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NTU50235100

周元昉04/23

PRESSURE MEASUREMENT

NTU50235100

周元昉04/23

Standards and Calibration

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Air piston gage

It produces an accurate level of pressure by balancing the vacuum section (the upper part) and the constant-pressure section (the lower part). Pressure in the lower section is determined by placing an approved high accuracy weight on the upper section. Pressure in the lower section is adjusted with the vacuum pump and pressure adjuster so that it balances with the weight on the upper section. The pressure in the lower section is led to the air inlet of the pressure gauge to be calibrated.

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Ref: Vern E. Bean, NIST MEASUREMENT SERVICES: NIST Pressure Calibration Service, NIST Special Publication 250-39, 1994.

The pressure under the piston

Oil piston gage

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Note: The National Bureau of Standards (NBS) of US was established by US Congress in 1901. Its name was changed to the National Institute of Standards and Technology (NIST) in 1988.

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High vacuum calibration system(Sandia National Lab.)

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Pressure Gages• Direct reading gages

• Manometers

g

pph

ρ21 −=

• Different fluid provides different uncertainty

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• Elastic pressure transducersBourdon-tube gage (0.1% accuracy)

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• Diaphragm and Bourdon gages

Diaphragm gage Bourdon gauge

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Electro-optic pressure transducer Piezoelectric transducer with acceleration compensation

Mounted on a shaker Mounted on an exhaust pipe

4f1 with mechanical filterMounted on the wall of a shock tube with f1

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• Strain gage pressure sensors

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• Miniature pressure transducer

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( )( )VR R R R

R R R RVout in= −

+ +1 3 2 4

1 2 3 4

V

R1 2

34R

R

R

in

Vout

•The Wheatstone Bridge

For a balanced bridge

Bridge output

R R R R1 3 2 4= and Vout = 0

Resistance change Δ Δ Δ ΔR R R R1 2 3 4, , ,

( )( )V

R R

R R

R

R

R

R

R

R

R

RVout in=

+− + −

−1 2

1 22

1

1

2

2

3

3

4

4

1Δ Δ Δ Δ η

η =+ +

+

+ +

1

11

1

1

4

4

2

2

3

3

r

RR

RR

rR

RR

RΔ Δ Δ Δ

where rR

R

R

R= =2

1

3

4

and

NTU50235100

周元昉04/23

( )V

r

r

R

R

R

R

R

R

R

RVout in=

+− + −

1 21

1

2

2

3

3

4

4

Δ Δ Δ Δ

ΔR R<<For , that is η → 0

• Constant current source

VR R R R

R R R RIout in= −

+ + +1 3 2 4

1 2 3 4

VR R

R R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

RIout in=

+− + − + −

1 3 1

1

2

2

3

3

4

4

1

1

3

3

2

2

4

4Σ ΣΔΔ Δ Δ Δ Δ Δ Δ Δ

ΣR R R R R= + + +1 2 3 4 ΣΔ Δ Δ Δ ΔR R R R R= + + +1 2 3 4

ΔR R<<For VR R

R

R

R

R

R

R

R

R

RIout in= − + −

1 3 1

1

2

2

3

3

4

4ΣΔ Δ Δ Δ

,

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周元昉04/23

• Silicon based piezoresistor pressure sensors

Anisotropic etching of single crystalline silicon

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Normal stress distribution of a square plate

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-1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

mm

Contour of normal stress in [011] direction (MPa)

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- Fabrication of silicon based piezoresistor pressure sensors

(Brysek et. al., Silicon Sensors and Microstructures, Nova sensor, 1990 )

(Lee et. al., Transducers ’95, 379-C9, 1995)

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• General Design Considerations

Plate dimensions

- maximize a/h: large aspect ratios give the best pressure sensitivities

- : fabrication considerations

Resistor placement: high signal level, sufficient impedance,

and insensitive to alignment and patterning error

- High signal level: positions of largest stresses (or strains)

h hmin <

h a< 0 1. : thin plate theory valid

a amin < amin is determined by the geometry of piezoresistors and the ability to

place resistors on the plate- maximum bending stresses must not exceed fracture stress

sensitivity, strength, frequency response

- w hmax .< 0 2 : avoid nonlinear behavior

- check resonant frequency

-

- :

- High impedance: a) narrower resistors,b) more resistor segments, andc) higher resistivity.

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周元昉04/23Differential-pressure transmitter

“Diffused” strain-gage transducers

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• Capacitive differential-pressure transmitter

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•Resonant transducers

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•Cavity effects

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Vacuum Gages•A typical vacuum system

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• Pressure ranges for various gages

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McLeod gage

Served as a vacuum standard

hAVV

hA

hAV

hAp

hpp

hApVp

ii

i

ii

i

ii

>>≈−

=

+==

if 22 γγ

γ

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• Kundsen gage • Momentum transfer (Viscosity) gage

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• Capacitance manometer

-A diaphragm gauge in which the deflection of the diaphragm is measured by observing the change in capacitance between it and a fixed counter electrode

Double-sided capacitance manometer Single-sided capacitance manometer

Full scale pressaur range: 20 torrAccuracy: 0.25% of readingResolution: 0.001% of full scale

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Thermal conductivity gages

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• Pirani gauge

Basic Pirani gauge circuitCalibration curves for a Pirani gauge

- the electrical resistance of the wire being proportional to its temperature

- the heated wire forms one arm of a Wheatstone bridge

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• Indirect pressure measurement: measures pressure-dependent heat flow

• Based on change in thermal conductivity of a gas: at low pressure, linear relationship between conductivity and pressure

• Constant current is delivered to heat a filament that a tiny thermocouple is spot welded to its midpoint

• As pressure decreases, gas impingement rate decreases and less heat is transferred from filament

• Measured filament temperature (thermocouplepotential) is transformed into pressure units at the controller

• Thermocouple gauge

(Teledyne Hastings Instruments, THI)

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(A) Uncompensated, (B) Compensated

Calibration curve

A temperature shift in the AC heated thermocouples 1 and 2 (Fig. B). The resultant temperature shift causes a change in the DC output from couples 1 and 2 inversely with pressure changes. The DC thermocouple 3 (when installed) is in series with the circuit load. Thermocouple 3 provides compensation for transient changes in ambient temperature.

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• Hot cathode gauge

Circuit for a Bayard-Alpert ionization gauge

p: plate g: grid

emittergrid

150V

30V

(cathode)

plate (ion collector)

(I+) 1Sensitivity S = ----------

(I–) P

I+ = Ion Current in Amperes (from collector)I– = Emission Current in Amperes (from filament)P = Pressure in torr

Ionization gauges

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Sensitivity10 (torr)-1 (mbar)-1 (typical)Operating Ratings• 0 VDC (collector)• +180 VDC to ground (grid)• + 30 VDC to ground• 5 VAC nominal (filament)X-Ray Limit2 x 10-10 torr(2.6 x 10-10 mbar)Operating Pressure2 x 10-10 torr to 1 x 10-3 torr(2.7 x 10-10 mbar to 1 x 10-3 mbar)

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• Cold cathode gauge

Wire anode loop: 2-10kVPermanent magnet: 0.1-0.2 TeslaOutput current: 10-50 mA/PaOperation range: 1-10-6 Pa

Higher ionization efficiency than hot cathode gage