Sensors

Sensor s

N VENKAIAH N. VENKAIAH

Lecturer Mechanical Engineering Department NIT Warangal 506 004

Why Sensors? Sensors and actuators are two critical components of ever y closed loop control system (mechatronics system ). A sensing unit can be as simple as a single sensor or can consist of additional compon ents such as filters, amplifiers, modulators, and other signal conditioners.

A typical mechatronic system

The controller accepts the information from the sensing unit information from the sensing unit,

makes decisions based on the control algorithm, and outputs commands to the actuating unit. The actuating unit consists of an actuator and optionally a po wer supply and a coupling mechanism.

1

Sensor vs Transducer Sensor is a device that when exposed to a physical phenomenon (temperature, displacement, force, etc.) produces a proportional output p g signal (, , g,) (electrical, mechanical, magnetic, etc.). Transducer is a device that converts one form of energy into another form of energy. Thermocouple - Sensor or Transducer?

"Both!"

Actuators

A typical actuating unit Actuators are the muscle behind a mechatronics system Accept a control command and produces a change in the physical system. Actuators are used in conjunction with the power supply and a coupling mechanism

2

Characteristics Characteristics

o f Actuators Sensors and

5

Range & Span Range : Limits between which the input can vary. Span : Difference between max. and min. values of input If the lowest point p g pof calibration is X units and the highest point of calibration is Y units and the calibration is continuous between these two points, then Range = X to Y units Span units

=

(Y-X)

200 o c 300

150 o c

50 o c

Example 1

Range = 50 to 200 o c Span = 200 – 50 = 150

o

c

800 o c 700 o c 600 o c 500 o c 400 o c 300 o cc

Range = 300 to 800 o c Span = 800 – 300 = 500

250 o c 200 o c 150 o c 100 o c 50 o c 0o c

Range = 0 to 250 o c Span = 250 – 0 = 250

Example 2

o

o

c

c

6

3

Sensitivity Ability of a measuring device to detect small differences in a quantity being measured.

0

Ratio of the output per unit input

for m1

1 2

for m

3

2

4 5 kg

Ratio of the linear movement of the pointer on the instrument scale to the change in the value of the measured variable causing this m

motion xxcm ==kg Sensitivity cm ()kg() mm-2 1 21 mm

7

Sensitivity contd… xxcm == kg Sensitivity cm ()kg() mm -21 2 1 mm = slope Input (mass)

If response is linear, slope remains constant throughout. 1f 1

Sensitivityyp is same at all inputs

0 fo r m 2 3 4

Length of the scale Sensitivity = Span of the instrument

f or m

1

2

5kg

15 cm = = 3 cm 5 kg kg m

8

4

Sensitivity contd…

Input (mass) If response is non-linear, slope varies from point to point. Therefore, sensitivity is different at different inputs

If the movement of the pointer is angular, sensitivity is expressed in terms of degrees or radians of the angle per unit change in input In digital instruments, the term scale factor is used instead of sensitivity

Threshold & Resolution Threshold is the min. input which produces a small but definite change in output when the input is increased gradually from a ‘ zero’ value. Resolution is the min. input which produces a small but definite change in output when the input is increased gradually from a ‘ non-zero ’ value.

Moral : However sophisticated the transducer may be, it can’t be used to indicate an input less than its resolution

5

Hysteresis Hysteresis represents the dependence of physical systems

history

A sensor is said to exhibit hysteresis y when there is a difference in output depending on whether the value of measurand is approached from below or above

Error

O

Hysteresis = R

2

Measurand

-R

1

Causes a. Mechanical friction b. Elastic deformation c. Thermal effects d. Magnetic effects Input = 100 V

Accuracy Degree to which the measured value agrees with the true value In other words, it ,indicates p the deviation of the output from the known input Accuracy or error = RI As (R-I) decreases, error decreases but accuracy increases and vice-versa

R

Mhd Methods to express accuracy 1. As a % of F.S.R 2. As a % of known I/P

I

6

Accuracy contd… Case -1 Let the F.S.R be 200 V Let the F.S.R be 200 V Accuracy as specified by the manufacturer be ±1% It means that, R-I Accuracy = 100 = ±1% F.S.R R-I =

±1×200 100

= ±2 V If R =100 V at an instant, then 98 < I < 102 If R = 50 V, 48 < I <52 Moral : Error remains the same throughout the range.

Accuracy contd… Case -2 R-I Accuracy = 100 = ±1% I As I and R are close to each other,, for , ypthe y sake of evaluation, I in denominator may be replaced by R R-I 100 = ±1% R Let at an instant R be equal to 100 V ±1×R ±1×100= ±1 V R-I = 100 = 100 I=100 ±1V = 99 V - 101 V Let R=50, 1 R-I= ±=± 0.5 2 I= 50 ±= 0.5 49.5V - 50.5 V

Moral : As reading decreases, error also decreases. This characteristic is against the known tendency of instruments which exhibit higher errors at lower readings

7

Precision (Reproducibility) Ability of an instrument to reproduce certain reading with a given accuracy. Degree of agreement among repeated results Degree of agreement among repeated results Maximum deviation of the readings from the mean, expressed as a percentage of F.S.R

Conditions

V-V maxa Precision = 100 % F.S.R

Same measurement procedure Same observer Same measuring instrument, used under same conditions Same location Repetition over a short period of time.

Accuracy Vs Precision A Famous Example

Neither Precise Nor Accurate

This is a random like pattern, p neither precise nor accurate. The darts are not clustered together and are not near the bull's eye.

Precise, Not Accurate

This is a precise pattern, but not accurate. The darts are clustered together but did not hit the intended mark. 16

8

Accurate, Not Precise This is an accurate pattern, but not precise. The darts are not clustered, but their 'average' position is the center of the bull's eye.

Accurate and Precise This pattern is both precise and accurate. The darts are tightly clustered and their average position is the center of the bull's eye. 17

Another Example AB

Input = 100 V

Input = 100 V

Readings: 103, 105, 104, 105, 103 V Readings: 99, 102, 98, 100, 101 V

Va = 104 V,m a x = 105 V,m in V V 5V Accuracy = 100 = 2.5%× 2 V 200 V ± 1×±V2 V Precision = 100 = 0.5% 200 V

F.S.R = 200 V = 103 V V

a

= 100 V,m a x = 102 V,m in = 98 V V V

± ×± Accuracy = 100 = 1% 200 V ± ×± Precision = 100 = 1% 200 V

9

Stability Ability to give same output when used to measure a constant input over a period of time. Change in output over time is termed as drift

Linearity Maximum deviation from a ‘straight-line’ response Normally expressed as a percentage of the fullscale value scale value

10

Nonlinearities Linear systems have the property of superposition

Input Response (output) AA

’

BB

’

C (A+B) C

’ (A’+ B’)

Many real systems will exhibit linear or nearly linear behavior over Many real systems will exhibit linear orsome nearly linear behavior over range of operation. Therefore, linear system analysis is correct, at least over this portion of a system’s operating envelope. Unfortunately, most real systems have nonlinearities that cause them to operate outside this linear region, and many common assumptions about system behavior, such as superposition, no longer apply.

