20-AEEM-329

ENGINEERING MEASUREMENTS

Engineering Areas

Research and Development

Design (Product and Process)

Manufacturing

Service and Maintenance

Engineering Methods

Theoretical

Simulation (Computational and Experimental)

Experimental

Part 1

Basic Principles

Feedback-Control System

Process

Disturbances

Input variable(energy and/or material)

ControlElement

Controller

Desired value ofcontrolled variable

MeasuringSystem

Controlled variable

Measuring System

Variableelement

converison

Variable

elementmanipulation

Sensingelement

Primary

Datatransmission

element

Datastorageelement

Datapresentation

element

Observer

Measured medium

Measured quantity

Presented data

sensor

signalconditioner

Computer-Based Measurement

Analog-to-digitalconverter

Observer

Measured medium

Measured quantity

Presented data

Transducer

Signalconditioner

Computer

Part 2

Measurement Characteristics

Instrument Types

active versus passive instruments

proportional versus null-type

analog versus digital

indicating versus signal output

smart versus conventional

Instrument Characteristics

Static Characteristics • accuracy/inaccuracy (uncertainty) absolute, relative, re full-scale tolerance

• precision/repeatability/reproducibility

low-precisionlow-accuracy low-accuracy

high-precision high-precisionhigh-accuracy

• range/span • linearity/nonlinearity • sensitivity

outputreading

measuredquantity

outputreading

measuredquantity

Instrument Characteristics

Static Characteristics (continued) • threshold (absolute/relative) • resolution (absolute/relative) • sensitivity to disturbance (temperature, pressure, etc.) zero drift/sensitivity drift

outputreading

measuredquantity

zero drift

nominalcharacteristic

outputreading

measuredquantity

sensitivity drift

nominalcharacteristic

• dead space/backlash/hysteresis

outputreading

measuredquantity

dead space

outputreading

measuredquantity

dead space

Instrument Characteristics

Dynamic Characteristics qi measured quantity qo output reading • general linear, time-invariant dynamic instrument/general input

a q a ddt q a d

dtq a d

dtq b q b d

dt q b ddt

q b ddt

qo o o o i i i i0 1 222 3

33 0 1 2

22 3

33+ + + = + + +... ...

• general linear, time-invariant dynamic instrument/stepped input

a q a ddt q a d

dtq a d

dtq b qo o o o i0 1 2

22 3

33 0+ + + =...

• zero-order instrument

a q b qo i0 0= • first-order instrument

a q a ddt q b qo o i0 1 0+ =

• second-order instrument

a q a ddt q a d

dtq b qo o o i0 1 2

22 0+ + =

Instrument Characteristics

Dynamic Characteristics (continued) zero-order instrument response

measuredquantity

time

outputreading

timet

first-order instrument response

measuredquantity

time

outputreading

timet

63%~~

τ time constant

tsettling within≈ 5 0 5%)τ ( . t

Instrument Characteristics

Dynamic Characteristics (continued) second-order instrument response

measuredquantity

time

outputreading

timet

low damping

high damping

• delay time • dead time • transition time • settling time • transient frequency • slew rate

Part 3

Measurement Errors

Types of Errors

• intrinsic errors of the measurement process extrinsic errors during data transfer, storage, display, evaluation, etc. • systematic errors (< > ≠e 0) can be reduced by corrections and calibration random errors (< > =e 0) can be reduced by averaging Sources of systematic errors: disturbance in the measured system by the measurement tolerances of components wear, aging environmental influence, etc.

Sources of random errors: • truly random stochastic noise Brownian (thermal) motion of molecules Johnson (thermal) noise of resistors shot (electron) noise of current flow flicker (contact) noise Barkhausen (magnetic domain) noise partition noise generation-recombination noise, etc. • incoherent extraneous signals and disturbances rf (radio-frequency electromagnetic) interference mains (60-Hz power line) interference magnetic interference vibrations, shocks, sound temperature oscillations, etc.

