This study deals with a methodology for increasing the efficiency of dynamic process calculations in elastic elements of complex engineering constructions. We studied the complex dynamic processes in a simple engineering construction, a mechanical system of an elastic body–continuous flow of homogeneous medium. The developed methodology is based on the use of a priori information on some of the vibrations forms, the construction of a “simplified” mathematical model of system dynamics, and the obtaining of an analytical relationship that describe the overall range of factors on the elastic vibrations of system. The methodology is used for cases of complex vibrations of elastic bodies, and the obtained results can serve as a basis for choosing the main technological and operational parameters of elastic elements of mechanisms and machines that perform complex vibrations. The results obtained in this work are the basis for calculating the blast effect on the elements of protective structures in order to increase their protective capacity by improving the method of their attachment or by using additional reinforcement, buff load effects on the elements of drilling strings and dynamic processes that occur during surface strengthening by work hardening in order to avoid resonance phenomena, and technological processes of vibration displacement or vibration separation of granular media.

Methodology for Increasing the Efficiency of Dynamic Process Calculations in Elastic Elements of Complex Engineering Constructions

The article presents the results of theoretical and experimental studies of the process of moving bulk material in the inactive zone between hinged screw sections of a flexible screw conveyor. The influence of the gap between the edges of adjacent screw sections and the magnitude of their circular displacement on the process of continuous transportation of bulk material is presented. The results of theoretical and experimental studies are compared. This will allow choosing the optimal design, kinematic and technological parameters of the developed sectional screw working body when transporting bulk agricultural materials along curved paths, both in horizontal and inclined directions, as well as along curved paths. РЕЗЮМЕ В статті представлені результати теоретичних і експериментальних досліджень процесу переміщення сипкого матеріалу в неактивній зоні між шарнірно з’єднаними гвинтовими секціями гнучкого гвинтового конвеєра. Наведено вплив величини зазору між краями сусідніх гвинтових секцій та величини їх колового зміщення на процес неперервного транспортування сипкого матеріалу. Проведено порівняння результатів теоретичних і експериментальних досліджень. Це дозволить вибрати раціональні конструктивні, кінематичні та технологічні параметри розробленого секційного гвинтового робочого органу при транспортуванні сипких сільськогосподарських матеріалів по криволінійних трасах, як у горизонтальному та похилому напрямках, а також по криволінійних трасах. INTRODUCTION Screw conveyors are widely used in the movement of various bulk materials, mainly agricultural products, which include: grain, granular seeds, fodder flour, chaff, bran, compound feed, cereal, granules of fertilizers, etc. The results of studies on the contact interaction of such bulk materials with working surfaces of screw conveyors are described in (Loveikin V. and Rogatynska L., 2011; Lyashuk O.L., et.al., 2015; Rogovskii I.L., et.al., 2019; Wang D.-X., 2012, Pylypaka S.F., et.al., 2019). Research on mechanical and technological properties of agricultural materials is given in the works (Tsarenko O.M., et.al., 2003; Rogovskii I.L., et.al., 2019). Mainly for transportation of such cargoes rigid auger conveyors installed at different angles to the horizon are used, as well as flexible screw conveyors, the determination of the parameters and modes of which are described in the works (Hevko B.M., et.al., 2018; Haydl H.M., 1986; Mondal D., 2018; Owen Philip J.,2010, Qi J., et.al., 2017, Roberts Alan W., and Bulk Solids, 2015, Tian Y. et.al., 2018). Pneumatic conveyors, which can transport various loads of curved tracks, have been widely used. The main disadvantage of these types of conveyors is significant energy costs and price, which limits their use. The study of these types of conveyors, as well as screw feeders for feeding bulk materials are in the works of (Baranovsky V.M., et.al.,2018, Hevko R.B., et.al., 2018; Lech M., 2001; Manjula E.V.P.J., et.al., 2017; Naveen T. et.al., 2015). The combination of technological operations, such as transportation and mixing of feed mixtures, is possible with the use of conveyor washers that can work on different routes, but only stationary. Vol. 60, No. 1 / 2020 INMATEH – 262 The results of studies on such conveyors are given in (Hevko R.B., et.al., 2017; Hevko R.B., et.al., 2018; Lyashuk O.L., et.al., 2018; Yao Y.P., et.al., 2014). The results of theoretical and experimental developments, which are presented in this article, are a continuation of previous studies and are aimed at improving the efficiency of the work of screw conveyors, the constructive schemes and the working bodies of which are given in the studies (Hevko B.M., et.al., 2018; Hevko R.B., et.al., 2014, 2016, 2019). MATERIALS AND METHODS In order to increase the reliability of the flexible screw conveyor functioning, it is proposed that its working body is made of separate screw sections that are hinged to each other. Fig.1a shows the location of the edges of adjacent sections, the screw ribs 1 and 2 which are located in the axial direction with a gap δ (inactive zone). The screw sections are interconnected using a hinge mechanism 3, made on the principle of a universal joint with spaced axes that are mutually perpendicular and located in an elastic casing 4. In the circumferential direction, the edges of adjacent helical ribs are offset from each other by an angle α. The idea of the design of such a working body is that when the bulk material ascends from the edge of the screw rib 1, the distance δ must fly through after some time t1. At the same time, the edge of the screw rib 2 is the least (it is necessary to take into account the angle of the material flight) for a time t2 and it must be rotated through an angle α in order to capture the transported material. A general view of the sections of the working body located on the curvilinear region and its individual elements are presented in Fig.1b. The purpose of these studies is to establish rational parameters and operating modes of the developed working body, which will ensure stable transportation of bulk materials on various technological routes. Let’s consider the movement of bulk cargo through a fixed casing using the screw sector of the screw spiral. Let us single out its elementary volume, which simultaneously contacts the fixed casing and the rotating section of the screw spiral. From the side of the casing, a reaction acts on it, perpendicular to its surface and the corresponding friction force. The reaction from the side of the gutter is determined by the vector sum of the gravity efforts of the selected elementary volume and centripetal force. The elementary volume is also affected by the reaction from the surface of the screw rib directed perpendicular to the surface of the screw at the contact point and the corresponding friction force. Fig.1c shows the forces acting on the elementary volume of bulk material moving in the casing.

