Sensors of mechanical stress - Hook: relation of mechanical stress and deformation (strain, prolongation) - types: 1. Capacitive strain gages 2. Resonant strain gages 3. Sensors with metastable magnetic alloys (memory) 4. Resistive strain gages (gauges)

Torque

M k = Fr Hook`s law

σ = Eε

Mk ... torque F ...

force

r ...

arm

σ = F/S ... tension, stress ε = ∆l/l ... deformation E = Young`s module of elasticity

Resonant sensors (string strain gages) - resonant frequency fo of string with length l and mass m depends on stretching force F

stimul

1 F fo = 2 ml m m = V lS F σ = = εE S

ρ=

buzení ∆l = ε ... relative deformation l E ... Young module of elasticity σ ... mechanical stress

⇓ 1 σ 1 εE fo = = 2l ρ 2l ρ

response

t odezva

- application: mechanical stress in large objects (dam, bridges…) Resonant string gage signal conditioning circuits: -pulse of driving current in coil magnetises and atract string → after pulse termination string performs damped oscillations inducing voltage in a coil - feedback arrangements of driving coil and pick - up coil - output voltage of pick-up coil amplified and connected to driving coil ⇒ OSCILLATOR

Sensors based on metastable magnetic alloys - increase of stress acting on certain magnetic alloys causes a change of their crystallic structure =>behave as FERROMAGNETIC material - transformation of crystallic structure is IRREVESIBLE ⇒ disposable sensors „memory“ of mechanical stress changes - passive type of sensors UH UA[V] 6

2

4 2 1

0

0

0,2

1 strip of an alloy 2 Hall probe + permanent magnet

0,4

0,6 ε

Resistive strain gages free grid metal

wire foil layer

bonded vacuum sputtering

strain gages

bonded monocrystallic semiconductor

difused to Si substrate

polycrystallic (sputtered)

Principle of operation S - ∆S - basic relation:

l R= ρ S l + ∆l

- total differential:

∆R ∆l ∆S ∆ρ = − + R l S ρ 2

∆l ∆S ∆l  ∆l  = −2 µ +  µ  + ... ≅ −2 µ S l  l  l µ ... Poison`s constant ∆ρ ∆R

R = 1 + 2µ + ρ = 1 + 2µ + π E e ∆l ∆l l l π e ... piezoresistive coefficient E ... Young module of elasticity

∆l = ε ... relative deformation l ∆ρ - caused by microstructural ρ changes of gage material–

changes must not be irreversible!

∆S

- depends on ∆l

∆R = C1ε + C2ε 2 + C3ε 3 + ... R0, 0 d K ε ,0 =

∆R R0, 0

= C1 + 2C2ε + 3C3ε 2 + ...

dε K ε , 0 ... strain gage factor (constant) Metal strain gages: K ≈ 2,

C2 ≈ 0 pro ε < 10-3

- temperature coefficient of sensitivity : - temperature coefficient of resistance αK =

∆K K 0, 20

ϑ∆

αR =

∆R R 0 ,20 ϑ∆

- tempco of resistance should be minimal (