Disturbance by the Measurement

Example: loading by a voltmeter

unloaded

VoltmeterElectrical Circuit

V1 Vo Rm

loaded VoltmeterElectrical Circuit

V1 V = Vo m' Rm

equivalent circuit VoltmeterElectrical Circuit

V = Vo m'VoRo Rm

V V RR Ro o

mo m

' =+

e V V

VR

R RR

R RRR

m oo

mo m

oo m

om

= − =+

− = −+

≈ −1

Reduction of Systematic Errors

• careful instrument design low tolerance low temperature coefficient low aging, etc. • opposing inputs, differential measurements

VoltmeterElectrical Circuit

VoRo

Vd

Vref

V = Vo m' Rm

V V Vm ref d= +

V V V RR Rd o ref

mo m

= −+

( )

e V VV

RR

V VV

m oo

om

o refo

= − ≈ −−

• Feed-back measurements

VoltmeterElectrical Circuit

VoRo

Vd

Vref

V = Vo m' Rm

feedback

High-Gain Negative Feedback

VoltmeterElectrical Circuit

VoRo

VrefVd

V = Vo m' G K

Amplifier FeedbackDevice

VM+_

Rm

V V Vm ref d= +

V V V RR Rd o ref

mo m

= −+

( )

V V GKref d=

V R

R GK Vdom

o( )1 + + =

V V GKm d= +( )1

V V GK

RR GK

Vm o om

o= +

+ +≈1

1

e V V

VRR GK

m oo

om

= − ≈ − ≈1 0

Random Deviations

xi is the result of the ith measurement (i = 1, 2, ... n) average value

< > = = ∑=

x x n xmean ii

n11

median value (x, is in increasing number)

x xmedian n= +( )/,

1 2 if n is odd

x x xmedian n n= + +12 2 2 1( )/

,/

, if n is even

deviation from the mean value

d x xi i= − < > variance

V n dii

n=

− ∑=

11

21

standard deviation

σ = V

Frequency Distributions

histogram of n = 50 measurements

<x> = 405.16, σ = 1.91

Measured Value

Num

ber o

f Mea

sure

men

ts

0123456789

10

400 401 402 403 404 405 406 407 408 409 410

frequency distribution and probability density

Measured Value

Freq

uenc

y D

istri

butio

n

0

0.05

0.1

0.15

0.2

0.25

400 402 404 406 408 410

Probability Distributions

The probability that a measurement is between x and x dx+ is dP p x dx= ( ) ,

where p x( ) is called the probability density distribution.

0( ) 1p x dx

∞=∫

0( )meanx x x p x dx

∞< > = = ∫

The probability that a measurement is smaller than x is

0( ) ( )

xP x p x dx= ∫

P x( ) is the cumulative probability

lim ( )

xP x

→∞= 1

P xmedian( ) .= 0 5

Normal (Gaussian) distribution

p x ex x

( )( )

=− − < >

12

2

22σ π

σ

68.0 % of data points is within ±σ of the mean 95.4 % of data points is within ±2σ of the mean 99.7 % of data points is within ±3σ of the mean

Error Estimates

Estimated range from n measurement (68% confidence level):

x x e= < > ± Standard error from the mean:

e

n= σ

Combined effects of m unrelated errors

e e e em2

12

22 2= + + +...

Error in a sum

S a e b e a b ea b= ± + ± = + ±( ) ( ) ( )( )1 1 1

ea e b e

a ba b=++

2 2 2 2

Error in a difference

S a e b e a b ea b= ± − ± = − ±( ) ( ) ( )( )1 1 1

ea e b e

a ba b=+−

2 2 2 2

Error in a product/quotient

S a e b e a b ea b= ± × ± = × ±( ) ( ) ( )( )1 1 1

e e ea b= +2 2

Regression

Regression is the process of finding a simple mathematical relationship

y f x= ( )

between two variables x and y based on a series of measured quantities

xi and yi (i = 1, 2, ... n)

Fitting with a given functional form

e.g., y f x a xjj

j

m= = ∑

=( )

0 or f x a b x cj j j

j

m( ) sin( )= +∑

=0

difference:

d y f xi i i= − ( )

least-squares (or least-mean-squares difference)

S d y f xi

ni i

i

n= ∑ = −∑

= =2

12

1[ ( )] (or S n d n y f x

i

ni i

i

n= ∑ = −∑

= =

1 121

21[ ( )] )

least-squares regression (or fitting)

min{ ( , , ... )} , , ...S a a a a a am m1 2 1 2⇒

initial guess best-fitting curve

Position [m]

Dis

plac

emen

t [m

m]

-40-30-20-10

010203040

0 5 10

theoryexperiment

Position [m]

Dis

plac

emen

t [m

m]

-40-30-20-10

010203040

0 5 10

theoryexperiment

Part 4

Signal Processing

Signal-to-Noise Ratio

Over a given bandwidth B:

10log 20logS S

N N

P VSNRP V

⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

PS signal power

PN noise power

VS signal voltage

VN noise voltage

Time [a. u.]

