Download LINEAR VARIABLE DIFFERENTIAL TRANSFORMERS

LINEAR VARIABLE DIFFERENTIAL
TRANSFORMERS
WHITE PAPER BY
KAVLICO CORPORATION
KAVLICO PROPRIETARY
June 1997
Revised: May 2000
Kavlico Proprietary
DESCRIPTION........................................................................................................................... 2
Excitation................................................................................................................................... 2
Output ....................................................................................................................................... 3
Resolution.................................................................................................................................. 3
Repeatability............................................................................................................................... 3
Construction ............................................................................................................................... 3
Temperature Range....................................................................................................................... 3
Mechanical Design ....................................................................................................................... 4
Length ....................................................................................................................................... 4
Typical Armature Length............................................................................................................... 4
Diameter................................................................................................................................. 4
Measurement Range ..................................................................................................................... 5
Configurations ............................................................................................................................ 5
LVDT CHARACTERISTICS ........................................................................................................ 6
FAULT DETECTION ................................................................................................................ 11
DIFFERENCE OVER SUM OUTPUT.......................................................................................... 12
NOMINAL VALUES.............................................................................................................. 13
LVDT ENVELOPE REQUIREMENTS ......................................................................................... 14
COST CONSIDERATIONS ........................................................................................................ 14
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DESCRIPTION
The Linear Variable Differential Transformer (LVDT) is a Displacement Transducer that
produces an electrical signal proportional to the displacement of a moveable core (armature)
within a cylindrical transformer.
The transformer consists of a primary and two secondary windings, coaxial wound, with each
secondary located on opposite ends. The nickel-iron armature is positioned within the coil
assembly providing a path for magnetic flux linking the primary coil to the secondary coils.
When the primary coil is energized with an alternating current, a cylindrical flux field is
produced over the length of the armature. This flux field produces a voltage in each of the two
secondary coils as a function of the armature position.
For the longer strokes, the primary winding is designed to maintain a flux field that is a
constant magnitude for any position within the linear range. A change in the position of the
armature will then move the flux field into one secondary and out of the other. This results in
an increase in the voltage induced in one secondary and a corresponding decrease in the other.
The secondary coils are normally connected in series with opposing phase. The net output of
the LVDT is the difference between the two secondary voltages. When the armature is
symmetrically positioned relative to the two secondary coils the differential output is
approximately zero, since the voltage in each secondary is equal but opposite in their phase
relationship (see Null Voltage).
There are several coil configurations that are used for LVDT’s. The very short strokes require
a high sensitivity to produce a reasonable output. They are normally wound with the primary
coil located between the secondary coils with the armature extending into each secondary
(commonly known as three coils design). This configuration has the highest sensitivity, the
lowest phase shift, and a low temperature coefficient of the sensitivity. It should be pointed
out that the individual secondary voltages of this configuration contain an X2 term, where X
is the displacement, and they are inherently non-linear. The differential output is very linear
(the squared terms subtract out) but the sum is not linear. For three coil designs, if the stroke
is larger than ±0.025 inches a difference over sum output is not recommended. The coil
configuration used on older four-wire LVDT designs with strokes longer than 0.25 inches
have a primary winding which is wound across the entire length with each secondary starting
in the center and ramping up to the end. This produced a linear differential output but if the
center tap was brought out, it was usually obvious that the sum was not linear. The computer
controlled winding machines allowed ramping the secondary coils from one end to the other
with a linear output that provides a constant sum.
Excitation
An LVDT requires an AC voltage for operation. Aircraft power or low impedance AC source
specifically designed for the LVDT normally supplies this excitation. In today’s aerospace
and aircraft industry, multi-channels with individual excitation sources are often used to
obtain the highest possible system reliability.
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Output
The output voltage of an LVDT is proportional to the voltage applied to the primary. To
avoid problems of excitation tolerances the output should always be stated in volts/volt.
