20-AEEM-329 ENGINEERING MEASUREMENTS Engineering Areas Research - - PDF document

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) Control Element Controller Desired value of controlled variable Measuring System Controlled variable

Measuring System

Variable element converison Variable element manipulation Sensing element Primary Data transmission element Data storage element Data presentation element Observer Measured medium Measured quantity Presented data sensor signal conditioner

Computer-Based Measurement

Analog-to-digital converter Observer Measured medium Measured quantity Presented data Transducer Signal conditioner 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-precision low-accuracy low-accuracy high-precision high-precision high-accuracy

• range/span
• linearity/nonlinearity
• sensitivity
• utput

reading measured quantity

• utput

reading measured quantity

Instrument Characteristics

Static Characteristics (continued)

• threshold (absolute/relative)
• resolution (absolute/relative)
• sensitivity to disturbance (temperature, pressure, etc.)

zero drift/sensitivity drift

• utput

reading measured quantity zero drift nominal characteristic

• utput

reading measured quantity sensitivity drift nominal characteristic

• dead space/backlash/hysteresis
• utput

reading measured quantity dead space

• utput

reading measured quantity dead space

Instrument Characteristics

Dynamic Characteristics

qi

measured quantity

qo

• utput reading
• general linear, time-invariant dynamic instrument/general input

a q a d dt q a d dt q a d dt q b q b d dt q b d dt q b d dt q

• i

i i i 1 2 2 2 3 3 3 1 2 2 2 3 3 3

+ + + = + + + ... ...

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

a q a d dt q a d dt q a d dt q b q

• i

1 2 2 2 3 3 3

+ + + = ...

• zero-order instrument

a q b q

• i

=

• first-order instrument

a q a d dt q b q

• i

1

+ =

• second-order instrument

a q a d dt q a d dt q b q

• i

1 2 2 2

+ + =

Instrument Characteristics

Dynamic Characteristics (continued)

zero-order instrument response

measured quantity time

• utput

reading time

t first-order instrument response

measured quantity time

• utput

reading time

t

63% ~ ~ τ time constant

tsettling within ≈ 5 0 5%) τ ( . t

Instrument Characteristics

Dynamic Characteristics (continued)

second-order instrument response

measured quantity time

• utput

reading time

t

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

Voltmeter Electrical Circuit V1 V

• Rm

loaded

Voltmeter Electrical Circuit V1 V = V

• m

' Rm

equivalent circuit

Voltmeter Electrical Circuit V = V

• m

' V

• Ro

Rm

V V R R R

• m
• m

' =

+ e V V V R R R R R R R R

m

• m
• m
• m
• m

= − = + − = − + ≈ − 1

Reduction of Systematic Errors

• careful instrument design

low tolerance low temperature coefficient low aging, etc.

• pposing inputs, differential measurements

Voltmeter Electrical Circuit V

• Ro

Vd V

ref

V = V

• m

' Rm

V V V

m ref d

= + V V V R R R

d

• ref

m

• m

= − + ( ) e V V V R R V V V

m

• m
• ref
• =

− ≈ − −

• Feed-back measurements

Voltmeter Electrical Circuit V

• Ro

Vd V

ref

V = V

• m

' Rm feedback

High-Gain Negative Feedback

Voltmeter Electrical Circuit V

• Ro

V

ref

V

d

V = V

• m

' G K Amplifier Feedback Device V

M

+

_

Rm

V V V

m ref d

= + V V V R R R

d

• ref

m

• m

= − + ( ) V V GK

ref d

= V R R GK V

d

• m
• (

) 1 + + = V V GK

m d

= + ( ) 1 V V GK R R GK V

m

• m
• =

+ + + ≈ 1 1 e V V V R R GK

m

• m

= − ≈ − ≈ 1

Random Deviations

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

=

x x n x

mean i i n

1

1

median value (x, is in increasing number) x x

median n

=

+ ( )/ , 1 2 if n is odd

x x x

median n n

= +

+

1 2

2 2 1

( )