Am

plitu

de [a

. u.]

Time [a. u.]

Am

plitu

de [a

. u.]

Frequency [a. u.]

Spec

trum

[a. u

.]

Frequency [a. u.]

Spec

trum

[a. u

.]

Analog Signal Filtering

low-pass filter

Normalized Frequency

Gai

n [d

B]

-40

-30

-20

-10

0

0.1 1 10 100

1st-order (-20dB/D)2nd-order (-40dB/D)4th-order (-80dB/D)

high-pass filter

Normalized Frequency

Gai

n [d

B]

-40

-30

-20

-10

0

0.1 1 10 100

1st-order (-20dB/D)2nd-order (-40dB/D)4th-order (-80dB/D)

band-pass filter

Normalized Frequency

Gai

n [d

B]

-40

-30

-20

-10

0

0.1 1 10 100

1st-order (-20dB/D)2nd-order (-40dB/D)4th-order (-80dB/D)

Coupling

DC coupling

R

Electrical Circuit

VoRo

VoltmeterIdeal

KR

R Ro=

+≈ 1

HF or AC coupling

R

Electrical Circuit

VoRo

VoltmeterIdeal

C

KR

R R i CR

R i Ci

io=

+ +≈

+=

+1 1 1/ //

/ω ωωωΩΩ

Ω = =2 1π f RCc / , K ≈

+

ω

ω

/

( / )

Ω

Ω1 2 (1st-order high-pass filter)

LF coupling

R

Electrical Circuit

VoRo

VoltmeterIdeal

C

Ki C

R i C i≈

+=

+1

11

1/

/ /ωω ω Ω

, K ≈+

1

1 2( / )ω Ω (1st-order low-pass filter)

Signal Amplification

Amplifier

VoutRout

RinVin Vout,

gain (open circuit): G VVoutin

= or G VVoutin

[ ] logdB = 20

input impedance Rin output impedance Rout

Differential Amplifier

Vin(+)

Vin(-) Vout

+

-

differential gain: G VV V

out

in in=

−+ +( ) ( )

Operational Amplifier

Vin(+)

(-)Vin

Vout

+

-

G R Rin out→ ∞ ≈ ≈ ∞ > ≈ <( ), ( ), ( )10 10 0 106 8Ω Ω

Feed-Back Amplifiers

Inverting Amplifier:

Vout

+

-VinR1

R2

V ( )+ = 0

V V RR R V R

R Rin out( )− =

++

+2

1 21

1 2

V G V Vout o= −+ −( )( ) ( )

V G V RR R V R

R Rout o in out= −+

−+

( )0 21 2

11 2

V VG R

R R

G RR R

out ino

o= − +

+ +

21 2

11 2

1

G VV

RR

outin

= ≈ − 21

R VI

VV V

R Rininin

in

in= =

−≈−( ) 1 1

Rout ≈ 0

Feed-Back Amplifiers

Non-Inverting Amplifier:

Vout

+

-

Vin

R1

R2

V Vin( )+ =

V V RR Rout

( )− =+1

1 2

V G V Vout o= −+ −( )( ) ( )

V G V V RR Rout o in out= −+

( )11 2

V V G

G RR R

out ino

o=

+ +1 11 2

G VV

R RR

outin

= ≈ +1 21

Rin ≈ ∞

Rout ≈ 0

Feed-Back Amplifiers

Differential Amplifier:

VinB

Vout

+

-VinAR1

R2

R1

R2

G VV

RRA

outinA

= ≈ − 21

G VV

RR R

R RR

RRB

outinB

= ≈+

+ =21 2

1 21

21

G VV V

RR

outinB inA

=−

≈ 21

R VI RinAinAinA

= ≈ 1

R VI R RinBinBinB

= ≈ +1 2

low Common Mode Rejection (CMR) due to imperfect symmetry

Instrumentation Amplifier

Vout+

-

VinA

R1

R2

R1

R2

+

-

+

-

VinB

Vsignal

Vnoise

V V VinB inA signal− =

V V G V G CMRout signal noise= + /

Common Mode Rejection (CMR) > 104 - 108

Signal Addition

Simple summation:

Vout

+

-

R

VinAR

VinBR

VinCR

VinDR

VinER

V V V V V Vout inA inB inC inD inE= − + + + +( )

Weighted summation:

Vout

+

-

R

VinA

VinB

VinC

VinD

VinE

RA

RB

RC

RD

RE

V RR V R

R V RR V R

R V RR Vout

AinA

BinB

CinC

DinD

EinE= − + + + +( )

Signal Sampling

over-sampling minimum-sampling f fsampling ≈ 6 f fsampling ≥ 2

Time [a. u.]

