20-AEEM-329 ENGINEERING MEASUREMENTSpnagy/ClassNotes/AEEM329 Engineering... · 2008. 3. 5. · d dt...
Transcript of 20-AEEM-329 ENGINEERING MEASUREMENTSpnagy/ClassNotes/AEEM329 Engineering... · 2008. 3. 5. · d dt...
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