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Research of the of bulk material movement process in the inactive zone between screw sections.

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Advanced asymptotic approaches and perturbation theory methods in the study of the mathematical model of single-frequency oscillations of a nonlinear elastic body

The theoretical calculations of the dynamics of the conveyor drive chain oscillations for different speeds of bulk material movement as a result of motion internal perturbations have been presented in the article. Resonant oscillations have been studied. It has been established that the amplitude of the transition through the resonance is greater for higher speeds of the conveyor drive chain and the maximum dynamic tension in the chain increases with increasing speed of transportation of bulk material. The dependences of the natural frequency of the system "drive chain of the conveyor line - grain" on the parameters of the system and the amplitude, as well as the amplitude of the resonant oscillations of the system on the speed of grain movement have been obtained. The dependence of the resonance amplitude of the system "conveyor chain drive - grain mass" on the speed of the drive chain at certain parameters has been determined. Taking into account the obtained theoretical data, an improved construction of a tubular chain conveyor with various working bodies and stand equipment using the Altivar 71 frequency converter for complex tasks of the electric drive from 0.75 to 630 kW has been developed. The experimental researches have been carried out and the dependences for definition of productivity and a rotation moment at transportation by the tubular scraper conveyor on curvilinear routes for loose material (wheat and peas) have been received.

https://jacm.scu.ac.ir/article_16759_798efd857a27458442f213b3a8b2dea5.pdf

The Dynamics of the Working Body of the Tubular Conveyor with the Chain Drive

A methodology for researching dynamic processes of one-dimensional systems with distributed parameters that are characterized by longitudinal component of motion velocity and are under the effect of periodic impulse forces has been developed. The boundary problem for the generalized non-linear differential Klein–Gordon equation is the mathematical model of dynamics of the systems under study in Euler variables. Its specific feature is that the unexcited analogue does not allow applying the known classical Fourier and D'Alembert methods for building a solution. Non-regularity of the right part for the excited non-linear analogue is another problem. This study shows that the dynamic process of the respective unexcited motion can be treated as overlapping of the direct and reflected waves of different lengths but equal frequencies. Analytical dependencies have been obtained for describing the aforesaid parameters of the waves. They show that the dynamic process in such mechanical systems depends not only on their main physical and mechanical parameters and boundary conditions, but also on the longitudinal motion velocity (relative momentum). As relative momentum increases, the frequency of the process decreases. To describe excited motion, we use the principle of single frequency of oscillations in non-linear systems with concentrated masses and distributed parameters as well as regularization of periodic impulse excitations. The main idea of asymptotic integration of systems with small non-linearity into the class of dynamic systems under study has been generalized. A standard equation for the resonance and non-resonance cases has been obtained. It has been established that for the first approximation, in the non-resonance case, impulse excitation affects only the partial change of the form of oscillations. Resonance processes are possible at a specific relation between the impulse excitation period, the motion velocity of the medium, and physical-mechanical features of the body. The amplitude of transition through resonance becomes higher when impulse actions are applied closer to the middle of the body. As the longitudinal motion velocity increases, it initially increases and then decreases.

Asymptotic method and wave theory of motion in studying the effect of periodic impulse forces on systems characterized by longitudinal motion velocity

The results of theoretical studies of simultaneous transporting  the components of feed mixtures along the curvilinear paths of tubular conveyors are presented in this article. The mathematical model of a technological process of moving a bulk material (grain) by means of a cable with a connected scraper is proposed. The model is presented as a system of elastic one-dimensional bodies, which are seamlessly moved by a bulk material. Nonlinear differential equations with partial derivatives that describe the dynamics of horizontal and vertical lines of a tube conveyor under the corresponding boundary conditions are deduced. Based on researches, the technique of determining the technological parameters, which ensure the reduction of energy consumption while bulk materials with the given quality of feed mixtures, is proposed.

Roman Ivasechko

Papers

Mathematical Model of a Dynamic Process of Transporting a Bulk Material by Means of a Tube Scraping Conveyor