Am

plitu

de [a

. u.]

Time [a. u.]

Am

plitu

de [a

. u.]

under-sampling serious under-sampling f fsampling < 2 f fsampling <<

Time [a. u.]

Am

plitu

de [a

. u.]

Time [a. u.]

Am

plitu

de [a

. u.]

Nyquist condition:

f fsampling > 2 max

Aliasing: sampling distortion due to high-frequency components being transmuted into low-frequency ones by insufficient sampling

Sample and Hold

S2

Vout

+

-

Vin

C

1S

Inpu

t Sig

nal

S 1

S 2

Sam

ple

& H

old

Multiplexing

IA

IA

IA

IA

IA

S/H

S/H

S/H

S/H

S/H

LPF

LPF

LPF

LPF

LPF

CH0

CH1

CH2

CH6

CH7

MUX

sampleenable

channeladdress

to A/DPGA

gaincontrol

Analog-to-Digital Converters

Parallel (Flash) Converter

(four-bit version)

+-

+-

+-

+-

Vref Vin

R

R

R

R/2

R/2

comparators

encoder

binary output

AD

C O

utpu

t

Input Voltage

2-bit converter

AD

C O

utpu

t

Input Voltage

3-bit converter

Analog-to-Digital Converters

Ramp Converter

+-

Vref

Vin

DAC

binary output

comparator

counter

reset

clock

register

write

AD

C O

utpu

t

Step

7-bit converter

0 16 32 48 64 80 96 112 128

inputvoltage

DAC output

τ τ τmin max, ,≈ ≈ ≈ −0 2 2 1nclock average

nclockT T

Analog-to-Digital Converters

Successive Approximation Converter

+-

Vref

Vin

DAC

binary output

comparator

reset

clock

register

write

controllogic

AD

C O

utpu

t

Step

7-bit converter

0 1 2 3 4 5 6 7 8

inputvoltage

DAC output

τ ≈ nTclock

Analog-to-Digital Converters

Voltage-to-Frequency Converter

Vin

Vrefbinary output

counter

reset

register

write

voltage-to-

converterfrequency

clocklow-frequecy

digital pulse trainhigh-frequecy

Integrating (Voltage-to-Time) Converter

+

-

C

integrator

Vin

VrefR

R

-

+-

comparator

clock

proportional time

Analog-to-Digital Converters

Error Types

AD

C O

utpu

t

Input Voltage

idealgain error

AD

C O

utpu

t

Input Voltage

idealoffset error

AD

C O

utpu

t

Input Voltage

ideallinearity error

AD

C O

utpu

t

Input Voltage

idealmissing code

ADC type Resolution Speed parallel (flash) 4-8 bits up to 1 GHz

ramp 6-10 bits 1 kHz - 100 kHz successive appr. 8-16 bits 10 kHz - 1 MHz

voltage-to-frequency 8-12 bits 1 - 60 Hz integrating 12-24 bits 1 - 60 Hz

Digital-to-Analog Converter

8-bit converter

R

2R

R

2R

R

2R

R

2R

R

2R

R

2R

R

2R

2R

+

-

Vref

Vout

2R

2Rb0

b1

b2

b3

b4

b5

b6

b7

V0

V1

V2

V4

V3

V5

V6

V7

-

V V V V V V V V Vout = + + + + + + +7

6 5 4 3 2 1 02 4 8 16 32 64 128

V V bi ref i=

V Vout ref= + + + + + + +( )b b b b b b b b7 62

54

48

316

232

164

0128

Part 5

Measurements with Variable Conversion Elements

Variable Conversion Elements

physical quantityto be measured electrical impedance

variable

resistive V R I=

inductive

V L dIdt=

capacitive

V QC C I dt= = �

1

Electrical Impedance:

