Mechatronics 2 course Ain Shams University

1. Faculty of Engineering
Ain Shams University
Mohammed Ibrahim
3/31/2017 1
MDP: Mechatronics (2)
Lecture 07:
Sensors II

2. Potentiometers

3. Potentiometers
•Construction
Electromechanical device containing
– Conductive film (resistive element)
– Wiper
– Slider
(a) Potentiometer (b) Schematic diagram of the potentiometer

4. •Construction
Potentiometers

5. Potentiometers

6. Potentiometers
Vo
Vs
V=0 to VexRp
Rx
xmax x
Vo
X
Ideal
Actual
According to the slider position [against a fixed
resistive element] the resistive element is “divided” at
the point of wiper contact.
•Can be Linear or Rotary potentiometer

7. Linear Potentiometer
• Terminal A connected to the
supply voltage
• Terminal B connected to the
Ground
• X=L*(Vout / VSupply)
X: Travelled Distance
L: Total Length

8. Angular Potentiometer
Single turn Multi-Turns
• The Same Like Linear Potentiometer
• But Vout is a Function of the Angular Position
• ⊖= Ф *(Vout / VSupply)
⊖: Rotated angle, Ф: Total angle

9. Differential
Transformers

10. Linear Variable Differential
Transformer (LVDT)
 LDVT is a robust and precise
device which produce a
voltage output proportional
to the displacement of a
ferrous armature for
measurement of robot joints
or end-effectors. It is much
expensive but outperforms
the potentiometer
transducer.
Linear Variable Differential Transformer (LVDT)

11. LVDT
An inductor is basically a coil of wire
over a “core” (usually ferrous)
It responds to electric or magnetic
fields
A transformer is made of at
least two coils wound over the
core: one is primary and
another is secondary
Primary Secondary
Inductors and tranformers work only for ac signals
A
B
A
B
BAout VVV 

12. LVDT

13. Vo=V1-V2
Vi
V1 V2
V1 > V2
Vo
Vi
How does a LVDT work?
Core moves toward Sec1
Sec1 Voltage goes up
In-Phase with Input
voltage

14. Vi
Vo
Vo=V1-V2
Vi
V1 V2
V1 = V2
Core in central position
No difference output voltage
How does a LVDT work?

15. Vo=V1-V2
Vi
V1 V2
Vi
Vo
V2 > V1
How does a LVDT work?
Core moves toward Sec 2
Sec 2 Voltage goes up
out-Phase with Input
voltage

16. Signal conditioning Scheme
A signal conditioning circuit that removes these difficulties is shown in
Figure , where the absolute values of the two output voltages are
subtracted. Using this technique, both positive and negative variations
about the center position can be measured.

17. LVDT for Force Measurement
 Force transducers are often
based on displacement
principles. There various type
force and torque transducer
available commercially
A force-measuring device based on
a compression spring and LDVT.

18. Rotary Variable Differential
Transformer (RVDT)

19. Strain Gauge

20. Common usages of strain gauge
• Used standalone for
 testing
 diagnostic
 monitoring
But the most common usage is as primary
transducer in the creation of another transducer
Elastic
structure
Strain
Gauges
Force
Pressure
Displacement
Acceleration
Strain

21. Strain gauges: resistive principle
FF
Sensitive
element
Assumptions:
• Strain gauge perfectly
glued to the measured
surface
• Strain gauge electrically
insulated
• Planar deformation
state
A
L
R   • R  resistance of the sensor []
•   resistivity of the material [m]
• L  conducer length [m]
• A  conducer area [m2]

22. Common values:
• Nominal resistance: R  120 , 350 
nominal resistance production tolerance: ± 1%
• Base length: 0,6-200 mm
• Materials: Constantan (Cu-Ni alloy), Karma, Ni-Cr
alloy, semi-condutors...
base
Strain gauges: resistive principle

23. Measuringbase
longitudinal axis
transversal
axis
Pigtail
connections
terminals
support
grid
reference markings
Strain gauges: resistive principle
Measuring
direction

