Abstract

We introduce a parameter called pointing error thermal sensitivity (PETS) for quantitatively determining the quality of a quadrupolar (QAD) fiber coil under radial temperature variations. We show both analytically and experimentally that the pointing error of a fiber gyro incorporating the fiber coil is linearly proportional to the final radial thermal gradient on the coil, with PETS as the proportional constant. We further show that PETS is linearly proportional to another parameter called effective asymmetric length of the coil. By thermally inducing different radial thermal gradients on the fiber coil and measuring the corresponding pointing errors in a gyroscopic measurement setup, we can confidently determine the PETS of the fiber coil and its associated effective asymmetric length caused by imperfections in coil winding. Consequently, we are able to precisely trim the coil to achieve best thermal performance.

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. R. P. Goettsche and R. A. Bergh, “Trimming of fiber optic winding and method of achieving same,” U.S.Patent:5528715, 6–18 (1996).
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    [CrossRef]
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    [CrossRef] [PubMed]
  10. W. Feng, X. Wang, and W. Wang, “Effect of turns’ difference in each layer on temperature performance of fiber optic gyroscopoe,” Journal of Chinese Inertial Technology19, 487–493 (2011).
  11. C. Mao, Z. Gong, X. Mou, and G. Yang, “Finite difference method for temperature field in fiber optical gyroscope,” Piezoelectrics and Acoustooptics25, 98–101 (2003).
  12. M. Li, T. Liu, Y. Zhou, J. Jiang, L. Hou, J. Wang, and X. S. Yao, “A 3-D model for analyzing thermal transient effects in fiber gyro coils,” Proc. SPIE, Advanced Sensor Systems and Applications III, 6830–6834 (2007).
  13. C. M. Lofts, P. B. Ruffin, M. D. Parker, and C. C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils,” Opt. Eng.34(10), 2856–2863 (1995).
    [CrossRef]
  14. J. Sawyer, P. B. Ruffin, and C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils, part II,” Opt. Eng.36(1), 29–34 (1997).
    [CrossRef]

2011

W. Feng, X. Wang, and W. Wang, “Effect of turns’ difference in each layer on temperature performance of fiber optic gyroscopoe,” Journal of Chinese Inertial Technology19, 487–493 (2011).

2003

C. Mao, Z. Gong, X. Mou, and G. Yang, “Finite difference method for temperature field in fiber optical gyroscope,” Piezoelectrics and Acoustooptics25, 98–101 (2003).

1997

J. Sawyer, P. B. Ruffin, and C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils, part II,” Opt. Eng.36(1), 29–34 (1997).
[CrossRef]

1996

H. C. Lefevre, “Fundamental of interferometeric fiber optic gyroscope,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 46–60 (1996).

G. A. Sanders, B. Szafraniec, R. Y. Liu, C. L. Laskoskie, L. K. Strandjord, and G. Weed, “Fiber optic gyros for space, marine, and aviation applications,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 61–71 (1996).
[CrossRef]

R. Dyott, “Reduction of the Shupe effect in fibre optic gyros; the random-wound coil,” Electron. Lett.32(23), 2177–2178 (1996).
[CrossRef]

F. Mohr, “Thermooptically induced bias drift in fiber optical Sagnac interferometers,” J. Lightwave Technol.14(1), 27–41 (1996).
[CrossRef]

1995

C. M. Lofts, P. B. Ruffin, M. D. Parker, and C. C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils,” Opt. Eng.34(10), 2856–2863 (1995).
[CrossRef]

1993

1980

1976

Chomát, M.

Dyott, R.

R. Dyott, “Reduction of the Shupe effect in fibre optic gyros; the random-wound coil,” Electron. Lett.32(23), 2177–2178 (1996).
[CrossRef]

Feng, W.

W. Feng, X. Wang, and W. Wang, “Effect of turns’ difference in each layer on temperature performance of fiber optic gyroscopoe,” Journal of Chinese Inertial Technology19, 487–493 (2011).