System accuracy will depend on providing a constant input voltage to the primary or
compensating for variations of the input by using ratio techniques. The output can be taken
as the differential voltage, or with a center tap, as two separate secondary voltages whose
difference is a function of the displacement. If the Sum of the secondary voltages is designed
to be a specific ratio of the difference voltage, overall accuracy can be significantly improved
using the (V1-V2)/(V1+V2) ratio as the output. (See Difference Over Sum Output). Figure 1
shows the AC input; and Figure 2 the two secondary output voltage waveforms as seen on an
oscilloscope. The Va secondary phase is shown referenced to the center of the coil and Vb
shown referenced to the end of the two secondary coils with the phase shift of Va at 2.5o and
Vb at 2.7o.
Resolution
Resolution of an LVDT is the smallest change in armature position that can be detected as a
change in the output. Sub-micro-inch resolution is not uncommon with LVDT’s. In practice,
the resolution is usually less than the noise threshold of external circuitry or resolution of the
equipment used to measure the output.
Repeatability
Repeatability of an LVDT is defined as the ability to reproduce the same output for repeated
exact positioning of the armature under the same operating conditions. The armature
displacement mechanism and test equipment normally limits the ability to measure the
repeatability of an LVDT.
Construction
Nearly all LVDT’s designed for aircraft or missile applications are wound on an insulated
stainless steel spool, magnetically shielded, and enclosed in a stainless steel housing using
welded construction. The armature is normally made from a 50% Nickel Iron alloy and brazed
to a stainless steel extension. Secondary leads are usually shielded to minimize channel to
channel crosstalk for multi channel units (See Crosstalk) and to keep RF energy from getting
into the signal conditioner. An LVDT does not contain electronic components and it is
unaffected by RF energy, making the LVDT nearly immune to EMI, EMP and lighting.
Temperature Range
The operating temperature range determines processes and materials used for construction.
LVDTs have been designed for operation from cryogenic temperatures of -440°F and to
operation submerged in liquefied metal (+1100°F). Construction and assembly for these
extreme conditions require very special materials and processes that assure complimentary
coefficients of expansion while maintaining good electrical and magnetic properties. Kavlico’s
standard construction provides operational temperature ranges from -65°F to +350°F. High
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temperature solder and special potting materials can extend this range from less than -80°F to
over 450°F.
Mechanical Design
The length and diameter of an LVDT must be sufficient to mechanically allow adequate
winding space to achieve the electrical performance:
¾ To meet pressure requirements
¾ To withstand the shock, vibration and static acceleration environments.
Where physical size is limited, electrical performance must be flexible. Although the LVDT is
basically a simple device, the operating characteristics and electrical parameters are complex
and depend to a large extent on the physical limitations.
Length
The minimum length of a coil housing for most aerospace applications can be estimated as
follows:
It will require approximately 0.5 to l.5 inches for the sum of the front and rear weld washers
plus possible lead connections. Small housing diameters (less than 0.5 inches), large lead wires
(larger than 26 AWG) or high pressures may require the longer length for lead connection
and/or support of a high pressure. Add the total electrical stroke and the length of the
armature and you have the housing length.
The length of the armature ranges from 0.6 inches, to up to twice the length of the electrical
stroke, depending on the frequency of the excitation and the actual stroke. Table 1 gives a
typical armature length for good performance at an excitation between 1800 to 3500 Hertz.
Additional housing length may be needed for mounting flanges, connectors, fluid passages,
cable routing or seal grooves which limit the coil length.
Typical Armature Length
Electrical
Stroke
(Inches)
Armature
Length
(Inches)
0.10 (+0.05)
0.50 (+0.25)
1.00 (+0.50)
2.00 (+1.00)
3.00 (+1.50)
4.00 (+2.00)
5.00 (+2.50)
7.00 (+3.50)
10.00 (+5.00)
14.00 (+7.00)
Table 1
Diameter
4
0.67
1.00
1.50
2.20
2.60
3.00
3.20
3.50
3.75
4.00
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The minimum diameter of the transformer housing will depend on electrical performance
criteria for the excitation frequency being used and housing wall thickness required to support
a pressure requirement.
Armature diameters less than 0.110 inches are easily damaged and are not recommended. The
armature extension should be slightly larger than the armature in diameter to protect the
armature from rubbing the bore. Ideally, the armature should have a short guide on the free
end that is the same diameter as the extension.
