (nickel-iron alloy plus other ingredients) is

used for dynamic tests. The higher gauge factor is a distinct advantage of good sensitivity where

dynamic strains of small magnitude are measured. However, it has poor stability.

5.24




5. 479PT (platinum-tungsten alloy): It shows an unusually high stability at elevated temperatures. It

also has a relatively high gauge factor for an alloy.

A gauge of this material is recommended for dynamic tests to 816°C and static tests to 649°C.

Strain gauge bonding agents:

The importance of the adhesive that bonds the strain gauge to the metal structure under test or as

part of a transducer cannot be overemphasized.

An ideal adhesive should be suited to its intended environment, transmit all strain from the surface

to the gauge, have high mechanical strength, high electrical isolation, low thermal insulation, and

be very thin.

Also, it should not be affected by temperature changes. The adhesive must provide a strong bond

while electrically isolating the gauge from the surface to which it is attached. In the case of wire

resistance strain gauge, commonly used bonding agents are Durofix, Eastman 910, Araldite,

Ceramic cement, Silicone varnish, etc.

Backing material:

The backing material is that portion of the strain gauge to which the strain sensitive grid structure

is attached.

In addition to the primary electrical insulation backing, it also helps retain the geometric shape of

the grid pattern and protects the gauge.

Commonly used backing material with wire strain gauge is paper, Bakelite, fiberglass, transfer

gauge, etc.

5.7 Wheatstone Bridge Circuit

The Wheatstone bridge is an electric circuit suitable for the detection of minute resistance

changes. It is therefore used to measure resistance changes of a strain gauge. The bridge is

configured by combining four resistors.

Fig.5.26 - Wheatstone bridge circuit

Null mode:

In the null model, the resistance, with no straining is so arranged that the galvanometer gives zero

deflection, V0 =0.

Normally, a strain gauge (resistance Rg) is connected in place of R1, R3 and R4 are fixed, and is

variable resistance.




5.25

Fig.5.27 - Wheatstone bridge circuit (null mode)

When the gauge is strained, its resistance Rg or R1 changes by an amount dR1. This change

unbalances the bridge resulting in deflection of output V0.

The balance (null) is then regained by adjusting R2 by an amount dR2. The rebalance condition gives

31 1

2 2 4

1 2 3 4 1 2 2

g

g g

RR +dR=

R +dR R

IfR = R = R = R , then dR =dR , the change in the value of R is directly measurement

of strain applied at R .

dR =F×e×R

5.8 Temperature Compensation in Strain Gauge

In the strain gauge and bridge configuration in addition to strain, temperature change would also

change the output.

This is due to resistance change of the wire in the strain gauge with a change in temperature and

due to different coefficient of expansion of gauges and metal to which they are bonded.

Different coefficient of expansion causes the differential expansion in gauges and metal to which

they are bonded.

In the strain gauge configuration, the temperature effect can be minimized or avoided by (i)

Compensation or cancelation method and (ii) evaluation as a part of the reduction problem.

The first method is extensively used for both metallic as well as semiconductor gauges while the

second method used only for semiconductor gauges.

Adjacent arm balancing or compensating gauge:

i. Use of dummy gauge,

ii. Use of two active gauges in adjacent arms,

iii. Use of four active gauges,

iv. Poisson's method

5.26




Self-temperature compensation

i. Selected melt gauge,

ii. Duel element gauge

Active Dummy method

The active-dummy method uses the 2-gauge system where an active gauge 1 is bonded to the

measuring object and a dummy gauge 2 is bonded to a dummy block which is free from the stress

of the measuring object but under the same temperature condition as that affecting the measuring

object.

Fig.5.28 - Dummy gauge for temperature compensation

The dummy block should be made of the same material as the measuring object.

Self-temperature compensation gauge

Theoretically, the active dummy method is an ideal temperature compensation method. But the

method involves problems in the form of an extra task to bond two gauges and install the dummy

block.

To solve these problems, the self-temperature compensation gauge is used with a single gauge.

Fig.5.29 - Self-temperature compensation gauge

With the self-temperature-compensation gauge, the temperature coefficient of resistance of the

sensing element is controlled based on the linear expansion coefficient of the measuring object.




5.27

Thus, the gauge enables strain measurement without receiving any thermal effect if it is matched

with the measuring object.

Let, consider the strain gauge resistor of linear expansion coefficient βg is bonded to the measuring

object of linear expansion coefficient βm.

The strain gauge bears thermally induced apparent strain is given by

et=α

F+ (βm- βg)

where, α = temperature coefficient of resistance of resistive element of a strain gauge,

F = gauge factor of strain gauge

From the above equation, it is clear that controlling the temperature coefficient of resistance (α) to

make the thermally induced apparent strain zero (eT = 0) in the equation

For eT= 0, α = (βg- βm)

The temperature coefficient of resistance (α) of the resistive element can be controlled through

heat treatment in the foil production process.

5.9 Temperature Measurement

Temperature is probably the most widely measured and frequently controlled variable encountered

in industrial processing of all kinds. Measurement of temperature potential is involved in

thermodynamics, heat transfer and many chemical operations.

All the properties of matter such as size, color, electrical and magnetic characteristics, and the

physical states (i.e. solid, liquid and gas) change with changing temperature.

The occurrence of physical and chemical changes is governed by the temperature at which a

system is maintained. Even the vast difference between life in the tropic, temperate and arctic

regions of the earth can be attributed to temperature.

The temperature may be defined as the:

I. Degree of hotness and coldness of a body or an environment measured on a definite scale;

II. Driving force or potential causing the flow of energy as heat;

III. The measure of the mean kinetic energy of the molecules of a substance.

IV. A change in the temperature of the system accounts for the change in the molecular motion

and hence the kinetic energy of the molecules.

5.9.1 Temperature Scales

A quantitative measure of the temperature of a body requires reference to some datum plane or

reference condition and the establishment of a suitable temperature unit.

Many temperature scales and reference points have been proposed; the important ones are listed

below:

Centigrade and Fahrenheit scales:

On both these scales, the freezing point and the boiling point water are used as fixed points. The

centigrade scale abbreviated ℃, assigns 0 ℃ to the ice point and 100℃ to the steam point and the

5.28




interval between these points is divided into 100 equal parts. The corresponding values on the

Fahrenheit scale, abbreviated ℉, are 32 ℉ and 212 ℉ with the interval divided into 180 equal parts.

Kelvin and Rankine absolute scales:

Thermodynamically, there does exist a condition of no molecular activity and hence no heat

content in a body The temperature at this condition is the lowest temperature possible and is

referred to as absolute zero. On the Kelvin and Rankine scales, the absolute zero temperature is

hypothetically placed at -273.2 C and - 459.7 F.

