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Force Transducer: resistive - strain gauge
►Definition: A strain gage is a sensor whose resistance varies with applied force. It converts force,
pressure, tension, weight, etc., into a change in electrical resistance which can then be measured.
L+L
W-W F F
Hooke equation:
A
F
YL
L
1 Applied force
Cross section area of the material
Elasticity module of the material
Poisson relationship:
allongitudin
ltransversa
- v = 0,5 (the volume is constant under tension);
- Metals have v values ranging from 0,3 to 0,4;
- v<0,5 (the volume increases when stretched out but decreases when
compressed).
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
► How does it work? It is based in the fact that a conductor material under tension changes
its electrical resistance. Found by Lord Kelvin in 1856. It consists of an insulating flexible
backing which supports a metallic foil pattern 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 is related to the strain by the quantity known as the gauge factor.
►Characteristics:
High precision;
Low cost;
High linearity;
Excellent time response;
Easy installation;
Can be used immersed in water and in corrosive gases;
Can be used in telemetry;
Used for measuring weight, pressure, torque, strain,
displacement, compression, acceleration e vibration.
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►The resistance of a conductor is:
LD
R
2
4
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
K usually vaires from 1,7 to 2,2.
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►The resistance of a conductor is:
Considering :
By definition, then:
Device type Typical range of
rated capacities
Typical total
uncertainty
±% fso
Temperature sensitivity
% fso per °C
(operating range)
Strain gauge load
cells: semiconductor 1 N to 10 kN 0.2 to 1 0.2 to 0.5 (-40°C to +80°C)
Strain gauge load cells: thin film 0.1 N to 100 N 0.02 to 1 0.02 (-40°C to +80°C)
Strain gauge load cells: foil 5 N to 50 MN 0.02 to 1 0.0015 (-40°C to +80°C)
Piezoelectric crystal 1.5 mN to 120 MN 0.3 to 1 0.02 (-190°C to +200°C)
Hydraulic 500 N to 5 MN 0.25 to 5 0.02 to 0.1 (5°C to 40°C)
Pneumatic 10 N to 500 kN 0.1 to 2 0.02 to 0.1 (5°C to 40°C)
LVDT, capacitive, tuning-fork,
vibrating wire 10 mN to 1 MN 0.02 to 2 0.02 to 0.05 (-40°C to +80°C)
Magneto-elastic 2 kN to 50 MN 0.5 to 2 0.03 to 0.05 (-40°C to +80°C)
Gyroscopic** 50 N to 250 N 0.001 0.0001 (-10°C to +40°C)
Force balance** 0.25 N to 20 N 1 part in 106 0.0001 (-10°C to +40°C)
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
Force transducer types and their broad characteristics
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Types:
X-Y planar Rosette
Rosettes at 2 directions
Rosettes at 3 directons
Diaphragm
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
Base of the strain gauge
Terminal for welding the
bolding wire Grid - resistive
element (foil)
►Measuring techniques:
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Measuring techniques:
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Measuring techniques:
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Measuring techniques:
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Measuring techniques:
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Measuring techniques:
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Wheatstone bridge:
Gauge factor greater than 100 and a sensibility
50 times greater than the one made of metal foil
Force Transducer: resistive - strain gauge
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
Position Transducer: types
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
A position transducer is any device that permits position measurement. It can either be an absolute position or a
relative (displacement sensor). Position sensors can be linear, angular, or multi-axis.
• Capacitive transducer
• Capacitive displacement sensor
• Eddy-current sensor
• Ultrasonic sensor
• Grating sensor
• Hall effect sensor
• Inductive non-contact position sensors
• Laser Doppler Vibrometer (optical)
• Linear variable differential transformer (LVDT)
• Multi-axis displacement transducer
• Photodiode array
• Piezo-electric transducer (piezo-electric)
• Potentiometer
• Proximity sensor (optical)
• Rotary encoder (angular)
• Seismic displacement pick-up
• String potentiometer (also known as string pot., string encoder, cable position transducer)
►Definition: the resistance is varied by a sliding contact which can be related by a
translation or rotation.
Position Transducer: resistive - potentiometer
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Exemple: sensor de posição do carro que contém os cartuchos de tinta em impressoras jato de tinta
iV
Vlx 0
Position of the sliding contact
Length of the resistive wire
Input voltage
Measured voltage
Characteristics:
- Range = 10 a 106 Ohms;
- This depends on the length;
- lmáx of 1 meter;
- contact noise
Position Transducer: resistive - potentiometer
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Equations:
+
_ Vin Rp t
o
+
-
V0
t
o
p
po
in R
R
V
V
0
+
_ Vin Rp t
o
+
-
V0 Rm
Voltmeter
to
m
p
o
tin
R
RV
V
/1
10
Position Transducer: resistive - potentiometer
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Linearity:
Position Transducer: resistive - potentiometer
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Linearity:
Position Transducer: resistive - potentiometer
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Theory: are non-contact devices capable of high-resolution measurement of the position and/or
change of position of any conductive targets. They are also able to measure the thickness or density
of non-conductive materials.
