Modelling an induction coil with fractional-order magnetic coupling in an ignition system of internal combustion engines

The introduction of methods for timely diagnostics of internal combustion engines allows maintaining the environmental indicators of the car fleet at the highest level. (Research purpose) The research purpose is in increasing the reliability of diagnostics of internal combustion engines by using data obtained by selective sampling of exhaust gases. (Materials and methods) Informational, mathematical and experimental research methods, including methods for statistical processing of results and analysis of data obtained during experiments were used during the study. (Results and discussion) The main systems that affect the environmental performance of internal combustion engines has been identified: the fuel supply system, the ignition system and the exhaust gas neutralization system. The article describes a generalized mathematical model for calculating the characteristics of exhaust gases. Authors conducted operational tests on 35 internal combustion engines with justification of their number according to standard methods. The actual value of diagnostic parameters was processed into relative percentages for drawing a nomogram. A zero value has been set for the reference state of the elements specified by the manufacturer. (Conclusions) It was found that the dominant number of failures accounted for internal combustion engines, in detail: the ignition system produces 15-25 percent of failures, the power system produces 30-44 percent, the exhaust system produces 10-15 percent. It was found that for unambiguous identification of any combination of factors, it is necessary to have output values of at least three evaluation criteria. It was found that the most sensitive parameters for evaluating the technical condition of the three systems are: changes in the engine crankshaft speed, the parameters of exhaust gas toxicity, CO, CO2, CH, O2 when providing test modes (operation of the internal combustion engine on 1 cylinder at 20 and 40 percent of the throttle opening). The article describes designed a gasoline engine loader for the implementation of diagnostic modes and control of diagnostic parameters, that allows to create operating loads with an accuracy of 0.1 percent.

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Properties of Fractional-Order Magnetic Coupling

Energies ◽

10.3390/en13071539 ◽

2020 ◽

Vol 13 (7) ◽

pp. 1539

Author(s):

Sebastian Różowicz ◽

Andrzej Zawadzki ◽

Maciej Włodarczyk ◽

Henryk Wachta ◽

Krzysztof Baran

Keyword(s):

Fractional Order ◽

Differential Calculus ◽

Internal Combustion Engines ◽

Classical Method ◽

Magnetic Coupling ◽

Delta Function ◽

Combustion Engines ◽

Switch Mode Power Supply ◽

Dirac Delta ◽

Selection Of

This paper presents the properties of fractional-order magnetic coupling. The difficulties connected with the analysis of two coils in dynamic states, resulting from the classical approach, provided motivation for studying the properties of fractional-order magnetic coupling. These difficulties arise from failure to comply with the commutation laws, i.e., a sudden power disappearance in the primary winding caused by a switch-mode power supply. Theoretically, under ideal conditions, a sudden power disappearance in the coil is, according to the classical method, manifested by a sudden voltage surge in the form of the Dirac delta function. As is well-known, it is difficult to obtain such ideal conditions in practice; the time of current disappearance does not equal zero due to the circuit breaker’s imperfection (even when electronic circuit breakers are used, the time equals several hundred nanoseconds). Furthermore, it is necessary to take into account phenomena occurring in real inductances, such as the skin effect, the influence of the ferromagnetic core and many other factors. It would be very difficult to model all these phenomena using classical differential calculus. The application of fractional-order differential calculus makes it possible to model them in a simple way by appropriate selection of coefficients and fractional-order derivatives. It should be mentioned that the analysis could be used, for example, in the case of high-voltage generation systems, including spark ignition systems of internal combustion engines. The use of fractional-order differential calculus will allow for more accurate modeling of phenomena occurring in such systems.

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