Fig.5.30 - Comparison of temperature scales

℃ =5

9(℉ − 32)

°𝐾 = (℃ + 273.2)

°𝑅 = (℉ + 459.7)

5.10 International Temperature Scale (ITC)

This scale has been established and adopted to provide an experimental basis for the calibration

of specific thermometers to indicate temperatures as close as possible to the Kelvin

thermodynamic scale.

The International temperature scale covers the range from the boiling point of oxygen to the

highest temperatures of incandescent bodies and flames. The main features of this scale, adopted

in 1948 at the Ninth General Conference on Weights and Measures are:

I. Temperatures are to be designated as °C and denoted by the symbol t. The name Celsius

was officially adopted to replace the name Centigrade.

II. The scale is based upon several fixed and reproducible equilibrium temperatures to which

numerical values are assigned. The fixed points and numerical values assigned to them are

tabulated in the following table.




5.29

Table 5.1 - Fundamental Fixed Points and their Numerical Values (At Standard Atmospheric Pressure of

1013250 dynes/cm2)

Fixed Point Temperature °C

Temperature of equilibrium between liquid oxygen and its vapor (Oxygen point) -182.97

Temperature of equilibrium between ice and saturated water (ice point)

Fundamental fixed point

0

Temperature of equilibrium between liquid water and its vapor (Steam point)

Fundamental fixed point

100

Temperature of equilibrium between liquid Sulphur and its vapor (Sulphur point) 444.6

Temperature of equilibrium between solid and liquid silver (Silver point) 960.8

Temperature of equilibrium between solid and liquid gold (Gold point) 1063.0

5.11 Temperature Measuring Instruments

Temperature measuring instruments may be classified either according to the range of

temperature measurement or according to the nature of change produced in the temperature

sensing element. The best classification is probably that given in ASME Code on Instruments which

is as follows:

1. Glass thermometers with mercury, alcohol, pentane, and other organic liquids.

2. Pressure-gauge thermometers with vapors or liquids as the actuating fluids. There are two

classes of these thermometers:

i. the vapor-pressure type partially filled with liquid ether, sulfur dioxide, ethyl chloride,

methyl chloride, etc., and

ii. those filled with a liquid or gas, such as mercury, alcohol, nitrogen, etc.

Instruments of the first type have scales that are made up of non-uniform divisions, whereas

the instruments of the second type have uniform divisions.

3. Differential expansion thermometers in which the differential expansion of two solids is

used as an indication of the temperature.

4. Electrical resistance thermometers with which temperature is determined by measuring

the resistance of a calibrated wire.

5. Thermocouple pyrometers in which the electromotive force set up at the junction of two

dissimilar metals is used as an indication of temperature.

6. Optical pyrometers with which temperature is determined by matching the luminosity of

the hot body with that of a calibrated source or by other means, which utilize the visible

radiation emitted from a hot body.

7. Radiation pyrometers with which temperature is estimated by absorbing radiation of all

wavelengths upon a small body and determining the temperature of the source from the

temperature attained by the absorber.

5.30




8. Fusion pyrometers with which temperature is determined by noting which of a series of

materials with graduated fusion temperatures melt or soften when exposed to the

temperature under investigation.

9. Calorimetric pyrometers with which temperature is determined by noting the quantity of

heat removed in bringing the body of known thermal capacity from the temperature to be

measured to some lower known temperature.

10. Color-temperature charts with which temperature is estimated by comparing the color of

a luminous hot body with colors given on the chart.

The instruments mentioned above can also be divided into electrical and non-electrical groups.

Table 5.2 - Temperature measuring instrument classification

Non-electrical methods Electrical methods

I. Liquid, vapor pressure, and gas

thermometers

I. Electrical resistance pyrometers

II. Bimetal strip thermometers II. Thermocouple pyrometers

III. Refractory cones, paints, and crayons III. Total radiation, photoelectric and optical

pyrometers

The term thermometry is sometimes applied without any scientific basis to the measurement

temperatures up to about 325 °C, and the term pyrometry to the measurement of high

temperatures. A summary of the operating range of the different temperature measuring devices

are given in the figure below.

Fig.5.31 - Operating range of thermometers




5.31

5.11.1 Liquid-in-glass thermometers

Liquid-in-glass thermometer is one of the most common types of temperature measuring devices.

The unit consists of a glass envelope, a responsive liquid, and an indicating scale.

The envelope comprises a thick-walled glass tube with a capillary bore, and a spherical or

cylindrical bulb filled with the liquid.

Fig.5.32 - Liquid in glass thermometer

The two parts are filled together and the top end of the capillary tube is sealed. The size of the

capillary depends on the size of the sensing bulb, responsive liquid and the desired temperature

range of the instrument.

Changes in the temperature will cause the fluid to expand and raise the stem. Since the area of the

stem is much less than the bulb, the relatively small changes of fluid volume will result in a

significant fluid rise in the stem.

The length of the movement of the free surface of the fluid column serves, by a prior calibration, to

indicate the temperature of the bulb.

The laboratory work thermometers have a scale engraved directly on the glass stem, while the

industry types have a separate scale located adjacent to the stem.

Quite often the top of the capillary tube is also bulb-shaped to provide safety features in case the

temperature range of the instrument is inadvertently exceeded.

The thermometer bulb is usually filled with mercury. It has the advantages of a broad temperature

span between its freezing and boiling points, a nearly linear coefficient of expansion, relative ease

of obtaining it in a very pure state and its non-wetting of glass characteristics.

When measuring temperatures above the boiling point of mercury (390°C at atmospheric

pressure), mercury may evaporate and condense at the top of the stem.

5.32




This is prevented by filling the space above mercury with nitrogen or carbon dioxide under high

pressure. This raises the boiling point and allows temperature up to 610 °C to be measured.

However, in many industrial applications, the escape of mercury through breakage causes

considerable damage to the products. This may necessitate the use of other liquids such as

alcohol, pentane, and toluene, etc., which do not cause contamination.

These liquids are also used for temperature measurements below the freezing point of mercury.

These liquids have further advantages of superior readability to mercury when colored with inert

dyes and of low cost.

However, they have low boiling points, a greater tendency to separate in the capillary, and wetting

glass characteristics. The range of applications of different liquids is stated in the table.

Table 5.3 - Liquids in glass thermometer with its temperature range

Liquid Range (°C)

Mercury -35 to 510

Alcohol -80 to 70

Toluene -80 to 100

Pentane -200 to 30

Creosote - 5 to 200

The choice in the type of glass used is a matter of economics influenced by the range of the

thermometer-the higher the range, the higher the cost.

