The calculations can be used in the preliminary assessment of the speed of operation of pneumatic braking systems and in the formulation of guidelines for the construction of a prototypical differential valve. A force rise time of 0.5 s causes the transition of the valve from the accelerating action to the tracking action, with 9.23% delay relative to the system without a valve. In the case of transition of the valve to the tracking action, this time increases only by 9.93%. Based on the calculations, it was found that the differential valve with large control pipe lengths can reduce the response time of the actuator by 42.77% relative to the system without the valve. These parameters can include the length of the control pipe, the throughput between chambers in the control part of the valve and the forcing rise time. The proposed valve can have two states of operation depending on the configuration of relevant parameters. Simplified mathematical models using the lumped method for systems without and with a differential valve are presented. This article presents simulation models of trailer air brake systems in configurations without a valve and with a differential valve, thus demonstrating the rationale for using a valve to improve system performance. The presented mathematical model can be modified for other injector design solutions. Correctness of mathematical description and determined in the course of opening and closing time calculations were related to the values declared by the manufacturer, showing differences below 3%. The calculations were performed in the Matlab/Simulink environment, creating current waveforms, acting forces and plunger displacement. The electrical part describes the generation of electromagnetic force by a circuit with a coil, in the mechanical equilibrium equation of forces acting on the plunger, and in the pneumatic part the air pressure on the plunger. The mathematical description includes three parts, i.e. Valtek plunger injector was chosen as the test object. The article presents a mathematical model that describes the operation of the low-pressure gas injector. It becomes necessary to know mathematical descriptions of the operation of individual components. Liquefied petroleum gas injection systems are among the most popular. In recent years, there has been a growing interest in alternative sources of power supply for internal combustion engines.
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