dept. of biomedical engineering 2003200449 younho hong resistive sensors
TRANSCRIPT
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