/ , / ,

if n is even deviation from the mean value d x x

i i

= − < > variance V n di

i n

= − ∑

=

1 1

2 1

standard deviation σ = V

Frequency Distributions

histogram of n = 50 measurements <x> = 405.16, σ = 1.91

Measured Value Number of Measurements 1 2 3 4 5 6 7 8 9 10 400 401 402 403 404 405 406 407 408 409 410

frequency distribution and probability density

Measured Value Frequency Distribution 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. ( ) 1 p x dx

∞

= ∫ ( )

mean

x x x p x dx

∞

< > = = ∫ The probability that a measurement is smaller than x is ( ) ( )

x

P x p x dx = ∫ P x ( ) is the cumulative probability lim ( )

x

P x

→∞

= 1 P xmedian ( ) . = 0 5 Normal (Gaussian) distribution p x e

x x

( )

( )

=

− − < >

1 2

2 2

2

σ 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 em

2 1 2 2 2 2

= + + + ... Error in a sum S a e b e a b e

a b

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

a b

= + +

2 2 2 2

Error in a difference S a e b e a b e

a b

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

a b

= + −

2 2 2 2

Error in a product/quotient S a e b e a b e

a b

= ± × ± = × ± ( ) ( ) ( )( ) 1 1 1 e e e

a 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 x

j j j m

= = ∑

=

( )

• r f x

a b x c

j j j j m

( ) sin( ) = + ∑

=0

difference: d y f x

i i i

= − ( ) least-squares (or least-mean-squares difference) S d y f x

i n i i i n

= ∑ = − ∑

= = 2 1 2 1

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

i n i i i n

= ∑ = − ∑

= =

1 1

2 1 2 1

[ ( )] ) least-squares regression (or fitting) min{ ( , , ... )} , , ... S a a a a a a

m m 1 2 1 2

⇒ initial guess best-fitting curve

Position [m] Displacement [mm]

• 40
• 30
• 20
• 10

10 20 30 40 5 10

theory experiment

Position [m] Displacement [mm]

• 40
• 30
• 20
• 10

10 20 30 40 5 10

theory experiment

Part 4 Signal Processing

Signal-to-Noise Ratio

Over a given bandwidth B: 10log 20log

S S N N

P V SNR P V ⎛ ⎞ ⎛ ⎞ = = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ P

S signal power

P

N noise power

VS signal voltage VN noise voltage Time [a. u.] Amplitude [a. u.] Time [a. u.] Amplitude [a. u.] Frequency [a. u.] Spectrum [a. u.] Frequency [a. u.] Spectrum [a. u.]

Analog Signal Filtering

low-pass filter Normalized Frequency Gain [dB]

• 40
• 30
• 20
• 10

0.1 1 10 100

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

high-pass filter Normalized Frequency Gain [dB]

• 40
• 30
• 20
• 10

0.1 1 10 100

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

band-pass filter Normalized Frequency Gain [dB]

• 40
• 30
• 20
• 10

0.1 1 10 100

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

Coupling

DC coupling

R Electrical Circuit V

• Ro

Voltmeter Ideal

K R R Ro = + ≈ 1 HF or AC coupling

R Electrical Circuit V

• Ro

Voltmeter Ideal C

K R R R i C R R i C i i

• =

+ + ≈ + = + 1 1 1 / / / / ω ω ω ω Ω Ω Ω = = 2 1 π f RC

c

/ , K ≈ + ω ω / ( / ) Ω Ω 1

2 (1st-order high-pass filter)

LF coupling

R Electrical Circuit V

• Ro

Voltmeter Ideal C

K i C R i C i ≈ + = + 1 1 1 1 / / / ω ω ω Ω , K ≈ + 1 1

2

( / ) ω Ω (1st-order low-pass filter)

Signal Amplification

Amplifier V

• ut

Rout Rin V

in

V

• ut

,

gain (open circuit): G V V

• ut

in

=

• r G

V V

• ut

in

[ ] log dB = 20 input impedance Rin

• utput impedance

Rout

Differential Amplifier V

in (+)

V

in (-)

V

• ut

+

• differential gain:

G V V V

• ut

in in

= −

+ + ( ) ( ) Operational Amplifier V

in (+) (-)

V

in

V

• ut

+

• G

R R

in

• ut

→ ∞ ≈ ≈ ∞ > ≈ < ( ), ( ), ( ) 10 10 10

6 8 Ω

Ω

Feed-Back Amplifiers

Inverting Amplifier:

V

• ut

+

• V

in

R1 R2

V ( )

+ = 0

V V R R R V R R R

in

• ut

( ) − =

+ + +

2 1 2 1 1 2

V G V V

• ut
• =

−

+ −

( )

( ) ( )

V G V R R R V R R R

• ut
• in
• ut

= − + − + ( )

2 1 2 1 1 2

V V G R R R G R R R

• ut

in

• = −

+ + +

2 1 2 1 1 2

1 G V V R R

• ut

in

= ≈ −

2 1

R V I V V V R R

in in in in in

= = − ≈

− ( ) 1 1

Rout ≈ 0

Feed-Back Amplifiers

Non-Inverting Amplifier:

V

• ut

+

• V

in

R1 R2

V Vin

( ) + =

V V R R R

• ut

( ) − =

+

1 1 2

V G V V

• ut
• =

−

+ −

( )

( ) ( )

V G V V R R R

• ut
• in
• ut

= − + ( )

1 1 2

V V G G R R R

• ut

in

• =

+ + 1

1 1 2

G V V R R R

• ut

in

= ≈ +

1 2 1

Rin ≈ ∞ Rout ≈ 0

Feed-Back Amplifiers

Differential Amplifier:

V

inB

V

• ut

+

• V

inA

R1 R2 R1 R2

G V V R R

A

• ut

inA

= ≈ −

2 1

G V V R R R R R R R R

B

• ut

inB

= ≈ + + =

2 1 2 1 2 1 2 1

G V V V R R

• ut

inB inA

= − ≈

2 1

R V I R

inA inA inA

= ≈

1

R V I R R

inB inB inB

= ≈ +

1 2

low Common Mode Rejection (CMR) due to imperfect symmetry

Instrumentation Amplifier

V

• ut

+

• V

inA

R1 R2 R1 R2

+

• +
• V

inB

V

signal

V

noise

V V V

inB inA signal

− = V V G V G CMR

• ut

signal noise

= + / Common Mode Rejection (CMR) > 104 - 108

Signal Addition

Simple summation:

V

• ut

+

• R

V

inA

R V

inB

R V

inC

R V

inD

R V

inE

R

V V V V V V

• ut

inA inB inC inD inE

= − + + + + ( ) Weighted summation:

V

• ut

+

• R

V

inA

V

inB

V

inC

V

inD

V

inE

RA RB RC RD RE

V R R V R R V R R V R R V R R V

• ut

A inA B inB C inC D inD E inE

= − + + + + ( )

Signal Sampling

• ver-sampling

minimum-sampling f f

sampling ≈ 6

f f

sampling ≥ 2

Time [a. u.] Amplitude [a. u.] Time [a. u.] Amplitude [a. u.] under-sampling serious under-sampling f f

sampling < 2

f f

sampling <<

Time [a. u.] Amplitude [a. u.] Time [a. u.] Amplitude [a. u.] Nyquist condition: f f

sampling > 2 max

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

Sample and Hold

S2 V

• ut

+

• V

in

C

1

S

Input Signal S

1

S

2

Sample & Hold

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 sample enable channel address to A/D PGA gain control

Analog-to-Digital Converters

Parallel (Flash) Converter (four-bit version)

+

• +
• +
• +
• Vref

V

in

R R R R/2 R/2 comparators encoder binary

• utput

ADC Output Input Voltage 2-bit converter ADC Output Input Voltage 3-bit converter

Analog-to-Digital Converters

Ramp Converter

+

• Vref

V

in

DAC binary

• utput

comparator counter reset clock register write ADC Output Step 7-bit converter 16 32 48 64 80 96 112 128 input voltage DAC output

τ τ τ

min max

, , ≈ ≈ ≈

−

2 2

1 n clock average n clock

T T

Analog-to-Digital Converters

Successive Approximation Converter

+

• Vref

V

in

DAC binary

• utput

comparator reset clock register write control logic ADC Output Step 7-bit converter 1 2 3 4 5 6 7 8 input voltage DAC output

τ ≈ nT

clock

Analog-to-Digital Converters

Voltage-to-Frequency Converter

V

in

Vref binary

• utput

counter reset register write voltage-to- converter frequency clock low-frequecy digital pulse train high-frequecy

