The operating principle is based on the following … linear behaviour with d !! 7 0 0 0 0 1 2 0 0...
Transcript of The operating principle is based on the following … linear behaviour with d !! 7 0 0 0 0 1 2 0 0...
1
Inductive sensors
The operating principle is based on the
following relationship:
L=f(x)
M=g(x)
•High robusteness against influencing
quantities (environmental)
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Basics
N
i
h1
h2
fmm = Ni = magnetic flux x reluctance= F x R [A-spire]
NiF
R[Weber]
The magnetomotive force is:
L variation based Inductive Sensors
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N
i
h1
h2
R
NL
di
dNL
2
Where the reluctance is:
l: flux path
A: area of the section interested by the flux (path
cross section)
m0 : permeability in vacuum m0 = 4p x 10-7 Hm-1
mr : relative permeability
A
lR
rmm
0
L variation based Inductive Sensors
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•Usually the variation of N, l or m are used to
convert physical quantities into elctrical signal.
N variation
L variation based Inductive Sensors
R
NL
di
dNL
2
A
lR
rmm
0
µ variation
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Advantages:
•Robustness against environmental quantities
•Reduced load effects
•High responsivity
Drawbacks:
•Sensitivity to magnetic field: shielding;
•Side effects reduce the operating range.
•Must work below the Curie Temperature.
Materials:
•In Vacuum: low responsivity, high frequency
operation
•Ferromagnetic core: high responsivity, low
frequency operation (<20kHz).
L variation based Inductive Sensors
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d air gap
N
i
h1
h’’2
Aμ
d
Aμμ
h
Aμμ
h
A
l
μA
l
μR
rr 00
2
0
1
0
0
0
22211
h’2
h2=h’2+h’’2
L variation based Inductive Sensors
Reluctance variation
A
lR
rmm
0
R
NL
di
dNL
2
7 Non linear behaviour with d !!
0
0
00
210
0
con )1(
222
R
kdxxRR
Aμk,
Aμμ
hhR
kdRR
r
0
2
0
0
0
22
eing
1)1(
R
NLb
x
L
xR
N
R
NL
L variation based Inductive Sensors
Reluctance variation
R0 takes into account
flux path through the coil
and not through the air!
Aμ
d
Aμμ
h
Aμμ
h
A
l
μA
l
μR
rr 00
2
0
1
0
0
0
22211
dair gap
N
i
h1
h’’2
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L variation based Inductive Sensors
Reluctance variation in differential configuration
0
02
00r
210
02
R
)xd(ky con )y1(RR
Aμ
2k,
Aμμ
h2h2R
)xd(kRR
0
2
20
20
0
2
2
2
2
R
NL eingb
y1
L
)y1(R
N
R
NL
0
2
10
10
0
2
1
2
1
R
NL eingb
y1
L
)y1(R
N
R
NL
Standard advantages coming from the differential configuration
(influencing quantities compensation, high responsivity, ….)
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Linear Variable Transducer
The core movement produces L1 and L2
variations which are then converted by suitable
bridges.
L variation based Inductive Sensors
m variation
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A primary coil and two secondary coils.
Linear Variable Differential Transformers
(LVDT)
The mutual inductance changes as a function
of the core position.
Core movement
M variation based Inductive Sensors
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•Primary coil: sinusoidal excitation signal,
frequency ranging between [60 Hz and
20.000 Hz]
•The amplitude of the induced voltage on
the secondary coils depends on the core position.
eo
1
eo
2
eex
x
i
eo
1
eo
2
eex
LVDT
M variation based Inductive Sensors
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LVDT
e01
e02
eexc
M variation based Inductive Sensors
NULL POSITION
e02
e01
eexc
In case the core is above the null position Max(e01)>Max(e02)
In case the core is below the null position Max(e02)>Max(e01)
This configuration allows for estimating the core position
by separately processing signals from the two coils!
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LVDT
Secondary coils in differential configuration
e0 eexc
M variation based Inductive Sensors
Advantages coming from the
differential configuration:
•influencing quantities compensation;
•high responsivity;
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LVDT
e01
e02
e0
e0
M variation based Inductive Sensors
How do extract from e0 the core position?
CORE ABOVE NULL
CORE BELOW NULL
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LVDT Modelling:
eex es1
es2
Ls/2
Ls/2
Rm
Rs/2
Rs/2
Rp
Lp
M1
M2
ip
is
M3 eo
2 1
3 2 1
3 2 1
02 2 2 2
0
ex p p p s
o m s
s s s sm s s p
s m s s s p
e i R sL i sM sM
e R i
R R L LR i s s sM i sM sM i
R R i s L M i s M M i
M variation based Inductive Sensors
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LVDT
eex
es1
es2
Ls/2
Ls/2
Rm
Rs/2
Rs/2
Rp
Lp
M1
M2
ip
is
M3 eo
Supposing Ls-M3 independent on
the core position, and assuming:
L2=Ls-M3
2 1
22
2 1 2 2
mo
ex p p p s p m p s m
s M M Re
e s M M L L s L R L R L R R R R
Assuming: 2
2 2 1pL L M M
2 1
2
2 2
mo
ex p p p s p m p s m
s M M Re
e s L L s L R L R L R R R R
-
M variation based Inductive Sensors
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The critical frequency nulling the phase lag is:
2
1
22
1
p
p
msp
cLL
)RR(Rf
2
210
LRL)RR(
)MM(R
e
e
ppms
m
ex
In this condition:
It can be demonstrated that under this condition the device
shows the maximum sensitivity.
