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1. ISSN 1064 2269, Journal of Communications Technology and Electronics, 2013, Vol. 58, No. 7, pp. 745–752. © Pleiades Publishing, Inc., 2013.
Original Russian Text © A.M. Kurbatov, R.A. Kurbatov, 2013, published in Radiotekhnika i Elektronika, 2013, Vol. 58, No. 7, pp. 735–742.
745
1 INTRODUCTION
It is well known that the characteristics of a fiber
optic gyroscope (FOG) are strongly worsened under
the influence of time varying thermal fields on its
sensing coil [1]. These fields cause the FOG tempera
ture bias drift, or the Shupe effect (SE), which is
treated as one of the FOG basic problems.
In Fig. 1, the FOG coil is depicted with a rectangu
lar cross section, and, four heat flows are shown in the
removed section. Let us call flows 3 and 5 radial and
flows 4 and 6 axial. Below, we call the fiber–compound
medium just the medium. In Fig. 1, the following coil
geometric parameters are also given: R1 and R2 are the
inner and outer diameters, respectively, and h is the
height. Coils with small h are referred to as low ones,
and coils with large h are referred to as high ones.
In papers [2–4], two equivalent expressions are
given for the thermal drift:
(1a)
(1б)
where D and L are the coil
diameter and fiber length, respectively; n is the fiber
refractive index; dn/dT is the fiber thermal sensitivity;
Т(z, t) is the temperature distribution along the fiber at
time moment t; and
1
The article was translated by the authors.
1
( ) ( ) ( ) ( )[ ]
2
0
2 , , ,
L
t B z L T z t T L z t dzΔΩ = − − −∫
( ) ( ) ( )
0
2 , ,
L
t B L z T z t dzΔΩ = −∫
( ) ( )1 ,B DL n dn dT=
is the time partial derivative of this distribution. Here,
we do not consider the contribution of fiber length
thermal changes, because it is small in conventional
quartz fibers. From (1à), it is seen that fiber sections
that are more distant from the fiber midpoint to SE
[1–7] more substantially contribute than less distant
ones. From (1a) and (1b), it is also seen that two ways
of reducing the SE influence are possible: (i) integra
tion paths specially chosen to minimize the integrals
and (ii) reduction of integrands.
Physical realization of the first way consists in spe
cial fiber winding techniques [2, 4]. They considerably
suppress the SE influence; however, they still do not
yield a necessary accuracy themselves [5].
The second way is thermal insulation and utiliza
tion of metallic screens [6]. Thermal insulation slows
down the temperature field variations (reduces the val
ues and ), metallic screens accelerate
temperature smoothing within the coil (reduce the
difference . In combination with
special fiber winding techniques, these steps allow
reaching the necessary accuracy. For example, in [6],
a coil with quadruple winding, air as a thermal insula
tor, and a copper carcass is described; the coil yields
the drift 0.04 (deg/h)/(°C/min). In [5, 7], a coil with a
drift lower than 0.01 (deg/h)/(°C/min) is described; it
is based on a quadruple winding [2–4], a carbon car
cass, and a compound that has high heat conductivity
(unlike that from [6]) and is deposited on the fiber dur
ing its winding.
In this paper, we describe a combination of special
fiber winding techniques with thermal insulation and
( ) ( ), ,T z t T z t
t
∂≡
∂
2
( ),T z t ( ),T L z t−
( ) ( ), ,T z t T L z t− −
Temperature Characteristics of Fiber Optic
Gyroscope Sensing Coils1
A. M. Kurbatov and R. A. Kurbatov
The Kuznetsov Research Institute of Applied Mechanics (a division of the Center for Ground Based Space Infrastructure
Facilities Operation), ul. Aviamotornaya 55, Moscow, 111123 Russia
e mail: akurbatov54@mail.ru
Received August 15, 2012
Abstract—In a 2D model, a fiber optic gyroscope (FOG) temperature drift is theoretically investigated
under the influence of temperature fields on its sensing coil for two techniques of fiber winding. The temper
ature field in the fiber cross section is calculated by means of the finite difference method. It is established
that, for the FOG temperature drift reduction to the level of 0.01 deg/h, the coil size being retained small
enough, it is effective to combine the thermal insulation, metallic screens, and compound with high heat con
ductivity.
