pforzheim university of applied sciences opto & measurements lab prof. dr. mohr fibergyroenvsens...
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FiberGyroEnvSens PF 30.04.03
Page 1Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Error signal buildup
in fiber gyroscopes
with their coil subjected to environmental influences
F. Mohr
FiberGyroEnvSens PF 30.04.03
Page 2Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Gyroscope basic operation
FiberGyroEnvSens PF 30.04.03
Page 3Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Sagnac effect
FiberGyroEnvSens PF 30.04.03
Page 4Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Basic configuration of fibre gyroscope
beam splitters
source
detector
light source
fiber couplers
sensorcoil
a
b
I0
I1 I2
FiberGyroEnvSens PF 30.04.03
Page 5Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Interferometric output signals of fiber gyroscope
I1
I2
)cos(12
II 01
)cos(12
II 0
2
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Page 6Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Gyro housing
FiberGyroEnvSens PF 30.04.03
Page 7Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Gyro source and
electronics module
FiberGyroEnvSens PF 30.04.03
Page 8Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
FiberGyroEnvSens PF 30.04.03
Page 9Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Formation of phase error
FiberGyroEnvSens PF 30.04.03
Page 10Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Phase delay of light wave after propagation through length L
zz=0 z=L
L
0
L
00 dz)z(ndz)z(
FiberGyroEnvSens PF 30.04.03
Page 11Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
L
000 dz)z()n
n(nL
Phase delay with the medium subjected to temperature gradients
zz=0 z=Lheatsource
cooler
(z)
L
000 dz)
c
zLt,z()n
n(nL)t(
Phase delay with time-constant thermal gradients
With the medium subjected to fluctuating temperature distribution
(t = time when light wave exits from fiber end)
FiberGyroEnvSens PF 30.04.03
Page 12Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Thermal error signal buildup
in fiber gyroscope
Phase delay of clockwise wave
L
000CW dz)
c
zLt,z(
nnL)t(
dzzCW
CCWBeamSplitter
z
I
L
... of counter clockwise wave
L
000CCW dz)
c
zt,z(
nnL)t(
Differential phase delay
L
0
0E dz)c
zLt,z()
c
zt,z(
n)t(
L
00
0E dzz2L)t,z(
nn
c)t(Same after some recalculation
L
0
E dzz2L)t,z(n
nDL
1)t(Error rotation rate
FiberGyroEnvSens PF 30.04.03
Page 13Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Calculation and measurement of temperature transients
FiberGyroEnvSens PF 30.04.03
Page 14Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Sensing coil geometries
A
B
A
B
View A-B
dz=0z=L
dz=0
z=L
ZYL
DIP
i
a
i
a
SYM
QAD
dz=0z=L a
i
d
z=0
z=L
i
a
FiberGyroEnvSens PF 30.04.03
Page 15Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Measurement arrangement for determination of
temperature transients and
rate error SagnacInter-fero-meter
(thermally isolated)
DataCaptureandProces-sing
Heating Cur-rent Source
Fiber EndsHeating Foilwith Current Leads
a b
c
Coil
HeatSource
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Page 16Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Measurement results
t
P
t=0 t=660s
E
P0
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Page 17Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Heat propagation model
I
R a
R a
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Page 18Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Thermal transients: theoretical and experimental results
Lines: calculated, with para-meters adjusted for best fit
dots: measured
time /sec
K
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Page 19Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Thermal transients and rotation rate error
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Page 20Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Sensor coil subjected to homogeneous
temperature change
• No travelling thermal wave!• Temperature homogeneous but
nonstationary• In spite of homogeneity of temperature
distribution:error effects arise because of elastic deformation of fiber
• cause: different thermoelastic properties of coil constituents (aluminum, glue, quartz fiber)
Schnitt-ebene
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Page 21Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Continuation of the project
• Basic goal: Taking into account elastical deformation of the fiber
• Potential causes of deformation: - Nonstationary temperature of whole coil - Vibration
FiberGyroEnvSens PF 30.04.03
Page 22Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Steps I:• Calculating elastical deformation of the fiber with homogeneous but unstationary
temperature distribution in coil • complicated thermoelastic problem, two attempts:
- closed-form analytical approach; - finite element modelling (FEM)• Compound modelled in two ways:
- fiber, glue, aluminum are homogeneous layers each- glue, aluminum homogeneous; fiber unidirectional laminate
• After elastic deformation is known: Determination of error rate
L
0r1211
3
z120
0
L
0r1211
2
z120
dzL
z21)t,z()pp(
2
n)t,z()p
2
2n1(n)t,z(
n
c
Ln
dzc
z2L)t,z()pp(
2
n)t,z()p
2
2n1()t,z(
n
n
1n)t(
p11, p12 = elastooptical constants of fiber, r, z = fiber strain
FiberGyroEnvSens PF 30.04.03
Page 23Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr
Steps II:
• After treatment of thermal problem is known and experienced:Extension to vibration and to elastic deformation resulting therefrom
• Experimental verification using electrodynamic shaker