Ukrainian Journal of Mechanical Engineering and Materials Science
Permanent URI for this communityhttps://ena.lpnu.ua/handle/ntb/31565
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Item Construction of a mathematical model of an unbalanced vibrating separator on a spring suspension(Видавництво Львівської політехніки, 2023-02-28) Topilnytskyy, Volodymyr; Vyshatytskyy, Volodymyr; Lviv Polytechnic National UniversityIn the article, a mathematical model of the oscillating motion of a vibrating separator is constructed. The methods of nonlinear mechanics and the calculation scheme of the vibration separator with an eccentric and a spring suspension, which is presented in the form of a flat mechanical system with four degrees of freedom, were used for its construction. The amplitude of oscillations of the vibration separator capacities in the vertical plane is greater than the amplitude of its oscillations in the horizontal plane. It is believed that the containers of the vibroseparator move only in the vertical plane, that is, they are in planar motion. The obtained mathematical model makes it possible to investigate the influence of the separator parameters with their arbitrary combination on the productivity of its work with the aim of its optimization.Item Nonlinear mathematical model of the five-container vibration system(Видавництво Львівської політехніки, 2022-02-22) Rebot, Dariia; Topilnytskyy, Volodymyr; Lviv Polytechnic National UniversityThe 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.Item Mathematical model of dynamics of vibrating systems working environments(Видавництво Львівської політехніки, 2022-02-22) Topilnytskyy, Volodymyr; Kabanov, Kostiantyn; Lviv Polytechnic National UniversityUsing 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.Item Evaluation of dynamic characteristics of DPKr-2 diesel train on straight sections of railway track(Lviv Politechnic Publishing House, 2017-10-19) Kuzyshyn, Andriy; Batig, Andriy; Lviv Research Institute of Forensic ScienceThe increase in motion speed of the trains moving along certain routs changes the operational conditions and interaction of the rolling stock and the track, and requires the solution of important issues related to the specifications of their maintenance, since there occur additional dynamic loads. In this case, the particular attention is paid to the interaction of the rolling stock and the railway track; to the problems of scientific substantiation of the criteria for assessing the dynamic characteristics of carriages; to the motion smoothness, traffic safety and travelling comfort; as well as to improvement of the maintenance specifications of the track and the rolling stock in the process of their operation and on the basis of scientific analysis and determination of top (safe) speeds of the trains motion. Using the three-dimensional mathematical model of the DPKr-2 Diesel train waggon, its basic dynamic characteristics were determined and analysed: coefficients of vertical and horizontal dynamics, maximum acceleration of the body both in vertical and in horizontal plane. The influence of the amplitude of vertical and horizontal obliques of the railway track on the dynamic characteristics of the Diesel train was investigated. The determination of the basic dynamic characteristics was carried out on the basis of the developed three-dimensional mathematical model of the waggon, which consists of 38 differential equations of the Diesel train motion. The simulation (solving) of the mathematical model was carried out using Maple software. The geometrical periodic equivalent obliques of the left and right rails were adopted as perturbations both in vertical and in horizontal plane. The determination of the basic dynamic characteristics of the DPKr-2 Diesel trane waggon will allow evaluating its vibro-protective properties. The determination of the coefficients of vertical and horizontal dynamics both in central and in axle leaf-spring suspension, of the maximum accelerations of the waggon body in vertical and in horizontal plane will allow carrying out the analysis of vibro-protective properties of the mechanical part of the Diesel train wagon. The obtained results may be used to define the safe interval of the Diesel train motion speeds on the track sections in the presence of vertical and horizontal obliques.Item Modelling of the articulated vehicle dynamics taking into account the elastically fastened freight(Lviv Politechnic Publishing House, 2017-01-01) Zhytenko, Oleksandr; Zalutskyi, Yurii; Lviv Polytechnic National University, Lviv, UkraineIn this article, some methodological statements of the formation of mathematical models in the problems of machine dynamics are elucidated. The presence of a cushioned freight in the form of the fastened vehicle complicates the system, so that the equations describing its oscillations are too complicated and unsuitable for practical usage. It is shown that with all the complexity of the research object, it is expedient to form the mathematical model at the level of the design diagram (model) with a relatively small number of degrees of freedom. The peculiarities of mathematical modelling of the motion processes of specialized articulated vehicles for transportation of cars, namely, formation of the design diagram (model), making the necessary assumptions, choosing the independent coordinates and writing down the second-order Lagrange equations describing the system oscillations, are presented. While modelling, the most typical case, namely, the motion over the unit prominence (road shock), the effect of which on the wheels of the articulated vehicle is of the impact type, is considered. The choosing of the initial perturbation in the form of a unit impact is caused by the possibility of obtaining an impact characteristic, which is defined as the reaction of the system on the δ-function. In addition, under the impact action, it is possible to carry out the direct visual analysis of non-interfered single-frequency oscillatory processes, which allows to quickly obtain the approximate express-evaluation of the amplitude values of the process, frequencies of oscillations, as well as the oscillations damping decrement of the two-section articulated vehicle, if it is necessary. The mathematical model of the articulated vehicle consisting of a tractor and a semi-trailer in the form of a linear system having 9 degrees of freedom is developed. It consists of three cushioned masses, namely, the frame of the truck tractor, the frame of the semi-trailer and three non-cushioned masses, which are axles with wheels as an assembly. Both sections of this system are connected by the saddle-coupling element that is not absolutely rigid. While moving, the frames of the truck tractor and of the semi-trailer performs oscillatory motion in the vertical plane and angular oscillations about an axis passing through the centre of masses. The axles with wheels in the assembly oscillate only in the vertical plane. The peculiarity of the model is that the elastic and damping properties of the suspension of vehicle fixed on the semi-trailer are taken into account. The solution of the mathematical model allows to obtain the impact characteristic, to calculate the amplitude-frequency characteristic and to obtain the required (unknown) values of the root-meansquare accelerations of the non-cushioned masses. The technology of systemic consideration of the problems of formation of mathematical models in the form of block diagrams (structure charts) which are equivalent in dynamic relation to the systems of automatic control is offered.