Development of the mathematical model of the magneto-contact thermal fire alarm

Mathematical models of a fire detector have been developed taking into account the dependence of the magnetization of the contacts of the sensitive element on the temperature and the parameters of the contact material. The obtained equations of the dynamics of the SP take into account the type and structure of the materials of the contact elements of the ЧЭ and the dependence of their magnetization on the temperature and correspond to the inertial positional link of the first order, written in relative variables with constant coefficients. As a result of studying the current literature, the characteristics of the material of the magnetic contacts have been taken into account in the models to determine its optimal dynamic parameters. The mathematical model of the detector is a system of equations consisting of the heat balance equation under conditions of non-stationary heat exchange with the assumption of uniform heating of the contacts of the sensitive element over the entire depth. The second is the equation of the relationship between the magnetization of contacts soldered in a reed switch and temperature. The obtained detector dynamics equations take into account the type and structure of the materials of the contact elements and the dependence of their magnetization on temperature and correspond to the inertial positional link of the first order. The variables of the equations are relative to the linearization point, with constant coefficients. The equations allow to study the detector operation parameters with the principle of the dependence of magnetic induction on temperature. The dynamics equations allow to study the dynamic parameters of the operation of thermal fire detectors, the relative error of the results does not exceed 5 %. The obtained results of the simulation of the fire detector operation confirm the correctness of the chosen hypothesis, and the determined parameters of the fire detector operation coincide with the experimental data. The results of the conducted studies allow to provide recommendations on the selection of the detector operation parameters, which will improve the quality of their operation: static and dynamic operation temperatures, inertia, operation time.