Various Nonlinearities Static (Coulomb) Friction Eccentricity Backlash Saturation Deadband

11

Static (Coulomb) Friction

Static friction has two primary effects on mechatronic systems 1. Some of the actuator torque or force is wasted in overcoming frictional forces, which leads to inefficiency from an energy viewpoint. 2. Loss of repeatability in mechatronic systems

Eccentricity

Gear eccentricity The true center of the gears pitch circle and the center of rotation will be separated by a small amount, known as the eccentricity. Small tooth-to-tooth errors can also cause local variations in the pitch circle radius. Eccentricity causes the mating gears, pulleys and chain drives to have nonlinear geometrical relationship between them Eccentricity impacts the accuracy of position measurements

12

Backlash If two gears are not mounted on a center-to-center distance that exactly matches the sum of the pitch radii, there will be a small clearance or there will be a small clearance, or

backlash, between the teeth. Gear backlash is just one of many phenomena that can be characterized as hysteresis

Gear backlash

Backlash exhibits effects similar to those for eccentricity, i.e., a loss of repeatability, particularly when approaching a measured point from different directions. The gear backlash problem is so prevalent and potentially harmful that many manufacturers go to great lengths to minimize the effect:

Backlash How to minimize backlash? • Gears mounted closer together than the theoretically ideal spacing, • Split “anti-backlash” gears that are spring loaded to force teeth to maintain engagement at all times, • External spring-loaded mounts for one of the gears to force engagement, or

13

Saturation All real actuators have some maximum output capability maximum output capability Input beyond a certain value does not cause any change in output This type of nonlinearity must be considered in mechatronic control system design, since maximum velocity and force or torque limitations affect system performance. Control systems modeled with linear system theory must be carefully tested or analyzed to determine the impact of saturation on system performance.

Deadband and Deadtime Deadband or deadspace of a transducer is the range of input values for which there is no output. Deadtime is the length of time from the application of an input until the output begins to respond and change

Thermostat deadband

14

Sensors - Classification By their measurement objective Position: Linear/Rotational sensors Proximity sensors Acceleration sensors Force, torque sensors Pressure sensors Flow sensors Temperature sensors Temperature sensors

Light sensors Smart material sensors Micro and nano-sensors

Position Sensors

15

LVDT

Transformer

16

Transformer The trans former so defined is a tightly coupled transformer (all flux links both coils) Loosely coupled transformers Loosely coupled transformers Only part of the flux produced by one coil links the second coil The magnetic path is said to be open These are more often used in sensors

Constructional Details A primary winding center ed between a pair of identically wound secondary windings, symmetrically spaced about the primary The moving element is a separate tubular armature of magnetically permeable material called the core, which is free to move axially within the coil's hollow bore and mechan ically coupled to the object whose position is being measured.

17

Working Principle Arm atu re (I ro n co re )

E1 E

E

in

E

in

E

ou t

ou t

= E -E 1

2

E2

Tr an sfo rme r Tr an sfo rme r

Voltage is proportional to the core displacement Displacement of core,

D = MEou t

Linear Variable Differential Transformer

18

LVDT - Application

41

Resistive Potentiometer Resistance of an electrical conductor L R = Where, A = Resistivity iii (h ) (ohms-m) L = Length of conductor, m A = Cross-sectional area of conductor, m

Potentiometer Valve Position Indicator

2

42

19

Capacitance Capacitance: the ratio between charge and potential of a body

V V V V

C

C =Q

coulombs/volt (or farad, F)

Capacitance is only defined for two conducting bodies, across which the potential difference is connected. Body B is charged by the battery to a positive charge Q and body A to an equal but negative charge –Q. Any two conducting bodies, regardless of size and distance

between them have a capacitance between them have a capacitance.

43

Capacitive Transducer Plates/Electrodes

Capacitance of a capacitor is given by

e

C d= ee 0

A r

r

farads

d C

where -12 e = Permittivity of vacuum = 8.854x10 F/m 0

e = Dielectric constant of the medium between the plates r

Am= Overlapping area between plates,

2

dm= Distance between the plates,

44

20

Capacitance Transducer Measurement of changes in capacitance enables the estimation of d, A, and er through suitable calibration Capacitance may be measured using a capacitance bridge Capacitance bridge expresses the capacitance changes in terms of capacitance impedance Z in ohms. 1 Z = p 2 fc where f = frequency, Hz c = capacitance, farads 45

Sensors - Classification By their measurement objective Position: Linear/Rotational sensors Proximity sensors Acceleration sensors Force, torque and pressure sensors Flow sensors Temperature sensors Light sensors Light sensors

Smart material sensors Micro and nano-sensors

21

Proximity Sensors

Proximity Sensors

22

Proximity Switches Mechanical limit switches Often called “microswitches” Often called microswitches Activation causes electrical contacts to either “break” (“normally closed” or NC switch) or “make” (“normally open” or NO switch) or both NC and NO

Switch Contact Configurations

23

Standard Basic Switches

Capacitive Proximity Sensor Metallic and non-metallic objects can be sensed Produces electrostatic field Max. sensing distance: up to tens of cm

24

Capacitive Proximity Sensor cont’d… Construction & Operation Typically, a hollow cylindrical conductor forms one plate of the sensor The second plate of the sensor is a disk at the opening of the cylinder. When an object nears the sensing surface it enters the electrostatic field of the electrodes and changes the capacitance in an oscillator circuit. As a result, the oscillator begins oscillating. The trigger circuit reads the oscillator ’s amplitude and when it reaches a specific level, the output state of the sensor changes. As the target moves away from the sensor the oscillator ’s amplitude decreases, switching the sensor output back to its original state.

Capacitive Proximity Sensor cont’d… Dielectric Constants

The larger the dielectric number of a material the easier it is to detect.

25

Capacitive Proximity Sensor cont’d… Relationship of the dielectric constant of a target and the sensor’s ability to detect the target

Rated sensing distance,

Capacitive Proximity Sensor cont’d… Detection through Barriers

Water has a much higher dielectric gp constant than that of plastic. This gives the sensor the ability to “see through” the plastic and detect the water.

26

Capacitive Proximity Sensor cont’d… Size Does Matter! • Dimensions Dimensions of the of the sensor sensor makes makes a big a big difference difference in span in span andand sensitivity • Large diameter sensors will have a larger span while small diameter sensor will have a shorter span

Capacitive Proximity Sensor cont’d… Commercial Capacitive Sensors

27

Inductive Proximity Sensor Metallic objects (best with ferrous metals) Oscillation amplitude changes Robust Max. distance 5 –15 mm

Inductance Two types of inductance: 1. Self inductance: the ratio of the flux produced by a circuit (a conductor dt il) i or it lfa dcoil) th tin th itself t d it and thecurrent that produces it. Usually denoted as Li . i

2. Mutual inductance: the ratio of the flux produced by circuit i in circuit j and the current in circuit i that produced it. Denoted as Mi . j

A mutual inductance exists between any two circuits as long as A mutual inductance exists between any two circuits long as field (flux) that couples the two. there is as a magnetic This coupling can be large (tightly coupled circuits) or small (loosely coupled circuits).

28

Inductive cont’d…

Proximity

Sensor

Inductive proximity sensor contains: At the very least a coil (inductor) Gt ti fi ld Generates a magnetic field

Operation As the sensor gets closer to the sensed surface the inductance of the coil increases if the sensed surface is ferromagnetic It is then sufficient to use a means of measuring this inductance to infer proximity and position

Practical Construction of Inductive Sensors

29

Eddy Current Sensor Many inductive proximity sensors are of eddy current type. If there is a metal object in close proximity to this alternating field, then eddy currents are induced in it then eddy currents are induced in it. The eddy currents themselves produce a magnetic field. This field distorts the original magnetic field. As a result, the impedance of the coil changes (Z=R+j Lto Z’=R’+j L’) and so the amplitude of the alternating current. At some preset level, this change can be used to trigger a switch. Used for detection of non-magnetic but conductive materials

Inductive Sensors

30

Eddy Current Sensors

Ultrasonic Proximity Sensor Works on reflection of ultrasound Cover long distances (several meters) compared to other prox. sensors Cover long distances (several meters) compared to other prox. sensors Sensitive to almost all surfaces Used mainly for distance measurements

31

Ultrasonic cont’d…

Proximity

Sensor

Operation

A high frequency voltage is applied to a disk, causing it to vibrate at the same frequency. The vibrating disk produces high-frequency sound waves. When transmitted pulses strike a sound-reflecting object, echoes are produced. The duration of the reflected pulse is evaluated at the transducer.

Ultrasonic cont’d…

Proximity

Sensor

Operation

The emitted pulse is actually a set of 30 pulses at an amplitude of 200 kv. The echo can be in microvolts.

