Mathematical Model of Thermal Drift of Fiber Optic Gyroscope Taking into Account Quadrupole Spooling of Fiber

The paper considers the development of a mathematical model of the thermal drift of a fiber-optic gyroscope (FOG) due to the thermo-optic effect, which takes into account the features of quadrupole spooling of fiber on the spool. Such devices are widely used in stabilization, orientation, and motion control systems of aerospace and ground techniques. The main task in achieving this goal is to separate the nonstationary temperature function into a temporal component and a spatial one (the function characterizing the temperature distribution along the fiber filament for the quadrupole spooling of fiber at radial temperature gradient). When developing the model, the initial assumption is that the array of fiber filaments on the spool is considered as a periodic continuous structure (successive layers with the same thermophysical characteristics). This allows taking into account only radial temperature gradients and assuming that the temperature at each instant in the corresponding fiber layer on the spool is distributed uniformly. The study provides the justification of the correctness of the proposed approach to constructing the thermal drift model by simulating the temperature in each layer of the fiber spool using the method of elementary balances. Modeling is performed in specially developed software, in which the functions of graphical output of calculation results are implemented. Based on computational experiments, it is substantiated that in real conditions of FOG operation at a relatively low rate of change in ambient temperature, the law of temperature variation in the fiber spool in the radial direction can be assumed as linear. The function of the spatial distribution of the temperature field along the fiber filament is determined. Using this function, an algorithm of its application for plotting the temperature distribution in a fiber spool with given geometric parameters close to the real ones is implemented. An example of calculating the thermal drift of the device for specified parameters of the fiber and geometric parameters of the spool, which are close to the parameters of devices used in practice, is given. The proposed model for calculating the thermal drift of a fiber-optic gyroscope extends and complements the potentialities of the method of elementary balances, which makes it possible to implement a simple and effective algorithm for calculating non-stationary temperature fields and thermal drift of almost any fiber-optic gyroscope of typical design without engaging costly software. The proposed model will allow developers of automated object motion control systems to implement effective algorithms for calibration and correction of thermal drift of a fiber optic gyroscope.