Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF...

FiberGyroEnvSens PF 30.04.03

Pforzheim 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



Gyroscope basic operation



Sagnac effect



Basic configuration of fibre gyroscope

beam splitters

source

detector

light source

fiber couplers

sensorcoil

a

b

I0

I1 I2



Interferometric output signals of fiber gyroscope

I1

I2

)cos(12

II 01

)cos(12

II 0

2



Gyro housing



Gyro source and

electronics module



Formation of phase error



Phase delay of light wave after propagation through length L

zz=0 z=L

L

0

L

00 dz)z(ndz)z(



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)



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



Calculation and measurement of temperature transients



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



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



Measurement results

t

P

t=0 t=660s

E

P0



Heat propagation model

I

R a

R a



Thermal transients: theoretical and experimental results

Lines: calculated, with para-meters adjusted for best fit

dots: measured

time /sec

K



Thermal transients and rotation rate error



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



Continuation of the project

• Basic goal: Taking into account elastical deformation of the fiber

• Potential causes of deformation: - Nonstationary temperature of whole coil - Vibration



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



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

Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF...

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