Gong, Z.

C. Mao, Z. Gong, X. Mou, and G. Yang, “Finite difference method for temperature field in fiber optical gyroscope,” Piezoelectrics and Acoustooptics25, 98–101 (2003).

Laskoskie, C. L.

G. A. Sanders, B. Szafraniec, R. Y. Liu, C. L. Laskoskie, L. K. Strandjord, and G. Weed, “Fiber optic gyros for space, marine, and aviation applications,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 61–71 (1996).
[CrossRef]

Lefevre, H. C.

H. C. Lefevre, “Fundamental of interferometeric fiber optic gyroscope,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 46–60 (1996).

Liu, R. Y.

G. A. Sanders, B. Szafraniec, R. Y. Liu, C. L. Laskoskie, L. K. Strandjord, and G. Weed, “Fiber optic gyros for space, marine, and aviation applications,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 61–71 (1996).
[CrossRef]

Lofts, C. M.

C. M. Lofts, P. B. Ruffin, M. D. Parker, and C. C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils,” Opt. Eng.34(10), 2856–2863 (1995).
[CrossRef]

Mao, C.

C. Mao, Z. Gong, X. Mou, and G. Yang, “Finite difference method for temperature field in fiber optical gyroscope,” Piezoelectrics and Acoustooptics25, 98–101 (2003).

Mohr, F.

F. Mohr, “Thermooptically induced bias drift in fiber optical Sagnac interferometers,” J. Lightwave Technol.14(1), 27–41 (1996).
[CrossRef]

Mou, X.

C. Mao, Z. Gong, X. Mou, and G. Yang, “Finite difference method for temperature field in fiber optical gyroscope,” Piezoelectrics and Acoustooptics25, 98–101 (2003).

Parker, M. D.

C. M. Lofts, P. B. Ruffin, M. D. Parker, and C. C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils,” Opt. Eng.34(10), 2856–2863 (1995).
[CrossRef]

Ruffin, P. B.

J. Sawyer, P. B. Ruffin, and C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils, part II,” Opt. Eng.36(1), 29–34 (1997).
[CrossRef]

C. M. Lofts, P. B. Ruffin, M. D. Parker, and C. C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils,” Opt. Eng.34(10), 2856–2863 (1995).
[CrossRef]

Sanders, G. A.

G. A. Sanders, B. Szafraniec, R. Y. Liu, C. L. Laskoskie, L. K. Strandjord, and G. Weed, “Fiber optic gyros for space, marine, and aviation applications,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 61–71 (1996).
[CrossRef]

Sawyer, J.

J. Sawyer, P. B. Ruffin, and C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils, part II,” Opt. Eng.36(1), 29–34 (1997).
[CrossRef]

Shorthill, R. W.

Shupe, D. M.

Strandjord, L. K.

G. A. Sanders, B. Szafraniec, R. Y. Liu, C. L. Laskoskie, L. K. Strandjord, and G. Weed, “Fiber optic gyros for space, marine, and aviation applications,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 61–71 (1996).
[CrossRef]

Sung, C.

J. Sawyer, P. B. Ruffin, and C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils, part II,” Opt. Eng.36(1), 29–34 (1997).
[CrossRef]

Sung, C. C.

C. M. Lofts, P. B. Ruffin, M. D. Parker, and C. C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils,” Opt. Eng.34(10), 2856–2863 (1995).
[CrossRef]

Szafraniec, B.

G. A. Sanders, B. Szafraniec, R. Y. Liu, C. L. Laskoskie, L. K. Strandjord, and G. Weed, “Fiber optic gyros for space, marine, and aviation applications,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 61–71 (1996).
[CrossRef]

Vali, V.

Wang, W.

W. Feng, X. Wang, and W. Wang, “Effect of turns’ difference in each layer on temperature performance of fiber optic gyroscopoe,” Journal of Chinese Inertial Technology19, 487–493 (2011).