DOI: 10.1134/S1064226913060107
PHYSICAL PROCESSES
IN ELECTRON DEVICES

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JOURNAL OF CJOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No. 7 2013
A.M. KURBATOV, R.A. KURBATOV
metallic screens. We consider the well known quadru
ple winding [2–7] and the Malvern winding [8],
which, as far as we know, previously was not investi
gated in the literature. In Section 1 of the study, the
calculation of thermal fields is described; in Section 2,
the general features and realization techniques are
described for chosen windings; in Section 3, the SE in
coils without thermal insulation and metallic screens
is calculated; and in Section 4,the SE suppression with
the use of thermal insulation and metallic screens is
described.
1. CALCULATION OF THERMAL FIELDS
To calculate the thermal fields in the coil cross sec
tion, we proceed from the heat equation in cylindrical
coordinates [9]:
(2)
where κ, ρ and c are the heat conductivity, density and
heat capacity at the point (r, z). The value κ/ρc is the
thermal conductivity [10]. The medium is inhomoge
neous, because it contains a fiber, a polymer coating,
and a compound. We replace this medium by a homo
geneous medium with parameters that are averaged
over all of the aforementioned materials according to
their volume fraction.
Assume that the coil cross section is rectangular, so,
the finite difference method is suitable for solving Eq.
(2). Let us introduce a uniform coordinate mesh with
( ) ( )
( ) ( )
( ) ( )
∂ρ
∂
∂ ∂⎡ ⎤= κ
⎢ ⎥⎣ ⎦∂ ∂
∂ ∂⎡ ⎤+ κ⎢ ⎥∂ ∂⎣ ⎦
, , ( , , )
1 , , ,
, , , ,
r z c r z T r z t
t
r r z T r z t
r r r
r z T r z t
z z
steps Δr and Δz in the radial and axial directions,
respectively, and a time mesh with step Δt. Grid func
tion = at time moment tn + 1 is deter
mined from its values = at time moment
tn with the help of Eq. (2) discretized according to the
following scheme [9, 11, 12]:
(3a)
(3б)
where
ξ is the parameter determining the type of discretiza
tion scheme (0 ≤ ξ ≤ 1). The index n + 1/2 corresponds
to the time moment tn + 1/2 = (tn + 1 + tn)/2. Here, a 1D
discretization scheme from [11] is taken as a basis. In
the calculation scheme determined by (3a) and (3b),
tridiagonal linear systems are solved by means of the
tridiagonal matrix algorithm (economical scheme)
[12]. We put ξ = 1/2, corresponding to the Crank–
Nicolson scheme, which, for values of Δt that are not
small enough, yields a large temperature field at the
1
,
n
i jT +
( )1, ,i j nT r z t +
,
n
i jT ( ), ,i j nT r z t
( )
( )
( )
+ + +
− +
+
+ + −
+ + +
⎡− = ξ − +⎣
⎤ ⎡+ + − ξ⎦ ⎣
⎤− + + ⎦
1 1 1
1
2 2 2
, , , 1, , 1, ,
2
1, 1, , 1,
, 1, , 1, 1,
1
,
n n n n
i j i j r i j i j i j i j i j
n n
i j i j r i j i j
n n
i j i j i j i j i j
T T c ar T ar ar T
ar T c ar T
ar ar T ar T
( )
( )
( )
+ + + +
− +
+ +
+ + −
+ +
− + +
⎡− = ξ − +⎣
⎤ ⎡+ + − ξ⎦ ⎣
⎤− + + ⎦
1
1
1 1
1 2 1 1
, , , , 1 , , 1 ,
1 2
, 1 1, , , 1
2 2
, , 1 , , 1 , 1
1
,
n n n n
i j i j z i j i j i j i j i j
n n
i j i j z i j i j
n n
i j i j i j i j i j
T T c az T az az T
az T c az T
az az T az T
, 1, 1
,
, 1, 1
2 2
,i j i j i
i j
i j i j i i
r
ar
r r
− −
− −
⎛ ⎞κ κ ⎛ ⎞
= ⎜ ⎟⎜ ⎟κ + κ +⎝ ⎠⎝ ⎠
, , 1
,
, , 1
2
,i j i j
i j
i j i j
az −
−
κ κ
=
κ + κ
2
,r
tc
r
Δ=
Δ 2
,z
tc
z
Δ=
Δ
h
R1
R2
1
2
3
z
4
8
5
6
r
O
R1 R2
h
7
Fig. 1. General diagram of a FOG coil and its cross section with indicated heat flow directions; 1 is a coil, 2 is the cross section,
3 and 5 are radial heat flows, 4 and 6 are axial heat flows, 7 is the fiber–compound medium, 8 is the coil carcass, R1 and R2 are
the inner and outer coil radii, and h is the coil height.

3. JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No. 7 2013
TEMPERATURE CHARACTERISTICS OF FIBER OPTIC GYROSCOPE 747
points of large thermal conductivity jumps. However,
the latter are absent in the medium; so, specifically for
the thermal drift, this scheme provides for rapid con
vergence in the case of time mesh refinement (step
reduction). The convergence is more rapid than that
for ξ = 1 (Yanenko method [12]) by, at least order, an
order of magnitude.
As the boundary conditions (BCs) at r = R1,2, z = 0,
and z = h (values R1,2 and h are shown in Fig. 1) we use
a combination of the BCs of the second and third
kinds (BC–2 and BC–3) [10]:
where α is the coefficient of heat exchange with the
environment (BC–2 for α = 0), θr1,2(z, t) are radial
external heat flows falling on the boundaries r = R1,2,
θz0,h(r, t) are the axial external heat flows falling on the
boundaries z = 0 and z = h (BC–3 for θr1,2 = θz0,h = 0),
and Т(t) is the environmental temperature. Calculated
by the described scheme, the temperature field is used
in (1a) and (1b), providing for a temperature drift.
2. FIBER WINDING TECHNIQUES
Consider the quadruple winding (QW) [2–4] and
winding from [8]. They are illustrated in Figs. 2a, 2b,
where the light propagates in one direction through
the turns designated by filled circles and in another
direction through the turns designated by empty cir
( ) ( )1,21,2
1,2( ) , ,r Rr R
T r T T t r z t==
κ∂ ∂ + α − = θ⎡ ⎤⎣ ⎦
( ) [ ] ( )0, 0,0,
( ) , ,z h hz h
T z T T t z r t==
κ∂ ∂ + α − = θ
cles [2]. On the basis of Fig. 2b, we call the second
winding a chess winding (its abbreviation CW should
not be confused with clockwise).
For the QW, the fiber midpoint is placed on the bot
tom left side, the first layer is wound in one direction,
the second layer is wound in the opposite direction,
the third layer is wound in the same direction as the
second layer, the fourth layer is wound in the same
direction as the first layer, and so on. Each four layers
are called quadrupoles, their number may be integer or
half integer. In the first case, the total lengths of filled
circle and empty circle layers are equal to each other,
unlike the second case. The latter means that the SE
can tend to a nonzero asymptotic value (similarly to
the dipole winding also described in [2–4]). Besides
this, in the case of the half integer number of quadru
poles, the winding is finished near the right wall, lead
ing to strong sensitivity to the axial temperature gradi
ent. Thus, number Nr of layers should be a multiple of
four. As a result, for the QW, the fiber sections equidis
tant from its midpoint can be brought together; so,
presently, the QW is regarded as the most suitable for
high performance FOGs [2–7].
As for the CW, the fiber midpoint is at point 2 in
Fig. 2b, and two fiber halves are wound in the opposite
directions to the vertical edges. After reaching these
edges (the first layer) fiber sections are wound away
from these edges to baffle 1; then, a transition of fiber
sections into other winding halves divided by baffle
1 takes place. Next, the fiber is again wound to vertical
edges; then, again to baffle 1; after that, there is one
r
z
r
z
(а) (б)
1
2
Fig. 2. FOG coil cross section with (a) QW and (b) CW. Filled and empty circles denote the turns along which the light propagates
in opposite directions; 1 is a baffle and 2 is the fiber midpoint.

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A.M. KURBATOV, R.A. KURBATOV
more transition to other winding halves, and so on.
This winding type is much easier to implement than
the QW due to smooth fiber transitions from one layer
to another (near vertical edges and through baffle 1 in
Fig. 2b).
For the CW, two modifications are possible: with a
single outer layer (Fig. 2b), when fiber ends are situ
ated near vertical edges, and without it (fiber ends are
together near baffle 1). It is clear that, in the case of the
high regularity of fiber layers forming, the CW is prin
cipally nonsusceptible to radial thermal flows and to
axial flows with equal powers (symmetrical axial tem
perature gradient).
