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INDUCTIVE TRANSDUCERS
Lecture 12Instructor : Dr Alivelu M Parimi
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OUTLINE
• LVDT, Synchros, Variable reluctance, eddy current
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INTRODUCTION
• When a current passes through a coil it produces a magnetic
field around and through the coil.
• A changing current will produce a changing magnetic field.
When a coil is in changing magnetic field, electromagnetic
induction occurs and an emf is induced in the coil.• Inductive transducers are those in which the self inductance of
a coil or the mutual inductance of a pair of coil is altered due
to variation in the value of measurand.
•
Change in inductance ∆L is MEASURED and is related tomeasurand
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TYPES OF INDUCTIVE
TRANSDUCERS
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The self inductance of a coil refers to the flux linkage within the coil due to current in the
same coil. Self Inductance L of a coil is given by
l
A 2
N L
Where N= no of turns of the coil
A = area of cross section of the coil
l = length of each turn of the coil
r 0 ,
0 = air = permeability of free space = 4 x 710
m
H (or
2A
N)
r = relative permeability, is the ratio of permeability of a specific medium to permeability
of free space (air)
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• Mutual inductance refers to the flux linkages in a coil due to
current in adjacent coil
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TYPES OF INDUCTIVE
TRANSDUCERS
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LINEAR VARIABLE DIFFERENTIAL
TRANSDUCER (LVDT)
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LVDT is one of the most commonly used inductive transducer used for displacementmeasurement. It can measure movements ±25 cm down to ±1 mm, is also capable of
measuring positions up to ±20 inches (±0.5 m). The typical range for LVDT sensitivity is 0.4
to 2.0)10)(( 3
cmV
mV
. Generally higher frequency results in higher sensitivity.
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LVDT
• There is one primary winding connected to an ac source (5-15
V, 50 Hz – 20 kHz). Core is made of high permeability soft iron
or nickel iron. Two secondary windings are connected in series
opposition. The voltages induced in SW1 and SW2 depend on
magnetic coupling between the core and the coils. Indifferential output configuration, transducer is so designed
that the effect of measurand in one part produces positive ∆L
and negative ∆L in another part. Difference of the effects is
taken ( 2∆L), giving the increased output.
• There are certain advantages gained by differentialarrangement such as increased sensitivity and accuracy and
the effects of interfering inputs like temperature changes,
variation in supply voltage and frequency getting cancelled 7
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LVDT
• Geometric centre of coil arrangement is called the NULL position.
• In null position the core is equally inside both secondary and thisposition is called the Null position.
• At null position the coupling between the primary and secondary isequal.
• The currents flowing in each of the secondary coil are equal. Sincethe secondary windings are connected in series opposition, so ifsecondary winding currents are equal, they will exactly cancel eachother and zero ac voltage (Null voltage) will appear.
• The output voltage at the null position is ideally zero but harmonics
in the excitation voltage, manufacturing defects and straycapacitance coupling between the primary and the secondaryusually result in a small non zero voltage called Null voltage.
• Under usual conditions this is less than 1 percent of the full scaleoutput voltage and may be quite acceptable. 8
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LVDT• When core is moved is moved to right/left, the coupling
between primary and one secondary increases while coupling
for the other decreases and the magnitude of output voltage
is proportional to the amount of core displacement,
• while the phase of the output voltage is determined by the
direction of the displacement. As can be seen form figure asthe core moves form left to right, output undergoes phase
difference of 180 degrees.
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LVDT
• For core variations near the centre of coil arrangement, the
output is very nearly linear. Linear range is clearly specified
and while LVDT is operating in linear range, it is called LVDT.
• Usually the AC output voltage is seen on CRO. But for further
processing and transmission it need to be converted bysuitable electronic circuitry to high level DC voltage or current
that is more convenient to display/store/transmit/progress..
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LVDT
• For a fixed constant core displacement, waveform seen at
output on CRO is sinusoidal whose peak to peak value can be
calibrated against core displacement. If the core movement is
varying with time, modulated waveform will be seen of CRO,
requiring demodulation and filtering to get output voltagewaveform similar to displacement waveform
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LVDT• LVDT signal conditioners available commercially generate a sine wave
for the primary coil and synchronously demodulate the secondary
output signal, so that the DC voltage that results is proportional to coredisplacement.
• The sign of the DC voltage indicates whether the displacement is to theleft or right.
• The signal conditioning for LVDTs consists primarily of circuits thatperform a phase-sensitive detection of the differential secondaryvoltage.
• A typical signal conditioner for LVDT provides
• Power supply
• Frequency generator to drive LVDT
• Demodulator to convert ac to dc
• DC amplifier to amplify the final output signal
•
LVDT that operates from battery or regulated power supply is calledDCDT (Direct Current Differential Transducers) or DC-LVDT
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RVDT (Rotational Variable
Differential Transducer) • The rotational variable differential transformer (RVDT) shown
in Figure is used to measure rotational angles and operates
under the same principles as the LVDT sensor.
• The LVDT uses a cylindrical iron core, while the RVDT uses a
rotary ferromagnetic core. The operation of a RVDT is similarto that of an LVDT.
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RVDT
• At the null position of the core, the output voltage ofsecondary windings S1 and S2 are equal in opposition.
• Therefore the net output is zero.
• Any angular displacement from the null position will result in a
differential voltage output.• The greater this angular displacement, the greater will be the
differential output.
• Hence the response is linear.
• Clockwise rotation produces an increase in voltage of a
secondary winding of one phase while counter-clockwiserotation produces an increasing voltage of opposite phase.