To determine the inside diameter of the spool tube, add the extension diameter and the
clearance to the tube. This diametrical clearance should be 0.010 inches minimum to 0.025
inches maximum. The wall of the spool tube should be at least 0.006 inches thick but must be
thick enough to contain any pressure requirement. It should be kept in mind that the tube
material and wall thickness does affect the performance.
The finished coil assembly diameter is determined by adding insulation to the spool tube,
winding the primary coil, insulating the coil, winding the secondary coils, insulating the
secondary, routing the magnet wire for lead connections, insulating the entire coil and
installing the shields. Typical coil assembly diameters for operating frequencies between 1800
and 3500 Hertz are 0.420 inches. A typical assembly for 400 Hertz would be 0.625 diameter.
This coil assembly must be installed in the housing that could have a wall thickness from
0.015 to 0.070 inches depending on the physical length, pressure and environment.
Measurement Range
The Full Scale or span is the displacement range of the LVDT’s armature for which the
electrical performance is required and is referred to as the Electrical Stroke. Since an LVDT
is inherently a center null device (zero output occurs at mid-stroke), the range or stroke is
normally specified as a plus and minus displacement from the null position. This does not
yield a 200% stroke or a 200% output. The Full Scale (100% of the stroke) being the total
end to end stroke and the Full Scale Output (100% of the output) the total end to end output
voltage. It is a common error to use the output at the end of the stroke as the Full Scale
Output.
Special winding placement of each secondary or the addition of a bias winding can reposition
the null to an off-center position. A bias winding is wound to produce a constant voltage over
the stroke and is added in series with the secondary coils to produce the required offset. The
full scale (span) is still the end to end stroke and full scale output is still the end to end
output. The null output of an LVDT has no sensitivity error and is the point in the stroke
with the highest overall accuracy. Sensitivity errors due to frequency variations, load effects
and temperature, have little effect on the null position.
Configurations
The Four Wire LVDT or Two Wire Output. A differential output only requires two
secondary wires and can be used directly in AC servo systems or synchronously
demodulated to a ±DC voltage.
The Five Wire LVDT or Three Wire Output. More elaborate signal conditioners use a
three wire secondary connection and use the two secondary voltages relative to a common
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connection. This arrangement facilitates fault detection and/or a difference over sum ratio.
(See Fault Detection or Difference over Sum Output)
The Six Wire LVDT. Performs the same as the five-wire unit but allows a differential
interface to each secondary to avoid shielding by using the common mode rejection.
Multiple LVDT’s. Where system reliability requires more than one output signal for
redundancy, up to four independent LVDT’s can be packaged in a single transducer
assembly. Coil placement may be in series (Tandem), or grouped side by side as a (Parallel)
cluster, see Figure 4. Multiple LVDT’s in one housing require less space, weight, and
installation time and are lower cost than purchasing quantities of single LVDT’s. Multiple
channels do present several new problems that must be considered. (See Tracking, Null
Difference and Crosstalk)
LVDT CHARACTERISTICS
Due to the principle of operation and the application of an LVDT, the parameters can
become very complex. The following requirements should be defined in a specification to
permit an optimum design for coil size and housing dimensions.
Electrical Stroke is the displacement range over which the specified performance and all
electrical parameters will be valid.
Mechanical Stroke is the guaranteed minimum physical stroke. Many LVDT’s will have
physical limitations for the actual Mechanical Stroke. When the displacement exceeds the
electrical stroke, the performance will be degraded. If specific output requirements for an
over-stroke are needed, these requirements should be specified to insure proper design since
these requirements could affect the physical length of the LVDT.
Excitation Voltage is the electrical potential intended to excite the transformer. This
voltage requires definition of amplitude, function, and frequency. An LVDT can be designed
for operation at less than 1 volt RMS to over l00 volts RMS. Normal excitation voltages for
missile or aircraft applications range from 3 to 26 volts RMS. Kavlico does not recommend
mixing RMS, Peak, or Peak to Peak specification requirements.
Excitation Frequency The best overall size and performance is obtained using excitation
frequencies in the range of 1800 to 3500 hertz. An LVDT can be designed for operation at
any frequency between 50 and l0, 000 hertz, but physical size or performance may be
compromised at the extremes.
