Issue №: 3 (130)
The journal solves the problems of creation and improvement of machinery and technologies for agriculture: 131 - Applied Mechanics, 132 - Materials Science, 133 - Industrial Engineering, 141 - Power Engineering, Electrical Engineering and Electromechanics, 208 - Agricultural Engineering
MATHEMATICAL MODEL OF CONTACT INTERACTION BETWEEN A ROTATING WORKING BODY AND PLANT STEMS FOR THEIR SHREDDING
Andrii BABII – Doctor of Technical Sciences, Professor, Head of Engineering Mechanics and Agricultural Machines Department Ternopil Ivan Puluj National Technical University (вул. Руська, 56, м. Тернопіль, Україна, 46001, e-mail: avbabiytntu@gmail.com, https://orcid.org/0000-0001-6198-0100).
Ivan VOVK – Postgraduate of Engineering Mechanics and Agricultural Machines Department Ternopil Ivan Puluj National Technical University (Ruska str., 56, Ternopil, Ukraine, 46001, e-mail: ivan_5479@ukr.net, https://orcid.org/0009-0000-5305-3550).
The paper proposes a mathematical model of contact interaction between the blade as the working body of a rotary shredder of plant residues and plant stems removed from the field surface. The method of removing such vegetation involves shredding it and scattering it over the field surface. The practical purpose of implementing the mathematical model is to determine the minimum circular speed of the working body when it interacts with the stems.
The mathematical model is based on the assumption that a plant stem can be modelled using Euler-Bernoulli beam theory. To theoretically reproduce the impact pulse interaction of the blade on the stem, a load approximation was used with delta functions having a narrow peak section. The model allows the deformation and oscillatory processes that occur in the stem after impact by the blade of the rotating working body to be evaluated. A solution to the Euler-Bernoulli equation for impulse impact has been constructed. The obtained expressions for the transverse displacements of the beam axis point have a modal decomposition for impulse impact. Since real stems have actual energy dissipation, modal damping, expressed by the corresponding coefficient, has been introduced into the model. For the numerical solution of the problem, a truncated series is considered: 10 modes for smooth pulses and 50 modes for very short pulses. This number of modes already gives a good approximation of the displacement and depends on the geometry and parameters of the interacting bodies.
The result of the numerical experiment is to obtain the values of the maximum bending moments that cause bending stress and compare them with the critical stresses that cause stem failure. For the reliability of the results obtained, the safety factor for bending has been increased to 1.2, which will ensure guaranteed stem failure. Based on this, the minimum speed of interaction between the blade and the stem when the breaking condition is met was found. This speed is 8-10 m/s, at which the stems will only be broken, but not crushed. Imposing the condition of shredding the stems into particles with a length of approximately 0.03 m, a series of peripheral circumferential speeds of the rotary working element's blade was obtained for various ground speeds of the machine. For example, at a forward speed of the unit of 3.0 km/h (0.83 m/s), the circular speed of the blade should be 12-14 m/s; for a forward speed of the unit of 4.0 km/h (1.11 m/s) – 16-18 m/s; for 5.0 km/h (1.39 m/s) – 20-22 m/s; for 6.0 km/h (1.67 m/s) – 24-28 m/s. Thus, the implementation of the mathematical model of the interaction between the blade of the rotary working element and the stems of the plants being removed, based on the Euler–Bernoulli beam model, allowed us to substantiate the minimum circumferential speed of the working element for various forward speeds of the unit and the required length of the shredded material.
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About the journal
G8 – Materials Science
G9 – Applied Mechanics
G10 – Metallurgy
G11 – Mechanical Engineering (by specializations)
The journal "Engineering, Energy, Transport AIC" is indexed according to the following databases and catalogs:
The All-Ukrainian scientific journal “Technology, energy, agriculture transport AIC” is an open-access scientific publication that publishes the results of original research, theoretical and applied developments, as well as scientific papers in the fields of engineering sciences, energy systems, and transport technologies of the agro-industrial complex.
The main objective of the scientific journal “Technology, energy, agriculture transport AIC” is to disseminate the results of modern scientific research and to promote the development of technical, energy, and transport solutions for the agro-industrial complex through the publication of scientific materials characterized by scientific novelty and practical significance in the field of design and modernization of machinery, equipment, and technologies.
The journal’s activities are focused on supporting the development of engineering science, stimulating the implementation of innovative approaches into industrial practice, as well as ensuring effective exchange of scientific achievements among researchers, educators, engineers, and other specialists in relevant fields.
Objectives of the Journal
To achieve its defined objective, the journal ensures the implementation of the following key tasks:
· publication of the results of fundamental and applied research covering the fields of applied mechanics, mechanical engineering, materials science, energy systems, electrical engineering, electromechanics, and transport systems of the agro-industrial sector;
· promotion of the implementation of advanced technical and technological developments aimed at improving the efficiency of machinery, equipment, and production processes;
· creation of conditions for active scientific exchange among research institutions, higher education institutions, industrial enterprises, and other interested organizations;
· support for the development of interdisciplinary research and expansion of cooperation among specialists in various fields of science and technology;
· promotion of the improvement of the scientific and technical level of research related to the design, modernization, and operation of technical equipment used in agro-industrial production;
· dissemination of information on modern achievements in science and technology and the implementation of innovative technologies in the fields of technical support, energy, and transport;
· development of a scientific information environment that facilitates effective scientific communication and the integration of national research into the international scientific community.
Publication frequency: 4 issues per year
Languages of publication: Ukrainian, English
Editor-in-Chief: Vitalii YAROPUD
State Registration: Decision of the National Council of Ukraine on Television and Radio Broadcasting № 1337 and № 1180. Media Identifier: R30-05173
EDRPOU Code: 00497236
Publisher ROR: https://ror.org/05m3ysc06
Publisher DOI Prefix: 10.37128
Technology, energy, agriculture transport AIC is a scholarly professional journal with a long-standing history and stable academic tradition, reflecting the evolution of engineering and technical sciences within the agro-industrial sector of Ukraine.
The journal was founded in 1997 under the title Bulletin of Vinnytsia State Agricultural Institute. According to the Resolution of the Presidium of the Higher Attestation Commission of Ukraine dated September 11, 1997, the publication obtained the status of a professional scientific journal, which enabled the publication of the main results of doctoral and candidate dissertations in technical sciences. From its inception, the journal positioned itself as an academic platform for addressing current issues of mechanization, electrification, and technical support of agricultural production. During 2001–2014, the journal was published under the title Proceedings of Vinnytsia National Agrarian University. Series: Technical Sciences (State Registration Certificate of Print Media KV No. 16644-5116 PR dated April 30, 2010). Throughout this period, a systematic approach to the selection and peer review of scientific manuscripts was established, the thematic scope of publications was expanded, and continuity of scientific directions as well as the development of sectoral engineering schools was ensured. Since 2015, the journal has been published under its current title, Technology, energy, agriculture transport AIC (State Registration Certificate No. 21906-11806 R dated March 12, 2016). The change of title reflected the expansion of the journal’s thematic coverage and its orientation toward interdisciplinary research in mechanical engineering, energy systems, electrical engineering, transport technologies, automation, and digital solutions for the agro-industrial complex.