Integrating (Voltage-to-Time) Converter +

• C

integrator V

in

Vref R R

• +
• comparator

clock proportional time

Analog-to-Digital Converters

Error Types

ADC Output Input Voltage ideal gain error ADC Output Input Voltage ideal

• ffset error

ADC Output Input Voltage ideal linearity error ADC Output Input Voltage ideal missing 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

V

• ut

2R 2R b0 b1 b2 b3 b4 b5 b6 b7 V V

1

V

2

V

4

V

3

V

5

V

6

V

7

• V

V V V V V V V V

• ut =

+ + + + + + +

7 6 5 4 3 2 1

2 4 8 16 32 64 128 V V b

i ref i

= V V

• ut

ref

= + + + + + + + ( ) b b b b b b b b 7 6 2 5 4 4 8 3 16 2 32 1 64 128

Part 5 Measurements with Variable Conversion Elements

Variable Conversion Elements

physical quantity to be measured electrical impedance variable

resistive V R I = inductive V L dI dt = capacitive V Q C C I dt = = 1 Electrical Impedance: ~ ~ ~ Z V I = resistive ~ ~ V R I = inductive ~ Z i L = ω capacitive ~ Z i C = 1 ω

Wheatstone Bridge

null-type dc bridge V

exc

+ _ + _ Vm R1 R2 R4 R3

unknown sensor resistance calibrated variable resistance A B C D

m BC DC

V V V = − 3 2 1 2 3 4 m exc

R R V V R R R R ⎡ ⎤ = − ⎢ ⎥ + + ⎣ ⎦

1 4 2 3

0 if

m

R R V R R = =

2 1 4 3

( ) R R p R R =

p is the physical parameter to be measured

Quarter-Bridge

deflection-type dc bridge V

exc

+ _ + _ Vm R2 R4 R3 R1

unknown sensor resistance A B C D

3 2 1 2 3 4

( ) ( )

m exc

R R V V R R R R ⎡ ⎤ ε = − ⎢ ⎥ ε + + ⎣ ⎦

2 3 4

R 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 2

m exc

V p V F ⎡ ⎤ = − ⎢ ⎥ + ε + ⎣ ⎦

• 0.5

0.5

• 1

1 ε F Vm/Vexc

exact approximation

For small strains (

0.01 F ε <

)

( ) 4

exc m

V V F ε ≈ − ε

Half-Bridge

deflection-type dc bridge V

exc

+ _ + _ Vm R1 R2 R4 R3

unknown sensor resistance A B C D unknown sensor resistance

3 2 2 1 2 1 1 2 2 3 4

( ) ( , ) ( ) ( )

m exc

R R V V R R R R ⎡ ⎤ ε ε ε = − ⎢ ⎥ ε + ε + ⎣ ⎦

3 4

R R R = =

and 1

1 1 2 2 2

(1 ), (1 ) R R F R R F = + ε = + ε

2 2 1 1 2 2

1 1 2 2

m exc

F V V F F ⎡ ⎤ + ε = − ⎢ ⎥ + ε + ε ⎣ ⎦

1 1 2 2

( ) 4

exc m

V V F F ≈ − ε − ε

Full-Bridge

deflection-type dc bridge V

exc

+ _ + _ Vm R1 R2 R4 R3

unknown sensor resistance A B C D unknown sensor resistance unknown sensor resistance unknown sensor resistance

3 3 2 2 1 2 3 4 1 1 2 2 4 4 3 3

( ) ( ) ( , , , ) ( ) ( ) ( ) ( )

