Published February 29, 2020 | Version v1
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A SEMI-ANALYTICAL METHOD FOR ANALYS OF CONTACT INTERACTION BETWEEN STRUCTURAL ELEMENTS ALONG ALIGNED SURFACES

  • 1. National Technical University «Kharkіv Polytechnic Institute»

Description

A significant share of structures includes the components that are in contact with each other. These include, for example, stamps, molds, machine tools, technological equipment, engines, etc. They are characterized by a varied load mode. Therefore, an important aspect in studying the stressed-strained state of such structures is to determine the dependence of contact pressure on the external forces applied to them. A superposition principle for contact problems is not applicable in a general case. However, for this type of structures, the linear dependence of contact pressure on the load level has been established. In this case, the contact area does not depend on the load level. It has been demonstrated that this pattern holds not only for a one-component but also for the multi-component load. As a result, the possibility for rapid determining the stressed-strained state of such structures is ensured, while maintaining the accuracy of the results obtained.

The applicability of the constructed method has been demonstrated by using the machine tools’ clamping accessories as an example. The established patterns are important when estimating the designs of structures. The derived direct proportional dependence of the solution on the applied loads makes it possible to shorten the design time of structures with the elements that interact when they are in contact at surfaces of the matching shape. In this case, we have considered different sets of loads, as well as the various varying variants of these loads. The examined cases have confirmed the direct proportionality of the components of the stressed-strained state of the magnitude of the applied forces for the case of their coordinated change. It has been also shown under an uneven change in the individual components of loads the dependence of contact pressure and components of the stressed-strained state of the examined objects on the applied forces demonstrates a complex character different from the directly proportional relation. The established dependences underlie the substantiation of the design and technological parameters of the structures that are designed, as well as their operational modes