32

Ultrasonic cont’d…

Proximity

Sensor

Operation

Depending upon the sensor, the blind zone is from 6 to 80 cm. An object placed in the blind zone will produce an unstable output

Ultrasonic cont’d…

Proximity

Sensor

33

Ultrasonic cont’d…

Proximity

Sensor

Microwave Proximity Sensor Based on radio waves (10 – 90GHz) Very long perception distance Very long perception distance Used mainly for distance measurement

34

Optical Proximity Sensor Based on reflecting light, usually (near) infrared Pf dd f i d tilf th bj t Performance dependsonsurface, size and material of theobject

Automatic Door Opener

35

Case Sorting – By Size

Production Counting

36

Sensors - Classification By their measurement objective Position: Linear/Rotational sensors Proximity sensors Acceleration sensors Force, torque and pressure sensors Flow sensors Temperature sensors Light sensors Light sensors

Smart material sensors Micro and nano-sensors

Acceleration Sensors

37

Acceleration Sensors

Seismic Accelerometers

(Inertial)

38

Piezoelectric Accelerometer What is piezoelectricity? Pi l t i ff t Piezoelectriceffect

Certain crystalline materials can generate charge when subjected to mechanical hildf ti deformation (t i) (strain) Converse is also true

Strain causes a redistribution of charges dipole (a dipole is kind of a battery!)

and results in a net electric 84

Piezoelectric Accelerometer cont’d Polarizing (poling) a piezoelectric material

(a) Random orientation of polar domains prior to polarization

(b) Polarization in DC electric field (c) Remnant polarization after electric field is removed

85

39

Piezoelectric Accelerometer cont’d Piezoelectric materials The piezoelectric effect occurs only in non conductive materials. Two main groups: crystals and ceramics. The most well-known piezoelectric material is

quartz (S i O2 ).

V

86

Piezoelectric Accelerometer cont’d Potential difference due to force applied is given by Egt= p where g = voltage sensitivity of the crystal (depends on the material of the crystal and the direction in which crystal surface is cut w.r.t crystal axis) t = thickness of the crystal p = lied app pressure

87

40

Piezoelectric Accelerometer cont’d

These sensors operate from frequency as low as 2 Hz and up to about 5 kHz Possess high linearity and a wide operating temperature range 88

Relative Acceleration Pick-up

89

41

Sensors - Classification By their measurement objective Position: Linear/Rotational sensors Proximity sensors Acceleration sensors Force, torque and pressure sensors Flow sensors Temperature sensors Light sensors Light sensors

Smart material sensors Micro and nano-sensors

Force, Torque Pressure Sensor s

and

91

42

Elastic Transducers Elastic Transducers Spring System is displacement Relationship F xand between force Relationship F xand is displacement between force

linear F = K x

where K is the spring constant

Gd 4 KD =N w 8 3 m

G G

= Shear Shear modulus modulus of of the the material material of of the the spring spring d = Diameter of the wire w

Dm = Mean diameter of the coil N = Number of coils in the spring. 92

Elastic Transducers Elastic Transducers

The force is applied to the end of the cylinder and the deformation is measured as the difference between the uncompressed and compressed length. All elastic devices share this common basis, but the method of measuring the distortion of the elastic element varies considerably. The material used - tool steel, stainless steel, aluminum or beryllium copper

93

43

Elastic Transducers Proving Ring Elastic Transducers Diameter of the ring changes when a force is applied along the diameter.

With an micrometer

Compression test on soil

With an LVDT sensor

94

Strain Gauge Load Cell Strain Gauge Load Cell Beam-Type R

1

R

R

R2

1

3

V

+

0

V

s Ai s

i Animation R R

+ e l b

2

R

t

4

e

R

4

V0 12 =RR VRRR

P

s

R

++

3

-

(1)

14 2 3

The bridge is said to be balanced and produces no output The bridge is said to be balanced and produces no output when

RR 12 = RR++ RR 14 2 3

or when

R 4 = RR++ RR

R

3

14 2 3

44

Strain Gauge Load Cell Strain Gauge Load Cell Beam-Type e Output voltage, isVproportional to strain ( )induced 0

V VG

0

V

=

e

s

To determine applied M fI = y y Pl e = bt 3E 12 2 t e = 6l bt2P E

force

Strain Gauge Load Cell Strain Gauge Load Cell Pillar-Type e =- =L

F

s

F

A·EE ·F

e =+ =T A ·E eL R

eT R

2

,R

3

4

,R

Poisson’s ratio

1

e

L L

R

+

R

1

2

V0 V

F

R

4

R

3

s

-

45

Strain Gauge Load Cell Strain Gauge Load Cell Ring-Type R

R2

1

+

V

0

V

s

R

R

4

Bridge Configurations Bridge Configurations -

-

3

Bending BendingLoads Loads

Quarter Bridge e

R

1

R2 V

0

V

S

R

R R

4

R

3

Assume that R1 is an active strain gage that has undergone a change in resistance, it ,when h ththe tt itest t hispecimen h it i bddhtowhich b it is bonded has been 1 subjected to stress. Equation (1) can then be rewritten as: V RR R + 0 1 =12 VR RRRR+ + + s

1 1423

46

Bridge Configurations Bridge Configurations -

Bending BendingLoads Loads

Quarter Bridge cont’d Assuming that all gauges have the same initial resistance, then equation (2) reduces to: V0 11 11 RR + 1 =-= RR () + VRR 2242 s 1 1 11 + RR RR But gauge factor, G = 11 e V0 e =+ G V 42 e s G Non-linearity Effect of Error axial loads 0.1% for every 1000 µ strans

e

R1

R2 V

0

V

S

R

R

4

Thermal effects

3

Magnitude output

of

Yes Yes Least

Quarter bridge is not recommended!

Bridge Configurations Bridge Configurations -

Bending BendingLoads Loads

Half Poisson Bridge

e V

0

V

S

-e

) Ge (1+ V0 =+Vs 42 1 e () G Non-linearity Error Effect of axial loads Reduced to apprx. (1- )% for every 1000 µstrans

Thermal effects

Magnitude output

of

Yes Ni l Increased by a factor of apprx. (1+ )

47

Bridge Configurations Bridge Configurations -

Bending BendingLoads Loads

Half Bridge

e V0 V

S S

e V0 G e = Vs 2 Non-linearity Error

Effect of axial loads

Thermal effects

Magnitude output

of

Nil Nil Nil About double that of single gauge

Bridge Configurations Bridge Configurations -

Bending BendingLoads Loads

Full Bridge

e -e

+ V

0

V

s s

-e e

-

V0 G = e Vs Non-linearity Error

Effect of axial loads

Thermal effects

Magnitude output

of

Nil Nil Nil Maximum

48

Bridge Configurations Bridge Configurations -

Axial AxialLoads Loads

2 Gauges in Opposite Arms e V 0 V 0

V

S

e V0 G e =+ +

2e VG e 2VG

s

Non-linearity Error

Effect of bending loads

0.1% for every 1000 µ strans

Nil Yes Less

Thermal output

Bridge Configurations Bridge Configurations -

effects Magnitude of

Axial AxialLoads Loads

Full Poisson Bridge

e-e

+ V

0

V V

s

-ee

-

) Ge (1+ V0 =+Vs 21 e () G Non-linearity Error Effect of bending loads Reduced to apprx. (1- )% for every 1000 µstrans

Thermal effects

Magnitude output

of

Nil Nil Increased by a factor of apprx. (1+ )

49

Hydraulic & Pneumatic Hydraulic Load Cells& Pneumatic Load Cells Used for sensing large static or slowly varying forces Used for sensing large, static, or slowly varying forces Typical accuracies: 0.1% of F.S.R. These load cells are comprised generally of a rig id outer structure , some medium that is used for measuring the applied force, and the measuring gage .

