Research of Optical Fiber Coil Winding Model Based on Large-deformation Theory of Elasticity and Its Application

Optical fiber coil winding model is used to guide proper and high precision coil winding for fiber optic gyroscope (FOG) application. Based on the large-deformation theory of elasticity, stress analysis of optical fiber free end has been made and balance equation of infinitesimal fiber is deduced, then deformation equation is derived by substituting terminal conditions. On condition that only axial tensile force exists, approximate curve equation has been built in small angle deformation scope. The comparison of tangent point longitudinal coordinate result between theory and approximation gives constant of integration, and expression with tangent point as origin of coordinate is readjusted. Analyzing the winding parameters of an example, it is clear that the horizontal distance from the highest point of wheel to fiber tangent point has millimeter order of magnitude and significant difference with fiber tension variation, and maintains invariant when wheel radius changes. The height of tension and accurate position of tangent point are defined for proper fiber guide. For application to fiber optic gyroscope, spiral-disc winding method and nonideal deformation of straddle section are analyzed, and then spiral-disc quadrupole pattern winding method has been introduced and realized by winding system. The winding results approve that the winding model is applicable.