However, for the CW, unlike the QW, fiber sections
equidistant from the fiber midpoint are not placed
together; so, the sensitivity to single sided axial ther
mal flow should take place (asymmetrical axial tem
perature gradient). One may think that the SE here
will be as large as for ordinary winding (OW), which is
made sequentially from lower layers to upper ones [2–
4], but this is not so. Indeed, the CW part situated
under the outer layer can be divided into pairs of layers
(Fig. 2b). Two layers of each pair give a contribution to
the SE with the same signs, but the contributions from
different layer pairs will be of the variable sign. On the
one hand, each following pair consists of sections
more distant from the fiber midpoint, than the previ
ous pair; so, there is no interpair SE cancellation. On
the other hand, this allows us to expect that, here, the
SE, at least, will be not as large, as for the OW.
Thus, the QW places together the fiber sections
equidistant from the fiber midpoint, thus, ensuring
maximally close physical conditions for them. In the
case of the CW this is not so, but this winding yields an
original way of summing the SE throughout individual
fiber turns, yielding a small resulting thermal drift.
3. CALCULATION OF THE THERMAL DRIFT
For the SE calculation, we set radial heat flows for
the QW ([4, 13]) and a single sided axial flow for the
CW (the worst situations for them). As will be shown
below, a low coil (see above) is better for both winding
techniques.
Assume that the medium is incorporated into a
metallic carcass of invar with 1 mm thick walls. The
thermal parameters of the rest materials correspond to
[4] and are listed in Table 1. Assume that the heat flow
has a power which warms up the wall the closest to its
carcass approximately by 10°С in 10 min. In Figs. 3a
and 3b, the SE time dependences are shown for the
outer and inner radial heat flows at 2R1 = 30 mm,
L = 1000 m, the fiber diameter 80 µm, the fiber coat
ing diameter 160 µm, the diameter of the fiber with
compound d = 200 µm, and the number of fiber layers
along the r axis Nr = 92. For the outer radial flow, the
SE peak value is 125 deg/h; for the inner flow, it is only
0.37 deg/h. Such difference is due to the fact that the
outer layers are most distant from the fiber midpoint,
and vise versa for the inner layers [4].
Note, that, under the axial heat flow, the SE
extreme value is 3.1 deg/h due to the thermal conduc
tivity jump at the carcass/medium boundary, which
Table 1
Material
Thermal conductivity,
m2
/min
Invar 2.18 × 10–4
Quartz fiber 5.08 × 10–5
Fiber coating 7.8 × 10–6
Potting compound 7.8 × 10–6
0
–20
–40
–60
–80
–100
–120
–140
3210
t, s
(a)ΔΩ, deg/h
0.05
0
–0.05
–0.10
–0.15
–0.20
–0.35
–0.40
3210
t, s
(б)ΔΩ, deg/h
–0.25
–0.30
Fig. 3. Temperature drift for QW in the presence of (a) external and (b) internal radial heat flows.

5. JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No. 7 2013
TEMPERATURE CHARACTERISTICS OF FIBER OPTIC GYROSCOPE 749
distorts the thermal field. In the absence of this jump,
the QW sensitivity to axial heat flow is small.
Let us give a physical explanation of the results.
While the coil is warmed, the function in the
medium exhibits the following behavior. At first, this
function is zero (heat did not pass through the car
cass); then, it becomes nonzero successively in the first
layers, but it is nonuniformly distributed over them
and sharply grows in time. Thus, these layers give sub
stantially different contributions to the SE; so, as a
result, it is large enough (Fig. 3a). However, then the
function involves more and more layers and
decreases in time, but the principal moment is that it
begins to be more and more uniformly distributed over
the medium. The latter means rather uniform sum
ming of SE contributions from individual quadru
poles, so that the SE value in Fig. 3a quickly goes
down.
Thus, it follows that, for the QW, it is not important
what number of winding layers will be after the first
layers, which form the SE extremum in Fig. 3a.
Besides this, the higher the coil, the larger the number
of turns within a layer; i.e., the larger the contribution
of each layer to the SE. This means that the low coil is
more advantageous.
In the presence of the radial heat flow from the
inside to the outside (Fig. 3b), the SE has a negative
extremum, then, reverses the sign (as in [4]), and,
next, tends to zero after 4 min. This slow decaying was
not observed in [4, 13], where the SE after the sign
T
T
reversal tends to zero within a few seconds. In our
case, such a long decaying is due to fast heat branching
through the side carcass walls to layers more distant
from the fiber midpoint (and their involvement from
the medium lateral sides), in comparison with direct
heat wave penetration into the medium after passing the
carcass wall that is the closest to the heat flow. Note that,
in the absence of side walls, our calculation results are in
good agreement with the data from [4, 13].