m exc

R R V V R R R R ⎡ ⎤ ε ε ε ε ε ε = − ⎢ ⎥ ε + ε ε + ε ⎣ ⎦

1 1 1 2 2 2 3 3 3 4 4 4

(1 ), (1 ), (1 ), (1 ) R R F R R F R R F R R F = + ε = + ε = + ε = + ε

3 3 2 2 1 1 2 2 4 4 3 3

1 1 2 2

m exc

F F V V F F F F ⎡ ⎤ + ε + ε = − ⎢ ⎥ + ε + ε + ε + ε ⎣ ⎦

1 1 2 2 3 3 4 4

( ) 4

exc m

V V F F F F ≈ − ε − ε + ε − ε

1 2 3 4

If F F F F F = = = =

1 2 3 4

( ) 4

exc m

V F V ≈ − ε − ε + ε − ε

Bridge Circuits

Maxwell bridge V

exc

Vm R1 Z2 R3

unknown sensor impedance calibrated variable resistance A B C D

~ ~ R4

C calibrated variable resistance

V Z Z Z Z

m =

=

1 2 4 3

if Z R

1 1

= , Z R i X

u u 2 =

+ , Z R

3 3

= , Z R i C R i C R i C R

4 4 4 4 4

1 1 1 = + = + ω ω ω Z Z Z Z

2 3 1 4

= R i X R R R i C R

u u

+ = +

3 1 4 4

1 ( ) ω R R R R

u = 3 1 4

and X C R R

u = ω 1 3

Strain Gages

wire type foil type Gage Factor 1 R F R ∂ = ∂ε Ohm’s Law ( ) ( ) ( ) ( ) R A ε ε = ρ ε ε

• Length contribution

( ) (1 ) ε = + ε

• Area contribution

2

( ) (1 ) (1 2 ) A A A ε = − νε ≈ − νε 0.25 0.35 ν ≈ − (Poisson’s ratio)

Strain Gages (cont.)

Resistivity contribution ( ) (1 ) ρ ε = ρ + βε 0.3 0.6 β ≈ − (strain coefficient of resistivity) Combined strain effect (1 ) ( ) (1 ) (1 2 ) R A + ε ε = ρ + βε − νε

• ( )

[1 (1 2 )] (1 ) R R R F ε ≈ + ε + ν + β = + ε Nominal resistance R A = ρ

• Gage factor

1 2 1.8 2.3 F ≈ + ν + β ≈ − Temperature coefficient

• 1

1 [ C

• r ppm/ C]

R a R T ∂ = ∂

• 1

1 1 1

gage

A a T T A T T ∂ρ ∂ ∂ ∂ρ ≈ + − ≈ − α ρ ∂ ∂ ∂ ρ ∂

• Temperature balanced gage

a ≈

• r 1

gage

T ∂ρ ≅ α ρ ∂

Strain Gages (cont.)

Temperature [°C] Thermal Strain [µin/in]

• 500
• 400
• 300
• 200
• 100

100 200 300 400 500

• 100

100 200 300

2024-T4 Aluminum

Thermal expansion coefficient 10ppm/ C

specimen

α ≈

• Self-temperature-compensated strain gages

specimen

a F ≈ − α

Part 6 Temperature Measurement

5 [ C] = ( [ F] -32) 9 T T ×

• 9

[ F] = [ C] 32 5 T T × +

• [K] =

[ C] 273.15 T T +

Thermal Expansion Methods

bulb fluid containing scale capillary tube

liquid-in-glass thermometer bimetallic thermometer

bimetallic strip motion of free 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 7 R0 R

Tungsten Copper Nickel Platinum

200 400 600 800 1000 Temperature °C General temperature-dependence

2 3 1 2 3

( ) (1 ... ) R T R a T a T a T = + + + + Linearized temperature-dependence

1

( ) (1 ) R T R a T ≈ +

Temperature Measurement with Thermocouples

Seebeck Effect

• Tm

T A B T

+

V

AB

( ) ( )

m m

T T AB A B AB AB m T T

V S S dT S dT S T T = − = ≈ − ∫ ∫ ,

A B

S S absolute thermoelectric powers

AB

S relative thermoelectric power T temperature

m

T temperature of “hot” junction (temperature to be measured) T temperature of “cold” junction (reference temperature)

Temperature Characteristics

• f Thermocouples

10 20 30 40 50 60

Chromel-Alumel Chromel-Constantan

400 800 1200 1600 Temperature [°C] Thermoelectric Voltage [mV]

Platinum/13%Rhodium- Platinum Platinum/10%Rhodium- Platinum 2 3 1 2 3

( ) ... V T a T a T a T = + + +

Temperature Measurement with Thermistors

semiconductor type

(1/ 1/ )

( )

T T

R T R eβ

−

= R resistance [Ω] R nominal resistance at 0 T [Ω] T reference (absolute) temperature [K] T absolute temperature [K] β temperature coefficient [K] 0.1 1 10