For temperatures up to 450 °C, normal glass is used. At high temperatures up to 520 °C,

borosilicate glass is used.

Above this temperature, quartz thermometers have been used but they are not common.

Salient features/characteristics:

a) The simplicity of use and relatively low cost

b) Easily portable

c) Ease of checking for physical damage

d) Absence of need for auxiliary power

e) No need for additional indicating instruments

f) Fragile construction; range limited to about 600 °C

g) Lack of adaptability to remote reading

h) The time lag between the change of temperature and thermometer response due to the

relatively high heat capacity of the bulb.




5.33

5.11.2 Bimetallic strip

Let's consider n as the ratio of moduli of elasticity of low to high expansion material, E1

E2

α1 is a lower coefficient of expansion

α2 is a higher coefficient of expansion

T is operating temperature

T0 is initial bonding temperature

If the 𝑡1 = 𝑡2 and if the materials are so chosen that 𝐸1 ≅ 𝐸2, then

r =2t

3(T − T0)(α2 − α1)

Generally, r is very large and the movement of the free tip is very small. However, the tip deflection

can be increased with the choice of materials that give a large value to the factor (𝛼1 − 𝛼2).

Normally the low expansion materials are invar (an iron-nickel alloy containing about 36% nickel)

and high expansion metal is brass. The respective coefficient of expansion for invar and brass are

0.009 × 10−4 𝑝𝑒𝑟 ℃ and 0.189 × 10−4 𝑝𝑒𝑟 ℃.

Fig.5.33 - Bi-metal strip

When a bi-metallic strip, in the form of a cantilever, is assumed to bend through a circular arc then,

𝑟 + 𝑑𝑟

𝑟=

𝑒𝑥𝑝𝑎𝑛𝑑𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑡𝑟𝑖𝑝 ℎ𝑎𝑣𝑖𝑛𝑔 ℎ𝑖𝑔ℎ𝑒𝑟 𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡

𝑒𝑥𝑝𝑎𝑛𝑑𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑡𝑟𝑖𝑝 ℎ𝑎𝑣𝑖𝑛𝑔 𝑙𝑜𝑤𝑒𝑟 𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡

=l [1 + α2(T − T0)]

l [1 + α1(T − T0)]

Simplification gives,

r =dr[1 + α1(T − T0)]

(α2 − α1)(T − T0)

5.34




With the low expansion metal of invar and the thickness of each metal strip 𝑡

2,

α1 ≅ 0 and dr =t

2

With these stipulations, the equation reduces to

r =t

2α2(T − T0)

The movement of the free end of the cantilever in a perpendicular direction from the initial

horizontal line is worked out as follows:

Angular displacement θ =l

r

Vertical displacement y = OB − OA = r − r cos θ = r (1 − cos θ)

When one end of the bimetallic strip is fixed, the position of the free end is a direct indication of

the temperature of the strip.

Bimetallic elements can be arranged in the flat, spiral, the single helix, and the multiple helix

configurations.

One end of the helix is anchored permanently to the casing and the other end is secured to a pointer

that sweeps over a circular dial graduated in degree of temperature.

In response to temperature change, the bimetal expands and the helical bimetal rotates at its free

end, thus turning the stem and pointer to a new position on the dial. Likewise, the curvature of the

bimetal spiral strip varies with temperature and causes a pointer to deflect.

The continuous strip wound into helical or spiral form has the advantages of compactness while

providing a long length of strip required for adequate indicator movement.

5.11.3 Pressure Thermometer

Fig.5.34 - Pressure thermometer

Pressure thermometers consist of a sensitive bulb, an interconnecting capillary tube, and a

pressure measuring device such as a Bourdon tube, bellows, or diaphragm.

When the system is filled with a liquid (mercury and xylene are common) under an initial pressure,

the compressibility of the liquid is often small enough relative to the pressure gage ∆𝑉

∆𝑝 that the

measurement is essentially one of volume change.




5.35

For gas or vapor systems, the reverse is true, and the basic effect is one of pressure change at

constant volume.

Capillary tubes as long as 60 m may be used for remote measurement. Temperature variations

along the capillary and at the pressure-sensing device generally require compensation, except in

the vapor- pressure type, where pressure depends on only the temperature at the liquid’s free

surface, located at the bulb.

Fig.5.35 - Compensation method

The motion of the compensating system is due to the interfering effects only and is subtracted

from the total motion of the main system, resulting in an output dependent on only bulb

temperature.

The “trimming” capillary (which may be lengthened or shortened) allows the volume to be changed

to attain accurate case compensation by experimental test. Bimetal elements also are used to

obtain cases and partial capillary compensation.

Fig.5.36 - Vapour-pressure thermometer

5.36




The volatile-liquid surface is always in the bulb. Capillary and case corrections are not needed in

such a device since the vapor pressure of a liquid depends on only the temperature of its free

surface.

Commonly used volatile liquids include ethane (vapor pressure changes from 140 kPa to 4 MPa

gage for a temperature change from -73 to 27°C), ethyl chloride (0 to 4 MPa gage for 4 to 180°C),

and chlorobenzene (0 to 400 kPa gage for 135 to 200°C).

The accuracy of pressure thermometers under the best conditions is of the order ±0.5 percent of

the scale range. Adverse environmental conditions may increase this error considerably.

5.12 Thermocouple

If two wires of different materials A and B are connected in a circuit with one junction at

temperature T1and the other at T2, then an infinite-resistance voltmeter detects an electromotive

force E, or if an ammeter is connected, a current is measured.

The magnitude of the voltage E depends on the materials and temperatures. The current ‘I’ is

simply E divided by the total resistance of the circuit, including the ammeter resistance.

Fig.5.37 - Thermocouple

5.12.1 Common Thermocouples

Thermocouples formed by welding, soldering, or merely pressing the two materials together give

identical voltages.

If the current is allowed to flow, the currents may be different since the contact resistance differs

for the various joining methods.

Welding (either gas or electric) is used most widely although both silver solder and soft solder (low

temperatures only) are used in copper/constantan couples. Special capacitor-discharge welding

devices (particularly needed for very-fine-wire thermocouples) are available.

Ready-made thermocouple pairs are, of course, available in a wide range of materials and wire

sizes.

5.12.2 Laws of Thermocouple

The thermal emf of a thermocouple with junctions at T1 and T2 is unaffected by temperature

elsewhere in the circuit if the two metals used are each homogeneous (Fig. a).

