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Purpose. To formalize the dependence of the eigenfrequencies of translational and torsional vibrations of the structural elements of the vibrating machine articulated by the connection node on their design parameters and mechanical characteristics, as well as regulatory requirements for vibration activity, strength and accuracy. To develop a method for selecting the design parameters of the elastic band element of the package, taking into account the specified values of the amplitude and frequency characteristics of the dynamic loads reproduced by the supporting structure and the coefficient of variation of the natural frequencies of translational and torsional vibrations.   Methodology. The research is based on fundamental approaches of applied mechanics, machine dynamics and vibration reliability.   Findings. The dependences of the eigenfrequencies of torsional vibrations of the body parts of the vibrating machine connected by the connection node on their design parameters and mechanical characteristics are obtained and analyzed. Vibrations around an axis orthogonal to the working direction of the node are considered. A comparative analysis of the natural frequencies of the node in the direction of the transmitted vibration and its circular vibrations from the design parameters and mechanical characteristics of the elastic band elements, their number in the package and the number of packages in the connection node is performed.   Originality. It is in the fact that for the first time the dependences describing the natural frequencies of translational and torsional vibrations of the body parts of a vibrating machine, articulated by a package of elastic band elements, are obtained. Also the paradigm for the choice of design parameters and mechanical characteristics of the elastic band element of the package, which is based on the results of a comparative analysis of the eigenfrequencies of vibrations in the working and connected directions through their coefficient of variation is innovative. This made it possible to include the criterion of vibration reproduction accuracy, which is formalized through the coefficient of frequency variation, together with the criteria of strength and rigidity, in the methodology of synthesis of the structural scheme of the vibrating machine.   Practical value. The proposed methodological solutions for the calculation and selection of design parameters and mechanical characteristics of tape elastic elements ensure the achievement of vibration activity indicators of articulated parts, as well as the ratio of natural vibration frequencies in the working and related directions at the level of the requirements of normative documents when upgrading existing machines and creating new modern equipment. As a result, the reliability, durability, safety, productivity and load-bearing capacity of machines, equipment and mechanisms of mining engineering, aviation, transport and space technology are increased.

Variation coefficient of torsional vibrations of the connection nodes of vibrating machines