• Hence, the amount of angular displacement and its directionmay be ascertained from the magnitude and phase of theoutput voltage of the transducer.
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Problem
• The output of an LVDT is connected to a 5 V voltmeter through
an amplifier whose amplification factor is 300. An output of
1.5 mV appears across the terminals of the LVDT when the
core moves through a distance of 0.5 mm. Calculate the
sensitivity of the LVDT and that of the instrument. The scale ofthe 5V voltmeter has 100 divisions. The scale can read to 1/5
of a division. Calculate the resolution of the instrument in
mm.
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Problem
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A steel cantilever is 0.25 m long, 25 mm wide and 5 mm thick
(a) Calculate the value of deflection at the free end for the cantilever when a force o
30 N is applied at this end. Modulus of elasticity of steel is 200 GN/m²
(b)
An LVDT with a sensitivity of 0.5 V/mm is used. The voltage is read on a 10 Vvoltmeter having 100 divisions. (2/10)
th of a division can be read with certainty.
Calculate the overall sensitivity ( N
V) of the system and the resolution of the
instrument (in Volts).
(c)
Calculate the minimum and the maximum values of force that can be measured
with this arrangement.
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Problem
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The equivalent electrical circuit of LVDT is shown in Figure E5.3. Find the transfer function
exe
e0 and phase variation from low to high frequencies when (i) When voltmeter having
infinite resistance is present (ii) When voltmeter having resistance R M is present..
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Variable inductance
transducers• The device consists of an arm that moves linearly according to the
displacement produced. Thus, reluctance ‘R’ will be produced due tothe flux path. The coil inductance of the device can be written by theequation, L= N2 /R.
• A linear movement of the arm to the right decreases the reluctance‘R’ of the flux path. Thus, according to the equation given above, the
inductance increases due to the decrease in reluctance and viceversa.
• This inductance ‘L’ can be calculated or recorded with the help of aninductance bridge or through a recorder. Thus the measure of thedisplacement of the arm can be obtained from the correspondingchange in inductance.
If the transducer is connected to the input of an oscillator tankcircuit, the change in frequency ‘f’ of the oscillator could be taken asthe measurement for the corresponding change in the displacementof the arm. A displacement of the arm changes the inductance andhence the frequency. Thus, the output can be measured in terms ofinductance and frequency.
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Variable Reluctance
transducer
21(b)
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Variable Reluctance
transducer• Due to the movement of the primary mover, the shaft moves
which has one protrusion of permanent magnet. For every
one revolution there will be one spike due to voltage induced
in the coil, which by proper signal conditioning would be
converted into a pulse. This is the principle behind non-contact variable reluctance transducer for speed
measurement.
• Figure (b) shows a rack having number of teeth made of
permanent magnet. The rate of pulses per minute would give
an indication of linear speed.
• On the shaft a gear made of permanent magnet can also be
mounted, knowing the number of teeth and counting number
of pulses in fixed time period will also give rpm of shaft.22
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Inductive transducer using
Eddy Currents • Figure depicts inductive transducer using Eddy Currents.
• An electric current called Eddy current is induced within the body of aconductor when that conductor either moves through a non uniformmagnetic field or is in a region where there is a change in magnetic
flux.
• When a conducting plate is placed near a coil carrying alternatingcurrent, eddy currents are produced in the conducting plate.
• Nearer the plate to coil, higher are the eddy currents and higher thereduction in inductance of the coil.
• Meter reading can be calibrated in terms of movement of plate.
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Synchros
• A synchro is an electromagnetic transducer commonly used to
convert an angular position of a shaft into an electrical signal.
• It is commonly known as a Selsyn or an autosyn.
• It is infact bidirectional transducer converting angular
displacement into an ac voltage and vice versa an ac voltageinto an angular displacement.
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Synchros
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The basic synchro unit is usually called asynchro transmitter. Its construction is similar
to that of a three-phase alternator.
The stator (stationary member) is of laminated
silicon steel and is slotted to accommodate a
balanced three-phase winding which is usuallyof concentric coil type (three identical coils are
placed in the stator with their axis 120° apart)
and is Y-connected.
The rotor is of dumb-bell construction and is
wound with a concentric coil
An ac voltage is applied to the rotor winding
through slip rings.
This voltage produces a magnetizing
current and voltages are induced in
three stator windings
Since the voltages in each stator
winding are produced by transformer
action, the three stator voltages may
have different values (as they link
with different values of flux) but theyare in time phase with each other.
Thus, the rotor acts as the primary
winding of a single phase transformer
and the three stator windings act as
secondary windings
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Synchros
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Let n3sn2sn1s VandV,V respectively be the voltages induced in the stator windings S1, S2, and
S3 with respect to neutral n. Then, for the rotor position of the synchro transmitter shown in
Figure 5.8. The rotor axis makes an angle θR with respect to axis of stator winding S2.
Vs1n = k Vr sin ωct cos (θR +120)
Vs2n = k Vr sin ωct cos θR
Vs3n = k Vr sin ωct cos (θR +240)
The three terminal voltages of the stator windings are:
Vs1s2 = vs1n - vs2n = √3K Vr sin(θR +240) sin ωct
Vs2s3 = vs2n -vs3n = √ 3 K Vr sin(θR +120) sin ωct
Vs3s1 = vs3n -vs1n = √3K Vr sin θR sin ωct
This position of the rotor is
defined as Electrical Zero of
the transmitter and is used asreference for specifying
angular position of the rotor.
Vs3s1 can be calibrated in terms
of rotor movement.
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Synchros
• Study
• Synchro Error Detector used in Position Control Mechanism
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