If a third homogeneous metal C is inserted into either A or B (see Fig. b), as long as the two new

thermal junctions are at like temperatures, the net emf of the circuit is unchanged irrespective of

the temperature of C away from the junctions.




5.37

If metal C is inserted between A and B at one of the junctions, the temperature of C at any point

away from the AC and BC junctions is immaterial. As long as the junctions AC and BC are both at

the temperature T1, the net emf is the same as if C were not there (Fig. c).

If the thermal emf of metals A and C is EAC and that of metals B and C is ECB, then the thermal

emf of metals A and B is EAC + ECB (Fig. d).

If a thermocouple produces emf E1 when its junctions are at T1 and T2, and E2 when at T2 and T3,

then it will produce E1 + E2 when the junctions are at T1 and T3 (Fig. e).

Fig.5.38 - Thermocouple laws

5.12.3 Thermocouple Materials

Platinum/platinum-rhodium thermocouples are employed mainly in the range of 0 to 1500°C. The

main features of this combination are its chemical inertness and stability at high temperatures in

oxidizing atmospheres.

Reducing atmospheres cause rapid deterioration at high temperatures as the thermocouple metals

are contaminated by absorbing small quantities of other metals from nearby objects (such as

protecting tubes). This difficulty, causing loss of calibration, is unfortunately common to most

thermocouple materials above 1,000°C.

5.38




Chromel (Ni90Cr10)/Alumel (Ni94Mn3Al2Si1) couples are useful over the range 200 to +1,300°C.

Their main application, however, is from about 700 to 1,200°C in non-reducing atmospheres. The

temperature/voltage characteristic is quite linear for this combination.

Fig.5.39 - Thermocouple temperature/voltage curves

Copper/constantan (Cu57Ni43) is used at temperatures as low as -200°C; its upper limit is about

350°C because of the oxidation of copper above this range.

Iron/constantan is the most widely utilized thermocouple for industrial applications and covers the

range -150 to +1,000°C. It is usable in oxidizing atmospheres to about 760°C and reducing

atmospheres to 1000°C.

5.13 Total Radiation Pyrometer

The radiation pyrometers are intended to measure the total energy of radiation from a heated body.

The energy is represented by the area under the spectral distribution curve and is given by the

Stefan -Boltzmann law.

Practical radiation pyrometers respond to a wide band of radiation of approximately 0.1 to 8.0

microns within the visible and infrared, and the actual width of this band depends entirely on the

physical construction of the radiation receiver.

The pyrometer is designed to collect the radiations from the radiating object (furnace) and focus

it using mirrors or lens onto a detector (say hot junction of a thermocouple).

The emf developed by the thermocouple circuit is measured by a suitable mili voltmeter or

potentiometer, which after suitable calibration becomes a measure of the temperature of the

radiating object.




5.39

The pyrometer consists of a blackened tube T open at one end to receive radiations from the object

whose temperature is desired. The other end of the tube carries the sighting hole E which is

essentially an adjustable eyepiece.

Fig.5.40 - Typical radiation pyrometer

The thermal radiations impinge on a concave mirror M whose position can be adjusted by a rack

and pinion. The mirror is centrally pierced to allow light to reach the eyepiece.

The mirror provides a maximum reflection of the incoming radiations onto a thermocouple C which

is shielded from the incoming radiations and carries a blackened copper target disk.

Two small semicircular flat mirrors are inclined at a slight angle from the vertical plane. The

resulting hole is smaller than the target and this allows radiation from the concave mirror to reach

the thermocouple.

The eyepiece and concave mirror are adjusted to focus the radiation from the furnace onto the

target. Small mirrors help in the focusing process. These mirrors appear as shown at (i) when the

radiation is not focused onto the target and when focusing, is achieved they appear as at (ii).

The object of directing radiations from the measured surface onto the temperature sensing

element can also be achieved by a parabolic reflector [Fig. (b)], or by a lens system [Fig. (c)].

5.13.1 Characteristics of radiation pyrometer

High speed of response (0.01 to 0.02 min), a fast response is due to the small thermal capacitance

of the detector. Accuracy ± 2% of the scale range.

No direct contact is necessary with the object where the temperature is to be measured. This fact

allows its use in situations where it is impossible or undesirable to bring the measuring instrument

in contact with the object under consideration.

Primarily used to measure temperatures in the range 700 - 2000 °C where thermocouple and

resistance thermometers cannot be employed.

5.40




Capable to measure the temperature of an object which may be either stationary or moving, and

so adaptable to continuous industrial processing.

Suitable for measuring temperatures where the atmospheric or other environmental conditions

prevent satisfactory operation of other temperature sensing devices.

Relatively independent of the distance between the measuring element and the heated body. The

intensity of radiation decreases as the square of the distance between the object and the

pyrometer, but the area of the cone of radiation received by the pyrometer increases in the same

proportion within the limits of the size of the radiating source. However, for optimum working the

distance from target to receiver should not be greater than 10 or 20 times the maximum useful

diameter of the target. The fraction (target diameter/distance from target to receiver) is called the

target area factor.

Fig.5.41 - Cone of radiation

If the temperature of the radiation body is not uniform, the total emitted radiation will not be directly

proportional to the area. Further, with an increase in the distance there will be greater opportunity

for gases, smoke, etc. to intervene and absorb some of the radiant energy. This would tend to

reduce the indicated temperature.

The effect of dust and dirt on the mirrors or lens is to cause the instrument to read too low.

Cooling is required to protect the instrument from overheating where the temperature may be high

because of operating conditions.

Pyrometer is calibrated under black body conditions. Because the emissivity of most substances

is less than unity, the temperature would be a function of the emissivity of the surface whose

temperature is desired. If emissivity of a surface is known, its actual temperature may be

determined by the following relation,

𝑇𝑎𝑐𝑡𝑢𝑎𝑙 =𝑇𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑

∜𝜖

Radiation detectors: The pyrometers use some means (a tube, parabolic reflector, a lens system)

to direct the radiations from the measured surface onto some sort of radiation detectors which

produce an electrical signal. Detectors may be classified as thermal detectors and photon

detectors. Commonly used thermal detectors are thermocouple or thermopile, metallic bolometer

(resistance thermometers) and semi-conductors bolometers (thermistors). These detectors are

blackened to improve their ability to absorb maximum radiant energy at all the wavelengths. A

thermopile detector gives a comparatively large output, has a quite low response time and is

adaptable in industrial fittings. Resistance thermometers have adequate sensitivity, fast speed of




5.41

response but cost more. Thermistors have the lowest response time but are generally not used

because of poor repeatability and compensation difficulties.

