Mathematical model of air flow movement in a motorized filter respirator

Abstract

Purpose. Development of a mathematical model of the air flow movement in a motorized filter respirator (hereinafter referred to as MFR), which allows ensuring the control of the fan parameters, taking into account external and internal influences on the duration of the protective action and favourable operating conditions. Methodology. To describe linear objects of the “input-output” type, it is convenient to use their transfer functions as mathematical models. In this case, to determine the mathematical description of the MFR operation, two tasks need to be solved. The first is related to finding the structure of the mathematical model, and the second involves determining the coefficients of the polynomials in the numerator and denominator of the transfer function that describes the motion of the air flow in the MFR. Findings. A mathematical model of airflow in a MFR has been developed in the form of a transfer function of the third order; it can be used to develop a pressure control system for the air in the under-mask space in accordance with the user’s work mode in order ensure comfortable working conditions. The presented mathematical model of airflow in the MFR differs from the existing approaches by taking into account the influence of the following external and internal parameters of the system on the performance indicators: the user’s work mode, atmospheric pressure, filter resistance, pressure drop in air ducts with the effect of air accumulation in the under-mask space based on the “capacity-resistance” principle. Numerical coefficients of the mathematical model of airflow in the air duct of the MFR have been determined, which allow adjusting the number of fan rotations according to the time of operation, the increase in resistance on the filters, and the operating mode. Originality. A correlation has been established between the external and internal parameters of the MFR: atmospheric pressure, pressure drop in the air duct, filter resistance, and the user’s work mode with the effect of air accumulation in the sub-mask space reflected according to the “capacity-resistance” principle. Practical value. The parameters of the mathematical model have been determined, which can be used when developing a control system for the airflow movement in the MFR: changes in air flow rate in accordance with different conditions of physical exertion of the user when performing professional activities.