106

Hydraulic Load Cell

Applied force tends to compress the liquid (oil) within the cylinder The generated pressure is directly proportional to the applied force F=PA Suitable for use in explosive atmospheres

50

Hydraulic Load Cell

108

Pneumatic Load Cell

Force-balance principle Force is applied on one side of a piston or a diaphragm and is Force is applied on one side of a piston or a diaphragm andpneumatic is balanced by pressure on the other side. This counteracting pressure is proportional to the force

51

Pneumatic Load Cell Applications To measure relatively small weights in industries where cleanliness and safety are of prime concern.

Merits Inherently explosion proof Insensitive to temperature variations No contamination

Demerits/Limitations • Relatively slow speed of response • Clean, dry and regulated air or nitrogen is needed

Piezoelectric Methods Charge amplifier

is required to integrate the electric charges

No need of power supply Under a force of 10 kN, piezoelectric transducer deflects only 0.00l mm. Very much suitable for dynamic measurements. Extremely fast events (like shock waves in solids, or impact printer and punch press forces) can be measured They can operate over a wide temperature range and survive temperatures 0 C. They can operate over a wide temperature range and temperatures ofsurvive up to 350

Industrialized piezoelectric load washers

111

52

Piezoelectric Methods cont’d Multi-component crystal force sensor Measures the forces in three orthogonal axes Each ring is cut along a specific axis and the orientation of the sensitive Each ring is cut along a specific axis and the orientation of the sensitive axis coincides with the axis of the force component to be measured. Each disc produces a charge proportional to the force component specific to that disc.

112

Inductive Method A change in mechanical stress on a ferromagnetic material causes its permeability to alter. The changes in magnetic flux are converted into induced voltages in the The changes in magnetic flux are converted into induced voltages in the effect or ma gnetostriction. pickup coils. Villari Force to be measured is applied on the core, stressing it and causing a change in its permeability and inductance. Strong in nickel–iron alloys. Poor linearity and hysteresis problems

113

53

Capacitive Transducer Plates/Electrodes

Capacitance of a capacitor is given by

e

C d= ee0

A r

r

farads

d C

where -1 2 e = Permittivity of vacuum = 8.854x10 F/m 0

e = Dielectric constant of the medium between the plates r

Am= Overlapping area between plates,

2

dm= Distance between the plates,

114

Capacitance Transducer

Fi d F t l t d Fixed or Foot electrode

P

Diaphragm (Movable electrode)

115

54

What is torque? Torque is a measure of how much a force acting on an object causes that object to rotate Torque = Force x Distance Torque = Force x Distance

Example 1: Distance = 1 m, Force = 100 N, Torque = 100 Nm. Example 2: Distance = 2 m, Force = 100 N, Torque = 200 Nm.

116

Fundamentals Concepts angular displacement ,

, over some time interval,

angular velocity , = /

t

angular acceleration , a = /

t

t.

Tangential force Ft = Fcosß

The off-axis force F at P produces a torque T =( Fcosß) l tending to rotate the body in the CW 117

55

Fundamentals Concepts The resultant , of any number of torques acting at different locations along a body is found from their algebraic sum of each such torque is subjected to an equal, but The source Theeach such torque is subjected to an equal, but source of oppositely directed,

reaction torque.

A nonzero resultant torque will cause the body to undergo a proportional angular acceleration (Newton’s second law) Tr = Ia polar moment of inertia), (kg m polar moment of inertia), (kg m )

where I = Moment of inertia of the body around the axis (i.e., its 2 ) When a =0,

Tr is also zero; the body is said to be in equilibrium .

For a body to be in equilibrium, there must be either more than one applied torque, or none at all 118

Fundamentals Concepts In a typical shaft, the shear stress t varies linearly from zero at the axis to a maximum value at the surface. The shear stress, t , at the surface of a shaft of m diameter, d , transmitting a torque, T , is found from

t p = 16T d3

m

Real materials are not perfectly rigid but have instead a modulus of rigidity , G , which expresses the finite ratio between t and shear strain , . The ma im m strain in a solid ro nd shaft therefore also eistsat its srface The maximum strain in a solid round shaft also exists andtherefore can be found from at its surface

p = m3

t

m

G

=

16T dG 119

56

Fundamentals Concepts

Transmitting torque T over length L twists the shaft through angle f . Manifestation of shear strain as an angular displacement between axially separated cross sections separated cross sections

f p=

32LT 4 dG

120

Torque Measurement

Schematic arrangement of devices for torque and power measurement

121

57

Torque Transducer Technologies Surface Strain

Convert surface strain ( the transmitted torque.

m

) into an electrical signal proportional to

Strain gauges are aligned along a the axis)

principal strain

direction (45° to 122

Torque Transducer Technologies Surface Strain

ee ==-=e 24 1 3 e 16T ==2e dG ma x 1 3 3 p dG But we know that V Fe F 0max =·= g age ga ge 1 V s

=

2

T = Torque Fg age

==G +

Gage factor E 2(1 )

Shear modulus

58

Torque Transducer Technologies Shear Stress Principal stresses and the shear stress are identical

124

Torque Transducer Technologies Twist Angle

Difference in tooth-space phasing between two identical “toothed” wheels attached at opposite ends of a compliant “torsion bar” is wheels attached at opposite ends of a compliant torsion bar is the torque used to determine The phase displacement of the periodic electrical signals from the two “pickups” is proportional to the peripheral displacement of salient features on the two wheels, and hence to the twist angle of the torsion bar and thus to the torque.

59

Dynamometers (Dynos ) 127

Classification of Dynamometers (Dynos) 1. Absorption dynamometers Energy or Power - Frictional resistance – Heat a. Prony brake (Mechanical) dynamometer b. Water brake (Hydraulic) dynamometer 2. Transmission dynamometers Neither add to nor subtract from the transmitted energy or power Placed at appropriate location

128

60

Absorption Dynamometer Prony Brake Dynamometer T=Fr P = T= 2p

While the drag torque tends to rotate the clamped-on apparatus, it is held stationary by the equal but opposite reaction torque Used to test large electric motors and engines

NT/60

Fr. 129

Water Brake Dynamometer

Principle of viscous coupling Engine shaft is coupled to a rotor that spins inside a concentric housing.

61

Water Brake Dynamometer Fill the housing with water until the engine is held at a steady rpm against the load. Th t i hi d d b Thewater iswhipped aroun d by

the spinning rotor Housing pushes the water back on to the rotor. Housing tends to rotate in response to the torque produced But is restrained by the load cell Torque = Force measured at the load cell

x Distance

131

Water Brake Dynamometer Merits Low acquisition cost Limited maintenance High durability.

132

62

Eddy-Current Dynamometer The varying flux intensity in the magnetic face, or inductor ring, magnetic face, or inductor ring,

develops eddy currents which flow near the inner surface of the ring. These eddy currents set up a magnetic field which react with the fields centered in the rotor teeth.

Reaction between the two sets of magnetic fields causes an attraction in tangential direction between the two members of the dynamometer thereby developing a braking torque which is in proportion to the strength of the eddy current reactive fields developed by the rotor teeth. 133

Eddy-Current Dynamometer

134

63

Transmission Dynamometers Passive devices neither appreciabl y add to nor subtract from the energy involved in the test system 2P 2P

Annular gear

P F

P Lever

S S

w Spur gear Pinion

W a L

Epicyclic Train Dyno 2P a = WL Torque, T PR

=

R = Pitch circle radius of the spur gear in m 135

Pressure Measurement

136

64

What is Pressure? Pressure is defined as force per unit area that a fluid exerts on its surroundings. The SI unit for pressure is the pascal (N/m

2

)

Why Measure Pressure? Pressure is invariably an important

process parameter

.