Thus, the QW indeed does not provide for coil
acceptable performance itself.
Figure 4 illustrates the SE for the CW under the
single side axial heat flow with the same power as in
the case of the QW. It is seen that the SE extremum for
the CW with an outer layer is seven times smaller than
the absolute value of the SE extremum for the CW
without an outer layer, which is in good agreement
with the data from [8]. This is explained by the fact
that the total contribution of layer pairs that precede
the outer layer to the SE is close to the contribution of
the outer layer, but has the opposite sign. As it is seen
from Fig. 4, in both cases, the absolute value of the SE
extremumappearstobemuchsmallerthanthatinFig.3a.
Thus, although in the CW, equividistant sections are
not put together, the SE values are much smaller than
for the QW and OW.
Note that raising of compound heat conductivity
by 10 times leads to the absolute value of the SE extre
mum for the CW in the presence of an outer layer is
reduced by 3 times, and, in the absence of an outer
layer, it i reduced only by 5 deg/h. This is probably due
0
–10
–20
–30
15129630
t, s
(b)
4
3
2
0
1512963
t, s
(а)
1
ΔΩ, deg/h
Fig. 4. Temperature drift for CW (a) with and (b) without an outer layer.

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JOURNAL OF CJOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No. 7 2013
A.M. KURBATOV, R.A. KURBATOV
to the fact that, near the outer layer, the temperature
field distortion due to the jump of the medium and
carcass’s thermal parameters now is smaller. That is
why the SE contribution of the outer layer becomes
closer in the absolute value (and retains the opposite
sign!) to the contribution of the rest layers. However, it
is clear that, in itself, the CW, similarly to the QW, does
not provide for coil acceptable performance either.
4. THERMAL INSULATION
AND METALLIC SCREENING
For coil protection from thermal fields one can
thermally insulate it, for example, by an air layer, as it
is described in [6]. Howeve,r in this case, convection
heat flows can be formed; therefore, for thermal insu
lation, it is better to use a solid medium. As an insula
tor, let us consider foamed polyurethane, which has a
low heat conductivity (0.03 W/(m K)), high heat
capacity (1500 W/(sec kg K)), and high enough den
sity (200 kg/m3
). According to the calculation, for the
SE to be not not higher than a value of 0.01 deg/h for
both winding cases, a layer with a thickness of several
tens millimeters is required, which strongly increases
the coil size. The situation is a little better for the lower
coil (Nr = 112) and for a heat conductive compound,
but this is still not enough.
On the contrary, if one tries to suppress the thermal
drift with the help of a copper carcass, then, its thick
ness also should be several tens of millimeters,
although the drift time duration here is smaller by two
or three 2–3 orders of magnitude.
In [6], a combined application of the QW, thermal
insulation (air), and metallic screening of the coil
wound on a copper carcass is described. Let us show
that, combining the thermal insulation, metallic
screens, and a heat conductive compound, for the CW,
one can reach a required accuracy, while keeping the
coil size small enough. We consider only a low coil
(Nr = 112) with the compound thermal conductivity
#10 times larger than in Table 1.
Consider a coil with the cross section shown in Fig. 5.
The coil contains a Permalloy screen, which is also a
magnetic shield, foamed polyurethane and copper
layers, a carcass with a baffle, and a medium. The geo
metric parameters of the coil and layers are summa
rized in Table 2. In Fig. 6, the SE behavior is shown for
this coil. It is seen that the CW with and outer layer
provides for the accuracy 0.01 deg/h at a rather small
coil dimension (even with a 3 mm thick Permalloy
screen). Note that a similar structure (but with 2.5
mm thick radial insulator and 1.5 mm thick lateral
thermal layers) yields for the QW the extreme SE value
~0.1 deg/h, which is larger by an order of magnitude
than for the CW with an outer layer but smaller by an
order of magnitude than for the CW without an outer
layer.
It is also clear that metallic screens reduce the
thickness of ths lateral layer of the thermal insulator to
the value 2.5 mm; however, even this thin layer plays an
important role, because, without it, the SE extremum
increases more than by an order of magnitude. Besides
1
2
3
4
5
r
z
Fig. 5. FOG coil cross section; 1 is a Permalloy screen, 2 is a thermal insulator, 3 is copper, 4 is a carrying carcass, 5 is a medium.