The primary impedance of an LVDT is quite complex and must be designed for a specific
frequency when low phase shift and high accuracy are desired. The range of frequencies over
which an LVDT will operate with low phase shift and good accuracy is highly dependent on
its physical size, coil geometry, displacement range and sensitivity. To achieve the best
overall performance, it is recommended that the range of the excitation frequency be kept as
low as possible. When multiple channels are used with different frequencies, a specific
frequency with a reasonable tolerance should be assigned to each channel.
Excitation Waveform It is recommended that only sine excitation is used for LVDT’s.
Both triangular and square waves contain several odd harmonics of significant magnitude.
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Phase shift of harmonics through an LVDT will be a similar multiple of the phase shift for the
fundamental frequency.
The geometry necessary for an LVDT design can produce significant primary to secondary
capacitance and the high harmonics of a square wave will produce large leading and trailing
spikes on the output signal. The secondary circuit of an LVDT is slightly inductive and when
using square wave excitation, shunt capacitance across the secondary, both inter-winding as
well as load capacitance, will lower the self resonance of the secondary circuit, which will
cause severe ringing of the output signal. The primary current with square wave excitation is a
triangular waveform and the IR drop across the primary resistance will cause the secondary
voltage to have a dropping slope.
Both triangular and square waves have been used successfully for LVDT excitation but
accurate calibration is difficult and severe limitations on impedance, sensitivity and load are
required for good performance. These waveforms often cause calibration correlation
problems using commercial test equipment and may require using the actual circuit to
determine the proper sensitivity. It is recommended that after the proper sensitivity is
established, sine excitation be used for calibration using the standard commercial test
equipment.
Input Power describes the real power in watts, or apparent power in volt-amperes, required
for the excitation of the LVDT. Since the input impedance of an LVDT is not purely
resistive, input power is generally given in Volt-Amps. This limits the input current rather
than actual power dissipated. It is recommended that the maximum volt-amperes be specified.
Practical limits for lower frequencies (26 VRMS, 400 Hz.) could be as high as l.5 VA down to
0.1 VA when using 7.0 VRMS at 3500 Hz.
Power Factor describes the ratio of the real power in watts, to the apparent power in volt
amps. This ratio is normally computed from the complex impedance. The Rs/Z (See Input
Impedance) will yield the power factor. Typical power factors for an LVDT are in the range
of 0.4 to 0.9.
Input Impedance will define the load the primary coil of the LVDT will present to the
excitation source. The input impedance of an LVDT is complex and is best described with
both the resistive and reactive components (Rs +jXL). It should be noted that the Rs term is
not just the DC resistance but includes the equivalent series real part of a complex impedance.
Eddy current losses and shunt capacitance across the inductance will add an AC resistance to
the DC resistance to produce the Rs term of the complex impedance. The vector sum of Rs
and XL, (impedance Z), is normally specified as a minimum value for design purposes. The
maximum volt-amperes will limit the minimum input impedance - both requirements need not
be specified. Quality assurance requirements normally require a specific value with a
tolerance for the impedance. It is recommended that if the specific impedance value is
required, it should be taken from the actual measurement when the design is
completed. A +20% tolerance is practical for primary impedance.
Output Impedance describes the maximum source impedance of the secondary voltage.
The source impedance of the LVDT secondary will depend on input power limitations,
sensitivity requirements and the constraints on the wire size due to physical space available.
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It is extremely difficult to predict the actual output impedance of an LVDT and this value is
normally taken from the actual coil design.
The output impedance will form a voltage divider with the load (see Load). The open circuit
voltage of the secondary will be reduced by the ratio of the load impedance divided by the
load impedance plus the output impedance of the LVDT. Errors due to loading are minimized
by calibrating with the equivalent of the actual interface load. A tolerance of +15% is
practical for secondary impedance.
Load. The load is the impedance of the circuit that the secondary of the LVDT is connected
to. The equivalent of the actual in-service load should be specified for proper calibration. If
long cable connections or RF filters are used, the shunt capacitance should be included with
the description of the load. When a center tap secondary is used, the load across each coil and
any additional differential load should be specified.
