ME 220 Measurements & SensorsME 220 Measurements & Sensors

Mechanical Measurements Applications

Chapters # 8, 9,10, 11 ( Figliola)

and 18 (Beckwith)

Thermometer

Thermometry based on thermal expansion

Liquid-in-glass thermometers (accuracy from ±0.2 to ±2°C)

CH. # 8 Temperature MeasurementsCH. # 8 Temperature Measurements

Bimetallic ThermometersIf you take two metals with different thermal expansion coefficients and bond them together, they will bend in one direction

Resistance Temperature Detectors RTD

R1

R2

R3 r1RRTD r3

RRTD R3 r1 r3

RR0 1 A T T0

Thermistors

RR0e 1/T 1/T0

Usually made of a semiconductor and have Much larger dR/dT (more sensitive) than RTD and has Fast Response

Thermocouple (Thermoelectric) (Thermoelectric)

Thermoelectric EffectsSeebeck effect: Generates voltages across two dissimilar materials when

a temperature difference is present.

Peltier effect: Moves heat through dissimilar materials when current is applied.

ThermocouplesThermocouples measure the difference in temperature between two points. One of those points at a known temperature.

Thermocouples in Series and in Parallel

THERMOCOUPLE TIME CONSTANT • The conservation of energy:

m cp dT / dt = h A (To – T) m : mass of thermocouple junction, Cp: specific heat of thermocouple junction h : heat transfer coefficient , A : surface area of thermocouple

T : junction temperature , To : environs temperature

θ =T – To / Ti - ToTi = initial measurement junction temperature, then the solution is

θ = e (-t / τ )

The time constant for this process is

τ = m cp /h A

Error Sources in Temperature Measurements

Conduction: Your probe can conduct heat to/from the environment to/from your desired measurement location

Radiative Temperature Radiative Temperature Measurements (Pyrometry)Measurements (Pyrometry)

Eb T 4

Temperatures greater than 500ºC

= 5.67•10-8 W/m2K4

Optical Pyrometer

CH. # 9 Pressure and Velocity MeasurementsCH. # 9 Pressure and Velocity MeasurementsDynamic Pressure = Total Pressure - Static Pressure

Use of Manometers

Pitot Tube Principles

Deadweight Testers

Elastic Pressure Transducers

Bourdon Tube Gauge

INCLINED MANOMETER

Flow velocity measurementsThermal Anemometry

Laser Doppler Anemometer (LDA)

Particle Image Velocimetry (PIV)

CH. # 10 Flow Measurements Turbine

Obstruction Flow Meter

Obstruction Meters

P1 P2

V2

2 V12

2gc

Qideal V2A2 A2

1 A2 /A1 2 1/ 2

2gc P1 P2

Rotameter or Area meter

Rotameter

CH. # 11 Strain Measurements

a dL

LL2 L1

L1

LL1

Strain Gauges

RLA

LCD2

The resistance across that conductor is

Where conductor of resistivity

If you strain this conductor axially, its length will increase while its cross sectional area will decrease. Taking the total differential of R,

dRRd R

LdL R

CD2 d CD2

1

CD2Ld dL 2L dD

D

dR

RdL

L 2dD

Dd

dR /R

dL /L1 2

dD /D

dL /L d /dL /L

dR

RdL

L 2dD

Dd

a dLL

L dD

D

La

F dR /R

dL /LdR /R

a1 2v

d /dL /L

For most strain gauges, = 0.3. If the resistivity is not a function of strain, then F only depends on poisson’s ratio, and F ~ 1.6.

Gage factor

Strain Gauge

lateral strain

axial strain

La

F dR /R

dL /LdR /R

a1 2v

d /dL /L

1

F

RR

F and R are supplied by the manufacturer, and we measure ∆R.

Strain Gage

Strain Gage [Gage Factor = (∆R/R)/(∆L/L)

& Young’s Modulus = (P/A) / (∆L/L) ]

Strain Gage Bridge CircuitStrain Gage Bridge Circuit

eoei

R1 /R

4 2 R1 /R

1

F

RR

eo eiF

4 2F

Wheatstone Bridge

eo eiR2

R1 R2

R4

R3 R4

make R2 = R4 = R

eo eiR

R1 R

R

R3 R

eo eiR

R1

1R

R3

1

eoei

R1

R1

1

R3

Multiple Gauge BridgeMost strain gauge measurement systems allow us to make 1, 2, 3 or all 4 legs of the bridge strain gauges.

Eo E iR1

R1 R2

R3

R3 R4

Say that unstrained, all of these have the same value. If they are then strained, the resultant change is Eo is

dEo EoRii1

4

dRi

Eo

Multiple Gauges•All gauges have the same nominal resistance (generally true)

•All gauges have matched gauge factors

EoE i

F

41 2 4 3

Eo

Force Measurements

Torque & Power MeasurementsTorque T = FRPower P = T

ACOUSTICS

• Acoustics is the study of Sound.