Pressure difference is used many a time as a means of measuring the flow rate of a fluid. Measurement of pressure helps in

force measurement

137

Units of Pressure 1 atm. pressure = 1.013 25 bar = 760 mm of Hg 1 bar = 10

5

1 Pa = 1 N/m

Pa = 100 kPa 2

138

65

Terminology

Atmospheric reference

Absolute reference

139

Static & Dynamic Pressure

66

Static Pressure Static pressure is the pressure at a point in an equilibrium fluid The absolute pressure at a depth H in a liquid P =P+( gH) P

= P + ( gH) Where: P = absolute pressure at depth H. ab s P = the external pressure at the top of the liquid. For most open systems this will be atmospheric pressure. = the density of the fluid. g = the acceleration due to gravity (g = 9.81 m/s 2 )). H = the depth pp at which the pressure is desired. abs

Dynamic Pressure Dynamic pressure is the component of fluid pressure that represents fluid kinetic energy

The dynamic pressure of a fluid with density and speed

1 = P d ynam i c 2 u

2

u is given by

PPP = +

Total static dynamic

67

P Mi Pressure Measuring Systems & Transducers u

143

Pressure Measuring Devices 1. Gravitational type a. Piston or loose diaphragm and weights (E.g. Dead weight pressure gauge tester) b. Liquid column (E.g. U-tube manometer) 2. Elastic element type a. Diaphragm b. Bellows c. Bourdon tube 3. Others a. Variable capacitance transducer b. Strain gauge transducer

144

68

Dead Weight Pressure Gauge Tester Used to calibrate other pressure gauges

Gauge under Test

Secondary Piston Piston

Weight of piston and platform + weights Oil pressure = Effective area of piston 145

Dead Weight Pressure Gauge Tester

146

69

Manometer Can be used to measure the pressure of both Limited to low pressure measurement

liquids and gases

.

(Near atmospheric pressure)

mass density of the manometric fluid should be more than that The The density of the manometric fluid should be more mass thanfluid that whose pressure is being of the measured should not be able to mix readily - that is, they must be

andthetwofluids immiscible .

Tubes must be vertical + ve pressure Vacuum

147

Sensitivity of a Manometer P

PP h P - P gh

1

P

2

12

=

O/P 1 h Sensitivity = I/P == P Pg 12

Sensitivity may be improved Se s t ty ay be po ed 1. by using manometric fluids having smaller and smaller mass density, 2. by reducing

g value 148

70

U-Tube Manometer Pressure in a continuous static fluid is the same at any horizontal level. Therefore, Fluid density

Pressure at B = Pressure at C P

=

C B P B C

For the

A

left leg

Pressure at B = Pressure at A + Pressure due to height h

1

of fluid being measured P

B

=P

A

Manometric fluid density

+ gh

m

1

righttheleg For For theleg right Pressure at C = Pressure at D + Pressure due to height h P

C

=P

A t mo s phe ri c

+

ma n o

As we are measuring gauge pressure, P

A

=

m a no

gh

2

- gh

gh

2

of manometric fluid

2

PA t m os phe ri c can be dropped

149

1

Well or Cistern Type Manometer

h =

Area of left side Area of left side

Volume moved

1

h2 = h

p 2 hd(/4) 2 p D 2 /4

d = hD ()

1

2

2

d ()

PP-= ghhD + 1222

=+ gh D 1( )

d

2

2

2

Only one reading (h ) is enough to 2 measure the pressure difference. Relatively large pressure differences may be measured

Clearly if D is very much larger than d d then ( ) is 2very small so D PP-= gh 122

150

71

Inclined Tube Manometer The sensitivity to pressure change is increased by tilting the manometer arm

h

2

h

1

-=gh PP 12 2 =

gl sin

151

Pros and Cons of Manometers Pros They are very is required No calibration the pressure can be calculated from the Norequired is calibration - the pressure can be calculated from the

simple .

first principles.

Cons Slow response – only useful for very slowly varying pressures - no use at all for fluctuating pressures For ver y accurate measurement the relationship between For ver y accurate measurement, the relationship between temperature and

must be known

152

72

Diaphragm-Type Transducer

Pressure signal is

converted

to a displacement

The diaphragm (thin metal disc) acts as a displacement under the action of the pressure.

spring element

that undergoes a

One side of the disc is exposed to the pressure to be measured, other side is exposed to atmospheric or areference pressure. f Distortion of the diaphragm is transmitted to a gauge dial Deflection curve is linear only for a small range of low pressures and low vacuum applications

Bellows-Type Transducer Pressure signal is converted to a displacement The bellows acts as a spring element displacement under the action of the pressure.

that u nderg oes a

Extremely sensitive to low pressures (0.034 to 5.17 bar gauge) The flexibility of a metallic bellows is similar in character to that of a helical coiled compression spring

73

Bourdon Tube Pressure applied causes the flat sections to deform into elliptical shape. This change in cross-section causes the tube to straighten g gy slightly. Since the tube is permanently fastened at one end, the tip of the tube traces a curve that is the result of the change in angular position with respect to the center. The tube is bent lengthwise into an arc of a circle of 270 to 300 o . Within limits, the movement of the tip of the tube can then be used to position a pointer to indicate the value of the applied internal pressure. 155

Variable Capacitance Transducer Consists of two flexible conductive plates and a dielectric fluid. As pressure increases, the flexible conductive pla tes will move farther apart, changing the capacitance of the transducer. This change in capacitance is measurable and is proportional to the change in pressure.

156

74

Strain Gauge Pressure Transducer An increase in pressure at the inlet of the bellows causes the bellows to expand. The expansion of the bellows moves a flexible beam to which a strain gauge has been attached. Th f h b h i f h i The movement of the beam causes theresistance ofchange thestrain gauge to Change in resistance is proportional to the applied pressure

Strain gauge used in a bridge circuit

Measuremen t o f High Pressure and Pressure

Low

158

75

Measurement of High Pressure Ranges from 1 000 to 20 000 bar Conventional devices are limited to 10 000 bar only

159

Principle

Bridgman Gauge Cell body

Resistance of an electrical conductor undergoes a change when subjected to a bulk compression (volume compression)

Kerosene filled Bellows Terminal

Pressure connection Sensing element

Sensing element is a loosely wound coil Sensing element when subjected to a bulk compression, undergoes a change in resistance Change in resistance is measured by a Wheatstone bridge Change in resistance is measured by a Wheatstone bridge Applied pressure is estimated from the measured resistance change through suitable calibration Sensing element materials: Manganin (Cu 84%, Mn 12 %, Ni 4%) Goldchrome (Cr 2.1 %, rest gold)

160

76

Measurement of Low Pressure Any pressure < atmospheric pressure = Low pressure or vacuum Atm. pressure

Atm. Pressure

Atm. pressure

Vacuum source

Units commonly used: torr Zero ref.

1torr=1mmHg

Hg

Bourdon pressure gauge up to 10 torr Manometers or bellows typeyp gauges gg p up to1torr Diaphragm gauges up to 10

-3

torr

For pressures less than above,

special type of gauges

aretobeused 161

McLeod Vacuum Gauge Modified mercury manometer

PV PV= cc B

V

PP= c

(1)

B

V

c

PPhor -= c

PPh=+

(2)

c

P PPP

c

V

c

Substituting for in Peq.1 V

PhPV +=

B c

T ub e CaS re a a B ul b a cnd ap il l aryl um e VB vo Fl u id si t y Den

V

hP=-= P

VV -

1

B

VV

Bc

cc

hV c then, P VV = VV Bc

If c-s area of capillary is a, then

Vah= c

ah 2

= P Vah B

Vah>>

By design,

B

ah a == = PKhK V 2

B

2

V

B

162

77

McLeod Vacuum Gauge Covers the vacuum ranging between 1 and 10

-6

torr.