►Equation:
h
AKkC
..
Capacitance (pF)
Proportionality constant
(=0,00885 for dimension in millimetres
Distance between plates
Sensor plate area (=D2/4)
Dielectric constant (K=1 if air)
Position Transducer: capacitive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
Shield
Sensor
Head
Electrostatic field
Target
►Equation:
If the distance between the sensor and the target by amount of h, then:
hh
AKkCC
hh
hh
C
C
1
/Non-linear equation
The solution is to measure the reactive impedance instead of a capacitance
C
jZC
CC
jZZ CC
1
and
Position Transducer: capacitive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Equation:
CC
CC
Z
Z
C
C
/1
/
Therefore:
h
h
Z
Z
C
C
The sensitivity of this type of sensor is given by:
AKkhCh
Z
h
ZS CC
11
Position Transducer: capacitive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Exemple of a measuring system:
Position Transducer: capacitive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
Preamplifier
Demodulator Filter Linearization
Circuit
Output
Amplifier
Voltage controlled
current source Oscillator
Power Supply
Gain
►Applications:
Position Transducer: capacitive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Linearity:
Position Transducer: capacitive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
Response voltage of a
capacitive displacement
sensor nearby its
resonance frequency
30.4 kHz using spacing
variation.
► Theory: The inductance of a wire depends on the number of turns, width of the winding or the area of the turn,
length of the winding and the permeability of the core.
Single layer coil with a cylindrical shape
KNr
L
22
Form factor
Position Transducer: inductive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Practical measuring techniques:
Varying the permeability of the core: it uses a moving ferromagnetic core within the
winding, or a section of the winding to the fixed one;
Varying the permeability of the medium: it uses metal detectors to detect the frequency
variation from a LC oscillator and the frequency deviation measured by a FM demodulator;
Measuring the position: it uses a mutual inductance. One coil moves to each other,
which increases the coupling and the AC signal measured by the second coill.
Position Transducer: inductive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Operational basics: it is based on the Eddy current induced on a conducting surface when the
magnetic flux lines are intercepted by it.
Position Transducer: inductive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
Inactive
coil
Active
coil
Displacement
Target
Impedance bridge
demodulator and the
high frequency power
supply
Output
Characterisitcs:
- The coils are connected in an impedance bridge;
- The bridge output is demodulated;
- The output signal is proportional to the distance from
the target;
- The sensor sensitivity depends on the material of the
target ;
- Low output variation due to temperature;
- The sensing operation depends on the coil diameter;
- The ratio gap/diameter is equal to 0.25;
- The frequency response is between 20 and 50 kHz.
Position Transducer: inductive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Operational basics:
Resistivity (Ω-cm)
No
rma
lize
d o
utp
ut
in r
es
pe
ct
to A
lun
iniu
m
Perfect conductor
Position Transducer: inductive
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Operational basics:
Magnetic materials
Non-magnetic materials
Platinum
Copper
Gold Magnesium
Tin
Aluminium Phosphorus
Brass
Nickel
Steel 1030
Steel 416
Graphite
Output for non-
magnetic materials
►Theory: É baseado na variação do acoplamento entre indutâncias, onde a saída é
proporcional ao deslocamento linear.
►Descrição: o movimento do
cilindro magnético ao longo do
núcleo sem contato, provoca a
mudança no fluxo magnético
que liga a bobina central e as
laterais.
Position Transducer: LVDT
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Esquema de ligação: as bobinas são ligadas em série e de fase oposta.
►Características:
-VS é uma excitação AC entre
50 Hz e 25 kHz;
-V0=0 quando o núcleo estiver
centrado entre as duas bobinas
laterais;
- O intervalo de operação
varia entre 2 a 150 mm,
dependendo da sensibilidade;
Position Transducer: LVDT
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Esquema de ligação: as bobinas são ligadas em série e de fase oposta.
►Características:
-VS é uma excitação AC entre
50 Hz e 25 kHz;
-V0=0 quando o núcleo estiver
centrado entre as duas bobinas
laterais;
- O intervalo de operação
varia entre 2 a 150 mm,
dependendo da sensibilidade;
Position Transducer: LVDT
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho
►Esquema de ligação: as bobinas são ligadas em série e de fase oposta.
►Circuito prático:
Oscilador 21
21
VV
VV
Filtro saída
-
Position Transducer: LVDT
POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING
Subject: Sensors & Transducers (4 credits)
Prof.: Dr. Pedro Bertemes Filho