Table 2
Parameter Value, mm
First (inner) fiber layer diameter 30
Coil outer diameter 86.4
Coil height 25.8
Permalloy screen width 3
Thermal insulation lateral side layers width 2.5
Thermal insulation radial layers width 1.5
Copper layers width 0.5

7. JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No. 7 2013
TEMPERATURE CHARACTERISTICS OF FIBER OPTIC GYROSCOPE 751
this, the SE time duration appears to be shorter by two
orders of magnitude than in the above case, corre
sponding to thermal insulation alone. This could be
explained by the fact that the Permalloy layer effec
tively branches the heat to the coil lateral wall opposite
to the one where the heat flow falls, a circumstance
that is critical for the CW.
Besides this, the copper layer yields additionally
reduces the SE value by a factor of four, which is prob
ably due to more rapid equalization of axial heat flows .
In the considered coil, it is also possible to deposit
copper onto the inner carcass walls in each of the two
regions containing the fiber. However, according to
the calculation, this technique does not lead to a sub
stantial change in the SE value.
Note in addition that the increase of the compound
thermal conductivity, in turn, yields the two fold SE
value reduction. Thus combined application of the
CW fiber, thermal insulation, metallic screens, and a
heat conductive compound allows reaching the FOG
coil low temperature sensitivity, relatively small
dimensions of the coil being retained.
5. ON THE SHUPE EFFECT
OF THE SECOND KIND
The purely thermal drift considered above is usually
called as SE of the first kind or SE 1 [5], because, in
[5, 6, 14], a conception of the SE of the second kind
1
(SE 2) is introduced. The latter effect is considered to
mean the FOG drift due to thermal mechanical
stresses. These arise from the difference of the thermal
expansion coefficients (TECs) of coil composing
materials. Due to the photoelastic effect, these stresses
induce fiber refractive index variations in time in addi
tion to the value dn/dT, which is responsible for SE–1.
According to [5, 14], a feature, differing SE–2
from SE–1, is the presence of a drift even in the case
when time varying temperature is uniformly distrib
uted over the coil cross section. This is due to the fact
that mechanical stresses in this situation at any time
moment (unlike the temperature) are distributed over
the coil cross section nonuniformly. This means that
the SE 2 time duration can be much longer than that
of SE 1. Note, however, that, in [5, 6, 14], the case of
the QW is considered. In this situation, SE 2 disap
pears only after temperature equilibrium distribution
over the coil cross section is settled; i.e., (for
example, as a result of equalization of the external heat
flow by the convective heat exchange with the envi
ronment). At the same time, for the CW, it is obvious
that SE–2 disappears not only for the uniform field
distribution over the coil cross section, but even for its
symmetrical distribution over it. Thus, the above
described ways of quick temperature equalization over
the coil cross section for tyhe CW should also reduce
the SE 2 time duration.
0T =
,T
0
–0.2
–0.4
–0.6
–0.8
543210
t, s
ΔΩ, deg/h
0.010
0.005
0
–0.005
543210
t, s
ΔΩ, deg/h
(a)
(b)
Fig. 6. Temperature drift in the case of CW for the coil cross section, shown in Fig. 5 for CW (a) with and (b) without an outer
layer.

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JOURNAL OF CJOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS Vol. 58 No. 7 2013
A.M. KURBATOV, R.A. KURBATOV
The quantitative calculation of SE 2 requires an
additional investigation. Note that, as certain addi
tional practical measures preventing from SE 2, in
[5, 7], it is suggested applying a carbon coil carcass
(low TEC, high heat conductivity) and its advantage
over an aluminum carcass with a higher TEC is dem
onstrated. Due to exactly this reason, we have consid
ered above the carcass of invar (low TEC), whose rel
atively low thermal conductivity can be compensated
for by the copper layer that has also been considered
above.
CONCLUSION
According to quantitative 2D modeling of SE 1
(purely temperature drift), of various fiber winding
techniques for FOG sensing coil, the chess winding
with a single outer layer [8] provides for the best results
for the coil temperature sensitivity, leaving behind even
the quadruple winding, which is now regarded as the
best for high–accuracy FOGs. Besides this, according
to qualitative consideration, the CW should be advanta
geous in terms of the time duration of SE 2 induced by
thermal stresses. Note that, here, we have assumed that
fiber turns are placed with ideal regularity, whereas their
displacements and coil asymmetry, unavoidable in
practice, can lead to and additional drift.
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1
SPELL: 1. Shupe, 2. integrands