Based on dynamics of average method for Markov processes we developed a mathematical model of functioning of conveyer transport systems with serial and parallel connection of conveyer and hoppers, and also with dendritic and self-similar structures. We obtained recursive algorithm which determines capacity of these systems.

На основании метода динамики средних для марковских процессов разработана математическая модель функционирования систем конвейерного транспорта с последовательным и параллельным соединением конвейеров и бункеров, а также с древовидной и самоподобной структурами. Получен рекуррентный алгоритм определения пропускной способности этих систем.

На підставі методу динаміки середніх для марківських процесів розроблено математичну модель функціонування систем конвеєрного транспорту з послідовним і паралельним з'єднанням конвеєрів і бункерів, а також з деревовидною і самоподібною структурами. Одержано рекурентний алгоритм визначення пропускної здатності цих систем.

На підставі методу динаміки середніх розроблено математичну модель функціонування систем конвеєрного транспорту самоподібної деревовидної структури з акумулюючими бункерами, що працюють в режимі підтримки в них об'єму вантажу в заданих межах. При цьому враховувалися простої конвеєрів і бункерів. Визначено середню пропускну спроможність цих систем конвеєрного транспорту, яка перевищує на 15 % пропускну спроможність тих же систем, але з некерованими бункерами.

Purpose. To determine the dependence of the coefficient of local losses of mechanical energy of flow of a two-component mixture of charge material on its depth, content of components, and average equivalent diameter of particles in the case of their free-dispersed motion. Methodology. The value of the coefficient of local losses of mechanical energy was determined by the value of the hydraulic resistance of the fluid during its movement in open channels and pipes. In this paper, methods were used of comparative analysis, mathematical modeling and forecasting of dynamic processes in the flow of granular material. Findings. Based on the results of theoretical studies, a mathematical model was obtained, the use of which allows calculating the coefficient of local losses of mechanical energy for the flow of a two-component mixture of charge materials with agglomerate particle sizes from 15 to 50 mm, pellets from 6 to 12 mm, coke from 10 to 60 mm. The developed model with satisfactory accuracy makes it possible to evaluate the movement of the charge from the indicated materials along the paths of the charging devices of blast furnaces at a speed in the range from 1,5 to 20 m/s and to determine the trajectories of the mixture of charge materials on the top with an accuracy of 0,2 m. It is noted that the calculation of the above coefficient by the known techniques is not accurate enough, which is associated with the uncertainty in the choice of a single average equivalent diameter of the particles of the two-component charge. Comparative analysis of the developed model with the known models and experimental data indicates that the accuracy of calculating the dynamic parameters of a two-component flow of charge materials using the developed model increases by 5 - 10 % in comparison with calculations using the previously known models. Originality. For the first time, regularities of changes in the coefficient of internal mechanical losses of a two-component flow of charge materials from its depth, content of components, average equivalent particle diameters when moving along the paths of charging devices of blast furnaces have been established. Practical value. Mathematical dependencies have been developed and can be used to determine the technological parameters of the charge of a modern blast furnace with different characteristics of the granulometry of the charge and the ratios of its components. This will increase the accuracy of predicting the course of the process under consideration, the degree of automation of the control systems for the technological process of the charge supply of blast furnaces, will make it possible to use expensive charge materials more efficiently, reduce energy consumption and reduce the harmful impact on the environment.