basic sensors and principles. ① strain gages measurement of extremely small displacement ①...
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BASIC SENSORS AND PRINCIPLES
① Strain gages• Measurement of extremely small displacement
① Potentiometers• Translational and Rotational displacement
② FSR
and so on…
A = xy
F = mg
On the surface,The average force per area is denoted as
F
A
2
( )
( )
N
m
; Stress-solid
(cf. Pressure)-liquid, gas
F is sometimes called as “LOAD”
( )
( )
m
L m
; Strain (unitless)
L
F
F
① Brittle material (ex. glass)
ruptureBroken : Brittle material’s property
; Non-linear
n
Linear region; elastic region (like spring)
Not linear ; over a wide range
② Ductile material (ex. Al, Steel)
For elastic region ( Linear region )
( < ) PLYoung’s modules (cf. y = kx)
E (modules of elasticity)
rupture
PLrupture
; Steel
n
ysPL
; Al
rupture
elastic region plastic region
elastic region
plastic region
F
A
L
E
E
FE
A L
E : constantA & L are almost constant
AEF AE
L ; Provided that you know
, it is possible to measure F
Strain gage is widely used to measure F
L
F
The Principle of Weighing MachineThe Principle of Weighing Machine
F • None of our business, • All about for mechanics in terms of a variety of structures.
F mg Able to derive ‘m’
Strain GagesStrain Gages
Electrical wire
A
L
: resistivity
Substrate
LR
A ; The relation between
Strain and Resistor
All variables changed for volume constant
F Length ( elastic region )F Length
8 X L Eight times
Electrical lengthX
R L LR
A A
L
RR L
L A A
2 2A
R L LR A
A A A
Strain GagesStrain Gages
Partial Derivative in order to know the relation to each component
LR
A
Strain GagesStrain Gages
L AR R R R
2
L Ld dL dA
A A A
R L A
R L A
Resistor
Strain
Measurable size
Strain GagesStrain Gages
Poisson’s ratio with
D L
D L
(1 2 )R L
R L
Piezo-resistive effect
Dimensionaleffect
L
D D D
Gage factor 1 2R RR RGL LL L
Strain GagesStrain Gages
• For metal strain gage G : ~1.6• For semiconductor strain gage G : 100 ~ 170
(High temperature coefficient)
Problem (3)Problem (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].
Problem (3)Problem (3)
10 10R R LRGL R LL
1&2 :
3&4 :
Gage L L L
Gage L L L
1f
AE
Load cell : force sensor (Structure + Strain gage)
Lk f
L
f AE
① ②
③ ④
① ②
Top view
( )o a BV Av V V
①
② ③
④ And LPF
Problem (3)Problem (3)
1
1 3
5 5 52a
R R R R RV
R R R R R R R
4
2 4
5 5 52b
R R R R RV
R R R R R R R
105 10
2o
R LV Av Av
R L
50oV Avkf Part of it is your design
5 X 10 Your design
Given by structure and material
Register VariableRegister
ResistiveSensor
Problem (4)Problem (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.
(a)Design a circuit including a bridge circuit having four strain
gages as well as instrumentation amplifier in order to magnify output. Specify the type of each strain gage composing the bridge circuit.(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.
Problem (4)Problem (4)
P-type Si Strain gage S1 & S2 : G = 100N-type Si Strain gage S3 & S4 : G = -100
S1 S2
S3 S4
<Top View> <Bottom View>
RRGLL
S1
S4
S3
S2
( )o a BV Av V V
S1
S4
S3
S2
And LPF
Problem (4)Problem (4)
1
1 3 2a
R R R R RV E E E
R R R R R R R
4
2 4 2b
R R R R RV E E E
R R R R R R R
Problem (4)Problem (4)
o
RV AvE
R
5L
Av GL
max5 100 0.0005oV Av
0.25 5Av V
max 0.0005L
L
200R
520
0.25Av
Problem (4)Problem (4)
Calibration
F : 0 – 100N
Change f by using different mass to measure V0
Use Least Square Method to find the Calibration Eqution.
Problem (6)Problem (6) 2 P-type Si strain gages and 2 N-type Si strain gages areattached below diaphragm of Pressure sensor.
In case of pressure on diaphragm, same strain occur at the each strain gage with its sensitivity of %/mmHg, its resistor is 50 without any pressure.
Assuming that it is linear between pressure and strain.
Catheter Liquid Sensor
Diaphragm
S1
S4
S3
S2
510
(a) In variation of pressure from 0 to 500mmHg , how each resistor of P-type and N-type Si strain gages changed.
Problem (6)Problem (6)
oR R G Sensitivity pressure
50 100 0.0000001 500PR
50 100 0.0000001 500NR
50.005
49.995
Problem (6)Problem (6)
(b) Design a bridge circuit included 4 strain gages and specify each strain gage in the circuit.
S1
S4S3
S2
(c) Add instrumentation Amplifier to vary from 0V to 1V with dc 1V. Specify its gain.
Problem (6)Problem (6)
( )o a BV Av V V
S1
S4S3
S2
And LPF
1
1 3 2a
R R R R RV E E E
R R R R R R R
4
2 4 2b
R R R R RV E E E
R R R R R R R
o
RV AvE
R
1L
Av GL
max1 100 0.0000001oV Av
0.00001 1Av V
max 0.00005(@500 )L
mmHgL
50R
1100000
0.00001Av
Problem (6)Problem (6)