24. A
L
R  
The gauge resistance varies due to two different effects:
• Dimentional alteration (L, A) due to strain;
• Resistivity variation () due to volume alteration
(piezoresistive effect).
2
A
LdA
A
Ld
A
dL
dR


A
dAd
L
dL
R
dR



Strain gauges: resistive principle
ELASTIC
RANGE

25. ELONGATION PIEZORESISTIVITY
)/(
)/(
21
)/(
)/(
LdLLdL
RdR
GF




Common value: k=2 (for metallic alloys).
GAGE FACTOR
Strain gauges: resistive principle
2
22
2
V
dVL
V
dL
V
LdL
dR


L
dL
R
dR
2
00  ddV
V
L2
 
A
L
R  
2
)/(
)/(

LdL
RdR
GF
PLASTIC
RANGE

26. Strain gauges: resistive principle
 Calibration information
 Manufacturer provides “gage factor” or GF
 2.x typical
dL/L
dR/R
m=GF

27. Painting layers removal
Strain gauges application:

28. Application spot cleansing
Strain gauges application:

29. Strain gauge positioning
Strain gauges application:

30. Adhesive glue application
Strain gauges application:

31. Strain gauge application: BE CAREFUL! AVOID BENDING!
Strain gauges application:

32. Pressure application (the thinnest glue layer possible)
Strain gauges application:

33. Terminal welding
Strain gauges application:

34. Cables strain release fixing
Strain gauges application:

35. Protective layers application
Strain gauges application:

36.  fast acting glues:
(short duration measurement application)
• cyanacrilate:
• short time polymerization
• ambient temperature
 slow acting glues:
(long duration measurement application)
• epossidic glue:
• a catalyst is needed
• high temperature accelerates polymerization
• fenolic glue:
• high temperature
• high pressure
Adhesive used:

37. Strain-gage temperature
compensation

38. measure
1 2
3 4
5
I5
dummy
E
Temperature effect: DUMMY
GAGE

39. Wheatstone Bridge




















43
4
21
2
21
43
4
2
21
2
1
RR
R
e
RR
R
e
VVe
RR
R
eV
RR
R
eV
ii
o
ii
ei

40. Steel beam with E  210000 Mpa
Stress applied a=100 Mpa uniaxial
R=120  Gage factor (GF): k=2
Resistance variation:
R=0.114 
MEASURING R/R requires a workaround
a
a
 
E
m m4 762. /x10m / m = 476
-4
R
R
GF  9 5. x10
-4
1
Measuring resistance variation

41. VOLTAGEREADING
11 22
33 44
II55
EE
AA
BB
CC
DD
E
RR
R
VAB
21
1


E
RR
R
VAD
43
3


Wheatstone bridge: principle
  
E
RRRR
RRRR
V
4321
3241



Introducing resistance variations and assuming small
variation form the same nominal resistance we have:
0
4321
4R
RRRR
E
V 

ii RRR  0
ii RR 

42.  Opposing branches signals add themselves up
R1+R1
R4+R4
V
R2
R3
E
21
Wheatstone bridge: principle
0
41
4R
RR
E
V 

04
2
R
R
E
V 

If the signal is the same we
have:

43. R1+R1
R4
V
R2
R3+R3
E
22
 Adjacent branches signals are subtracted
Wheatstone bridge: principle
0
31
4R
RR
E
V 

0
E
V
If the signal is the same we
have:

44. R1, R2, R3, R4 having the same
nominal resistance
As a first step a balancing
resistance is introduced, whose
resistance can be altered until
the reading of the
UNSTRAINED configuration is
null
THIS allows for offset
compensation and makes the
actual brigde closer to satisfy
the assumptions made in the
model
Rbal
I5
1 2
3 4
E
Wheatstone bridge: principle

45. QUARTER BRIDGE
1 2
3 4
E
V
Wheatstone bridge: configuration

46. HALF BRIDGE
1 2
3 4
E
V
Wheatstone bridge: configuration

47. HALF BRIDGE
Wheatstone bridge: configuration

48. FULL BRIDGE
1 2
3 4
E
V
Wheatstone bridge: configuration

49. Connection cables resistance is not
compensated by the dummy (RL)
1 2
3
4
dummy
RL
RL
E
Wheatstone bridge: 2 wire
connection

