Medical Instrumentation II. 1. (Axial) Stress On the surface, the (average) force per unit area is...

Medical Instrumentation II

1. (Axial) Stress

On the surface, the (average) force per unit area is denoted as σ: “Stress” (cf. pressure)

][2m

N

A

F

M

)8.9( NgMgf

y

x

xyareaA )(

A


F(force) is sometimes called “load”

2. Strain


L(length)

wall

F(force)

<Stick>

wall

)(

F(force)

<Stick>

][)(m

m

Lstrain

Strain is unitless!

3. & curve 1. Brittle material (ex. Glass)

rapture

n

n

Linear region : elastic region (ex. Spring)

Ultimate stress

After this rapture, material is broken by force and no stress & strain state


Not linear over a

wide range

2. Ductile material (ex. aluminium, steel)


n

PLys

PL

Elastic region

Yield region

Plastic region

rapture Aluminium


PLrapture Steel

Elastic region

For elestic region : linear region (σ ≤ σPL)

EE : young’s modulus (modulus of elasticity)

//Summary//


Estress )(

A

Fstress )(

Lstrain

)(

4. Cantilever


L(length)

wall

F(force)Al

XX = 0

LE

A

F

E

LE

A

F

Constant

E is ConstantA&L are almost Constant

AEL

AEF

AEL

AEforceF )(

5. Strain gage


Substrate

Electrical wire

L(length)

Resistivity

+ -A(Surface area)

IRV

A

LR

6. Partial differentiation


AR

L

A

LR

AR

L L

2A

LR

A A

AA

LRA

2

LA

RL

A

LR


AL RRRR

AA

LL

AA

L

2

Fractional A

A

L

L

R

R

Poisson’s ratio L

L

D

D


L(length)

D

DD LL

2DA

L

L

R

R

)21(

Piezoresistive effect

Dimensional effect


Gage factor

For metal strain gage G : ~ 1.6

For semiconductor strain gage G : 100 ~ 170

LL

RR

LLR

RG

21

(High temperature coefficient)

Problem (3) Solution.

Metal strain gage four (gage factor is 10) set up in a tool. F is authorized a tool. gage 1 & 2 are increase ΔL, gage 3 & 4 are decrease ΔL. ΔL/L = kF (k is constant) . design by bridge circuit (out voltage proportionate force). Represent out voltage by force. Drive voltage is dc 5v.



10

LLR

RG

L

L

R

R

10

wall

F(force)1 2

3 4

wall

1 2

3 4

Gage 1 & 2 : L -> L + ΔLGage 3 & 4 : L -> L - ΔL

kFL

L

Side view


wall

Cf.

F(force)

AEF

FAE

1

Resistor Variable Resistor

Resistive Sensor


V 10V dc

U 1

O PAMP

+

-

O U T5v

R3

R1 R4

R2

reference

in = 0

ip = 0

IA

V0 = AvV0 = Av(Va – Vb)

V 10V dc

Va Vb

Va Vb


52

5)()(

5

52

5)()(

5

42

4

31

1

R

RR

RRRR

RR

RR

RV

R

RR

RRRR

RR

RR

RV

b

a

52

5)()(

5

52

5)()(

5

42

4

31

1

R

RR

RRRR

RR

RR

RV

R

RR

RRRR

RR

RR

RV

b

a

R

RA

R

RAVVAoV vvbav

55

2

2)(

kFAL

LA vv 50105

kFAV vo 50

Your design

Given by structure & material

Part of it is your design

Problem (4) Solution. Two p - type Si strain gage (Gage factor is +100)

and two n - type Si strain gage (Gage factor is -100) use system (measure force)

(a) Bridge circuit consist of four strain gage. Design circuit that bridge’s output is amplified by instrumentation amplifier. (clear state strain gage type consist of bridge circuit) drive voltage is dc 1V.

(b) When cantilever is authorized force, cantilever’s increase & decrease length is equal. Strain gage’s maximum length rate is ±0.05%, when no load, strain gage resistance is 200Ω. Output by authorized force is change ±5v. Define instrumentation amplifier’s gain.

(c) Propose calibration method in force instrumentation.



wall

S1 S3

S2 S4

wall

S1S3

S2 S4

V 10V dc

U 1

O PAMP

+

-

O U TE[v]

S3

R1 S2

S4

reference

in = 0

ip = 0

IAVa Vb

S1 : ∆L increase / ∆R increaseS2 : ∆L decrease / ∆R decreaseS3 : ∆L increase / ∆R decreaseS4 : ∆L decrease / ∆R increase

Gain is positive

Gain is negative


ER

RRE

RRRR

RRE

RR

RV

ER

RRE

RRRR

RRE

RR

RV

b

a

2)()(

2)()(

42

4

31

1

R

REAV vo

200

0005.0max

RL

L- 5 ≤ V0 ≤ 5 [v]


L

LGA

R

REAV vvo

5

VAAV vvo 525.00005.01005max,

VVAv 2025.0

5

V0

F

(C) Use least square method Second & third order polinominal

Problem (6) My Solution.

Two p - type Si strain gage (Gage factor is +100) and two n - type Si strain gage (Gage factor is -100) use system (measure force). When diaphragm is authorized pressure, each strain gage generate same strain and sensitivity is 10⁻⁵ %/mmHg. when no pressure, strain gage resistance is 50Ω. (Suppose that pressure proportionate strain).

(a) When pressure changing 0 – 500mmHg, How change p & n type Si strain gage’s resistance?

(b) Draw bridge circuit consist of four strain gage. and Where are each strain gage? Mark it!

(c) drive voltage is dc 1v, Output by authorized pressure is change 0 - 1v. define instrumentation amplifier’s gain



(a)

Strain gage

pressure

50

52.5

47.5

mmHg/%0001.010 5

50005.0: pR xytypep0 < Xp < 500

50005.0: pR xytypen

Pressure 0 : 50Pressure 500 : 52.5 & 47.5Pressure & strain is linear

P-type

n-type


(b)

V 10V dc

U 1

O PAMP

+

-

O U TE[v]

S1

S3 S4

S2

reference

in = 0

ip = 0

IAVa Vb

(c)

12

1)()(

1

12

1)()(

1

42

4

31

3

R

RR

RRRR

RR

RR

RV

R

RR

RRRR

RR

RR

RV

b

a


R

RA

R

RAVVAoV vvbav

1

2

2)(

vvvo AAL

LGAV 01.00001.0100

L

LG

R

R

R is 50ΩL/L = 0.0001G = 100

Av = 100

10 0 VI’m sorry prof. woo,,,, problem is so difficult,,,

Medical Instrumentation II. 1. (Axial) Stress On the surface, the (average) force per unit area is...

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