The load on the output of an LVDT will affect the sensitivity, phase shift and temperature
error. If the correct load is used for calibration, all performance requirements will be met with
the service load. To minimize load errors, tolerances should be kept as small as possible and
the load impedance should not be less than l0, 000 ohms. Shunt capacitance of the load circuit
should be kept under 7500 pF when using excitation frequencies over 1000 hertz.
Sensitivity, gain and scale factor are the same requirement. They are the slope of the output
voltage Vs displacement. Kavlico prefers to define sensitivity as the slope of a best-fit
straight line drawn through the output data. An LVDT is a ratiometric device and the
sensitivity should be expressed as the ratio of the volts out, per volt in, per Inch of
displacement (V/V/Inch).
A practical upper limit for the sensitivity of short stroke units (less than 0.065 inches) that
operate at frequencies less than 500 hertz would be in the range of 3.0 V/V/Inch. Up to 6.5
V/V/Inch can be achieved for short stroke units that operate at frequencies around 3500 hertz.
This limit will decrease with longer strokes and should not exceed 0.5 Volts/Volt at the end of
stroke for the lower frequencies or 0.85 Volts/Volt at the higher frequencies.
Synchronous type demodulators will only produce a DC output for the in-phase component
of it’s input signal. A simplified way of looking at a phase shifted signal is that it contains the
sum of two sine waves, one that is in-phase with the reference and one that is at 90°
(quadrature). When a synchronous type demodulator is used, phase shift errors are eliminated
if the LVDT output is measured using an analyzing (phase sensitive) voltmeter that can
measure the component of the output that is inphase (0 or 180 degrees) with the excitation.
Looking at the waveforms of this type of demodulator it is not obvious but it does rectify the
in-phase component. Non-synchronous (rectifier) type demodulators are used on some five
or six wire LVDTs and the LVDT output is measured using the total voltage ratio (without
regard to phase). A requirement for Sensitivity should include a statement for the ratio of the
in-phase component or the total voltage.
Temperature Coefficient Temperature error for the sensitivity is normally specified as a
coefficient of the sensitivity. The temperature coefficient of the sensitivity of an LVDT is
not linear over wide temperature ranges. It should be expressed as the maximum allowed
change in sensitivity, as a percentage of the nominal sensitivity, averaged over 100° of
temperature change. Typical coefficients range from +0.5% to -3.0% per 100°F.
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Accuracy is a term that has no specific definition and requires the user to provide
one. This term is often incorrectly used as being synonymous with linearity. Accuracy
should be used when a group of independent errors, such as linearity, sensitivity and
temperature effects, are combined. For many applications only the total error is important
and not the individual error sources.
Once components of accuracy are defined, it becomes useful to state the minimum and
maximum deviations allowed from a specified reference (usually the nominal output) as a
percent of Full Scale output. These bounds are called Accuracy or the Error Band and are the
bounds of uncertainty for any measurement point under defined conditions. Acceptance
testing of the LVDT is conducted at room temperature and both room temperature limits and
environmental limits should be stated. Room temperature accuracy is very useful for
calibration, since it establishes specific limits for acceptance and the individual error sources
need not be computed.
Linearity describes the maximum deviation of any calibration point from a specified straight
line. The error is usually expressed as a percentage of Full Scale output. Unless linearity
errors are to be included in an “Accuracy” definition, the type of straight line used for the
reference must be stated. The most commonly used line is the “Best Fit Straight Line”
(BSFL).
Null Voltage is the minimum differential output voltage of an LVDT that can be obtained
with the armature position. For most LVDTs this is at a balanced center where an equal
number of secondary turns are engaged for both secondary coils. The null position is
normally defined as the position where the inphase components of the differential output are
zero (this is 0 VDC for a synchronous demodulator). The null voltage is primarily due to
slight differences in phase shift of one secondary to the other at the null position. When
taking the difference of two voltages with different phase, the in-phase components being
equal, the quadrature is not and this difference is the null voltage. Figure 5 shows the null
quadrature that results from taking the difference in two secondary voltages with only 0.2
degrees of phase difference. It is possible to bias the null position with an additional coil that
will have a constant output over the stroke.