The photon detectors produce an output because the photons associated with the arriving thermal

radiation release electrons from the detector material. These electrons migrate to electrodes and

produce a voltage output. The photon detectors have a fast speed of response, quite large

sensitivity but their application is limited due to limited spectral sensitivity.

5.14 Optical Pyrometers

A metallic surface is usually dark and dull-colored at room temperature. When the surface is

heated, it emits radiations of different wavelengths; these radiations are, however, not visible at

low temperatures.

As the temperature is progressively increased beyond 540 °C, the surface becomes dark red,

orange and finally white. The high temperature is the result of the concentration of radiations in a

short wavelength portion of the spectrum.

A color variation with temperature growth may thus be taken as an index of the probable

temperature; the possible temperature -the color chart is given below:

Table 5.4 - Temperature -color chart of optical pyrometers

Temperature ℃ Colour

540-650 Dull cherry red

700-820 Orange

870-1050 Yellow

1100+ White, radiation is harmful to the naked eye

The typical old-time black-smith was trained by experience to judge the temperature of hot metals

by noting the color of the metal surface. The method is, however, subjective, i.e., it depends on the

judgment of the observer and its accuracy and sensitivity cannot be relied upon.

Fig.5.42 - Disappearing-filament optical pyrometer

5.42




This principle of temperature measurement by color or brightness comparison is utilized in optical

pyrometers designed to measure temperatures in the range of 700 - 3000 °C.

These pyrometers compare the energy emitted by a body at a given wavelength with that of a black

body calibrated lamp.

Radiations from the target surface are focused by an objective lens (L) upon the plane filament (F)

of an incandescent electric light bulb. The eye price (is) is also adjusted until filaments are in sharp

focus and under these conditions, the filament is seen superimposed on the image of the target

surface.

A red filter (R) is placed between the eyepiece and filament, and it allows only a narrow band of

wavelength 0.65 p to pass through it. Matching of the brightness of the lamp filament with that of

the target surface is achieved by adjusting current through the standard lamp by changing the value

of circuit resistance.

The variable resistance or the magnitude of milli ammeter reading (a measure of current through

the lamp) may then be calibrated in terms of the target temperature.

When the filament is indistinguishable, in terms of brightness, from the image of the target surface,

then it is radiating at the same intensity as the target surface.

When the filament is colder than the target surface, it appears as a dark wire against a light-colored

background. Filament brightness is then increased by causing more current to pass through the

filament.

A filament hotter than the object would appear brighter than the target surface. The current through

the filament is then reduced to provide correct merging of filament and the object.

In an alternative approach, the current through the lamp filament is maintained constant. An optical

wedge of absorbing material is moved up and down and its variable thickness accentuates the

incoming energy to match the filament. The wedge position is then calibrated for temperature.

The pyrometer is calibrated by sighting it upon a black body at various known temperatures.

5.14.1 Characteristics of an optical pyrometer

No direct contact is necessary with the object whose temperature is to be measured. This aspect

allows their use in situations where the measuring target is remote and inaccessible such as

molten metals, furnace interiors, etc.

Excellent accuracy; the temperature in the useful operating range (700 -1000°C) can be determined

within ± 5 °C. This pyrometer has been accepted as the standard means for determining

temperatures on the International Temperature Scale from the gold point and upwards.

Measurement is independent of the distance between the target and the measuring instrument.

The image of the target, however, should be sufficiently large to make it possible to secure a

definite brightness match with the filament of the test spot.

The skill in operating the thermometer can be acquired readily. However, the skill of the operator

has more effect on the resulting temperature measurements when an optical pyrometer is used

than when a radiation pyrometer is used.

Because of its manual null-balance operation, this pyrometer is not suitable for continuous

recording or automatic control applications.

The lower measuring temperature is limited to 700℃. Below this temperature, the eye is incentives

to wavelength characteristics.




5.43

5.15 Resistance Thermometers and Thermistors

The resistance R (ohms) of an electrical conductor of resistivity 𝜌(ohms.c), length L (cm) and

cross-sectional area A (cm2) is given by,

𝑅 =𝜌𝐿

𝐴

As temperature changes, the resistance of the conductor also changes. This is due to two factors:

(i) dimensional change due to expansion or contraction and (ii) change in the current opposing

properties of the material itself.

For an unconstrained conductor, the latter is much more than 99% of the total change for copper.

This change in resistance with temperature is used for measuring temperature.

5.15.1 Resistance thermometers

Most metals become more resistant to the passage of electric current as they become hotter, i.e.,

their resistance increases with growth m temperature. An adequate approximation of the

resistance-temperature relationship is given by:

𝑅𝑡 = 𝑅0(1 + 𝛼𝑡 + 𝛽𝑡2)

Where 𝑅𝑡 is resistance at any temperature𝑡 ℃, 𝑅0 is resistance at zero °C, 𝛼, and 𝛽 are constants

depending on the material. The constants R0,𝛼, and 𝛽 are determined at the ice, steam and Sulphur

points respectively. For platinum resistance thermometer, 𝑅𝑡

𝑅0 must not be less than 1.39 for 𝑡 =

100℃ to indicate the purity of the metal and the stability.

Fig.5.43 - Resistance thermometers

The thermometer comprises a resistance element or bulb, suitable electrical leads, and an

indicating-recording or resistance measuring instrument.

The resistance element is usually in the form of a coil often fine platinum, nickel or copper wound

non-conductively onto an insulating ceramic former which is protected externally by a metal

sheath.

A laboratory-type of resistance thermometer is often wound on a crossed mica former and

enclosed in a pyrex tube. The tube may be evacuated or filled with an inert gas to protect the metal

wire.

5.44




Care is to be taken to ensure that the resistance wire-free from mechanical stresses. A metal that

has been strained will suffer a change in the resistance characteristics; the metal is therefore

usually annealed at a temperature higher than that at which it is so operated.

Leads are taken out of the thermometer for the measurement of changes in resistance to

determine the value of temperature.

The change in resistance is usually measured by a wheat stone bridge which may be used either

in the null (balanced) condition or the deflection (out of balance) condition.

For steady-state measurements, the null condition suffices whereas transient conditions usually

require the use of the deflection mode.

A metal used for the fabrication of sensing elements is required to satisfy the following

characteristics:

1. The linearity of resistance - temperature relationship for convenience in measurement

2. Relatively large change in resistance with temperature to produce a resistance

thermometer with good sensitivity

3. No change of phase or state within a reasonable temperature change

4. Resistant to corrosion and absorption under conditions of use

5. Availability in a reproducible condition, consistent resistance-temperature relationship to

provide reliable uniformity

6. High resistivity so that the unit can be fabricated in a compact and convenient size

Industrial resistance thermometers, often referred to as resistance temperature detectors (RTD)

are usually made with elements of platinum (shows little volatilization below 1000℃), nickel (up

to 600 ℃) and copper (upto250℃).

