Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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TITLE: SENSOR COIL FOR LOW BIAS FIBER OPTIC GYROSCOPE
BACKGROUND
Field of the Invention
The present invention relates to fiber optic
gyroscopes. More particularly, this invention pertains to
an improved sensor coil design that addresses factors
contributing to various bias errors and minimizes gyro
bias sensitivity to dynamic thermal and vibration
environments.
Description of the Prior Art
A fiber optic gyroscope comprises the following
main components~ a light source, (2) a beamsplitter
(either a fiber optic directional coupler or an
integrated-optics Y-junction), (3) a fiber optic coil, (4)
a polarizer (and sometimes one or more depolarizers), and
(5) a detector. Light from the light source is split by
the beamsplitter into copropagating and counterpropagating
waves travelling in the sensing coil. The associated
electronics measures the phase relationship between the
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two interfering, counter-propagating beams of light that
emerge from opposite ends of the coil. The difference
between the phase shifts experienced by the two beams
provides a measure of the rate of rotation of the platform
to which the instrument is fixed.
Environmental factors can affect the measured
phase shift difference between the counterpropagating
beams, thereby introducing a bias or error. Such
environmental factors include variables such as
temperature, vibration (acoustical and mechanical) and
magnetic fields. Such factors are both time-varying and
unevenly distributed throughout the coil. These
environmental factors induce variations in the optical
light path that each counterpropagating wave encounters as
it travels through the coil. The phase shifts induced
upon the two waves are unequal, producing a net
undesirable phase shift which is indistinguishable from
the rotation-induced signal.
One approach to attain a reduction of
sensitivities arising from environmental factors has
involved the use of various symmetric coil winding
configurations. In such coils, the windings are arranged
so that the geometrical center of the coil is located at
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the innermost layer while the two ends of the coil are
located at the outermost layers.
N. Frigo has proposed the use of particular
winding patterns to compensate for non-reciprocities in
5 "compensation of Linear Sources of Non-Reciprocity in
Sagnac Interferometers". Fiber optics and Laser Sensors
I, Proc. SPIE Vol. 412 p. 268 (1989). Furthermore, United
States patent 4,793,708 of Bednarz entitled "Fiber optic
Sensing Coil" teaches a symmetric fiber optic sensing coil
formed by dualpole or quadrupole winding. The coils
described in that patent exhibit enhanced performance over
the conventional helix-type winding.
United States patent 4,856,900 of Ivancevic
entitled "Quadrupole-Wound Fiber optic Sensing Coil and
Method of Manufacture Thereof" teaches an improved
quadrupole-wound coil in which fiber pinching and
microbends due to the presence of pop-up fiber segments
adjacent the end flanges are overcome by replacing such
pop-up segments with concentrically-wound walls of turns
for climbing between connecting layers. ~oth of the
aforementioned United States patents are the property of
the assignee herein.
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While appropriate coil winding techniques
minimize some of the bias errors found in the output of a
fiber optic gyro, they are not capable of eliminating all
of such biases. In particular, the design of the gyro
sensor coil can impact the gyro's random walk, bias
stability, temperature sensitivity, bias temperature-ramp
sensitivity, bias vibration sensitivity, bias magnetic
sensitivity, scale factor temperature sensitivity, scale
factor linearity and input axis temperature sensitivity.
SUMMARY OF THE INVENTION
The foregoing and additional shortcomings and
disadvantages of the prior art are addressed by the
present invention that provides a sensor coil for a fiber
optic gyroscope. Such a coil includes optical fiber. The
fiber is arranged into a plurality of concentric
cylindrical layers. Each of the layers comprise a
plurality of turns of the fiber and each of the turns is
arranged in a predetermined winding pattern. The turns
are encapsulated by a potting material of predetermined
composition.
The preceding and other features and advantages
of the invention will become further apparent from the
detailed description that follows. Such description is
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accompanied by a set of drawing figures. Numerals of the
drawing figures, corresponding to those of the written
text, point to the various features of this invention with
like numerals referring to like features throughout.
