Development of a Homogenized Thermomechanical Model for the Optimized Design of Fiber Optic Gyroscopes

Fiber Optic Gyroscopes (FOG) are high-precision measurement devices that measure the rotation rate of a fiber optic coil along its axis thanks to the Sagnac effect. Two counterpropagative waves are sent into an optical fiber coil. The interferometric phase difference measured between the two waves is proportional to the rotational rate of the coil around its axis. Under thermal loadings, the coil will expand, modifying the optical path of the two waves, thus altering the rotational rate measurement (Mohr effect). In order to understand and reduce this thermal drift, an axisymmetric Finite Element model (M0-model) of the fiber-optic coil has been proposed to evaluate the strain along the entire fiber coil. However, this model is extremely expensive. Indeed, the coil's geometry and the materials' arrangement are complex as they result from the winding of several thousand turns held together by resin. The fiber itself is made of three materials whose thermomechanical properties vary significantly over the wide temperature range that needs to be evaluated. A homogenized model of the coil is proposed here, taking advantage of its periodical internal structure. The obtained orthotropic model allows the use of very coarse meshes, resulting in drastic reductions in computational time over the tested temperature range. The homogenized model is first used on the fine mesh (M1-model) and compared to the M0-model to assess the homogenization error. The homogenized model is then used on a coarse mesh (M2-model) and compared to the M1-model to assess the discretization error. In order to limit the impact of the homogenization error on the Mohr effect estimation, a hybrid model is developed. It is based on a fine model, similar to the M0-model, in the areas where the error is considered too large and on a homogenized M2-model elsewhere.