Modeling the impact of elastic bodies taking into account dry positional friction and the coefficient of velocity restoration

• Autorzy: Bohomolov Olexiy , Zavhorodnii Oleksiy , Hurskyi Petro , Bredykhin Vadym , Bohomolov Oleksandr , Shchur Taras , Walichnowska Patrycja , Kruszelnicka Weronika , Tomporowski Andrzej

Identyfikatory

DOI

10.12913/22998624/203280

• Języki publikacji: EN

Abstrakty

EN

Considering dry positional friction in the model of collinear elastic impact, the stiffness of the system during compression is greater than its stiffness during decompression. The coefficients of the relative motion equation of the bodies involved in the impact have different values at these stages. They depend not only on the geometry of the bodies in the interaction region and the mechanical properties of their materials, but also on the velocity restitution coefficient, which is one of the input parameters of the model, determined a priori through experiments. In the case of power-law nonlinearities in the stiffness of the dynamic system, which corresponds to the solutions of the contact problem in the theory of elasticity, the equation of relative motion of the bodies has closed analytical solutions. During the compression phase, the solution is expressed with an Ateb-sine and its powers, while during the decompression phase, it is expressed with an Ateb-cosine and its powers. To simplify the numerical implementation of the solutions, an approximation of these special functions by trigonometric functions is proposed. This approximation ensures a calculation accuracy of three significant digits after the decimal point. Examples of calculations are provided, demonstrating that accounting for positional friction leads to a decrease in the maximum compression of the bodies, an increase in the peak impact force, and an extension of its duration over time. Variations of impacts between bodies with surfaces of second- and fourth-order in the dynamic interaction region are calculated. The model has much in common with the classical model, but additionally considers the actual value of the velocity restitution coefficient, which is less than one, in collinear impacts. The presented theory applies only to elastic impacts with low initial collision velocities, where no plastic deformations occur.

Słowa kluczowe

EN

quasi-static collinear impact; elastic bodies; positional friction; analytical solution; periodic Ateb-functions

• Wydawca: Lublin University of Technology ; Polish Society of Ecological Engineering (PTIE), Branch of PTIE in Lublin
• Czasopismo: Advances in Science and Technology. Research Journal
• Rocznik: 2025
• Tom: Vol. 19, no. 7
• Strony: 25--35
• Opis fizyczny: Bibliogr. 27 poz., fig., tab.

Twórcy

autor

Bohomolov Olexiy

• Department of Equipment and Engineering of Processing and Food Production, State Biotechnological University, Kharkiv, Ukraine

autor

Zavhorodnii Oleksiy

• Department of Physics and Mathematics, State Biotechnological University, Kharkiv, Ukraine

autor

Hurskyi Petro

• Department of Equipment and Engineering of Processing and Food Production, State Biotechnological University, Kharkiv, Ukraine

autor

Bredykhin Vadym

• Department of Reliability and Durability of Machines and Structures Named After V.Ya. Anilovich, State Biotechnological University, Kharkiv, Ukraine

autor

Bohomolov Oleksandr

• Department of Equipment and Engineering of Processing and Food Production, State Biotechnological University, Kharkiv, Ukraine

autor

Shchur Taras

• Department of Agricultural Engineering State Biotechnological University, Kharkiv, Ukraine

autor

Walichnowska Patrycja

• Department of Renewable Energy Sources Engineering and Technical Systems, Faculty of Mechanical Engineering, Bydgoszcz University of Science and Technology, Al. Prof. S. Kaliskiego 7, 85-796 Bydgoszcz, Poland

• https://orcid.org/0000-0002-3012-5803

autor

Kruszelnicka Weronika

• Department of Renewable Energy Sources Engineering and Technical Systems, Faculty of Mechanical Engineering, Bydgoszcz University of Science and Technology, Al. Prof. S. Kaliskiego 7, 85-796 Bydgoszcz, Poland

autor

Tomporowski Andrzej

• Department of Renewable Energy Sources Engineering and Technical Systems, Faculty of Mechanical Engineering, Bydgoszcz University of Science and Technology, Al. Prof. S. Kaliskiego 7, 85-796 Bydgoszcz, Poland

