Dept. of Biomedical Engineering2003200449

YOUNHO HONG

RESISTIVE SENSORS

Stress (axial), Strain

M

xy A=xy

F=mg

On the surface,the average force per unit area isdenoted as σ

: “stress” [N/m²]

L

F

F

δ

: “strain” [unitless]

Stress-Strain Curve

Brittle Materials ( ex. glass, concrete)

1 : ultimate stress2 : rupture

# Do not have a yield point# ultimate strength and breaking strength are the samenonlinear

over a wide range

Stress-Strain Curve

Ductile material (ex. Al, steel)

1 : ultimate stress2 : yield stress3 : rupture4 : elastic region5 : plastic region

A : AlB : steel

For elastic region ( linear region )[σ ≤ σ PL]σ = E ε (E : Young’s modulus)

σ PL

cf) Less ductile materials such as aluminum and medium to high carbon steels do not have a well-defined yield point.

Cantilever

L

F

F

δ

Al

Al

σ = E ε If a material of a cantilever is a aluminum,A and L are almost constant.

L+ ε

F

F = αε

Strain gage

(electrical wire)

A

L

+ -Vρ

resistivity is low

Strain gage

If A, L, ρ change at the same time,

Poisson’s ratio

L

D

L+ ∆L

D- ∆D

Gage factor

for metal strain gage, G : ~1.6for semi-conductor strain gage, G : 100~170

100 Ω -> 100.01 Ω100 Ω -> 101 Ω

for a bit of changes of resistance,use Bridge Circuit method

I A

+

-

O U T

Problems and Solutions

Top view

Bottom view

Gage 1

Gage 2

Gage 3

Gage 4

Gage 1&2 : L => L + ∆LGage 3&4 : L => L - ∆L

f = ε AEε = (1/AE)f

(3) Four metal strain gages which gage factor is 10 are attached on a plain. By forcing F to the plain, Gage1 and 2 are expanded as long as ∆ L, whereas Gage3 and 4 are shorten in the same length. It has a relation that ∆ L/L = kf ,k is constant. Design a bridge circuit getting output voltage in proportion to F, describe output voltage as F. Voltage source of the bridge circuit is dc 5[V].

Problems and Solutions

Vo = Av(Va-Vb)R 2 R 4

I A

+

-

O U T

5 V

R 1R 3

Problems and Solutions

p-type Si strain-gage S1&S2 : G=100n-type Si strain-gage S3&S4 : G=-100

Top view

Bottom view

Gage 1

Gage 3Gage 2

Gage 4

(4) Consider to design a system measuring force by using both two P-type Si strain gages which gage factor is 100 and two N-type Si strain gages which one is -100.

R 2 R 4

I A

+

-

O U T

E (v )

R 1R 3

Problems and Solutions

R=200Ω -5 ≤ Vo ≤ 5

Vo.max = Av*5*100*0.0005 = Av*0.25 = 5V Av = 20

(b) Assuming that both top and bottom of cantilever is changed in the same length in case that forced. By forced F, maximum change of the length of strain gage is +0.05%, resistor is 200 without any load. Specify gain in order output to vary in the range between -5V to +5V.

(c) Derive to calibrate this kind of instrument.

f

Vo

Change f by using different metal,and measure Vo

# Use least square method to find the calibration equation.

Problems and Solutions(6) Four metal strain gages are attached on the diaphragm below. Two of them whichare p-type Si strain gages have 100 gage factor and the others which are n-type Si strainGages have -100 gage factor. When the diaphragm is pressed, each of strain gages hasthe same strain and sensitivity is (1/100000)%/mmHG. When It isn’t pressed, resistanceis 50. Assume the relation between pressure and strain is linear.

(a)How much does each resistance of p-type and n-type Si strain gages change, when the pressure is changed ?

The sensitivity is (1/100000)%/mmHG and the resistance is 50 when pressure is zero.So, when the pressure is 500mmHG, the resistance of p-type is 50 + 0.00005 and the resistance of n-type is 50-0.00005.

(b) Design Bridge circuit with four strain gages. Make the positions of strain gages.

p-type Si strain-gage S1&S2 : G=100n-type Si strain-gage S3&S4 : G=-100R 2 R 4

I A

+

-

O U T

E (v )

R 1R 3

Problems and Solutions

R 2 R 4

I A

+

-

O U T

1 V

R 1R 3

(c) Define the Voltage Gain of the op-amp. Input voltage is DC 1V. Output voltage changes 0-1V.

Av = 100000

Thank for your attention