For precise temperature measurements, platinum is preferred because it is physically stable (i.e,

relatively indifferent to its environment, resists corrosion and chemical attack and is not readily

oxidized) and has high electrical resistance characteristics.

It is stated that with careful and in scientific hands, the accuracy attainable with a platinum

resistance thermometer is of the order of ± 0.01 °C up to 500℃)., and within ± 0.1 °C up to 1200℃).

Because of accuracy, stability, and sensitivity, the platinum resistance thermometer has been used

to define International Temperature Scale from the boiling point of oxygen (−182.9℃) to the

freezing point of antimony (630.5℃).

Act of temperature measurement by a resistance thermometer affords the following advantages:

1. Simplicity and accuracy of operation

2. Possibility of easy installation and replacement of the sensitive bulb

3. Easy check on the accuracy of the measuring circuit by substituting a standard resistance

for the resistance element

4. Flexibility about the choice of the measuring equipment, and interchangeability of element

and assembly of components

5. Possibility of much large distance between the temperature-sensitive element and the

indicating element than that with the pressure-actuated thermometers

6. Absence of any reference junction, and so more effective at room temperature when

compared to a thermocouple

7. Possibility of average temperature measurements by suitably connecting the temperature-

sensitive element

8. A positive temperature coefficient of resistance is relatively well-behaved function

compared with the output of a thermocouple




5.45

9. Higher working signal level, simplicity of lead wires and termination schemes compared

with a thermocouple

However, the performance of a resistance thermometer is affected by

1. Resistance change due to temperature changes of measuring resistors

2. More lag because the thermometer is invariably enclosed in a protecting sheath

3. Possibility of current leakage between the resistance element and the ground

4. Generation of thermoelectric emf at the junction of similar metals; its elimination requires

the use of only copper switches and copper wire connections

5.15.2 Thermistors

A thermistor is a contraction of the term Thermal Resistor. They are essentially semi-conductors

which behave as resistors with a high negative temperature coefficient.

As the temperature increases, the resistance goes down, and as the temperature decreases, the

resistance goes up. This is just opposite to the effect of temperature changes on metals.

A high sensitivity to temperature changes (decrease in resistance as much as 6% for each 1℃ rise

in temperature in some cases) makes the thermistors extremely useful for precision temperature

measurement, control, and compensation in the temperature range of −100℃𝑡𝑜 300℃.

Thermistors are composed of a sintered mixture of metallic oxides such as manganese, nickel,

cobalt, copper, iron, and uranium. These metallic oxides are milled, mixed in appropriate

proportions, are pressed into the desired shape with appropriate binders and finally sintered.

The electrical terminals are either embedded before sintering or baked afterward. The electrical

characteristics of thermistors are controlled by varying the type of oxide used and the physical size

and configuration of the thermistor.

Thermistors may be shaped in the form of beads, disks, washers, rods, etc. Disks and rods are

used more as time delay elements, temperature compensators and for voltage and power control

in electrical circuits. Glass and metal probes less than 2 mm diameter are used for temperature

measurements of metal surfaces, gases, and liquids.

Fig.5.44 - Typical thermistor forms

5.46




Thermistors may be used bare but are usually glass coated or positioned under a thin metal cap.

The change in resistance is measured by using circuitry similar to that of metal conductors.

Thermistors differ from metal resistors in the following aspects:

1. Resistance change in metals is positive (increase in resistance with temperature growth).

Thermistors have a relatively large but negative resistance change (reduced resistance with

temperature rise)

2. Metals have an approximately linear temperature-resistance relationship. The

corresponding relation for a thermistor is:

𝑅𝑡 = 𝑅0𝑒𝛽 (1

𝑇−

1

𝑇0)

Where 𝑅𝑡 is the resistance at 𝑇 °𝐾, 𝑅0is the resistance at absolute temperature 𝑇0, 𝛽 is constant

depending on the thermistor's formulation or grade, the typical range is (3400 − 4000°K).

Fig.5.45 - Resistance-temperature curve for a thermistor and platinum resistance thermometer

The practical operating range of thermistors lies between approximately −100℃to 300℃. The

range for resistance thermometers is much greater, being from −160℃ to 600℃.

Thermistors have the advantages of high sensitivity, availability in very small sizes, fast thermal

response, fairly low cost and easy adaptability to electrical read-out devices.

5.16 Introduction to Pressure Measurements

The pressure is an essential component of the everyday life of human beings. We talk about

atmospheric pressure, blood pressure, gauge pressure, vacuum, etc. Hence, it becomes imperative

to know the elementary details about pressure and its measurement. Pressure can be defined in

many ways.

The pressure is the force exerted by a medium, usually a fluid, on a unit area. Measuring devices

usually register a differential pressure—gauge pressure. The pressure is also defined as the force

exerted over a unit area. Force may be exerted by liquids, gases, and solids.

Pressure may be measured in atmospheres, bars, or in terms of the height of a liquid column.

Standard atmospheric pressure is usually referred to as 760 mmHg.




5.47

The standard atmospheric level is always measured at the sea level. It is to be noted that

atmospheric pressure decreases with increasing altitude. The units of pressure normally depend

on the context in which pressure is measured.

Measurement of pressure becomes an important aspect due to the following reasons:

1. It is a quantity that describes a system.

2. It is invariably a significant process parameter.

3. Many a time, the pressure difference is used as a means of measuring the flow rate of a fluid.

4. From the lowest to the highest pressures usually encountered in practice, the level of pressure

has a range of nearly 18 orders of magnitude.

5.16.1 Pressure Measurement Scales

The following basic scales are employed in pressure measurement:

1. Gauge pressure is measured above the local atmospheric pressure.

2. Total absolute pressure is the total pressure measured from zero pressure as the datum point.

When the absolute pressure exceeds the local atmospheric pressure, it may be considered to

be the sum of the gauge pressure and the local atmospheric pressure. The total pressure is the

sum of atmospheric pressure and gauge pressure.

Total absolute pressure = Atmospheric pressure + Gauge pressure

3. Differential pressure is the difference in pressure measured between two points.

4. When the pressure to be measured is less than the local atmospheric pressure, it is called

vacuum pressure. In other words, when the gauge pressure is negative, it is termed as the

vacuum.

