Pressure Measurement Theory

8/20/2019 Pressure Measurement Theory

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Pressure sensors

dSdF p =

- definition:

F .. force [ N]S .. area [m2]

p → F → ε deformation element → change in dimensions

Strain gaugedirect (intrinsic) sensor

2 ways of measurement:1 atm = 100 kPa


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Basic principles of pressure sensors

p→F

Element type:

direct

(intrinsic)

F→ε

Deformation

element

ε → …

• el.charge – piezoelectric

• magnetic (L,Φ )

• optical (O. fibre sensor)• el. resistance

strain type ε converted to

• bending

• strain, pressure

• shear

• torsion

Mech. strain:

• strain gauge• resonator

position:

• capacitive• inductive

• optical

membrane tube Bellows, drum cantilever


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1. Membrane with strain gages

- most widely used

z h2

r R

h

p2

p1

- membrane deformation:

r σ

tσ

12 p p p −=∆Action of pressure results in strain σ composed of:

- radial component

- tangential component


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-1

σ

σt

σr

1′r

R

0 ′′r

R

0 r

R

Distribution of radial and tangential

strain under pressure-deformation

Metallic membrane:

• glued semiconductive strain gauges

• metallic foil strain gauges

• thick layer deposition technology

)/( Rr r r =σ

)/( Rr tt =σ


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Strain gauge „roseta“

- ideal strain gauge (-foil) for membranes

- 2 sensors at periphery and 2 in the middle


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semiconductive membrane

substrát N

R 3R 4

R 2

R 1

∅ 3,5

difuzní odporytypu P

+ difusion implemented piezoresistors- made by integrated circuit technology ⇒ cheap

- Si, SiC, diamond

Substrate N

P-type

piezoresistors


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Thin-layer pressure sensors

1

2

2 0

−ε −ε

+ε +ε

1 – four beams = deformation element

2 – connecting rod from outer membrane

-Separation of measured environment from the sensor ⇒ use e.g. Inmeasuring pressure in melting (transfer of deformation from outer durable

membrane via connecting rod)


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−ε

−ε

−ε

+ε

+ε

+ε

Deformation elements with cantilever and bellows


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Immersible pressure sensors

-Measuring of liquid level

- separation membrane, hermetic cable


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−

+

+−

+−

2

4 3

R 4

R 4

R 1

R 1

R 3

R 3

R 2

R 2

1 P

2

3

4 1

Membrane sensor with separating membrane

Separating

membrane

Silicon oil

Si

membrane


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2. Deformation pressure sensors - tubes

P

Bourdon tube


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3. Capacitive pressure sensors

- capacitor – usually differential

-Deformation element = pre-strained metallic membrane – serves asgrounded electrode

-Range: ∆ p = 1 mbar – 10 bar, total p up to 400 bar

C1

C2

p1 p2

OM

I

K

M

Differential capacitor with separating liquid

Glass

Membrane


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123

4

5

p1 p2C1 C2

ϑR

Pressure sensor with ceramic membranes

1- membrane2 – central piece Al2O33 - hydraulic liquid

4 - electrodes

5 - temperature sensor

0,1 %, max. 350°C

Range 2,5 to 300 kPa


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sklo

Si p

elektrody

prstencovýmagnet

pevnáelektroda

pohybliváelektroda

cívka vlnovec s nosníkem stálý magnet

p

S J

MEMS sensor

Feedback sensor with bellows

- combination of Si membrane and capacitive sensor

- returning membrane to

idle position throughelectrostatic force

- range – up to 200 kPa

Very precise and expensive

Glass

electrodes

Coil Permanent magnetBellows with cantilever

Fixed

electrode

Moving

electrode

Ring magnet

4 Piezoelectric pressure sensor


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4. Piezoelectric pressure sensor

membrána

vývodyelektrod

př edpětí

zesilovač

kompenzacezrychlení

k ř emennévýbrusy

konektor

M

- mechanical pre-strain of crystal is

necessary

- vibration compensating necessary

- for measuring fast pressurevariations

(e.g. engine pistons)

Vibration

compensation

Piezo crystals

Connector

Amplifier

Mech. pre-strain

Electrodes

membrane


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7. Resonant pressure sensors

p

SiO2

IDMIDM

IDM IDM

f R

f p

f f p R ± F)( p=∆

Surface acoustic wave (SAW)


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Examples of pressure sensors• (separating metallic membrane) Si measuring membrane,

piezoresistors, (integrated amplifier):PTX 120

• Process pressure sensor: HART or current loop: Capacitive

STX 2100

• Resonant sensor „double fork“

Cressto, Druck, Yokogawa,…


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Very low pressures


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Very low pressures

Principle: LVDT

SCHAEVITZ

Piezoresistive pressure sensors KELLER


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Piezoresistive pressure sensors

SPECIFICATIONS (at 4 mA excitation)

Pressure Ranges (FSLinearity

Stability

Operating Temperature Range

Storage Temperature

Temperature-Coefficients of…

- Zero (without Comp.)- Sensitivity

1-20 bar 0,25% FS typ. 1% FS max.

0,5 mV typ. 2 mV max.

-10…80°C (optionally)

-20…100°C

0,05 mV/K typ. 0,2 mV/K max.0,01%/K typ. 0,02%/K max.

KELLER

Integrated pressure sensors


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– Pure CMOS based sensor

– calibrated to automotivespecifications

Integrated pressure sensors

Pressure Measurement Theory

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