~ ~~Z VI

=

resistive

~ ~V R I= inductive

~Z i L= ω capacitive

~Z i C= 1ω

Wheatstone Bridge

null-type dc bridge

Vexc+_

+_Vm

R1

R2

R4

R3

unknownsensor

resistancecalibratedvariable

resistance

A

B

C

D

m BC DCV V V= −

32

1 2 3 4m exc

RRV VR R R R⎡ ⎤

= −⎢ ⎥+ +⎣ ⎦

1 4

2 30 ifm

R RVR R

= =

2

1 43

( ) RR p RR

=

p is the physical parameter to be measured

Quarter-Bridge

deflection-type dc bridge

Vexc+_

+_Vm

R2

R4

R3

R1unknown

sensorresistance

A

B

C

D

32

1 2 3 4( )

( )m excRRV V

R R R R⎡ ⎤

ε = −⎢ ⎥ε + +⎣ ⎦

2 3 4 0R R R R= = = and 1 0 (1 )R R F= + ε

ε is the physical parameter to be measured F is the so-called gage factor (sensitivity of the gage)

1 1( )

1 1 2m excV p VF

⎡ ⎤= −⎢ ⎥+ ε +⎣ ⎦

-0.5

0

0.5

-1 0 1ε F

V m/V

exc

exact

approximation

For small strains ( 0.01Fε < ) ( )

4exc

mVV Fε ≈ − ε

Half-Bridge

deflection-type dc bridge

Vexc+_

+_Vm

R1

R2

R4

R3

unknownsensor

resistance

A

B

C

D

unknownsensor

resistance

32 21 2

1 1 2 2 3 4

( )( , )( ) ( )m exc

RRV VR R R R⎡ ⎤ε

ε ε = −⎢ ⎥ε + ε +⎣ ⎦

3 4 0R R R= = and 1 0 1 1 2 0 2 2(1 ), (1 )R R F R R F= + ε = + ε

2 2

1 1 2 2

1 12 2m exc

FV VF F

⎡ ⎤+ ε= −⎢ ⎥+ ε + ε⎣ ⎦

1 1 2 2( )4exc

mVV F F≈ − ε − ε

Full-Bridge

deflection-type dc bridge

Vexc+_

+_Vm

R1

R2

R4

R3

unknownsensor

resistance

A

B

C

D

unknownsensor

resistanceunknown

sensorresistance

unknownsensor

resistance

3 32 21 2 3 4

1 1 2 2 4 4 3 3

( )( )( , , , )( ) ( ) ( ) ( )m exc

RRV VR R R R⎡ ⎤εε

ε ε ε ε = −⎢ ⎥ε + ε ε + ε⎣ ⎦

1 0 1 1 2 0 2 2 3 0 3 3 4 0 4 4(1 ), (1 ), (1 ), (1 )R R F R R F R R F R R F= + ε = + ε = + ε = + ε

3 32 2

1 1 2 2 4 4 3 3

112 2m exc

FFV VF F F F

⎡ ⎤+ ε+ ε= −⎢ ⎥+ ε + ε + ε + ε⎣ ⎦

1 1 2 2 3 3 4 4( )4exc

mVV F F F F≈ − ε − ε + ε − ε

1 2 3 4If F F F F F= = = =

1 2 3 4( )4

excm

V FV ≈ − ε − ε + ε − ε

Bridge Circuits

Maxwell bridge

Vexc

Vm

R1

Z2R3unknown

sensorimpedance

calibratedvariable

resistance

A

B

C

D~~

R4

C

calibratedvariable

resistance

V ZZ

ZZm = =0 1

243

if

Z R1 1= , Z R i Xu u2 = + , Z R3 3= , ZR i C

R i C

Ri C R4

4

4

44

1

1 1=+

=+

ω

ωω

Z Z Z

Z2 314

=

R i X R R

R i C Ru u+ = +314

41( )ω

R R R

Ru = 314

and X C R Ru = ω 1 3

Strain Gages

wire type foil type

Gage Factor 1 RFR∂

=∂ε

Ohm’s Law

( )( ) ( )( )

RAε

ε = ρ εε

Length contribution

0( ) (1 )ε = + ε

Area contribution

20 0( ) (1 ) (1 2 )A A Aε = − νε ≈ − νε

0.25 0.35ν ≈ − (Poisson’s ratio)

Strain Gages (cont.)