The only known purpose of a low null voltage is for rigging the stroke to a zero position
(adjusting the physical position of the LVDT housing with respect to the armature
extension). This is often done using the null output measured with a non-phase-sensitive
voltmeter. If the null voltage is low, a more precise zero position can be achieved for the inphase component.
Imperfections in the core material, high flux densities and non-uniform hardness of metal in
the flux path will generate harmonic distortion, which, if not equal in the two secondary coils,
could also contribute to the null voltage.
Offset Null. The Null with a biased offset winding is not at a balanced position of the
secondary coils and larger phase differences in the secondary voltages will produce a larger
null voltage. For a biased null position, three voltages produce the in-phase zero and will
never have the same phase shift. This will result in a higher than normal null voltage. Null
Voltage for a biased offset could be as high as 5.0% of the maximum output. For most
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applications, only the Inphase Component is used and the null voltage will have little or no
significance on the accuracy.
Null Shift. Kavlico defines null shift as the change in null position that cannot be attributed
to material growth. Temperature error of the null position of an LVDT may result from a
number of sources but for most applications is negligible. The most significant null position
errors are from different linear expansions of the materials that close the loop from the
mounting point of the housing to the mounting point of the armature extension. When
possible, linear expansions can be matched to minimize null shift. Most aircraft or aerospace
LVDT are constructed from 300 series stainless steel and the change in length from the
mounting point of the housing to the mounting point of the armature extension will be about
9.3 to 9.6 PPM/oF.
Phasing. As noted in LVDT description, the differential output voltage will be in phase or
l80o out of phase with the primary voltage as the armature is displaced through the null
position. Phasing is used to determine in which direction the armature is displaced from the
null position. When specifying the phase for a specific direction of core displacement, the
common elements (low side of both primary and secondary) must be specified.
Phasing for a three-wire secondary can be specified by indicating the desired phase of each
secondary with the low side of the primary connected to the center tap and specifying which
secondary voltage is to increase for a specific direction of the armature displacement.
Phase Shift for an LVDT normally refers to the difference in angular degrees between the
primary excitation voltage and the secondary output voltage when the output is taken
differentially.
For LVDTs that use three wire or split secondary, the phase shift requirement should
indicate the specific output voltage for which the requirement applies (the differential voltage
or each individual secondary voltage).
Limiting the phase shift will limit the quadrature voltage. In some applications a limit on
quadrature is necessary since it appears as quadrature on the output of an error amplifier in a
servo system or as a reverse voltage across the switch of a synchronous demodulator.
Phase Difference is used to describe the maximum allowed difference in the phase shift of
the two secondary voltages when using a three wire or split secondary. It should be pointed
out that this is NOT the differential phase shift. Both magnitude and phase shift of each
secondary must be considered when computing differential phase shift. Typical phase
difference for the two secondary voltages, at the end of the stroke, is 3 to 8 degrees. At the
end of the LVDT stroke, one secondary will be at its highest voltage and have its lowest
phase shift when the other secondary will be at its lowest voltage with its highest phase shift
(See Figure 6).
Tracking is used to define the uniformity of performance between channels of multiple
channel LVDTs. Calibration data is taken from a single reference point (normally the first
channel null position). Each channel’s output is compared and the maximum difference
between any two channels is termed “tracking.” This is normally expressed as a percent of
Full Scale.
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Null Difference tracking at the null position is sometimes specified as a maximum “Null
Difference” and may have a different requirement than at other stroke positions. The smallest
practical Null Difference is 0.001 inch or 0.15% of the stroke whichever is larger. Null
differences less than 0.010 inches will require trimming the extension prior to final calibration.
Crosstalk is a term used for multiple channel units to describe the voltage produced in the
secondary of one channel by the primary excitation of another channel. When separate drivers
are used for different channels they may not be synchronous and slight differences in
frequency will produce a beat frequency (difference frequency), which may produce an
apparent oscillation of the system. Frequencies for different channels are sometimes
separated such that the beat frequency is above the system response. Typical crosstalk for
tandem construction is less than 0.0010 V/V and for parallel construction 0.0010 to 0.0025
V/V.
