basic mechanical sensors and sensor principles. definitions transducer: a device that converts one...
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Sensors : definition and principlesTRANSCRIPT
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BASIC MECHANICAL SENSORS
ANDSENSOR PRINCIPLES
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Definitions
• Transducer: a device that converts one form of energy into another.
• Sensor: a device that converts a physical parameter to an electrical output.
• Actuator: a device that converts an electrical signal to a physical output.
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Sensors :definition and principles
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Sensors : taxonomies• Measurand
– physical sensor– chemical sensor– biological sensor(cf : biosensor)
• Invasiveness– invasive(contact) sensor– noninvasive(noncontact) sensor
• Usage type– multiple-use(continuous monitoring) sensor– disposable sensor
• Power requirement– passive sensor– active sensor
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Potentiometers
Translational Single turn
Helical
𝑣0=𝑅 𝑖
𝑅 𝑣𝑠=𝑥 𝑖
𝑙 𝑣𝑠
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The Wheatstone bridge
Eb A
B
C
D
R1 R2
R3 R4
Rg
Ig
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Circuit Configuration
+ VAC -
+ VC -
Eb A
B
C
D
R1 R2
R3 R4 + VA -
E0 = VAC
VA = EbxR4/(R1+R4)
VC = EbxR3/(R2+R3)
E0 = VAC = VA – VC =
))(()(
3241
3142
32
3
41
4
RRRRRRRRE
RRR
RRRE bb
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Null-mode of Operation
Eb= 10 V A
B
C
D
R1= 1000
R2= 600
R3 R4= Rx
0 + -
Ig
At balance:
R2R4 = R1R3 or R1/R4 = R2/R3 and the output voltage is zero
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9
Example 1
Eb= 10 V A
B
C
D
R1= 1000
R2= 600
R3 R4= Rx
0 + -
Ig
Assume that the bridge shown is used to determine the resistance of an unknown resistance Rx. The variable resistance is the resistance box that allows selection of several resistors in series to obtain the total resistance and it is set until null position in the meter observed. Calculate the unknown resistance if the variable resistance setting indicates 625.4.
The bridge will be balanced if R1/R4 = R2/R3 . Hence, R4 = Rx = R1/(R2/R3) = 1000x625.4/600 = 1042.3 .
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Deflection-mode of OperationAll resistors can very around their nominal values as R1 + R1, R2 + R2, R3 + R3 and R4 + R4. Sensitivity of the output voltage to either one of the resistances can be found using the sensitivity analysis as follows
241
4
232
241
31423232413
1
0
)(
)()())((())((
1
RRRE
RRRRRRRRRRRRRRRE
RES
b
bR
232
3
2
0
)(2 RRR
ERE
S bR
232
2
3
0
)(3 RRRE
RES bR
241
1
4
0
)(4 RRRE
RES bR
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+ Eg -
ETh = E0
A
B
C
D
RTh
Rg R3 R4
R1 R2
RTh
Ig
ETh = E0 = VAC (open circuit)
RTh = R1//R4 + R2//R3
Ig = E0/(RTh + Rg)
Eg = E0Rg/(RTh + Rg) In case of open-circuit (Rg) Eg = E0
The equivalent circuit
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Stress and strain
L
T
A
Tension: A bar of metal is subjected to a force (T) that will elongate its dimension along the long axis that is called the axial direction. Compression: the force acts in opposite direction and shortens the lengthA metal bar
Stress: the force per unit area a = T/A (N/m2)
Bar with tension
L
T
L+dL
dL
StrainStrain: The fractional change in lengtha = dL/L (m/m)
D
L T
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Hooke’s lawStress is linearly related to strain for elastic materials
a = a /Ey = (T/A)/Ey
Ey : modulus of elasticity ( Young’s modulus)
Elastic Region
Plastic Region
Strain (a)
Stress (a)
Elastic Limit
Breaking point
The stress-strain relationship
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Transverse strainThe tension that produces a strain in the axial direction causes another strain along the transverse axis (perpendicular to the axial axis) as
t = dD/D
This is related to the axial strain through a coefficient known as the Poisson’s ratio as
dD/D = - dL/L
The negative sign indicates that the action is in reverse direction, that is, as the length increases, the diameter decreases and vice versa. For most metals is around 0.3 in the elastic region and 0.5 in the plastic region