Resistivity contribution

0( ) (1 )ρ ε = ρ + βε

0.3 0.6β ≈ − (strain coefficient of resistivity)

Combined strain effect

00

0

(1 )( ) (1 )(1 2 )

RA

+ εε = ρ + βε

− νε

0 0( ) [1 (1 2 )] (1 )R R R Fε ≈ + ε + ν + β = + ε

Nominal resistance

00 0

0R

A= ρ

Gage factor 1 2 1.8 2.3F ≈ + ν + β ≈ −

Temperature coefficient

-11 [ C or ppm / C]RaR T∂

=∂

1 1 1 1gage

AaT T A T T∂ρ ∂ ∂ ∂ρ

≈ + − ≈ − αρ ∂ ∂ ∂ ρ ∂

Temperature balanced gage

0a ≈ or 1gageT

∂ρ≅ α

ρ ∂

Strain Gages (cont.)

Temperature [°C]

The

rmal

Str

ain

[µin

/in]

-500-400-300-200-100

0100200300400500

-100 0 100 200 300

2024-T4 Aluminum

Thermal expansion coefficient

10ppm / Cspecimenα ≈

Self-temperature-compensated strain gages

specimena F≈ − α

Part 6

Temperature Measurement

5[ C] = ( [ F] -32)9

T T ×

9[ F] = [ C] 325

T T × +

[K] = [ C] 273.15T T +

Thermal Expansion Methods

bulb

fluidcontaining

scale

capillarytube

liquid-in-glass thermometer bimetallic thermometer

bimetallicstrip

motion offree end

scale

needle

International Practical Temperature Scale: triple point of hydrogen -259.34 °C boiling point of oxygen* -182.96 °C boiling point of water* +100.00 °C freezing point of zinc * +419.58 °C freezing point of silver* +961.93 °C freezing point of gold* +1,064.43 °C

(*at atmospheric pressure)

Resistance Temperature Devices (RTDs)

1

2

3

4

5

6

7R0R

Tungsten

Copper

Nickel

Platinum

200 400 600 800 1000Temperature

°C

General temperature-dependence

2 30 1 2 3( ) (1 ... )R T R a T a T a T= + + + +

Linearized temperature-dependence

0 1( ) (1 )R T R a T≈ +

Temperature Measurement with Thermocouples

Seebeck Effect

-

Tm

T0

AB

T0+

VAB

0 00( ) ( )

m mT TAB A B AB AB m

T TV S S dT S dT S T T= − = ≈ −∫ ∫

,A BS S absolute thermoelectric powers

ABS relative thermoelectric power

T temperature

mT temperature of “hot” junction (temperature to be measured)

0T temperature of “cold” junction (reference temperature)

Temperature Characteristics of Thermocouples

0

10

20

30

40

50

60Chromel-Alumel

Chromel-Constantan

400 800 1200 1600Temperature [°C]

ThermoelectricVoltage [mV]

Platinum/13%Rhodium-Platinum

Platinum/10%Rhodium-Platinum

2 31 2 3( ) ...V T a T a T a T= + + +

Temperature Measurement with Thermistors

semiconductor type

0(1/ 1 / )0( ) T TR T R eβ −=

R resistance [Ω]

0R nominal resistance at 0T [Ω]

0T reference (absolute) temperature [K]

T absolute temperature [K]

β temperature coefficient [K]

0.1

1

10

-100 0 100 200 300

Temperature [°C]

Nor

mal

ized

Res

ista

nce,

R/R

0

Thermal Radiation

Planck’s law 2

5 /2

( 1)b hc KThcL

e λ=

λ −

Lb spectral radiance of black body 3[W / m srad]

h Planck constant -34= 6.626 10 [J s]×

c speed of light 82.998 10 [m/ s]= ×

λ wavelength 0.1 100 [ m]≈ ÷ μ

Κ Boltzmann constant 231.381 10 [J/K]−= ×

T absolute temperature [K]

0

5

10

15

0.1 1 10 100Wavelength [µm]

Spec

tral R

adia

nce

[W/m

3sr

ad]

1000 K

300 K

3000 K

100 K

visible10

10

10

100

5

10

15

0.1 1 10 100Wavelength [µm]

Spec

tral R

adia

nce

[W/m

3sr

ad]

