Kulik N. Mathematical modeling of reflecting elements of LED devices

Mathematical modeling of reflecting elements of LED devices. - Manuscript. The thesis for PhD (technical sciences) degree, speciality 05.09.07. - lightning engineering and sources og light. - O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, 2018. The thesis is devoted to the development of mathematical models and methods of calculating the reflector on the basis of surfaces of arbitrary shape for the LED source, as well as verification of the feasibility of the methodology in practice. In the work the analysis of existing methods of calculation of light devices is carried out. As an initial approximation, the method of balance of incident and reflected light flows is used. This method was improved by using the approximation by a power function to obtain the analytical equation of the profile curve of the reflecting element. The problem of calculating the brightness of the luminous body of the LED source was considered. An analytical calculation leads to a big error, because the complexity is to determine the shape of the luminous body. It was decided to obtain a spatial distribution of the luminous body from experimental data, or to find a method of analytical calculation based on data provided by the manufacturer in the form of curve of the force of light source. For verification verification of light distribution with a source of linear size, the method of elementary mappings, which uses a direct beam of rays, was chosen. This method helps to solve the problem of the initial data given not by the brightness of the light in this direction, but by the curve of the force of light source. The method and algorithm of calculation of reflecting surface for the reflector of variable diameter of the output light aperture is developed. The given technological decision is substantiated, the choice of the amperage of the source has been made and the cooling system of the crystal of the LED is calculated. According to the calculation data a prototype sample was made and laboratory tests were carried out. To assess the adequacy of the model Pearson's criterion was used. The empirical value turned out to