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 is a perspective view of a sensor coil
for a fiber optic gyroscope in accordance with the
invention;
Figure 2 is a cross-sectional view of the sensor
coil of the invention taken at line 2-2 of Figure 1;
Figure 3 is a graph of the gyro bias versus the
temperature rate of change (or temperature time-
derivative) for a coil made in accordance with the prior
art, that is, a dry-wind in an aluminum spool. The slope
of this curve is referred to as the "Shupe coefficient"
and has units of bias change (deg/hr) per rate of
temperature change (degC/hr);
Figure 4 is a graph of the gyro bias versus the
temperature rate of change for a coil made in accordance
with this invention, that is, a potted coil on a carbon
composite spool;
Figure 5 shows graphs of the output bias of a
fiber optic gyroscope versus time and of the gyroscope
temperature versus time for a coil made in accordance with
the prior art (aluminum spool);
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Figure 6 is an enlarged cross-sectional view of
a representative portion of the layered windings of a
sensor coil in accordance with the invention;
Figure 7 is a graph of the relationship between
frequency of axial vibration and A.C. bias for two potted
sensor coils; and
Figure 8 is a table of values for judging the
appropriateness of sensor coil potting material in
accordance with the invention.
DETAILED DESCRIPTION
Turning to the drawings, Figure 1 is a
perspective view of a sensor coil 10 in accordance with
the present invention. As mentioned earlier, the sensor
coil 10 provides a critical element of a fiber optic gyro
system. In use, it is rigidly fixed to a platform whose
rotation rate is to be measured.
The sensor coil 10 is a particular example of a
coil in accordance with the invention. It comprises an
optical fiber 12 that is wound upon a supportive spool 14
and serves as an optical guide for receiving a
counterpropagating beam pair emitted from a common light
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source (not shown). The supportive spool 12 in Figure 1
shows flanges. However, the presence of flanges is not
required in this invention.
Figure 2 is a cross-sectional view of coil lo, a
particular example of a sensor coil in accordance with the
invention, taken at line 2-2 of Figure 1. As can be seen,
a disk-like support 16 is press-fit within the spool 14.
The support 16 has a central aperture 18 for receiving a
fastener whereby the sensor coil 10 can be tightly secured
to the platform. An annular shoulder 20, formed at the
inner surface of the spool 14, acts as a stop to maintain
the position of the support.
In contrast to a conventional aluminum or like
spool for a rotation rate sensor, the spool 14 (including
the support 16) is of a carbon composite material~or
another material with similar thermomechanical properties.
.
Such material includes woven carbon fibers such as those
commercially available from such sources as the Amoco
Corporation under the trademarks "P-25, "P-55", "P-105" or
the like. The spool 14 is formed of such fibers which
have been built up into multiple fiber layer tubes or
sheets by means of a bonding matrix of, for example,
phenolic material. The spool 14 can be formed from such
tubes or sheets by a number of known processes including,
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for example, cutting sections therefrom. Alternatively,
the woven fiber can be arranged into predetermined
orientations and shapes in a dye and the bonding material
cast around it. Another process employs transfer molding
in which the chopped fiber is mixed with a transfer
molding material and then transferred or pressure injected
into a transfer mold. The fibers are preferably oriented
at right angles withi~ the bonding matrix material,
aligned both longitudinally and circumferentially with
respect to the spool's axis of rotation 22. By so
arranging the fibers, the spool 14 will expand
symmetrically both longitudinally and radially with
temperature.
The inventors have developed a theoretical model
of bias non-reciprocities in the fiber optic gyroscope.
In particular, they have found that gyro bias errors under
a dynamic thermal environment can be due to thermal
stress. This effect is very similar to the standard
temperature Shupe effect reported in "Thermally Induced
Non-Reciprocity in the Fiber Optic Interferometer", D.M.
