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 coil. These devices are widely used in stabilization, orientation and motion control systems of aerospace and ground techniques. The main task in achieving this goal was to separate the non-stationary 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 allowing is to consider the array of fiber filaments on the spool 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 moment of time in the corresponding fiber layer on the spool is uniformly distributed. The study provides justification of the correctness of the proposed approach in constructing the thermal drift model by simulating the temperature in each layer of the fiber coil using the method of elementary balances. Modeling was 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 change in the fiber coil 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 coil with given geometric parameters close to the real one is implemented. An example of calculating the thermal drift of the device for specified parameters of the fiber and geometric parameters of the coil, closed 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 capabilities 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. The developed model will allow developers of automatic object motion control systems to realize effective algorithms for calibration and correction of thermal drift of a fiber optic gyroscope.