• Sound is caused by variations in Pressure transmitted through air or other materials.

• The pressure, and the resulting sound, can vary in both Amplitude and Frequency.

• Humans can detect sound over a wide range of frequencies and amplitudes.

What is Sound?• Sound is a propagating disturbance in a fluid or in

a solid. The disturbance travels as a longitudinal wave.

• Airborne sound Sound in air is called airborne sound generated by

a vibrating surface or a turbulent fluid stream. • Structure borne sound Sound in solids is generally called structure borne

sound.• Sound: is measured by a microphone and has

Amplitude and Frequency

SOUND WAVESrapid pressure variation

cycles of compressions and rarefactions

SOUND WAVES• Sound energy is transmitted through air as a pressure wave.• Frequency : The frequency of a sound (cycles / sec.) hertz (Hz). f = 1/T (Hz) The range for human hearing is from 20 to 20.000 Hz. • Wavelength :The distance between analogous points of two

successive waves. λ = c / f where c = speed of sound (m/s)

f = frequency (Hz)

Frequency (Hz) 63 125 250 500 1K 2K 4K 8K Wavelength (m) 5,46 2,75 1,38 0,69 0,34 0,17 0,085 0,043

Frequency Independent of sound-pressure level.

The speed of sound in air = 344 m/s fn (Temp)

The speed of sound in water = 1000 m/s

The speed of sound in solid = 3000 m/s

Speed of Sound and Wavelength

Sound Waves

Pure Tone and Noise

Human Ear

External, Middle and Inner Ear

Middle &Inner ear

Hearing

Noise to Outside

• From Machines such as Airplanes, Pumps, Compressors and generators.

• From Air conditioning such as condensers, Chillers, Ventilation Opening, Louvers

• Nose Control by: Relocation, Use of Vibration Damping, Use of Attenuator and Use of Enclosure.

Typical Noise Sources

The Decibel (dB) & Sound Power LevelThe Decibel (dB) & Sound Power Level

dB = ten times the logarithm to base 10 of the ratio of two quantities.

Power Level = 10 log (w1 / w2) dB

where w1 and w2 are the two powers.

SWL = 10 log (sound power)/(ref. power)

Reference power  (Watt) = 10-12 W, which is the threshold of hearing ( lowest detectable sound).

Sound Energy Decreases with (distance)2

Sound intensity• Sound intensity, power per unit area.• The intensity passing a spherical surface around source in a

free field is: I = W / A = W / 4 π r2   = p2 / ρ c   (W/m2)where W = power     (W)

A = area   ( m2) r = radius   (m) p = root mean square pressure  (N/m2) ρ = density     (kg/m3) c = velocity of sound   (m/s)

   

• SOUND INTENSITY LEVEL LI = 10 log (I / I0)  (dB)Where Io = reference intensity  = 10-12 W/m2.

Sound pressure level (SPL)• Sound measuring device respond to sound pressure .

• Sound pressure level in decibels vary with distance from source.

• SPL = 10 log (p2 / p02) = 20 log (p / p0)

where p= rms pressure (N/m2)

& po = 20x10-6 N/m2.

For Free Field : SWL=SPL +20 log r +11 dB

Sound Pressure

The reference value used for calculating sound-pressure level is 2 ×10-5 Pa.

Note the unit of the equation

Sound Level Meter

Adding two sound pressure levels

Diff between 2-Levels Total= Larger +

0 or 1 3

2 or 3 2

4 or 9 1

10 or more 0

Total SPL =

10

SPLloglog10 i1

10

ni

1i10

Addition of two sound pressure levels Addition of two sound pressure levels

Noise criteria (NC)

1) NC relates SPL with frequency to show how SPL varies with frequency

2) The highest curve crossed by the data determines the NC rating. NC-39

A , B, and C - Weighting

A- Weighting (dBA)The ear is less sensitive with decreasing frequency.To simulate ear response use A weighting (dBA).

63 125 250 500 1kHz 2kHz 4kHz Fan Octave Band dB: 85 86 85 80 73 70 60 A-weighted : -25 -16 -9 -3 0.0 +1 +1 60 70 76 77 73 71 67 70 80 75 67 80 76

81 dBA

SOUND INSULATION• Source - Transmission Path- and Receiver

• Air-borne noise and Structure-borne noise

• Reduction of Air-borne sound:

- Relocation of source and/or receiver

- Use floating floors, Use absorbent material

- Use local insulation, and local attenuators

- Use fans with backward curved impellers

- Lined duct work and avoid crosstalk