1000 K

300 K

3000 K

100 K

visible10

10

10

10

Thermal Emissivity

Pincident

Ptransmitted

Preflected

Pabsorbed

Pradiated

Pradiated

incident reflected transmitted absorbedP P P P= + +

radiated absorbedP P=

emissivity absorption=

Radiation Thermometers

Heat Source

Testpiece

Film or CameraInfrared

Stefan-Boltzmann law of thermal radiation:

40

( )b bI L d kT∞

= π λ λ =∫

8 -2 -45.67 10 [Wm K ]k −= ×

40

( ) ( )bI L d kT∞

= π ε λ λ λ ≈ ε∫

Advantages:

fast, remote sensing large specimens without scanning

Disadvantages:

material sensitive (ε emissivity) low dynamic range/sensitivity

Part 7

Pressure Measurement

Absolute pressure

Difference between the pressure of the fluid

and the absolute zero pressure (vacuum)

Gauge pressure

Difference between the pressure of the fluid

and atmospheric pressure

Differential pressure

Difference between the pressures at two different points

Manometers

h

pA

pB

A B A Bp p p phg

− −= =

γ ρ

γ weight density of the fluid [ 3N/m ]

ρ mass density of the fluid [ 3kg/m ]

g gravitational acceleration ≈ 9.81 [ 2m/s ]

Elastic Element Pressure Sensors

diaphragms: bellows:

unknown pressure

translational movement

unknown pressure

translational movement

read-out:

mechanical

strain gage

piezoelectric

capacitive

inductive

fiber-optic

Part 8

Flow Measurement

Coriolis Flowmeters

mass flow rate of liquids

inlet

outlet

driversensor 1

sensor 2

no flow with flow

amplitude

time

τ = 0

amplitude

time

τ

Differential Pressure Flowmeters

venturi-type

P1 P2

orifice-type

P1 P2

Variable Area Flowmeters

(rotameters)

inlet

outlet

float

Turbine Flowmeters

inlet

outletmagnetic pick-up

turbine wheel

Contrapropagating Ultrasonic Flowmeters

Doppler shift

transducer #2

transducer #1

fluid flow

no flow low flow rate high flow rate

Part 9

Mass, Force, and Torque Measurements

Electronic Load Cells

1. elastic elements 2. displacement or strain sensor

cylindrical block proof ring

load

load

Accelerometers

casingpiezoelectric

plates

inertia mass

electric output

Piezoelectricity (Quartz or silicon dioxide, SiO2)

+

-+

-

-

+

- -

+

+

- + -

- -

+

+

++ + + + + + +

- - - - - - -+ + + + + + +

- - - - - - -

SiSiSi

O O O+

-

-

-

VV

+_ +_

+_

F F

F F

Torque Cells

12

3 4

end view

±45°torgue

side view

Vexc+_

+_Vm

R1

R2

R4

R3

A

B

C

D

2 4 1 3( ) ( )4

excm

V FV ε ≈ ε + ε − ε − ε

torque amplified: 2 4 1 3ε = ε = − ε = − ε

tension eliminated: 2 4 1 3ε = ε = ε = ε

bending eliminated: 2 4 1 3andε = − ε ε = − ε

Part 10

Translational Motion Measurements

Resistive Potentiometer

V0

R0

V mV0

R1

R20 2V m

20

α =

1 0 2 0(1 ) andR R R R= − α = α

2

0 01 2

mRV V V

R R= = α

+

Linear Variable Differential Transformer (LVDT)

~~VpVa

Vb

Vm = V -a Vb

displacement

ferriticcore

no friction

some nonlinearity (odd symmetry)

sin( ) and sin( )a p a b p bV V K t V V K t= ω − ϕ = ω − ϕ

( ) sin( )m p a bV V K K t= − ω − ϕ

Optical Decoders

linear decoder

displacementtransmitter

receiver

circular decoder

rotation

transmitter

receiver

Fiber-Optic Proximity Sensors

Fotonic Fiber

receiver fiber

transmitter fiberstainless steel casefiberglass bundle

transmitterfiber

receiverfiber

displacement reflector

Gap Thickness [mm]

Nor

mal

ized

Opt

ical

Sig

nal

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

Region 1

Region 2

Eddy Current Proximity Sensors

eddy currents

magnetic field

probe coil(ac excitation)

lift-offspecimen

conductive

Ultrasonic Ranging

solids

liquids

gases

Testpiece

ReflectedWave Wave

Incident

EchoExcitation

& ReceiverTransmitter

UltrasonicTransducer

transducer

immersion tankliquid