Download Medical Instrumentation

Homework # 1
2004200456
Lim Myeong-Jun
Index
 (Axid) Stress
 δ & ε Curve
 Cantilever
 Strain gage
 Gage factor
 Problem solution
(Axid) Stress
y
x
A=x*y
A
On the surface, the average force
per unit area is denoted as δ.
M
“ stress ” cf) Pressure
F is sometimes called “ Load ”
F =M*g
L
F
ε : Strain(unitless)
F
δ
δ & ε Curve
 Brittle material ( ex. Glass)
Linear : elastic region =>
Not linear over a range
δn : Ultimate stress
δ & ε Curve
 Ductile material ( ex. Al, Steel)
δn : Ultimate Stress
δy : yield Stress
δ pl : Proportional Limit
δ & ε Curve
For elastic region (linear
region) (δ ≤ δpl)
δ=E*ε
∵ E : Young’s modulus
( Modulus of elastivity)
Cantilever
L
F
F
δ
E : constant , A & L : almost constant
∴ If we know ε , then we can find F (force).
Strain gage
 A strain gauge (alternatively: strain gage) is a device used to
measure the strain of an object. Invented by Edward E.
Simmons and Arthur C. Ruge in 1938, the most common
type of strain gauge consists of an insulating flexible
backing which supports a metallic foil pattern. The gauge is
attached to the object by a suitable adhesive, such as
cyanoacrylate. As the object is deformed, the foil is
deformed, causing its electrical resistance to change. This
resistance change, usually measured using a Wheatstone
bridge, is related to the strain by the quantity known as the
gauge factor.
Strain gage
The black line is electrical wire.
L
ρ
+
V
A
-
The equation shows relation
between strain and resistance.
If we push the strain, ρ, A and
L was changed.
Strain gage
when you differentiate each variable,
Total change of resistance
The third equation’s ‘-’ sign means
that opposite change as compared
with change of resistance.
-> R ∝ L, R ∝ 1/A
Strain gage
Where
μ : Poisson’s ratio
εD : △D/D = strain along the
diametrical(horizontal) axis.
εL : △L/L = strain along the
longitudinal(vertical) axis.
Strain gage & Gage factor
Piezoresistive
effect
Dimensional
effect
Gage factor
For mental strain gage : G = ~1.6
For semi conductor strain gage : G = 100 ~ 170
high temperature coefficient
Gage factor
 The gauge factor GF is defined as:
where RG is the resistance of the undeformed gauge, ΔR is the change in
resistance caused by strain, and ε is strain.
 For metallic foil gauges, the gauge factor is usually a little over 2. For a
single active gauge and three dummy resistors, the output v from the
bridge is:
where BV is the bridge excitation voltage.
 Foil gauges typically have active areas of about 2-10 mm2 in size. With
careful installation, the correct gauge, and the correct adhesive, strains up
to at least 10% can be measured.
Problem # 3
 Gage factor : 10
F
1
2
3
4
Gage 1 & 2 : L -> L + △L
Gage 3 & 4 : L -> L - △L
Side view
L
1
2
Top view
F
Problem # 3
Cf)
R3
V1
5V
R2
Va
R1
: Resistor
: variable Resistor
Vb
: Resistive Sensor
R4
-
+
IA
V0 = Av(Va – Vb)
A : Differential-mode
voltage gain
Problem # 3
R3
5V
R2
Va
R1
Vb
R4
Problem # 3
- The constant 50 defined by gage factor(10) and voltage source(5v).
- Av is changeable factor by resistor connected IA(Instrument
Amplifier)
- k is given by structure and material.
- There are linearity between Vo and F.
Problem # 4
F
1
3
2
4
Side view
1
3
Top view
 Gage factor :
p-type Si strain gage S1 & S2 : G = 100
n-type Si strain gage S3 & S4 : G = -100
Problem # 4
E
Problem # 4
Problem # 4
Use least squares method to find the
calibration equation.
Force range : 0~100N
F
1
3
2
4
Side view
Problem # 6
 In the below pressure sensor, diaphragm is equipped with two p-
type Si strain gage of gage factor of +100 and two n-type Si strain
gage of gage factor of -100. As pressure is placed in the
diaphragm, the same strain occurs in the each strain gage and
the responsiveness is 10-5%/mmHg. As not, the strain gage is 50.
suppose the relationship between pressure and strain is linear.
 (a) When pressure is changed from 0 to 50mmHg, What is the
resistance of the p-type and Si strain gage changed?
 (b) Sketch the bridge circuit consisting of four strain gage and
mark where each strain gage is placed.
 (c) Let the driving power source have voltage of 1 and add
instrumentation amplifier for the final output to be converted
from 0 to 1V. What is the gain?
Problem # 6
2
4
1
3
 Gage factor :
p-type Si strain gage S1 & S2 : G = 100
n-type Si strain gage S3 & S4 : G = -100
Problem # 6
저항
(Ω)
50.25
p-type
50
n-type
49.75
0
500
압력(mmHg)
Problem # 6
1
Problem # 6
Thanks for your attention!!