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Nowadays offset printing method is actively used in modern printing houses for printing graphic arts products, and makes it possible to obtain large print runs of high-quality full-color images. Offset printing technology allows to automate a large number of processes and due to this get a low cost of production, and equipment utilization rate. The purpose of this research is to create a scientific basis for structural and mathematical modeling of the inking apparatus of an offset printing machine. To achieve this goal, a discrete model of the ink apparatus was built as a control object associated with the movement and ink flow of the printing process, and the research results were summarized in the form of a mathematical model. Also, a methodology for the distribution of ink layers in the inking apparatus was developed. The inking apparatus is considered a dynamic system formed by a set of rollers and cylinders. The discrete model is based on the actual movement pattern of ink layers, considered as a directed graph. The sections of the trajectory of the ink layer movement are considered as arcs of the graph, and the contact points of rollers are considered as nodes of the graph, which correspond to the thickness of the ink layer for certain nodes and discrete moments of time. The necessary mathematical basis for computer modeling of an inking apparatus of complex structure has been created. The process of dividing the ink layer was described using difference equations. For computer implementation, based on the Gauss method of numerical solution of the systems of linear algebraic equations, software has been developed using the Visual Basic program, which allows to determine the divisions and thickness of the ink layer on the surfaces of the elements of the inking system. The discrete model with the help of difference equations describes the discrete process of division of the ink layer taking into account the time of displacement of the layer on the surfaces of rollers and cylinders. The result of modeling is cyclic processes of ink layer division, generalized in the form of dynamic characteristics. The extension of the proposed methodology to the inking apparatus of complex structure makes it possible to apply this methodology to the study of the inking apparatus of different designs.
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