0µ 0.1 µ 0.2 µ 1µ 100 µ 200 µ

Commercial McLeod gauge calibrated in terms of microns 163

McLeod Vacuum Gauge

164

78

Sensors - Classification By their measurement objective Position: Linear/Rotational sensors Proximity sensors Acceleration sensors Force, torque and pressure sensors Flow sensors Temperature sensors Light sensors Light sensors

Smart material sensors Micro and nano-sensors

Flow Sensors

166

79

Terminology 1. Point velocity measurement—the fluid’s velocity at a fixed point across the pipe’s cross section (m/s) 2 Mean flow velocity measurement—average fluid velocity across the 2. Mean flow velocity measurement average fluid the (m/s) crossvelocity section across of the pipe 3. Volumetric flow rate measurement—the rate of change in the volume of fluid passing through the pipe with time (m 3 /s) 4. Total volume measurement—the total volume of fluid which has passed through the pipe (m 3 ) 5. Mass flow rate measurement—the rate of change in the mass of the fluid passing through the pipe with time (kg/s) 6. Total mass measurement—the total mass of fluid passing through the pipe (kg) 167

Flow Characteristics Velocity is maximum at the center and zero at the wall As the flow rate is increased, particle motion becomes random Critical velocity - Velocity at which disturbance occurs Reynolds number,

R= e

vD

µ

D = Pipe diameter, m = Mass density of the fluid, kg/m 3 v = Mean fluid velocity, m/s µ = Absolute viscosity of the fluid, kgs/m2

Laminar flow Turbulent flow

Velocity distribution 168

80

Classification of Flow Measuring Devices I. Primary or quantity methods Positive displacement flow meters II. Secondary rate and inferential methods a) Obstruction meters i Flow nozzle i. Flow nozzle

ii. Venturi iii. Orifice iv. Variable area flow meter (Rotameter) b) Velocity probes i. Total pressure probes ii. Static pressure probes

iii Direction sensing probes (Yaw meters) iii. Direction sensing probes (Yaw meters)

c) Others i. Turbine meter ii. Electromagnetic meter iii. Hot-wire anemometer iv. Sonic flow meters v. Mass flow meter

Positive Displacement The oval-gear positive displacement flowmeter Meter Fluid is “

displaced

169

Flow

” from the inlet side of

the flowmeter to the outlet side using a series of compartments of known volume. The number of compartments of fluid that have been transferred are counted to determine the total volume that has passed through the flowmeter, and if time is also measured then volumetric flowrate can be measured. For liquids - piston, sliding vane, oval-gear, bi-rotor, tri-rotor, and disc types of flowmeter and for gases roots, bellows (or diaphragm), or CVM flowmeters are popular.l High accuracy measurement (typically ±0.5% of F.S.R for liquids and ±1% of reading for gases) Complex mechanical devices, with moving parts which of course wear with time. Fluids should be free of solid particles so as to reduce wear of the seals and reduce the need for excessive maintenance.

170

81

Measurement of Flow Rate - Obstruction Meters Bernoulli’s Equation Assumptions Assumptions Inviscid fluid Incompressible fluid No heat addition Along a streamline

11 22 22 11

P vghP ++=++ vgh 1112 22 22 p = pressure along the streamline , N/m 3 = density of the fluid, kg/m v = fluid velocity along the streamline, m/s 2 g = acceleration due to gravity, m/s h = height of the fluid, m

2

Measurement of Flow Rate - Obstruction Meters They measure flow based on the relation between pressure and velocity

Type s Venturi

Flow-nozzle Flow nozzle

Orifice 172

82

Measurement of Flow Rate Venturi and Flow Nozzle

173

Measurement of Flow Rate Orifice Since the actual flow profile at location 2 downstream of the orifice is quite complex, thereby making the effective value of A2 uncertain, the following substitution introducing a flow coefficient K is made,

where A is the area of the orifice. As a result, the volumetric flowrate o real flows is given by the equation,

Q for

174

83

Obstruction Meters for Compressible Fluids

1

2

175

The Variable Area Flow Meter (Rotameter) The rotameter is a tapered tube and a float. Principle: Flow of the media will alter the position of a float in the tapered tube. The position of the float in the tapered tube is proportional to the volumetric fl ow rate The float reaches a stable position p in the tube when the upward force equals the downward gra vitational force exerted by weight of the float. With liquids, the float is raised by a combination of the buoyancy of the liquid and the velocity head of the fluid. With gases, buoyancy is negligible, and the float responds to the velocity head alone.

176

84

Rotameter A change in flo wrate upsets this balance of forces. The float then moves up orpdown, , gg changing the annular area until it again reaches a position where the forces are in equilibrium A variable area flow meter norma ll y requires vertical installation and a straight pipe run (minimum length of five times the diameter of the pipe) five times the diameter of the pipe)

before the flow meter’s inlet

It is the most widely used variable area flow meter because of its low cost, simplicity, low pressure drop, relatively wide range, and linear output

177

Rotameter - Pros & Cons Advantages Low cost Simple to install Easy to use and virtually maintenance free Easy to use and virtually maintenance free

Disadvantages Lower accuracy compared to many other flow meter technologies Affected by pulsation Sensitive to fluid changes such as viscosity , density temperature

and

Typical Applications Liquid or gas flow meter where high accuracy is not required Measuring water and gas flow in plants or labs Monitoring chemical lines Monitor makeup water for food & beverage plants 178

85

Typical Rotameters

179

Typical Rotameters

180

86

Pitot Tube

Manometer reads Pd = ( Ps + Pd ) – Ps P

s

(P + P ) s

d

Pitot tube arranged to measure fluid velocity

181

Pitot Static Tube To tal p re ssu re h ol e N os e pi ec e Stati c p res su re h ol es

Du ct sta tic p re ssu re (Ps ) Vel oc ity p re ssu re (Pd )

Acc ess h o le i n d u ct

To tal p re ssu ret ) (P

() – P P+P= P )( PP d d

Man om eter r ead s + P P s

s

I n cl in ed man o mete r

182

87

Pitot Static Tube Pros Simple construction. Relatively inexpensive. Almost no calibration required. Induces minimal pressure drops in the flow.

Cons A d ti l l ti t b hi h h f Accuracy and spatial resolution may not be high enough for some applications. Tube must be aligned with the flow velocity to obtain good results. Any misalignment in yaw should not exceed ±5°

183

Turbine Flow Meter

A multi-bladed rotor is placed in the flow and rotates as fluid passes through it. Rotor’s speed is proportional to the velocity of the fluid flowing through the meter. The rotor’s speed of rotation is detected using a proximity sensor Average velocity of fluid in the pipeline is measured Since the pipe diameter is known, volumetric flowrate can be determined

184

88

Turbine Flow Meter Pros Medium initial set up cost Medium initial set up cost Reliable, time tested proven technology

Cons For clean fluid only Low to medium pressure drop Low to medium pressure drop

185

Electromagnetic Flow Meter (Magmeter) Faraday's Law When a conductor moves perpendicular to a magnetic fiel d, the voltage induced across theconductor th dt i ti l it lit is proportional itsvelocity. The conductor is the fluid being metered, while the induced voltage is measured using electrodes in the pipe wall. Faraday's Formula E a vML

E = Voltage generated in the conductor v = Velocity of the conductor M = Magnetic field strength L = Length of the conductor

89

Electromagnetic Flow (Magmeter) cont’d

Meter

A measurement accuracy of typically ±0.5% of reading over a range of at least f t lt10 10:1 1 The flowmeter’s accuracy is also unaffected by changes in fluid viscosity and density , and may be used to meter difficult mixtures such as slurries and paper pp pp pulp. Not suitable for use with liquids such as oil.

gases , steam ,or

non-conducting

The flowmeter’s calibration is also sensitive to changes in flow velocity profile although requiring a shorter straight length of pipe upstream of the meter than the orifice plate or turbine meter.

Hot-Wire Anemometer Basically involves the power that is dissipated by a hot wire (few µmdiameterandacoupleofmmlong tungsten wire) to an ambient fluid that is moving past it. away takes Passage fluid from of the heat wire at a Passage fluid away takes from of the heat wire at a

rate proportional

to its velocit y .