Shupe, APPlied optics, Vol. 19, p. 654 (1980). One of the
drivers of this thermal-stress induced bias error is the
thermal mismatch that exists between the glass optical
fiber and the metallic spool. That is, the bias error
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results partly from the termal stress exerted upon the
coil windings through mismatched thermal expansions of the
metallic spool (greater expansion) and the glass fiber
(lesser expansion). Another driver is thermal stress due
to expansion /contraction of the coil potting material
(discussed below). The differences between the standard
temperature-Shupe effect and the thermal-stress induced
Shupe effect are clea~ly noticeable when a coil is
subjected to a steady-state temperature ramp. While the
bias error due to the standard Shupe effect dies away as
soon as the temperature gradients become constant with
time, the bias error due to the thermal-stress effect is
non-zero as long as the temperature of the coil is
changing and that effect remains even after the
temperature gradients have reached steady-state.
Contrasting the effects, the standard Shupe effect is
mainly a function of the rate of change of the temperature
gradients across the coil while the termal-stress induced
Shupe-effect is mainly a function of the rate of change of
the coil average temperature.
In the present invention, as a result of careful
selection of the carbon composite material of the spool
14, its coefficient of thermal expansion may be made to
closely match the coefficient of the windings of the glass
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optical fiber 12, thereby, minimizing thermal stress on
the optical fiber. This is in contrast to the design of
sensor coils in accordace with the pior art in which the
optical fiber is conventionally wound upon an aluminum
spool. As discussed below, careful selection of the coil
potting material can also reduce thermal stresses in the
optical fiber.
Figure 3 is a graph of the gyro bias error
versus rate of change of temperature (temperature time
derivative) for a coil made in accordance with the pior
art. The data were taken from a sensor coil formed of
inch thick aluminum. Approximately 200m of 185 micron
wide optical fiber was wound thereon in a symmetric
pattern. As predicted by the model developed by the
inventors, the Shupe-effect bias is predominantly linear
with the temperature time derivative. The slope of the
curve has been designated the "Shupe coefficient" by the
inventors and is a direct indication of the coil and
the gyro bias sensitivity to temperature ramps. For a
coil made in accordance with the prior art, the Shupe
coefficient is large, 0.22 (deg/hr)/(degC/her) in Figure
3. Many coils wound on aluminun spools were measured to
have Shupe coefficients between 0.1 and 0.4. In contrast,
potted coils wound on carbon-composite spools exhibit a
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significant reduction in the Shupe coefficient. Figure 3
is a graph of the gyro bias error versus the temperature
rate of change for a coil made in accordance with this
invention. This data was taken from a sensor coil
approximately 200 m long, consisting of 165 micron fiber
wound on a carbon composite spool and potted with an UV-
curved adhesive. The Shupe coefficient of this coil is
about one order of magnitude lower than that of pior art
coils.
In addition to the linear dependence of the bias
with the temperature rate of change predicted by the
inventors model, they have experimentally found that
significant second order effects can also be observed in
coils made in accordance with the prior art and such
effects are a function of the change in temperature.
Figure 5 shows graphs of the outpt bias of a fiber optic
gyroscope versus time and of the gyroscope temperature
versus time. These two graphs reveal the relationship
between gyroscope output bias and temperature. This
data was taken from a sensor coil having a spool formed of
0.06 inch thick aluminum in accordance with the prior art.
Approximately 1000 m of 185 micron fiber was wound thereon
in a symmetric pattern. The variation of coil temperature
(or temperature profile) is shown by the curve 24. The
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solid line or curve 22 is a plot of the time derivative of
the temperature profile. As can be seen from the graph,
significant departures from the linear dependence of the
bias with the temperature rate of change were measured at
the areas 26 and 28. The inventors believe that these
significant departures are due to a second order thermal-
stress induced Shupe effect. The significant temperature
time-derivative have not been observed in coils made in
accordance with this invention.
Other features of the invention address
additional sources of bias. Figure 6 is an enlarged
cross-sectional view of a representative portion of the
layered windings of optical fiber 12 that form the optical
guide of the gyro.
As can be seen in Figure 6, the windings of
optical fiber 12 are potted within a matrix of adhesive
material 30. Generally, the presence of such adhesive
material 30 provides a number of useful advantages for the
gyro. These include facilitating the precision of coil
winding. That is, the adhesive potting material 30 can be
applied and cured layer-by-layer so that smooth surfaces
will be presented for the winding of subsequent layers.