FAULT DETECTION
Many technological advances in the design, construction and use of the Linear Variable
Differential Transformer (LVDT) have been made in the last 15 years. Utilizing computer
aided winding machines, the state of the art in LVDT performance has made significant
advances.
Much of the progress that has been made is due to achieving the ability to produce an LVDT
where the two secondary windings provide not only the normal differential signal, but also a
constant sum. Add to this, the ability to adjust the sum for a specific differential output, and
a whole new dimension for the LVDT is opened.
The first benefit one can realize is the ability to fault detect the signal on a real time basis
without affecting performance or placing the signals in jeopardy should the fault detection circuit fail. Using the LVDT output as two discrete signals relative to the center tap of the
secondary can do this. From this point of reference, (assume the center tap is the signal
ground) the two secondary voltages will both be linear with armature displacement and both
will have the same phase relationship relative to the excitation. They may be either in-phase
or out-of-phase (should be specified for the application) and neither will have a zero voltage
output. At this point, two approaches are possible.
The first approach would be to either actively rectify or synchronously demodulate each
secondary voltage and then use the DC voltages to produce a difference and sum. Accurate
calibration can be accomplished using a total voltage ratio for active rectification or calibrating
using only the in-phase component of the output voltage (See Figure 7) when synchronous
demodulation will be used. No phase shift correction is required when the proper calibration
is performed.
A second approach would be to use the AC signals, Va and Vb, directly to produce both a
difference and a sum voltage (See Figure 8) using both a differential and summing amplifier,
then demodulating these voltages. It should be pointed out that this approach, when used
on the AC signals, must be used with caution.
The individual secondary voltages have differences in phase (see Phase Difference) and the
output of a differential amplifier will not be the exact algebraic difference of the secondary
voltages. When only the inphase components are used, this phase difference is not significant.
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When using the total component, the LVDT can be calibrated using the differential output
that will yield the same voltage as the output from a differential amplifier.
A differential amplifier can cause a not so obvious error in that it does not present a fixed load
to its inverting input due to the common mode voltage generated by the non-inverting side.
This will cause the Va secondary to be loaded differently than Vb. The input resistors for a
differential amplifier should be 20K ohms or larger to minimize load errors.
Also an open circuit fault in the LVDT on the inverting side will result in the differential
amplifier producing a false signal to the summing amplifier due to the common mode signal
produced on the non-inverting side.
When using a differential and summing amplifier the ideal configuration would have a noninverting buffer for each secondary signal with the summing resistors on its input. This will
present a fixed load to each half of the secondary of the LVDT and act as a pull down and not
allow the input to float in the event of an open circuit in the secondary of the LVDT. The
buffer will also isolate the common mode voltage from the differential amplifier since the sum
is taken in front of the buffer (see Figure 9)
When using a flight or engine control computer the best configuration would be to simply
demodulate the Va and Vb to DC signals, digitize them and then let the computer do the rest.
In any case, by establishing a minimum value for the sum voltage, any value below this would
indicate a fault in the signal. The total loss of the sum would most likely indicate an open in
the primary side if the excitation were still present. All significant fault conditions (opens or
shorts), which could occur in the LVDT, would be detected.
DIFFERENCE OVER SUM OUTPUT
In addition to fault detection, a constant sum provides another possible advantage when using
an LVDT. Nearly everything that affects the differential output voltage also affects the
sum voltage. If the output of an LVDT is taken as the difference over sum ratio, nearly all
excitation changes, temperature effects, frequency effects, loading and long term gain loss do
not produce an error.
(Va/Ex. - Vb/Ex.) / (Va/Ex. + Vb/Ex.) = (Va-Vb)/(Va+Vb)
[The Excitation Voltage drops out]
This five/six-wire configuration presents many possible alternatives for the signal
conditioning of an LVDT, but also presents a few new specification clarifications that must
be addressed.
Definition of the difference over sum gain with its tolerance and the sum with its
tolerance, describe the requirements for this use. The limits of the individual secondary
voltages can be determined working from these requirements.
A typical requirement might be as follows:
1.
2.
3.
4.
Excitation: 7.07 VRMS with a +5% tolerance.
Stroke: +3.000 inch.
Sum: 0.6000 V/Vex. (4.242 VRMS) with a +10% tolerance.