If M1-M2=kx:
eo=eexk’’x
M variation based Inductive Sensors
2 1
2
2 2
mo
ex p p p s p m p s m
s M M Re
e s L L s L R L R L R R R R
-
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LVDT
As it can be observed the amplitude of eo
does NOT give information on the
displacement direction.
e0
eo=eexk’’x
M variation based Inductive Sensors
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LVDT
In case of a time changing displacement x:
the sensor output is a sinusoidal signal (driving signal) modulated by x.
M variation based Inductive Sensors
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LVDT
A rough demodulation producing the
output signal envelope:
• will give information on the
displacement amplitude;
•will NOT give information on the
displacement direction.
M variation based Inductive Sensors
Two different x(t) produces similar outputs!!!
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The mean value of e0 allows to estimate the
absolute position of the core.
A phase sensitive demodulation will produce
information on both the amplitude and the
direction of the displacement.
M variation based Inductive Sensors
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LVDT
A phase sensitive demodulation will produce
information on both the amplitude and the
direction of the displacement.
.
M variation based Inductive Sensors
Demodulating AM signals
Many sensors show an output signal which is
given by:
e0(t)=keexc(t)x(t)
Where:
k is a gain
eexc(t) is the excitation signal (carrier)
x(t) is the unknown quantity (modulating signal)
Es.: LVDT, ac bridges, etc;
eexc e0
x
e0 is a suppressed carrier AM signal!
AM modulation
Full carrier:
In this case the
modulated signal is
always phase locked to
the carrier independently
on the sign of the
modulating signal.
Suppressed carrier:
In this case the
modulated signal and the
carrier:
are in phase if the
modulating signal is
positive;
are in counterphase if the
modulating signal is
negative.
tcostcosAkV
e
)tcos(Ax
)tcos(Ve
ss
s
exc
000
0
00
2
e0(t)=keexc(t)x(t)
suppressed Carrier
AM modulation
In case of a LVDT in differential configuration:
e0(t)=keexc(t)x(t)
• The magnitude of e0 gives information on the core
displacement while its position as respect to “null”
(direction) cannot be estimated.
• The phase lag between e0 and eexc can produce
information on the displacement direction.
eexc
e0
e0
e0
eex es1
es2
Ls/2
Ls/2
Rm
Rs/2
Rs/2
Rp
Lp
M1
M2
ip
is
M3 eo
The Asynchronous demodulation will not produce
information on the displacement direction!
Carrier suppressed AM modulation
e0(t)
eref(t)
ed(t) em(t)
Synchronous demodulation
tcostcostcosAVkV
)tcos(tcostcosAVkV
e
tcostcosAkV
e
)tcos(Ve
sssr
ssr
m
ss
rref
00
0000
000
0
0
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2
2
Two steps:
A low pass filter is required to
eliminate 20+s component.
Carrier suppressed AM modulation
1
2
Differential LVDT output
Asynchronous
demodulation
Snchronous
demodulation
Carrier
X(t)
Modulated
signal
Modulated
signal
The Synchronous demodulation can
be implemented by a
CARRIER AMPLIFIER
Carrier suppressed AM modulation
Dedicated electronics must be used to detect
the displacement direction!
Datasheet AD598
…LVDT conditioning …
Demodulating AM signals
…another example…
The PO2211 is a differential microcoil inductive
sensor to measure the speed or position of a
gear PO2211 datasheet
Demodulating AM signals
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Advantages:
•Good resolution;
•Friction free operation;
•MTBF =2x106 h=228 years);
•Elctrical insulation between primary and secondary coils;
•Linearity and responsivity;
•High dynamic range.
Operating range 100mm;
25cm.
Power supply 1V, 24V;
50Hz, 20kHz.
Responsivity
(normalized to
power supply
voltage)
0.1V/cm;
40V/ mm.
Resolution Up to 0.1 mm
LVDT
M variation based Inductive Sensors
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LVDT
Behavior of the output signal as a function of the core position
M variation based Inductive Sensors
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Drawbacks
•Offset voltage in the null position due to
parasitic capacitance
•3° armonic distorsion due to the
ferromagnetic core saturation;
•Self heating of R.
LVDT
M variation based Inductive Sensors