Such a winding environment enhances control of the
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resulting coil geometry including such essential factors
as inter-fiber spacing, turns per layer and layers per
coil minimizing the presence of winding defects such as
"missing turns".
Various manufacturing methods can be employed to
create a coil in which the turns or windings are embedded
in a matrix of adhesive potting material. Such methods
include, for example, application of the adhesive by means
of a syringe-type dispenser followed by curing. Such
methods assure that smooth surfaces will be presented for
the winding of subsequent layers. A uv-curable adhesive
which permits rapid hardening is most appropriate for such
methods.
Other methods of manufacture include dry coil
winding followed by vacuum impregnation with a very low
viscosity adhesive. An alternative wet winding technique
employs a thermally-curable adhesive that is applied as
the coil is wound. The adhesive is left uncured (in
liquid form) during winding. The completed (wound) coil
is then thermally cured.
While the potting of the coil is seen to provide
the above-identified benefits, the inventors have found
that the design of the potting material matrix, including
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the type of adhesive potting material employed, can be
manipulated to improve the performance of the gyro
significantly. In particular, as demonstrated below,
careful selection of adhesive potting material 30 for
encapsulating the coil can significantly reduce the
sensitivity of the sensor coil 10 to vibration-induced
bias errors.
The inventors have found that gyro vibration
sensitivity can be minimized in a potted sensor coil
through careful selection of the potting adhesive. The
vibration sensivity of a potted sensor coil results from
processes within the coil that introduce a non-reciprocal
phase error into the output that is indistinguishable from
the rotation rate signal. The bias vibration sensitivity
is caused by a non-reciprocal phase shift in the
counterpropagating waves that, in turn, results from
changes in fiber length and refractive index brought about
by vibration dynamic strains via the photoelastic effect.
This bias error is similar in nature to the Shupe bias
error described earlier, the main difference being that
the environmental perturbation is vibratory strain rather
than changing temperature. It has been observed
experimentally that, when resonance frequencies are
greatly removed from the instrument performance bandwidth
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(and the noise factor is negligible), the open loop
response of gyro output to a sinusoidal vibration sweep is
a linear function of vibration frequency.
This is true when the direction of vibration is
either parallel to the coil input axis (axial vibration)
or perpendicular to it (transverse vibration). The
inventors have found that the fiber optic gyro bias
vibration sensitivity is a linear function of vibration
frequency. Furthermore, they have found that, under
transverse vibration, gyro output exhibits an azimuthal
dependence that is nearly sinusoidal, (i.e., varies as the
SIN of the azimuth angle.)
The consequences of the vibration dependence are
significant. Even though a direct D.C. bias effect,
called "D.C. rectification, " has not been observed,
saturation of the electronic components can prevent the
closed-loop electronics from monitoring the rotation rate
at certain vibration frequencies. This can be manifested
as an apparent D.C. rectification. Angle rate noise may
also result from the vibration as well as pseudo-coning at
the system level.
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The inventors have found that the above-
described vibration-associated problems may be minimized
or eliminated by arranging the matrix comprising potting
adhesive and fiber windings so that the vibration dynamic
stresses experienced in the fiber windings are minimized.
High stresses and strains in the fiber core are produced
by dynamic amplification. The inventors have further
found that this harmf~l dynamic amplification effect can
be traced to the use of an adhesive potting material of
insufficient elastic stiffness.
Accordingly, the present invention addresses the
problem of vibration-induced bias error, firstly, by
providing that the design of the dynamic system that
includes the spool, windings, adhesive potting medium and
coil mount possesses a natural resonant frequency that is
outside the operational bandwidth of the gyro.
Second, the effects of vibration-induced bias
error are also reduced through the use of a potting
material that is capable of meaningfully sharing dynamic
loads with the fiber to reduce the vibratory stresses and
strains in the fiber.
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The inventors have found that vibration-induced
bias errors may be reduced by employing adhesive potting
material having a relatively-high Young's modulus (i.e.