The larger the velocity of the fluid, larger the heat dissipation from the wire for a fixed wire temperature. Alternately, larger the velocity of the fluid, smaller the wire temperature for a fixed heat dissipation rate from the wire. Velocityy information is converted to thermal either temperature change or change in the heat dissipation rate information. By measuring the change in wire temperature under constant curre nt or the current required to maintain a constant wire temperature, the heat lost can be obtained. The heat lost can then be converted into a fluid velocity in accordance with convective theory

.

90

Hot-Wire Anemometer

tf transfer

h h

Consider a wire that is immersed in a flui d flow. Assume that the wire, heated by an electrical current input, is in thermal equilibrium with its environment. The electrical power input is equal to the power lost to convective heat,

I = Input current Rw = Resistance of the wire Tw and Tf = Temperatures of the wire and fluid respectively Aw = Projected wire surface area and = Heat Httf ffi transfer i t f thcoefficient i of thewire The wire resistance to,

R

w

is also a

function temperature

a = Thermal coefficient of resistance R = Resistance at the reference temperature Re f

of

according

T

Re f

Hot-Wire Anemometer The heat transfer coefficient King's law,

h is a function of fluid velocity

vf according to

Where a, b and c are coefficients obtained from calibration. Combining the above three equations allows us to el iminate the heat transfer coefficient h,

Continuing, we can solve for the fluid velocity,

91

Hot-Wire Anemometer

Hot-Wire Anemometer Pros : - Excellent Excellentspatial spatialresolution resolution. - High frequency response > 10 kHz (up to 400 kHz)

Cons: - Fragile, can be used only in due to dustrecalibration frequent accumulation (unless the flow frequent due to dustrecalibration accumulation (unless the flow

clean gas flow s

.

- Needs Needs is very clean). - High cost.

92

Ultrasonic Flowmeter Requires particulates or bubbles in the flow. Ideal for wastewater applications conductive dti t bd or water based. Generally does not work

or any dirty liquid which is

with distilled water

or drinking water.

Ideal for applications where low pressure drop compatibility, and low maintenance are required.

, chemical

194

Ultrasonic Flowmeter

PRINCIPLE OF OPERATION Employs the frequency (Doppler effect) of an ultrasonic signal shift Ultrasonic sound (typically 1 MHz) is transmitted into a pipe with flo wing liquids, and the discontinuities (suspended particles or gas

.

bbbl ) fl h li ih li h l diff f bubbles) reflect theultrasonicwavewith aslightly different frequency. The difference in between the transmitted a nd received signalsfrequency (the Doppler frequency shift) is directly proportional to the velocity of the flow. Liquid sho uld contain at least 100 parts per million (PPM) of 100 micron or larger suspended particles or bubbles

195

93

Ultrasonic Flowmeter

196

Ultrasonic Flowmeter Pros - No obstruction in the flow path,p,nop pressure p drop - No moving parts, low maintenance cost - Can be used to measure corrosive or slurry fluid flow

Cons - Higher initial set up cost

197

94

Sensors - Classification By their measurement objective Position: Linear/Rotational sensors Proximity sensors Acceleration sensors Force, torque and pressure sensors Flow sensors Temperature sensors Light sensors Light sensors

Smart material sensors Micro and nano-sensors

Temperature Measurement

95

Contents 1. Introduction 2. Classification of devices 3. Bimetallic Thermometers 4. Liquid-in-Glass Thermometer 5. Thermocouple Thermometer 6 Resistance Thermometers 6. Resistance Thermometers 7. Thermistors 8. Total Radiation Pyrometer 9. Optical Pyrometer

200

Introduction What is Temperature? The sensation of warmth or coldness felt by touching it The sensation of warmth or coldness felt by touching it. Temperature is a measure of the average kinetic energy of the particles in a sample of matter, expressed in units of degrees on a standard scale. Fundamental property like length, mass and time but fundamentally ydifferent in nature from them Measured with help of some physical property of a substance that changes with temperature in a reliable, reproducible and quantifiable way.

201

96

Classification of Devices Based on the effect they use 1. Mechanical effects a. Expansion of metals - Bimetallic thermometers b. Expansion of fluids - Liquid-in-glass thermometers - Pressure thermometers

2. Electrical effects a. Thermo-electric effects - Thermocouple thermometer b. Electrical resistance changes - Electrical resistance thermometer - Thermistors

3. Radiation effects a. Total radiation pyrometers b. Optical pyrometers

202

Bimetallic Thermometers Two dissimilar metals A temperature change causes A temperature change causes

differential expansion y

()L TT-

2

12

t

Temperature change is estimated from measured deflections Invar (Nickel steel) - Low thermal expansion

L t

Brass or stainless steel - High thermal expansion y

Strips are bonded by brazing or welding Combined thickness of strips: 0.01 mm to 0.3 mm Temperature range:

-75

o

c to 550

o

c

203

97

BMT Configurations

204

Liquid-in-Glass Thermometer Principle

: Fluid expands on heating Safety bulb

Used in science, medicine, metrology and industry for almost 300 years. The fluid is contained in a sealed glass bulb, and its expansion is measured using a scale etched in the stem of the thermometer. The most widely used fluid is

mercury

Stem ( -38 °C to 356 °C

Introduction of a gas into the instrument can increase the range to 600 °C or beyond.

) Capillary

Other working fluids include ethyl alcohol, toluene and technical pentane, which can be used down to -200 °C. Delicate. One has to read them without dropping them!

Temp. sensitive bulb

Liquid-in-glass thermometers have largely been replaced by more robust electrical devices which can be digitized and automated.

205

98

Thermocouple Thermometer Seebeck Effect (1821)

T

1

T >T 1

2

T

2

Thermocouple original discovery

When a conductor is placed in a temperature gradient, electrons diffuse along the gradient Result is generation of emf

206

Thermocouple Bi-metallic junction

207

99

Thermocouple A

T T

1

2

BB

V

The difference in the emfs generated by the two conductors is then given by:

() AB12 ()B 1 2 A

ES=TT E = Net emf generated S

AB

Seebeck coefficient

T1 , T2 Junction temperatures in K

209

Materials

The simplicity, ruggedness, low cost, small size and wide temperature range of thermocouples make them the most common type of temperature sensor in industrial use.

210

100

Thermocouple temperature Vs Voltage curves

211

Special Materials Material Temperature

(o C)

Sensitivity (µV/o C)

Rhodium-Iridium / Rhodium 2200 6 Boron / Graphite 2500 40 Tungsten / Rhenium 2760 6

212

101

Laws of Thermocouple Law -I A

T3

T

T1

=

T2 T

5

A

T7

4

T

T8

T2

1

T6

T

B

T 9

10

B

Thermal emf of a thermocouple with its junctions at T1 and T2 is unaffected by the temperature of the wires away from the junctions as long as each of the wires is homogeneous.

213

Laws of Thermocouple contd… Law -II C T4 A T1

T B

2

=

T

A T1

T

T

3

B

5

AT 3

T

2

=

A T

1

BB

T

6

T7

T2

6

T8 C

With the insertion of a third homogeneous metal C either into A or B, as long as the two new junctions formed are at the same temperature, the net emf of the circuit is unaffected irrespective of the temperature of C away from the junctions. 214

102

Laws of Thermocouple contd… Law - III

A T

T2

1

=

T

4

T

A

1

C

B

T

T 3

T2

=T

T

B

T

T

2

5

C

1

B

1

A

T6

2

If a metal C is inserted between A and B at one of the junctions If a metal C is inserted between A and B at one the junctions, theoftemperature of C at any point away from 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.