A vacuum is defined by the following relation:

Vacuum = Atmospheric pressure − Absolute pressure

5. Absolute pressure is measured above the total vacuum or zero absolute. Zero absolute

represents a total lack of pressure.

Fig.5.46 - Absolute, gauge, and barometric pressures

5.48




The following are the units and conversion factors that are normally used:

a) 1 Pa = 1 N/m2

b) 1 atm = 760 mmHg = 1.013 × 105 Pa

c) 1 mmHg = 1 Torr

d) 1 Torr = 1.316 × 10−3 atm = 133.3 Pa

e) 1 bar = 105 Pa

5.16.2 Classification of Pressure Measuring Devices

The different instruments/devices used for the measurement of pressure can be classified as

follows:

1. Gravitation-type manometers

2. Mechanical displacement-type manometers:

(a) Ring balance

(b) Bell-type

3. Elastic pressure transducers:

(a) Bourdon tube pressure gauges

(b) Diaphragm-type gauges

(c) Bellow gauges

4. Electrical pressure transducers:

(a) Resistance-type pressure transducer

(b) Potentiometer devices

(c) Inductive-type transducer

(d) Capacitive-type transducer

(e) Piezoelectric pressure transducer

(f) Bridgman gauges

6. Low-pressure measurement gauges:

(a) McLeod gauges

(b) Pirani or thermal conductivity gauges

(c) Ionization gauges

7. Engine indicator (for varying pressure measurements)

5.17 Pitot Tube

The pitot tube is a device that is used to measure the local velocity and total pressure of a fluid, as

against the velocity measured across the tube in case of an orifice plate and a venturi meter. It

finds extensive application in aircraft.

A pitot tube consists of an ‘L’ shaped structure held upfront against the fluid flow. It consists of a

static probe and an impact probe.




5.49

The impact probe should face a direction that is against the fluid flow. While the static probe

measures the static pressure in the system, the impact probe is meant to measure the total

pressure of the system.

Fig.5.47 – Pitot tube

When the fluid flows against the tip of the impact probe, it is brought to rest. This affects (rise) on

the pressure (P2) corresponding to P1 at the static probe.

Applying Bernoulli’s Theorem for an incompressible fluid, we get the following equation:

𝑉 = √2(𝑃2 − 𝑃1)

𝜌

5.18 Elastic Transducers

Single diaphragms, stacks of diaphragms, and bellows are some of the important elastic

transducers used for pressure measurement.

Diaphragms are generally used as primary transducers for dynamic pressure measurement. These

may be of a flat or corrugated type, as shown in the figure below.

Fig.5.48 - Types of diaphragms (a) Flat diaphragm (b) Corrugated diaphragm

Flat diaphragms are used along with electrical secondary transducers for better amplification of

small-diaphragm deflections.

5.50




For large deflections, corrugated diaphragms are preferred. Corrugated diaphragms generally find

application in static pressure measurement due to their increased size and deflection, which affect

the dynamic response.

A single diaphragm in its simplest form is shown in the figure below. It is a thin, flat, circular plate

fixed at the two ends; upon application of pressure, it will deflect and the resulting differential

pressure is given by P1 − P2.

Fig.5.49 - Simple diaphragm

This can be used only for relatively small movements wherein the relationship between pressure

and deflection is linear. The deflection attained by flat diaphragms is limited by linearity constraints

or stress requirements. However, for practical applications, some modification is required.

Sometimes, a mechanical linkage system or an electrical secondary transducer needs to be

connected to the diaphragm at its center. To enable this, a metal disc or any other rigid material is

provided at the center with diaphragms on either side.

The diaphragm may be made up of a variety of materials such as nylon, plastic, leather, silk, or

rubberized fabric. This type of transducer, which is used for pressure measurement, is known as

the slack diaphragm or fabric diaphragm differential pressure gauge.

The construction of a fabric diaphragm is shown in the figure below.

Fig.5.50 - Fabric diaphragm




5.51

It comprises a rigid centerpiece, which is held on either side by diaphragms made of fabric. A

secondary transducer, which may be an electrical or a mechanical linkage system, or a recording

pen, is connected to the center.

The slack diaphragm is used to measure low pressures. Since the centerpiece is rigid, there may

be a reduction in the flexibility of the diaphragm.

A pressure capsule or a metal capsule can be formed by joining two or more diaphragms, as shown

in the figure below.

Fig.5.51 - Pressure capsule

The use of corrugated diaphragms increases linear deflections and reduces stress.

Differential pressure can be created by applying one pressure from inside the capsule and another

from the outside. In a metallic capsule, the relationship between deflection and pressure remains

linear as long as the movement is not excessive.

Metallic bellows can be employed as pressure-sensing elements. A thin-walled tube is converted

into a corrugated diaphragm by using a hydraulic press and is stacked as shown in the figure

below.

Fig.5.52 - Metallic bellow

Due to the differential pressure, there will be a deflection, y0. Normally, materials such as phosphor

bronze, brass, beryllium copper, and stainless steel are used for making bellows.

5.52




Metallic bellows are often associated with zero shift and hysteresis problems.

The modification of a metallic bellow for differential pressure measurement is shown in the figure

below. An industrial gauge, called an industrial bellows gauge, has a double-bellow arrangement.

Fig.5.53 - Industrial bellow gauge

One end of the double bellow is connected to a pointer or a recorder pen. High pressure of P2 and

low pressure of P1 are applied to create a differential pressure.

5.19 Bourdon tube

The most widely used gauge for pressure measurement is the Bourdon tube. It was first developed

in 1849 by E. Bourdon.

This tube is composed of a C-shaped hollow metal tube having an elliptical cross-section.

One end of the Bourdon tube is fixed and can be used as the pressure inlet, as shown in the figure

below.

Fig.5.54 - Bourdon tube




5.53

The other end is free and closed. Due to the applied pressure, the tube straightens out and tends

to acquire a circular cross-section. Thus, the pressure causes the free end to move. This movement

is proportional to the difference between inside and outside pressures.

To measure pressure, movement of the free end is often magnified and transmitted to a pointer

that moves over the scale through linkage and gearing mechanism.

The pointer indicates gauge pressure since the reference pressure is atmospheric. In case higher

sensitivity is required, the Bourdon tube may be formed into a helix containing several turns.

Bourdon tubes can also assume helical, twisted, or spiral forms, and the operation of all these

gauges is similar to that of C-shaped tubes commonly employed for differential pressure

measurement.

Bourdon tubes are usually made of phosphor bronze, brass, and beryllium copper. However, the

choice of material depends on the range of pressure to be measured and the elastic limit of the

material under consideration.