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References

  • Johnson, K. L. (1985). Contact Mechanics. Cambridge University Press. doi: https://doi.org/10.1017/cbo9781139171731
  • Rogovyi, A. (2018). Energy performances of the vortex chamber supercharger. Energy, 163, 52–60. doi: https://doi.org/10.1016/j.energy.2018.08.075
  • Rogovyi, A., Khovanskyy, S. (2017). Application of the similarity theory for vortex chamber superchargers. IOP Conference Series: Materials Science and Engineering, 233, 012011. doi: https://doi.org/10.1088/1757-899x/233/1/012011
  • Rogovyi, A., Khovanskyy, S., Grechka, I., Pitel, J. (2019). The Wall Erosion in a Vortex Chamber Supercharger Due to Pumping Abrasive Mediums. Advances in Design, Simulation and Manufacturing II, 682–691. doi: https://doi.org/10.1007/978-3-030-22365-6_68
  • Gaydamaka, A., Kulik, G., Frantsuzov, V., Hrechka, I., Khovanskyi, S., Rogovyi, A. et. al. (2019). Devising an engineering procedure for calculating the ductility of a roller bearing under a no-central radial load. Eastern-European Journal of Enterprise Technologies, 3 (7 (99)), 6–10. doi: https://doi.org/10.15587/1729-4061.2019.168145
  • Syomin, D., Rogovyi, A. (2012). Features of a Working Process and Characteristics of Irrotational Centrifugal Pumps. Procedia Engineering, 39, 231–237. doi: https://doi.org/10.1016/j.proeng.2012.07.029
  • Panchenko, A., Voloshina, A., Boltyansky, O., Milaeva, I., Grechka, I., Khovanskyy, S. et. al. (2018). Designing the flow-through parts of distribution systems for the PRG series planetary hydraulic motors. Eastern-European Journal of Enterprise Technologies, 3 (1 (93)), 67–77. doi: https://doi.org/10.15587/1729-4061.2018.132504
  • Panchenko, A., Voloshina, A., Kiurchev, S., Titova, O., Onopreychuk, D., Stefanov, V. et. al. (2018). Development of the universal model of mechatronic system with a hydraulic drive. Eastern-European Journal of Enterprise Technologies, 4 (7 (94)), 51–60. doi: https://doi.org/10.15587/1729-4061.2018.139577
  • Panchenko, A., Voloshina, A., Milaeva, I., Panchenko, I., Titova, O. (2018). The Influence of the form Error after Rotor Manufacturing on the Output Characteristics of an Orbital Hydraulic Motor. International Journal of Engineering & Technology, 7 (4.3), 1. doi: https://doi.org/10.14419/ijet.v7i4.3.19542
  • Voloshina, A., Panchenko, A., Boltynskiy, O., Panchenko, I., Titova, O. (2018). Justification of the Kinematic Diagrams for the Distribution System of a Planetary Hydraulic Motor. International Journal of Engineering & Technology, 7 (4.3), 6. doi: https://doi.org/10.14419/ijet.v7i4.3.19544
  • Voloshina, A., Panchenko, A., Boltyansky, O., Titova, O. (2019). Improvement of Manufacture Workability for Distribution Systems of Planetary Hydraulic Machines. Advances in Design, Simulation and Manufacturing II, 732–741. doi: https://doi.org/10.1007/978-3-030-22365-6_73
  • Martynyak, R. M., Slobodyan, B. S. (2009). Contact of elastic half spaces in the presence of an elliptic gap filled with liquid. Materials Science, 45 (1), 66–71. doi: https://doi.org/10.1007/s11003-009-9156-9
  • Slobodyan, B. S., Lyashenko, B. A., Malanchuk, N. I., Marchuk, V. E., Martynyak, R. M. (2016). Modeling of Contact Interaction of Periodically Textured Bodies with Regard for Frictional Slip. Journal of Mathematical Sciences, 215 (1), 110–120. doi: https://doi.org/10.1007/s10958-016-2826-x
  • Kravchuk, A. S., Neittaanmäki, P. J. (2007). Variational and Quasi-Variational Inequalities in Mechanics. Springer. doi: https://doi.org/10.1007/978-1-4020-6377-0
  • Vollebregt, E., Segal, G. (2014). Solving conformal wheel–rail rolling contact problems. Vehicle System Dynamics, 52 (sup1), 455–468. doi: https://doi.org/10.1080/00423114.2014.906634
  • Kalker, J. J. (1977). Variational Principles of Contact Elastostatics. IMA Journal of Applied Mathematics, 20 (2), 199–219. doi: https://doi.org/10.1093/imamat/20.2.199
  • Papangelo, A., Hoffmann, N., Ciavarella, M. (2017). Load-separation curves for the contact of self-affine rough surfaces. Scientific Reports, 7 (1). doi: https://doi.org/10.1038/s41598-017-07234-4
  • Ciavarella, M. (2015). Adhesive rough contacts near complete contact. International Journal of Mechanical Sciences, 104, 104–111. doi: https://doi.org/10.1016/j.ijmecsci.2015.10.005
  • Ciavarella, M., Joe, J., Papangelo, A., Barber, J. R. (2019). The role of adhesion in contact mechanics. Journal of The Royal Society Interface, 16 (151), 20180738. doi: https://doi.org/10.1098/rsif.2018.0738
  • Li, Q., Popov, V. L. (2018). Adhesive force of flat indenters with brush-structure. Facta Universitatis, Series: Mechanical Engineering, 16 (1), 1. doi: https://doi.org/10.22190/fume171220005l
  • Li, S., Yao, Q., Li, Q., Feng, X.-Q., Gao, H. (2018). Contact stiffness of regularly patterned multi-asperity interfaces. Journal of the Mechanics and Physics of Solids, 111, 277–289. doi: https://doi.org/10.1016/j.jmps.2017.10.019
  • Popov, V. L., Pohrt, R., Li, Q. (2017). Strength of adhesive contacts: Influence of contact geometry and material gradients. Friction, 5 (3), 308–325. doi: https://doi.org/10.1007/s40544-017-0177-3