215

Laws of Thermocouple contd… Law –IV: Law of Intermediate Metals

A T1 B

E

T AB

B

2

+

B T1 C

E

T BC

C

=T 2

A 1

C

E

AB

+E

BC

C

T2

If the thermal emf of metals A and B is E and that of metals B and that of metals B AB If the thermal emf of metals A and B is E and C is E , then the thermal emf of metals A and C is E +E BC

AB

BC

216

103

Laws of Thermocouple contd… Law –IV: Law of Intermediate Metals A B C D E have desirable properties to construct thermocouples A, B, C, D, E have desirable properties to construct thermocouples Possible Combinations: AB, AC, AD, AE, BC, BD, BE, CD, CE, DE Take A as a standard and calibrate for AB, AC, AD and AE AB AC Ref. temp. is constant (T

2

T1 Voltage

)

T

1

0.

0.

5.

5.

..

..

..

..

Voltage

217

Laws of Thermocouple contd… Law –IV: Law of Intermediate Metals

A T1 B

EA B

T B

From this E

2

+

A T

1

C

BC

EAC

T C

2

=T

B 1

C

E AB +E A C

C

T

2

can be calculated.

218

104

Laws of Thermocouple contd… Law –V: Law of Intermediate Temperatures

A T

1

B

E

T2

12

+

A T

2

B

B

If a thermocouple produces emf of E when its junctions are at T If a thermocouple produces emf of E and T 2 , and E 2 3 when at T when the junctions are at T

E2 3

T B

=T

A 1

3

B

E

12

+E

T B

23

when its junctions are at T 12 and T , then it will produce E 1 2 +E 2 3 and T 1 3

3

1 23

219

Laws of Thermocouple contd… Law –V: Law of Intermediate Temperatures A T T

B

E

T,30

E from the thermocouple tables from the thermocouple tables

T,30

+E

E

3 0, 0

30 12

B

=E

+

AA 30 B

E

=

0 23

B

B

E

12

+E

Couple AB Ref. Junction temp: 0

T

T, 0

is measured, E

30,0

is obtained

1

B

23

0

0

c

Voltage

0. 5. .. 30 E TE

30, 0 T, 0

220

105

Laws in a Nutshell

221

Special Configuration

H ot- ga s f low

222

106

Pitfalls wires should not be twisted together to form a junction Can be soldered to use up to temperatures not exceeding 200°C Can be soldered to use up to temperatures not exceeding 200°C. Welding the junction is preferred, but it must be done without changing the wires’ characteristics.

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Resistance Thermometers Electrical resistance changes in a reproducible manner with temperature ) Popularly RTDs called Resistance Temperature Detectors ( Popularly called Resistance Temperature Detectors ( )RTDs Resistance Vs temperature characteristics are stable , reproducible , and have a near linear positive temperature coefficient from -200 to 800 °C. Typical materials used: Nickel (Ni), Copper (Cu), and Platinum (Pt). The most common: 100-ohm or 1000-ohm

Platinum RTDs

,(PRTs,

Platinum Resistance Thermometers) Platinum Resistance Thermometers) A positive temperature coefficient RR -

a = ×1 0 0 0 100

R

0

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107

RTDs Contd… = Resistance, R A

L

= Resistivity (ohms) L = Wire length A = Wire area

Temperature Vs Resistance A = 3.9083 E-3 B = -5.775 E-7 C = -4.183 E -12 (below 0 °C), or C = 0 (above 0 °C)

For a PT100 sensor, a 1 °C temperature change will cause a 0.384 ohm change in resistance.

How do RTDs Work? RTDs use electrical resistance and require a small power source to operate to operate.

Wheatstone bridge

108

2-Wire Configuration

3-Wire Configuration

109

4-Wire Configuration

A Typical PT100 RTD

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11 0

Advantages and Limitations Advantages High accuracy High accuracy Wide operating range Suitability for precision applications

Drawbacks/Limitations RTDs in industrial applications are rarely used above 660 °C. At very low temperatures, the sensitivity of the RTD is zero and thus not useful. Less sensitive to small temperature changes and have a slower response time. More expensive than thermocouples and thermistors Require a current source

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Thermistors Work on the same principle as RTDs Oxides of cobalt, copper, iron, manganese, magnesium, nickel etc. Materials have high resistivity A plot of the temperature Vs resistance characteristic curves is provided Temperature Vs resistance is non-linear

1/T = A + B (loge R) + C (loge 3 R)

T = temperature, K A, B, and C = fitting constants R = resistance, ohms

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111

Types of Thermistors 1. PTC

(Positive Temperature Coefficient) device

Rit i ith iitt Resistance increases with increasing temperature. 2. NTC

(Negative Temperature Coefficient) device Resistance decreases with increasing temperature.

NTC thermistors are more commonly used than PTC thermistors NTC thermistors are more commonly used than PTC thermistors

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Typical resistance–temperature characteristics

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11 2

Thermistors cont… Characteristics/Advantages Low cost High sensitivity Rapid response due to small size of thermistor Stable devices Smaller and more fragile than thermocouples and RTDs, cannot tolerate much mishandling.

Drawbacks Highly nonlinear output - makes interfacing more difficult Relatively limited operating range (-100

oC

to 350°C)

High-quality constant current or voltage source is required

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Pyrometry Pyros means “ fire ” and metron means “ High temperature measurement (above 600

to measure ” o

c)

Pyrometer or Radiation thermometer Non-contact measurement Only surface temperature is measured Can be measured up to 4000

oc

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Theory Idea: Every object whose temperature is above absolute zero (-273 emits radiation. The total rate of radiation emission per second:

o c)

E = KT4

Radiant energy is in the form of electromagnetic waves, considered to be a stream of photons traveling at the speed of light. Cause: Internal mechanical movement of molecules. The spectrum of the radiation: 0.7 to 1000 µm wavelength. Lies within the red area of visible light ("infra"-red after the Latin)

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Electromagnetic Spectrum

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11 4

Power Spectral Density

Power spectral density of radiated energy emission at various temperatures.

240

Absorption, Reflection and Transmission

a+ +t=1

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11 5

Infrared Measuring System

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Types of Pyrometers 1 Total radiation pyrometer 1. Tot al radiation pyrometer 2. Optical pyrometer

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Total Radiation Pyrometer Total radiation is proportional to fourth power of absolute temperature

qCTT =-se

A

()

44

AB

q = radiant-heat transfer, Btu/hr-ft

2

s = Stefan-Boltzmann constant e = emissivity C A

= Configurationalfactor to allow for relative position and geometry of bodies

TT and Absolute = temperaturesof bodies A and B

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AB

Optical Pyrometer Designed for thermal radiation in the visible spectrum.

Principle p Match the brightness of the hot object to the brightness of a calibrated la mp filament

E ye pie c e L am p

Ab so r p t io n

O bje c ti ve

f ilt e r

Le ns

Schematic diagram of an optical pyrometer

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11 7

Optical Pyrometer

Image of Hot Target Image of Filament (Cooler)

Pointer indicating the center of the filament. 246

Optical Pyrometer

Image of Hot Target

Image of filament (Hotter)

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11 8

Optical Pyrometer

The filament’s image blends into the image of the target. The filament “disappears”. 248

Advantages 1. Fast measurement 2. Facilitates measurement of moving targetsg (conveyor g (yp) processes). 3. Measurements can be taken of hazardous or physically inaccessible objects (high-voltage parts, great measurement distance). 4. Measurements of high temperatures (greater than 1300°C) present no problems. In similar cases, contact thermometers cannot be used, or have a limited life. 5. No interference, no energy is lost from the target. 6. No risk of contamination and no mechanical effect on the surface of the object; thus wear-free. Lacquered surfaces, for example, are not scratched and soft surfaces can also be measured.

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Precautions 1. The target must be optically (infrared-optically) visible to the IR thermometer. High levels of dust or smoke make measurement less accurate. Concrete obstacles, such as a closed metallic reaction vessel,allow l ll f l for til tonly th iidtopical f th ti measurement. the insideof thecontainer cannot be measured. 2. The optics of the sensor must be protected from dust and condensing liquids. (Manufacturers supply the necessary equipment for this.) 3. Normally, only surface temperatures can be measured, with the differing emissivities of different material surfaces taken into account.

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