Mathematical Modeling of Operational Reliability of Ground-Based Navigation Systems

Abstract

The theoretical justification for improving the effectiveness of vibration isolation for navigation equipment by reducing the natural frequency of the elastic suspension through the use of an additional electromagnetic loading system on the moving part is presented. An overview of the main elements of primary sensors and vibration protection systems for reproducing vibrations is provided. It is emphasized that vibration isolation of navigation equipment in the low-frequency disturbance range, typical for terrestrial carriers, is a crucial component in preventing emergency situations on airborne and marine vessels. A detailed calculation scheme for a vibration test stand using vertically installed flat springs is presented. Relationships between the natural frequency of the suspension and the system parameters are determined. One method for reducing the natural frequency of an elastic suspension on flat springs is analyzed. The calculation scheme for the suspension with vertically installed elastic springs is outlined. The stability conditions of the linear system, which depend on the amplitude of oscillations, are analytically investigated. It is emphasized that there is no translational movement of the suspension other than the chosen one. It is proposed to consider the calculation scheme of the suspension in the absence of dry friction. The structural component of the magnetic system is analyzed. The system of dispersive fluxes and their concentration in the air gap is outlined. An analysis of the compensatory nonlinearity of the stiffness characteristic of elastic elements is carried out. The reduction of distortions in the shape of the moving oscillations of the moving platform in the horizontal plane is analyzed. Stiffness characteristics of the suspension with a magnet for several actual values of kkk and δ\deltaδ are provided. Experimental calculations demonstrate that this vibration isolation system for navigation equipment leads to a significant reduction in the natural frequency of the suspension, ensuring its operational reliability and maximum prevention of low-frequency horizontal vibrations.