50. 1
2
3
4
3 wires connection
and shielding
dummy
E
Wheatstone bridge: 3 wires
connection

51. 1 2
3 4
V+
V-
S+
S-
To be used with a
short connection cable
Wheatstone bridge: 4 wires
connection

52. 1 2
3 4
V+
V-
S+
S-
SENS+
SENS-
V
I  0
I  0
Wheatstone bridge: 6 wires
connection
Suitable for long
connection cables
AKA:
REMOTE
SENSING

53. Bridge calibration: offset nulling
1 2
3 4
E
V
Rbalance
As a first step any
discrepancy between
the actual resistance
and the nominal one
is balanced
introducing a variable
resistance between
two adjacent elements
and reading the
output.
The resistance is
changed until a null
reading of V is
reached.
OFFSET NULLING AND GAIN CALIBRATION CAN BE
PERFORMED ONLY WHEN ALL ELEMENTS ARE UNLOADED

54. Bridge calibration: gain calibration
1 2
3 4
E
V
Rcalibration
As a final step a calibrating
resistance is introduced in
parallel with one of the
elements, in order to create a
known resistance variation.
The reading of V as a result
of the calibration resistance
introduction is used to
compute a gain
compensation for the
measuring circuitry reading
V and nominal resistance
uncertainty.
1/R1=1/R0+1/Rcal V*=GV

55. Strain Gauges connection: bridge
1 2
3 4
E
V
Some likely assumption to make
calculation easier:
- ΔR/R is small
- All gage factors are equal
- All nominal resistances are
equal
-an equivalent strain is computed
by dividing the ratiometric output
by the common gage factor
V/E=(ΔR1+ΔR4-ΔR2-ΔR3)/R0
V/E=GF(ε1+ε4-ε2-ε3)
εT=(V/E)/GF=ε1+ε4-ε2-ε3
Δrj/R0=GFεj
1 2
3 4
V

56. Bridge configuration: traction and
bending
As cantilever beam is subject to
traction N, bending B, and to
temperature variation A.
Effects of torque are usually
negligible
Strain along the principal axis
on the upper side of the beam is
therefore:
εI=εN+εB+εA
While on the transversal axis
strain on the upper side will be
given by:
εII=-νεN-νεB+εA
On the lower sides the strains
become respectively:
εIII=εN-εB+εA
εT=(V/E)/GF=ε1+ε4-ε2-ε3
N
B
1 2
3 4
εI εII
εIII εIV
εIεII
I
εII
εIV

57. Strain Gauge configuration:
traction
Single strain gauge
Suitable only if:
•bending moment is
negligible
•temperature is constant or
autocompensated
ε1=εI=εN+εB+εA
ε2=0 ε3=0 ε4=0
εT=εN+εB+εA
N
B
1 2
3 4
QUARTER BRIDGE
1

58. Strain Gauge configuration:
traction
Orthogonal strain gauges
Compensates:
•Temperature
Is affected by:
•Bending moment
and amplifies sensitivity
ε1=εN+εB+εA
ε2=-νεN-νεB+εA
ε3=0
ε4=0
εT=(1+ν)εN+(1+ν)εB
N
B
1 2
3 4
HALF BRIDGE
1 2

59. Strain Gauge configuration:
traction
Temperature dummy gauge
Compensates:
•Temperature
Is affected by:
•bending moment
ε1=εI=εN+εB+εA
ε2=εA
ε3=0 ε4=0
εT=εN+εB
N
B
1 2
3 4
HALF BRIDGE
1
2

60. Strain Gauge configuration:
bending
Opposed faces
Compensates:
•Temperature
•Normal traction
and amplifies sensitivity
ε1=εN+εB+εA
ε2=εN-εB+εA
ε3=0
ε4=0
εT=2εB
N
B
1 2
3 4
HALF BRIDGE
1
2

61. Strain Gauge configuration:
bending
Orthogonal strain gauges
Compensates:
•Temperature
•Normal traction
and amplifies sensitivity
N
B
1 2
3 4
FULL BRIDGE
1 4
2 3

62. Questions
Questions
3/31/2017 62