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Electrical Resistance of Gage Wire
D
L T
R=L/A
dAARdL
LRdRdR
dAALdL
Ad
ALdR 2
AdA
LdLd
RdR
A = r2 = (/4)D2 and dA/A = 2 dD/D yields dD/D = - dL/L
)21(
L
dLdR
dR
Piezoresistive effect Dimensional effect
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Principles of strain measurement dR/R
dL/L
metals semiconductors
Gage factor - K
K = (dR/R)/(dL/L) = (dR/R)/a
For wire type strain gages the dimensional effect will be dominant yielding K 2
For heavily doped semiconductor type gages the piezoreziztive effect is dominant yielding K that ranges between 50 and 200
dR can be replaced by the incremental change R in this linear region yielding R/R = Ka
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Bonded Strain-Gages
Backing Resistive Wires
Direction of strain
Con
nect
ing w
ires
T
Strain Gage
Beam
Solid (fixed) platform
A bonded gage Fixing the gage
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Examples of bonded gages
Resistance-wire type Foil type Helical-wire type
K 2.0
R0 = 120 or 350 . 600 and 700 gages are also available
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Semiconductor strain-gage units
Unbonded, uniformly doped
Diffused p-type gage
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Fixing the gage
T
Strain Gage
Beam
Solid (fixed) platform
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21
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Strain gage on a specimen
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The unbonded gage
Poles
Prestrained resistive wire
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Unbonded strain-gage pressure sensor
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Example 2A strain gage has a gage factor 2 and exposed to an axial strain of 300 m/m. The unstrained resistance is 350 . Find the percentage and absolute changes in the resistance.
a = 300 m/m = 0.3x10-3; R/R = Ka = 0.6x10-3 yielding %age change = 0.06% and R = 350x0.6x10-3 = 0.21 .
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Example 3A strain gage has an unstrained resistance of 1000 and gage factor of 80. The change in the resistance is 1 when it is exposed to a strain. Find the percentage change in the resistance, the percentage change in the length and the external strain (m/m).
R/R (%) = 0.1 %; L/L (%) = [R/R (%)]/K = 1.25x10-3%, and a = [L/L (%)]/100 = 1.25x10-5 = 12.5 m/m
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Wheatstone bridge for the pressure sensor
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Integrated pressure sensor
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Integrated cantilever-beam force sensor
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Elastic strain-gageMercury-in-rubber strain-gage plethysmography (volume-measuring) using a four-lead gage applied to human calf.
Venous-occlusion plethysmography
Arterial-pulse plethysmography
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Effect of Temperature and Strain in other Directions
)](1[ 00 TTRR R0 is the resistance at T0 and is the temperature coefficient
This is very much pronounced in case of semiconductor gages due to high temperature coefficient.
Effects of wanted strain (sw), unwanted strain (su) and temperature (T) add up in the change in resistance as
R = Rsw + Rsu + RT
The effect of unwanted strain and temperature must be eliminated before the resistance change is used to indicate the strain
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Bridge Configurations For Strain Gage Measurements
Solid platform
Cantilever
Strain gage
Q
W
Eb A
B
C
D
R1 R2
R3 R4 = Rx
Rg
Ig
The cantilever beam with a single strain-gage element
A quarter bridge
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Analysis of quarter-bridge circuit
)2(2))(()(
))((
2
3241
31420 RR
RE
RRRRRRRRR
ERRRR
RRRREE bbb
Let R1 = R2 = R3 = R and R4 = Rx = R + R = R(1 + R/R), and let x = R/R. The open circuit voltage E0 = 0 at balance (R = 0). At slight unbalance (R 0)
Let x = R/R )
21(4)2(20 x
xE
xx
EE bb
...42
1)2
1(2
1 xxx...)
