Mathematical Model of Thermal Drift of a Fiber-Optic Gyroscope and its Experimental Verification

The article presents a model of thermal drift of a fiber-optic gyroscope (FOG), caused by the thermal transition process. The model includes thermooptical and elastooptical effects. To find the temperature and strain fields in the fiber circuit, we set up an uncoupled quasistationary thermoelasticity problem. As an impact, we considered the environment heating at a rate of 1 °C/min, followed by a steady-state output. We performed the numerical solution of the problem by the finite element method in the ANSYS software package. The study also shows the distributions of the temperature and strain rates along the fiber over time. The analysis of the calculated data allowed us to establish the qualitative and quantitative features of the drift components caused by the above effects, and to adopt simplifying hypotheses for the working drift model. The experiments performed with three fiber circuits showed satisfactory compliance with the calculated data

References

[1] Sheremet'yev A.G. Volokonnyy opticheskiy giroskop [The fiber-optic gyroscope]. Moscow, Radio i svyaz' Publ., 1987. 152 p.

[2] Herve C. Lefevre. The fiber-optic gyroscope. Boston, Artech House, 2014. 343 p.

[3] Sagnac G. L'éther lumineux démontré par l'effet du vent relatif d'éther dans un interféromètre en rotation uniforme. Comptes rendus de l’Académie des Sciences, 1913, vol. 95, pp. 708–710.

[4] Sagnac G. Sur la preuve de la réalité de l'éther lumineux par l'expérience de l'interférographe tournant. Comptes rendus de l’Académie des Sciences, 1913, vol. 95, pp. 1410–1413.

[5] Andronova I.A., Malykin G.B. Physical problems of fiber gyroscopy based on the Sagnac effect. Physics–Uspekhi, 2002, vol. 45, no. 8, pp. 793–817. DOI: 10.1070/PU2002v045n08ABEH001073

[6] Gromov D.S. Teplovaya zashchita i termostabilizatsiya volokonno-opticheskikh giroskopov. Dis. kand. tekhn. nauk [Thermal protection and thermal stabilization of fiber-optic gyroscopes. Kand. tech. sci. diss.]. Saint-Petersburg, 2014. 134 p. (in Russ.).

[7] Antonova M.V., Matveev V.A. Model of error of a fiber-optic gyro exposed to thermal and magnetic fields. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Priborostr. [Herald of the Bauman Moscow State Tech. Univ., Instrum. Eng.], 2014, no. 3, pp. 73–80 (in Russ.).

[8] Vakhrameev E.I., Galyagin K.S., Ivonin A.S., Oshivalov M.A. Prediction and correction of fiber-optic gyroscope thermal drift. Izvestiya vysshikh uchebnykh zavedeniy. Priborostroenie [Journal of Instrument Engineering], 2013, vol. 56, no. 5, pp. 79–84 (in Russ.).

[9] Shupe D.M. Thermally induced non-reciprocity in the fiber-optic interferometer. Appl. Opt., 1980, vol. 19, no. 5, pp. 654–655. DOI: 10.1364/AO.19.000654

[10] Mohr F., Schadt F. Bias error in fiber optic gyroscopes due to elasto-optic interactions in the sensor fiber. Proc. SPIE, 2004, vol. 5502, pp. 410–413. DOI: 10.1117/12.566654 Available at: http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=848587

[11] Schadt F., Mohr F. Error signal formation in FOGs through thermal and elastooptical environment influence on the sensing coil. Proc. Inertial Sensors and Systems, 2011, pp. 2.1–2.13.

[12] Ling W., Li X., Xu Z., Zhang Z., Wei Y. Thermal effects of fiber sensing coils in different winding pattern considering both thermal gradient and thermal stress. Optics Communications, 2015, vol. 356, pp. 290–295. DOI: 10.1016/j.optcom.2015.08.002

[13] Ling W., Li X., Xu Z., Wei Y. A dicyclic method for suppressing the thermal-induced bias drift of I-FOGs. IEEE Photonics Technology Letters, 2016, vol. 28, no. 3, pp. 272–275. DOI: 10.1109/LPT.2015.2494623

[14] Ling W., Li X., Yang H., Liu P., Xu Z., Wei Y. Reduction of the Shupe effect in interferometric fiber optic gyroscopes: The double cylinder-wound coil. Optics Communications, 2016, vol. 370, pp. 62–67. DOI: 10.1016/j.optcom.2016.02.064

[15] Trufanov A.N., Smetannikov O.Y., Trufanov N.A. Numerical analysis of residual stresses in preform of stress applying part for PANDA-type polarization maintaining optical fibers. Opt. Fiber Technol., 2010, vol. 16, no. 3, pp. 156–161. DOI: 10.1016/j.yofte.2010.02.001

[16] Hocker G.B. Fiber-optic sensing of pressure and temperature. Appl. Opt., 1979, vol. 18, no. 9, pp. 1445–1448. DOI: 10.1364/AO.18.001445

[17] Kinet D., Mégret P., Goossen K.W., Qiu L., Heider D., Caucheteur C. Fiber Bragg grating sensors toward structural health monitoring in composite materials: Challenges and solutions. Sensors, 2014, no. 14, pp. 7394–7419. DOI: 10.3390/s140407394

[18] Butter C.D., Hocker G.B. Fiber optics strain gauge. Appl. Opt., 1978, vol. 17, no. 18, pp. 2867–2869. DOI: 10.1364/AO.17.002867

[19] Narasimhamurthy T.S. Photoelastic and electro-optic properties of crystals. New York, London, Plenum Press, 1981. 514 p.

[20] Novatskiy V. Voprosy termouprugosti [Thermoelasticity issues]. Moscow, AN SSSR Publ., 1962. 364 p.