• 100

100 200 300 Temperature [°C] Normalized Resistance, R/R 0

Thermal Radiation

Planck’s law

2 5 /

2 ( 1)

b hc KT

hc L e

λ

= λ − Lb spectral radiance of black body

3

[W / m srad] h Planck constant

• 34

= 6.626 10 [Js] × c speed of light

8

2.998 10 [m/s] = × λ wavelength 0.1 100 [ m] ≈ ÷ μ Κ Boltzmann constant

23

1.381 10 [J/K]

−

= × T absolute temperature [K]

5 10 15

0.1 1 10 100

Wavelength [µm] Spectral Radiance [W/m3 srad]

1000 K 300 K 3000 K 100 K visible

10

10 10 100

5 10 15

0.1 1 10 100

Wavelength [µm] Spectral Radiance [W/m3 srad]

1000 K 300 K 3000 K 100 K visible

10

10 10 10

Thermal Emissivity

Pincident Ptransmitted Preflected Pabsorbed Pradiated Pradiated

incident reflected transmitted absorbed

P P P P = + +

radiated absorbed

P P = emissivity absorption =

Radiation Thermometers

Heat Source Testpiece Film or Camera Infrared Stefan-Boltzmann law of thermal radiation:

4

( )

b b

I L d kT

∞

= π λ λ = ∫

8

• 2
• 4

5.67 10 [Wm K ] k

−

= ×

4

( ) ( )

b

I 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 p

A

pB

A B A B

p p p p h g − − = = γ ρ γ weight density of the fluid [

3

N/m ] ρ mass density of the fluid [

3

kg/m ] g gravitational acceleration ≈ 9.81 [

2

m/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

• utlet

driver sensor 1 sensor 2 no flow with flow

amplitude time

τ = 0

amplitude time

τ

Differential Pressure Flowmeters

venturi-type

P1 P2

• rifice-type

P1 P2

Variable Area Flowmeters

(rotameters) inlet

• utlet

float

Turbine Flowmeters

inlet

• utlet

magnetic 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

casing piezoelectric plates inertia mass electric output Piezoelectricity (Quartz or silicon dioxide, SiO2)

+

• +
• +
• +

+

• + -
• +

+ +

+ + + + + + +

• - - - - - -

+ + + + + + +

• - - - - - -

Si Si Si O O O

+

• V

V + _ + _ + _ F F F F

Torque Cells

1 2 3 4 end view ±45° torgue side view

V

exc

+ _ + _ Vm R1 R2 R4 R3

A B C D

2 4 1 3

( ) ( ) 4

exc m

V F V ε ≈ ε + ε − ε − ε torque amplified: 2

4 1 3

ε = ε = − ε = − ε tension eliminated: 2

4 1 3

ε = ε = ε = ε bending eliminated: 2

4 1 3

and ε = − ε ε = − ε

Part 10 Translational Motion Measurements

Resistive Potentiometer

V R0 V

m

V R1 R2

2

V

m

2

α =

• 1

2

(1 ) and R R R R = − α = α

2 1 2 m

R V V V R R = = α +

Linear Variable Differential Transformer (LVDT)

~ ~

V

p

V

a

Vb V

m = V - a

Vb displacement ferritic core

no friction some nonlinearity (odd symmetry) sin( ) and sin( )

a p a b p b

V V K t V V K t = ω − ϕ = ω − ϕ ( ) sin( )

m p a b

V V K K t = − ω − ϕ

Optical Decoders

linear decoder

displacement transmitter receiver

circular decoder

rotation transmitter receiver

Fiber-Optic Proximity Sensors

Fotonic Fiber receiver fiber transmitter fiber stainless steel case fiberglass bundle transmitter fiber receiver fiber displacement reflector Gap Thickness [mm] Normalized Optical Signal 0.2 0.4 0.6 0.8 1 1 2 3 4 Region 1 Region 2

Eddy Current Proximity Sensors

eddy currents magnetic field probe coil (ac excitation) lift-off specimen conductive

Ultrasonic Ranging

solids liquids gases

Testpiece Reflected Wave Wave Incident Echo Excitation & Receiver Transmitter Ultrasonic Transducer

transducer immersion tank liquid