  • Ciavarella, M. (2017). A very simple estimate of adhesion of hard solids with rough surfaces based on a bearing area model. Meccanica, 53 (1-2), 241–250. doi: https://doi.org/10.1007/s11012-017-0701-6
  • Ciavarella, M. (2017). On Pastewka and Robbins' Criterion for Macroscopic Adhesion of Rough Surfaces. Journal of Tribology, 139 (3). doi: https://doi.org/10.1115/1.4034530
  • Argatov, I., Li, Q., Pohrt, R., Popov, V. L. (2016). Johnson–Kendall–Roberts adhesive contact for a toroidal indenter. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2191), 20160218. doi: https://doi.org/10.1098/rspa.2016.0218
  • Ciavarella, M. (2018). An approximate JKR solution for a general contact, including rough contacts. Journal of the Mechanics and Physics of Solids, 114, 209–218. doi: https://doi.org/10.1016/j.jmps.2018.03.005
  • Li, Q., Pohrt, R., Lyashenko, I. A., Popov, V. L. (2019). Boundary element method for nonadhesive and adhesive contacts of a coated elastic half-space. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 234 (1), 73–83. doi: https://doi.org/10.1177/1350650119854250
  • Li, Q., Popov, V. L. (2017). Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials. Computational Mechanics, 61 (3), 319–329. doi: https://doi.org/10.1007/s00466-017-1461-9
  • Rey, V., Anciaux, G., Molinari, J.-F. (2017). Normal adhesive contact on rough surfaces: efficient algorithm for FFT-based BEM resolution. Computational Mechanics, 60 (1), 69–81. doi: https://doi.org/10.1007/s00466-017-1392-5
  • Atroshenko, O., Tkachuk, M. A., Martynenko, O., Tkachuk, M. M., Saverska, M., Hrechka, I., Khovanskyi, S. (2019). The study of multicomponent loading effect on thin­walled structures with bolted connections. Eastern-European Journal of Enterprise Technologies, 1 (7 (97)), 15–25. doi: https://doi.org/10.15587/1729-4061.2019.154378
  • Atroshenko, O., Bondarenko, O., Ustinenko, O., Tkachuk, M., Diomina, N. (2016). A numerical analysis of non–linear contact tasks for the system of plates with a bolted connection and a clearance in the fixture. Eastern-European Journal of Enterprise Technologies, 1 (7 (79)), 24. doi: https://doi.org/10.15587/1729-4061.2016.60087
  • Tkachuk, M. M., Skripchenko, N. B., Tkachuk, M. A. (2016). Solving of problems on contact interaction of rough bodies using model of nonlinear winkler layer. Mekhanika ta mashynobuduvannia, 1, 3–14.
  • Tkachuk, M. (2018). A numerical method for axisymmetric adhesive contact based on Kalker's variational principle. Eastern-European Journal of Enterprise Technologies, 3 (7 (93)), 34–41. doi: https://doi.org/10.15587/1729-4061.2018.132076
  • Tkachuk, M. M., Skripchenko, N., Tkachuk, M. A., Grabovskiy, A. (2018). Numerical methods for contact analysis of complex-shaped bodies with account for non-linear interface layers. Eastern-European Journal of Enterprise Technologies, 5 (7 (95)), 22–31. doi: https://doi.org/10.15587/1729-4061.2018.143193
  • Tkachuk, M., Bondarenko, M., Grabovskiy, A., Sheychenko, R., Graborov, R., Posohov, V. et. al. (2018). Thin­walled structures: analysis of the stressed­strained state and parameter validation. Eastern-European Journal of Enterprise Technologies, 1 (7 (91)), 18–29. doi: https://doi.org/10.15587/1729-4061.2018.120547
  • Tkachuk, N. A., Kravchenko, S. A., Pylev, V. A., Parsadanov, I. V., Grabovsky, A. V., Veretelnik, O. V. (2019). Discrete and Continual Strengthening of Contacting Structural Elements: Conception, Mathematical and Numerical Modeling. Science & Technique, 18 (3), 240–247. doi: https://doi.org/10.21122/2227-1031-2019-18-3-240-347
  • Bondarenko, M., Tkachuk, M., Grabovskiy, A., Hrechka, I. (2019). Substantiation of Thin-Walled Structures Parameters Using Nonlinear Models and Method of Response Surface Analysis. International Journal of Engineering Research in Africa, 44, 32–43. doi: https://doi.org/10.4028/www.scientific.net/jera.44.32
  • Washizu, K. (1982). Variational Methods in Elasticity & Plasticity. Oxford-New York: Pergamon Press, 630.
  • Zienkiewicz, O. C., Taylor, R. L., Zhu, J. Z. (2013). The Finite Element Method: Its Basis and Fundamentals. Butterworth-Heinemann, 756. doi: https://doi.org/10.1016/c2009-0-24909-9
  • Karmanov, V. G. (2004). Matematicheskoe programmirovanie. Moscow: FIZMATLIT, 264.
  • Tkachuk, M. M., Grabovskiy, A., Tkachuk A., M., Hrechka, I., Ishchenko, O., Domina, N. (2019). Investigation of multiple contact interaction of elements of shearing dies. Eastern-European Journal of Enterprise Technologies, 4 (7 (100)), 6–15. doi: https://doi.org/10.15587/1729-4061.2019.174086
  • Tkachuk, M., Grabovskiy, A., Tkachuk, M. M., Zarubina, A., Saverska, M., Mukhin, D., Kutsenko, S. (2019). Contact interaction of molds elements and project-technological provision of their technical. Bulletin of the National Technical University «KhPI» Series: Engineering and CAD, 1, 58–66. doi: https://doi.org/10.20998/2079-0775.2019.1.07
  • Sea, Zh. (1973). Optimizatsiya. Teoriya i algoritmy. Moscow: Mir, 244.
  • Himmel'blau, D. M. (1975). Prikladnoe nelineynoe programmirovanie. Moscow, 534.