Wang, X.

W. Feng, X. Wang, and W. Wang, “Effect of turns’ difference in each layer on temperature performance of fiber optic gyroscopoe,” Journal of Chinese Inertial Technology19, 487–493 (2011).

Weed, G.

G. A. Sanders, B. Szafraniec, R. Y. Liu, C. L. Laskoskie, L. K. Strandjord, and G. Weed, “Fiber optic gyros for space, marine, and aviation applications,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 61–71 (1996).
[CrossRef]

Yang, G.

C. Mao, Z. Gong, X. Mou, and G. Yang, “Finite difference method for temperature field in fiber optical gyroscope,” Piezoelectrics and Acoustooptics25, 98–101 (2003).

Appl. Opt.

Electron. Lett.

R. Dyott, “Reduction of the Shupe effect in fibre optic gyros; the random-wound coil,” Electron. Lett.32(23), 2177–2178 (1996).
[CrossRef]

in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE

H. C. Lefevre, “Fundamental of interferometeric fiber optic gyroscope,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 46–60 (1996).

G. A. Sanders, B. Szafraniec, R. Y. Liu, C. L. Laskoskie, L. K. Strandjord, and G. Weed, “Fiber optic gyros for space, marine, and aviation applications,” in Fiber Optic Gyros: 20 Anniversary Conf., Proc. SPIE2837, 61–71 (1996).
[CrossRef]

J. Lightwave Technol.

F. Mohr, “Thermooptically induced bias drift in fiber optical Sagnac interferometers,” J. Lightwave Technol.14(1), 27–41 (1996).
[CrossRef]

Journal of Chinese Inertial Technology

W. Feng, X. Wang, and W. Wang, “Effect of turns’ difference in each layer on temperature performance of fiber optic gyroscopoe,” Journal of Chinese Inertial Technology19, 487–493 (2011).

Opt. Eng.

C. M. Lofts, P. B. Ruffin, M. D. Parker, and C. C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils,” Opt. Eng.34(10), 2856–2863 (1995).
[CrossRef]

J. Sawyer, P. B. Ruffin, and C. Sung, “Investigation of the effects of temporal thermal gradients in fiber optic gyroscope sensing coils, part II,” Opt. Eng.36(1), 29–34 (1997).
[CrossRef]

Piezoelectrics and Acoustooptics

C. Mao, Z. Gong, X. Mou, and G. Yang, “Finite difference method for temperature field in fiber optical gyroscope,” Piezoelectrics and Acoustooptics25, 98–101 (2003).

Other

M. Li, T. Liu, Y. Zhou, J. Jiang, L. Hou, J. Wang, and X. S. Yao, “A 3-D model for analyzing thermal transient effects in fiber gyro coils,” Proc. SPIE, Advanced Sensor Systems and Applications III, 6830–6834 (2007).

G. A. Sanders, B. Szafraniec, R. Y. Liu, M. S. Bielas, and L. Strandjord, “Fiber-optic gyro development for a broad range of applications,” Proc. SPIE, Fiber Optic and Laser Sensors XIII 2510, 2–11(1995).

R. P. Goettsche and R. A. Bergh, “Trimming of fiber optic winding and method of achieving same,” U.S.Patent:5528715, 6–18 (1996).

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Figures (7)

Fig. 1
Fig. 1

Illustration of a quadrupole-wound fiber coil, where A and B are used to denote fiber layers wound in CCW (solid line) and CW (broken line) directions respectively, and d is the fiber coil thickness. (a) The relative positions of CCW and CW layers. (b) The numbering of each fiber layer in CCW and CW directions, where the height of each grid cell indicates the diameter of the fiber and the lines represent the position of fiber’s center line in the vertical axis.