42(
4
32
0 xxxEE b
Since x<<1, higher order terms can be neglected yielding R
REx
EE bb
440
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Sensitivity analysis can also be used
241
1
4
0
)(4 RRRE
RES bR
RRER
RRRESRE b
bR
4)( 240 4
Sensitivity analysis
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Effect of Temperature and Tensile Strain
• R = RQ + RW + RT • The effect of unwanted strain and temperature must be
eliminated. • The circuit as it is provides no compensation.• Using a second strain gage of the same type for R1 can
compensate effect of temperature. • This second gage can be placed at a silent location
within the sensor housing, hence kept at the same temperature as the first one.
• As a result, both R1 and R4 have the same amount of changes due to temperature that cancel each other in the equation yielding perfect temperature compensation
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Wheatstone Bridge with Strain Gages and Temperature Compensation
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Bridge with Two Active Elements
Cantilever
Strain gages
Q
W
The cantilever beam with two opposing strain gages
Eb A
B
C
D
R1 R-R R2
R3 R4
R+R
Rg
Ig
Circuit for the half-bridge
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Circuit analysis
Let R2 = R3 = R; R1 = R - R; R4 = R + R, the open circuit voltage E0 = 0 at balance (R = 0). At slight unbalance (R 0)
))(( 3241
31420 RRRR
RRRREE b
))(()()(RRRRRR
RRRRRREb
RRE
RRE b
b
24
2
Eb A
B
C
D
R1 R-R R2
R3 R4
R+R
Rg
Ig
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Insensitivity of half-bridge Wanted
strain Unwanted
strain Temperature
R4
R1
Effects of wanted and unwanted strains and temperature on measuring gages
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Bridge with Four Active Elements (Full Bridge)
The force, when applied in the direction shown, causes tension on gages at the top surface (R + RQ) and compression on gages at the bottom surface (R - RQ).
The tensile force W causes (R + RW) on all gages.
The temperature also produces (R + RT) on all gages.
Q
W R1
R2 R4
R3
The cantilever beam with four strain gages (full bridge)
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Eb A
B
C
D
R1 R-R
R4 R+R
Rg
Ig
R3 R-R
R2 R+R
• The strain gages that are working together are placed into opposite (non-neighboring) arms of the bridge.
• The strain gage resistors are manufactured for a perfect match to have the open circuit voltage E0 = 0 at balance (R = 0).
• At slight unbalance (R 0) with R1 = R3 = R - R; R2 = R4 = R + R
))(( 3241
31420 RRRR
RRRREE b
RRE
RRRRRRRRRRRRRRRRE bb
))(())(())((
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L = n2G, where
n= number of turns of coil
G = geometric form factor
= effective permeability
Self-inductance
Inductive sensors
Mutual inductance
Differential transformer
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LVDT transducer
(a)electric diagram and
(b)cross-section view
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LVDT
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Capacitive sensors +QQ
x Area = A
xAC r0
dv/dt
i
1
C +
Cv
i
(a ) (b )
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Capacitive displacement transducer
(a)single capacitance and (b)differentialcapacitance
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20 xA
xCKysensitivit r
xdx
CdC
orxC
dxdC
0
0
00
1
)(
)()(
xARRCwhere
j
jxE
jXjV
r
I
Capacitive sensor for measuring dynamic displacement changes
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Piezoelectric sensors
kfq k is piezoelectric constant C/N
Akfx
Ckfv
r 0
Kxq
K is proportionality constant C/m
RCs iidtdxK
dtdqi
Rv
xtdxK
dtdvCii
dtiC
vv
Rs
CC
00
0
)(
)1(
1)()(0
jjK
jXjV S
KS=K/C, V/m; = RC, s
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Response to step displacement
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High-frequency response
High-frequency circuit model for piezoelectric sensor. RS is the sensor leakage resistance and CS the capacitance. Lm, Cm and Rm represent the mechanical system.
Piezoelectric sensor frequency response.
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51
Quantum Tunneling Composites
(a) Structure (b) Effect of pressure
Structure and effect of pressure for QTC
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52
Effect of Pressure on a QTC Pill
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53
QTC as a Pressure Sensor