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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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NTU50235100
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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.
NTU50235100
周元昉04/23
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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周元昉04/23
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.
NTU50235100
周元昉04/23
High vacuum calibration system(Sandia National Lab.)
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NTU50235100
周元昉04/23
NTU50235100
周元昉04/23
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)
NTU50235100
周元昉04/23
• 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
NTU50235100
周元昉04/23
• Strain gage pressure sensors
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NTU50235100
周元昉04/23
• Miniature pressure transducer
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周元昉04/23
( )( )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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NTU50235100
周元昉04/23
• Silicon based piezoresistor pressure sensors
Anisotropic etching of single crystalline silicon
NTU50235100
周元昉04/23
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)
NTU50235100
周元昉04/23
- 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.
NTU50235100
周元昉04/23
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NTU50235100
周元昉04/23Differential-pressure transmitter
“Diffused” strain-gage transducers
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周元昉04/23
• Capacitive differential-pressure transmitter
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•Resonant transducers
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周元昉04/23
•Cavity effects
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Vacuum Gages•A typical vacuum system
NTU50235100
周元昉04/23
• 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
NTU50235100
周元昉04/23
• Kundsen gage • Momentum transfer (Viscosity) gage
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周元昉04/23
• 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
NTU50235100
周元昉04/23
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
NTU50235100
周元昉04/23
• 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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周元昉04/23
(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.
NTU50235100
周元昉04/23
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NTU50235100
周元昉04/23
• 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)
NTU50235100
周元昉04/23
• 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