Bourdon gauges are employed to measure pressures of up to 500 MPa.

5.20 Measurement of Vacuum

Pressures below the atmosphere are generally termed as low pressures or vacuum pressures.

When the term vacuum is mentioned it means that the gauge pressure is negative.

However, atmospheric pressure serves as a reference and absolute pressure is positive. Low

pressures are more difficult to measure than medium pressures.

Pressures above 1 Torr can easily be measured by the direct measurement method, wherein the

force applied causes a displacement.

Manometers, diaphragms, bellows, and Bourdon tubes are some examples of the instruments used

in direct measurement of pressure. These devices are generally employed to measure a pressure

value of about 10 mmHg.

For measuring pressures below 1 Torr, indirect or inferential methods are often employed. In these

methods, the pressure is determined by drawing indirect references to pressure-controlling

properties such as volume, thermal conductivity, and ionization of the gas.

Some of the devices that fall under this category include McLeod gauge, Pirani gauge, and

ionization gauge.

5.20.1 McLeod Gauge

McLeod gauge, which was developed in 1874 by Herbert McLeod, is perhaps the most widely used.

It is employed as an absolute standard of vacuum measurement for pressures ranging from 10 to

10−4 Torr.

A McLeod gauge, which is also known as a compression gauge, is used for vacuum measurement

by compressing the low-pressure gas whose pressure is to be measured.

The trapped gas gets compressed in a capillary tube. The vacuum is measured by measuring the

height of a column of mercury.

McLeod gauge works on Boyle’s law, which states that by compressing a known volume of the low-

pressure gas to a higher pressure, initial pressure can be calculated by measuring the resulting

volume and pressure.

5.54




The following fundamental relation represents Boyle’s law:

𝑃1 =𝑃2 𝑉2

𝑉1

where P1 and P2 are the initial and final pressures, respectively, and V1 and V2 are the corresponding

volumes.

A McLeod gauge is composed of a capillary tube A, which is sealed at the top, and two limbs B and

C, which are connected to the vacuum system. Both limbs A and B are capillary tubes and their

diameters are the same.

The diameter of limb C is wider and hence reduces capillary errors. The McLeod gauge is

schematically represented in the figure below.

Fig.5.55 - McLeod gauge

Initially, the movable reservoir is lowered to allow the mercury column to fall below the opening

level O. In this position, the capillary and limbs are connected to the unknown pressure source. The

movable reservoir is then raised such that the mercury fills up the bulb.

The mercury level in capillary tube A also rises and compresses the trapped gas in the capillary

tube A according to Boyle’s law.

It is important to note here that, in practice, the mercury level in capillary tube B is raised to the

same level as that of limb C, which represents the zero level on the scale.

The difference in levels of the two columns in limbs A and B gives a measure of trapped pressure,

which can directly be read from the scale.

Let V1 be the volume of the bulb in capillary A above the level O, P1 the unknown pressure of the

gas in the system connected to B and C, P2 the pressure of the gas in the limb after compression,

and V2 the volume of the gas in the sealed limb after compression. Then,

P1V1 = P2V2

where P1 and P2 are measured in units of mmHg.




5.55

If the cross-sectional area of the capillary tube is a and the difference in levels of the two columns

in limbs A and B is h, then V2 = ah, where h is the difference between pressures P1 and P2, that is, h

= P2 − P1.

Therefore, one gets the following equations:

P1V1 = (P2)ah

P1V1 = (h + P1)ah

P1V1 = ah2 + ahP1

P1(V1 - ah) = ah2

∴ 𝑃1 =𝑎 ℎ2

𝑉1 − 𝑎ℎ

To measure low pressures, the value of V1 is made large compared to that of a. The ratio of V1 to

a is called the compression ratio.

If a is made too small, the mercury tends to stick inside the capillary tube; this restricts the upper

limit of the compression ratio. The compression ratio gets limited due to the excessive weight of

mercury if V1 is very large.

McLeod gauges are regularly employed to calibrate other high-vacuum measuring devices. The

presence of condensable vapors in the gas whose pressure is to be measured poses a serious

limitation as Boyle’s law is not followed, which may induce errors.

5.20.2 Pirani Gauge

The principle on which a Pirani gauge works is thus: when a heated wire is placed in a chamber of

gas, the thermal conductivity of the gas depends on its pressure. Hence, it follows that energy

transfer from the wire to the gas is proportional to the gas pressure.

Fig.5.56 – Pirani gauge

The temperature of the wire can be altered by keeping the heating energy supplied to the wire

constant and varying the pressure of the gas, thus providing a method for pressure measurement.

On the other hand, a change in the temperature of the wire causes a change in the resistance,

providing a second method for the measurement of pressure.

Three attributes, namely magnitude of the current, resistivity of the current, and the rate at which

heat is dissipated govern the temperature of the given wire through which an electric current flows.

The conductivity of the surrounding media determines the heat dissipation rate.

5.56




Thermal conductivity reduces due to the reduction in pressure and, consequently, for a given input

of electrical energy, the filament attains a higher temperature.

A resistance bridge is employed when the resistance of the wire filament is measured. The bridge

is balanced at some reference pressure and the out-of-balance currents are used at all other

pressures as a measure of the relative pressures.

Heat loss from the filament due to the variations in ambient temperatures can be compensated.

This can be accomplished by connecting the two gauges in the series in one arm of the bridge, as

depicted in the figure below.

Fig.5.57 - Pirani gauge with compensation for ambient temperature changes

One of the gauges whose pressure is to be measured is connected to a vacuum source and the

other is evacuated and sealed. Since both are exposed to the same ambient conditions, the

measurement gauge will respond only to variations in the vacuum pressure.

By adjusting R2, the bridge circuit can be balanced to give a null reading.

The deflection of the bridge from the null reading, due to the exposure of the measurement gauge

to test the pressure environment, will be independent of variations in ambient temperatures.

References:

1) Er. R K Rajput, ”Mechanical Measurements and Instrumentations", Kataria Publication.

2) R K Jain, ”Mechanical Measurement and Metrology”, Khanna Publisher.

3) N. V. Raghavendra & L. Krishnamurthy, "Engineering Metrology and Measurements", Oxford

University Press.

4) Anand Bewoor & Vinay Kulkarni, "Metrology and Measurement", Tata McGraw-Hill

Education Private Limited.

Documents

Contents...5.4 Prof. Sunil G. Janiyani, Department of Mechanical Engineering Mechanical Measurement and Metrology (3141901) | Unit-5 Force, Torque, Pressure, Strain & Temperature Measurement