Ukrainian Journal of Mechanical Engineering and Materials Science

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    Nonlinear mathematical model of the five-container vibration system
    (Видавництво Львівської політехніки, 2022-02-22) Rebot, Dariia; Topilnytskyy, Volodymyr; Lviv Polytechnic National University
    The construction of a non-linear mathematical model of movement and interaction of the commanding and executive components of vibration systems is an important task. It implements vibration technologies of separation, grinding, mixing, compaction, transportation, surface product processing and technology for regulating the vibration effect on systems and mechanisms for their further research to increase the efficiency of vibrating machines, devices, and mechanisms and relevant technological processes. The article presents a generalized diagram of a five-container vibration system. On its basis, a mathematical model was developed, which in the future will make it possible to research the effectiveness of vibration machines, devices, and mechanisms. The calculation scheme of the system and the methods of nonlinear mechanics were used to build the mathematical model. The obtained mathematical model makes it possible to determine the horizontal and vertical components of the amplitude of any point of the containers of the vibration system. This will make it possible to investigate the influence of different modes of operation of the system on the amplitude and nature of vibrations of the containers, in particular, established regimes, influence reversing of the drive, the influence of the processing environment of the containers of the vibration system, influence processed parts.
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    Mathematical model of dynamics of vibrating systems working environments
    (Видавництво Львівської політехніки, 2022-02-22) Topilnytskyy, Volodymyr; Kabanov, Kostiantyn; Lviv Polytechnic National University
    Using the apparatus of the special periodic Ateb-functions in combination with the asymptotic methods of nonlinear mechanics, the nonlinear mathematical models of motion of working environment of the oscillation system, which dependences take into account resilient and viscid making tensions from descriptions of the deformation state of environment, her physical and mechanical properties and features of co-operation of environment with the oscillation system, are worked out. The nonlinear model for describing the dynamics of the working environment of oscillating systems is more flexible, because the nonlinearity index, which depends on the type of working load, significantly affects the results of the oscillating loading process. It allows us to take into account the type of load, and, accordingly, increase the level of adequacy of the constructed analytical model of the oscillatory process that needs to be investigated. Taking into account this model, the study of various processes in oscillating systems can be carried out, in particular in different modes of vibration processing.