Fig. 2
Fig. 2

Illustration of asymmetrical fiber wounding. (a) CCW (denoted by A) and CW (denoted by B) wound fiber sections have the same length. (b) CWW section is short by a length of l, resulting in a shift of l/2 of the coil midpoint to the CW side.

Fig. 3
Fig. 3

Gyroscopic setup for measuring thermal induced error signals. Inset a) shows a ribbon heater with a width and a length equal to the width and the perimeter of the coil is wrapped around coil to apply a radial temperature gradient. TC1 and TC2 are the temperatures measured at the outer and inner surfaces of the fiber coil. Inset b) shows TC1 and TC2 as a function of time when a radial temperature excitation is applied, and are stabilized at 70.2°C and 54.3°C respectively, resulting a temperature gradient δT=TC1TC2=15.9 °C

Fig. 4
Fig. 4

(a) Measured rotation rate error (solid line) of a gyro system in Fig. 3 when the fiber coil’s outer layer is subject to a temperature change TC1 (dotted line). (b) Angular error of the gyro system steadily approaches asymptotic value (pointing error), despite the fast fluctuation of the corresponding rate error (solid line).

Fig. 5
Fig. 5

(a) Illustration of coil trimming with two fiber turns unwrapped from the outer layer of the coil. (b) Measured pointing error ψ e of fiber coil as a function of the trimming lengths l when a temperature excitation profile from room temperature to 70°C is applied to the outer layer of the coil.

Fig. 6
Fig. 6

The pointing error taken before coil trimming. The lines indicate the best linear fit through the data points.

Fig. 7
Fig. 7

(a) Pointing error of Coil-2 with different trimming lengths on the “A” portion fiber. The slope of each curve is the PETS of the coil. (b) PETS of Coil-2 as a function of trimming length l and the corresponding theoretical curve of Eq. (9c) for L = 240m, N = 24 and γ=0.0195

Tables (3)

Tables Icon

Table 1 Height and Length of Each Fiber Layer

Tables Icon

Table 2 Measurement Results of γδT and ψ e0 of Three Fiber Coils

Tables Icon

Table 3 Outer Surface Temperature, Final Temperature Gradient, and γ T of Three Coils Under Test

Equations (17)

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Δ φ e (t)= 2τ L β 0 n T [ 0 L/2 T(s,t) t sds 0 L/2 T( s ,t) t s d s ]
Ω e (t)= 4γ L [ 0 L/2 T(s,t) t sds 0 L/2 T( s ,t) t s d s ]
γ= n 2D n T
ψ e ( t )= 0 t Ω e (t) dt= 4γ L [ 0 L/2 ΔT(s, t ) sds 0 L/2 ΔT( s , t ) s d s ]
ψ e0 (t)= 4γ L i=1 4 [ ΔT( A i ,t)ΔT( B i ,t) ] (i1)L/8 iL/8 sds
ψ e (t)= 4γ L { i=1 4 [ ΔT( A i ,t)ΔT( B i ,t) ] (i1) L 8 + l eff 2 iL 8 l eff 2 sds + i=1 3 [ ΔT( A i ,t)ΔT( B i+1 ,t) ] iL 8 l eff 2 iL 8 + l eff 2 sds }
ΔT( A i )=Δ T inner +δT x i d ,( x i =d/16, 7d / 16 , 9d / 16 ,15d/16 )
ΔT( B i )=Δ T inner +δT x i d ,( x i = 3d / 16 , 5d / 16 , 11d / 16 , 13d / 16 )
ψ e0 =γ L 8 2 δT
ψ e =γ( L 8 2 7 8 l eff )δT
ψ e0 =γ L N 2 δT
ψ e = γ T δT= ψ e0 N1 N (γδT) l eff
γ T =γ( L N 2 N1 N l eff )=γ l all
l eff = l eff0 +l
ψ e = ψ e0 N1 N (γδT)l
ψ e0 = ψ e0 N1 N (γδT) l eff0
l eff0 =L/ [ N(N1) ] N l all / (N1 )

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