A difference over sum Gain: 0.16667 V/V/Inch (0.5000 V/V at each end of the stroke).
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5.
And the total accuracy: +1.0% F.S. (+2%) of the reading at either end of the stroke.
The nominal differential gain is the sum ratio multiplied by the difference over sum gain =
0.6000 V/Vex * 0.16667 V/V/Inch = 0.1000 V/Vex/Inch and this times 3.000 inches = 0.3000
V/Vex
NOMINAL VALUES
Stroke
Position
Inches
Va
V/Vex
Vb
V/Vex
Va-Vb
V/Vex
3.000
-0+3.000
0.1500
0.3000
0.4500
0.4500
0.3000
0.1500
-0.3000
0.0000
0.3000
Va+Vb
V/Vex
0.6000
0.6000
0.6000
(Va-Vb)/(Va+Vb)
V/V
-0.5000
-0+0.5000
See Figure 10
The worst case for secondary values is:
1.
For the sum tolerance, 0.6000 V/V +10% = 0.5400/0.6600 V/V and each secondary is
0.2700/0.3300 V/V.
2.
When the sum is 0.5400 V/V the nominal differential must be 0.5400*0.5000 or
0.2700 V/V. Adding +2% tolerance to the gain and calculating the outputs at the ends
of stroke yields 0.2754 V/V and for each secondary the change to the end of the
stroke=0.1377 V/V;
3.
When the sum is 0.6600 V/V the nominal differential must 0.6600*0.5000 or 0.3300
V/V. With the ±2% this is 0.3366 V/V and for each secondary =0.1683 V/V
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A. For the minimum low voltage;
0.2700 V/V minimum at the zero position -0.1377 V/V maximum change = 0.1323 V/V
and the lowest excitation = 6.7165 Volts, therefore the minimum value = 0.8886 volts.
B. For the maximum high voltage;
0.3300 + 0.1683 = 0.4983 V/V and the highest excitation is 7.4235 Volts, and the
maximum value = 3.6991 volts.
These values do not allow for rigging errors or mechanical over stroke.
Practical accuracy for a difference over sum unit is +0.5% of full scale at 75oF. This accuracy
will include errors due to sensitivity, non-linearity, input voltage variations, frequency
variations and load tolerances for the service life of the unit. The temperature coefficient of
sensitivity is normally less than +0.25% per 100°F. For strokes over 2 inches, frequencies
between 1500 and 2500 hertz will produce the highest accuracy.
The classic use of an LVDT was the differential connection, using only a four-wire
configuration. There is only one possible connection for the load, phase shift referred to the
differential signal at the end of the stroke, there was only one possible output impedance to
contend with and normally a null voltage occurred at mid-stroke. For nearly all applications,
only the in-phase component was used for calibration. For the five and six wire
configurations it gets more complicated.
The load for each secondary and any additional differential loading must be specified.
Phase shift for the Va or Vb outputs will change over the entire stroke with the highest
phase shift at the low voltage end. The highest quadrature will occur at the high voltage end of
the stroke and the phase shift for Va or Vb should be measured at that end of the stroke.
The output impedance of the Va or Vb coils changes over the stroke. The output impedance
is normally measured for quality purposes at the high voltage end for each secondary.
When the secondary center tap is to be the signal reference, the Null Position (Zero
Position) is normally defined as the place in the displacement where Va is equal to Vb (there
is no “Null” voltage). A Null voltage is only obtained from an LVDT when connected such
that the differential output is obtained. (see Null Voltage).
Calibration of the output can be done using the in-phase or total component.
Using the secondary sum for the switching circuit of a demodulator, phase shifting networks
or scaling sensitivity to correct for phase shift is not recommended.
LVDT ENVELOPE REQUIREMENTS
Once the electrical, mechanical and performance parameters have been determined, several
factors must be considered in packaging. Kavlico’s design team can provide the length and
diameter necessary to meet both the environmental and electrical performance.
COST CONSIDERATIONS
Boilerplate and over specifying performance attributes becomes costly in production. Design
options and cost savings are available when specific requirements and system performance
are analyzed and practical limits placed on all requirements.
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