"stiff" material). Figure 7 contains graphs of the
relationship between the vibration-induced A.C. bias
amplitude for two potted sensor coils and the frequency of
axial vibration. In the graph, the curve 32 presents the
relationship between bias error in the data output by a
gyro utilizing a sensor coil with fiber windings potted in
an adhesive characterized by a Young's modulus of less
than 300 p.s.i. As can be seen, the relationship between
the axial vibration frequency and A.C. bias effect is
substantially linear, reaching 10.0 degrees per second as
the shaker frequency swept from 0 to 1000 Hz.
The curve 32 presents the relationship between
bias error and axial shaker frequency for a gyro having a
sensor coil potted in an adhesive matrix of material of
Young's modulus in excess of 100,000 p.s.i. As can be
seen from this curve a dramatic and substantial
improvement in the performance is obtained by increasing
the stiffness of the potting material. When compared to
the bias error for a low modulus material as shown by the
curve 30, the A.C. bias that results from axial vibration
is relatively negligible as the shaker frequency is swept
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from 0 to nearly 2000 Hz. Similar results have been
obtained relating A.C. bias to transverse vibrations.
Thus the data confirms that, by increasing the stiffness
' of the potting material, the mechanical stresses imposed
by vibration will be shared to a greater extent by the
potting material and therefore they will be somewhat
removed from the optical fiber. Significantly reduced
sensitivity of gyro output to vibration can be observed
when potting material of a large Young's modulus is
employed.
While the benefit of potting the fiber coil
windings in a high modulus material to minimize bias
effects due to vibration are clear, the inventors have
further determined that the stiffness of potting material
must tempered in view of a number of factors. As the
stiffness of the potting material increases, the coil
becomes subject to greater thermal stress in response to
change's in temperature well above or well below the
(minimum stress) curing temperature Tc. Such excessive
thermal stressing of the sensor coil can produce the
problems of coil cracking, h-parameter (polarization
cross-coupling) degradation and large bias temperature-
ramp sensitivity. Coil cracking and degraded h-parameter
performance have been observed in a 200 meter potted coil
design.
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The coil cracking, h-parameter and temperature-
ramp sensitivity problems are all affected by the choice
of potting material since, as mentioned above, thermal
stress is a function of the modulus of the potting
material. Thermal stress o is proportional to ~E(T-TC)
where ~ is the difference between the coefficients of
thermal expansion of the adhesive and the optical fiber, E
is the elastic modulus of the adhesive material and T-TC
is the temperature excursion from the adhesive curing
temperature Tc. Stated in terms of design considerations,
an optimum adhesive for use as the coil potting material
should be one for which the thermal stress a is minimized
or made as small as possible over the maximum foreseen
temperature excursion T-TC while E is maintained as large
as possible to minimize vibration-induced bias effects.
Figure 8 is a table that presents data for
evaluating the suitability of various adhesive potting
materials. As can be seen, the adhesive marketed under
the trademark "NOA 83 H" of Norland, which possesses a
relatively-high elastic modulus E of 200,000 p.s.i. is
predictably characterized by excellent vibration
performance but sensor coils utilizing such potting
material have experienced some cracking. This adhesive
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exerts a maximum stress o over a 160 degree Centigrade
excursion of 3840 p.s.i. On the other hand, "SCOTCH CAST
235" of Minnesota Mining and Manufacturing Corporation,
which has an elastic modulus of approximately 40,000
p.s.i. exerts a maximum stress of 1200 p.s.i. and "NOA 65"
(Norland 65), which possesses an elastic modulus of about
20,000 p.s.i., exerts a maximum stress of 320 p.s.i. over
an 80 degree Centigrade thermal excursion. The inventors
have found that adhesives having Young's modulus between
1,000 and 20,000 p.s.i. are adequate to fulfill both the
bias vibration requirement and low thermal stress.
Thus, it is seen that the teachings of the
present invention provide sensor coils that are
substantially improved in terms of minimization of bias
sensitivities due to dynamic thermal and vibration
environments. By utilizing the teachings of the
invention, one can obtain gyro performance that is
substantially less subject to bias errors of environmental
origin that were formerly unrecognized or unaddressed by
the prior art.
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While this invention has been described with
reference to its presently preferred embodiment, it is not
limited thereto. Rather, this invention is limited only
insofar as defined by the following set of patent claims
and includes within its scope all equivalents thereof.
