1. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 1 Error signal buildup in fiber gyroscopes with their coil subjected to environmental influences F. Mohr

2. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 2 Gyroscope basic operation

3. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 3 Sagnac effect

4. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 4 Basic configuration of fibre gyroscope

5. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 5 Interferometric output signals of fiber gyroscope

6. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 6 Gyro housing

7. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 7 Gyro source and electronics module

8. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 8

9. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 9 Formation of phase error

10. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 10 Phase delay of light wave after propagation through length L

11. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 11 Phase delay with the medium subjected to temperature gradients Phase delay with time-constant thermal gradients With the medium subjected to fluctuating temperature distribution (t = time when light wave exits from fiber end)

12. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 12 Thermal error signal buildup in fiber gyroscope Phase delay of clockwise wave... of counter clockwise wave Differential phase delay Same after some recalculation Error rotation rate

13. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 13 Calculation and measurement of temperature transients

14. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 14 Sensing coil geometries

15. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 15 Measurement arrangement for determination of temperature transients and rate error

16. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 16 Measurement results

17. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 17 Heat propagation model

18. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 18 Thermal transients: theoretical and experimental results Lines: calculated, with para- meters adjusted for best fit dots: measured time /sec K

19. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 19 Thermal transients and rotation rate error

20. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 20 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)

21. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 21 Continuation of the project Basic goal: Taking into account elastical deformation of the fiber Potential causes of deformation: - Nonstationary temperature of whole coil - Vibration

22. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 22 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 p 11, p 12 = elastooptical constants of fiber, r, z = fiber strain

23. Pforzheim University of Applied Sciences Opto & Measurements Lab Prof. Dr. Mohr FiberGyroEnvSens PF 30.04.03 Page 23 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