Bibliografia

• 1. Yaseena M., Kumara M., Rawat S.K. Assisting and opposing flow of a MHD hybrid nanofluid flow past a permeable moving surface with heat source/sink and thermal radiation. Partial Differential Equations in Applied Mathematics, 2021; 4, 100168. https://doi.org/10.1016/j.padiff.2021.100168.
• 2. Olshanskii V., Olshanskii A., Kharchenko S., Kharchenko F. About motion of grain mixture of variable porosity in the cylindrical sieve of vibrocentrifuge. Teka Commission of Motorization and Power Industry in Agriculture, 2016; 16(3), 31–34.
• 3. Jagusiak-Kocik M., Bohomolov O., Hurskyi P., Bredykhin V., Lukyanov I., Shchur T., Dzhidzhora O. Optimizing the separation process of difficult to separate wheat and barley grain mixtures using vibrofriction technology. CzOTO 2024; 6(1): 360–370. https://doi.org/10.2478/czoto-202-0038.
• 4. Bredykhin V., Tikunov S., Slipchenko M., Alfyorov O., Bogomolov A., Shchur T., Kocira S., Kiczorowski P., Paslavskyy R. Improving efficiency of corn seed separation and calibration process. Agricultural Engineeringthis, 2023; 27(1): 241–253. https://doi.org/10.2478/agriceng-2023-0018.
• 5. Karaiev O., Bondarenko L., Halko S., Miroshnyk O., Vershkov O., Karaieva T., Shchur T., Findura P., Prístavka M. Mathematical modelling of the fruit-stone culture seeds calibration process using flat sieves. Acta Technologica Agriculturae, 2021; 24(3): 119–123. https://doi.org/10.2478/ata-2021-0020.
• 6. Wang P., Deng X., Jiang S. Global warming grain production and ats efficiency: Case study of major grain production region. Ecological Indicators, 2019; 105: 563–570. https://doi.org/10.1016/j.ecolind.2018.05.022.
• 7. Olshanskyi V.P. Pro udar viazko-pruzhnoho tila ob zhorstku pereshkodu. Visnyk NTU ‘KhPI’, Ser.: Dynamika i mitsnist mashyn, 2018; 38(1314): 37–41.
• 8. Olshanskyi V.P. Pro udar viazko-pruzhnoho tila ob zhorstku pereshkodu. Visnyk NTU ‘KhPI’, Ser.: Matematychne modeliuvannia v tekhnitsi ta tekhnolohiiakh, 2018; 27(1303): 73–78.
• 9. Brahinets M.V., Dmytriv V.T., Khmelovskyi V.S., Bohomolov O.V., Bohomolov O.O. Modeliuvannia protsesu separatsii nasinnia ripaku separatorom udarnoi dii. Tekhnika ta Enerhetyka. Zhurnal naukovykh doslidzhen silskohospodarskoho vyrobnytstva. Kyiv, 2020; 11(2): 157–164.
• 10. Bogomolov A.V. Separatsiya trudnorazdelimyih syipuchih smesey (nauchnoe obosnovanie energosberegayuschih protsessov i oborudovaniya). Monografiya. HNTUSG, 2013; 296.
• 11. Bohomolov O.V., Brahinets M.V., Mazunov A.R., Naumenko E.M., Bohomolov O.O., Bohomolova V.P. Udoskonalennia konstruktsii hravitatsiinoho bahatoiarusnoho udarnoho separatora. Visnyk KhNTUSH, 2019; 207: 75–81.
• 12. Havrylenko Y., Kholodniak Y., Halko S., Vershkov O., Miroshnyk O., Suprun O., Dereza O., Shchur T., Śrutek M. Representation of a monotone curve by a contour with regular change in curvature. Entropy. 2021; 23(7): 923. https://doi.org/10.3390/e23070923.
• 13. Olshanskyi V.P., Olshanskyi S.V. Uzahalnena zadacha mekhanichnoho udaru v teorii Hertsa. Vibratsii v Tekhnytsi ta Tekhnolohiiakh, 2018; 4(91): 70–75.
• 14. Bredykhin V., Shchur T., Kis-Korkishchenko L., Denisenko S., Ivashchenko S., Marczuk A., Dzhidzhora O., Kubon M. Determination of ways of improving the process of separation of seed materials on the working surface of the pneumatic sorting table. Agricultural Engineeringthis, 2024; 28: 51–71. https://doi.org/10.2478/agriceng-2024-0005.
• 15. Fu G. An extension of Hertz’s theory in contact mechanics. Journal of Applied Mechanics, 2007; 74(2): 373–374. https://doi.org/10.1115/1.2188017.
• 16. Gendelman O., Vakakis A.F. Transition from localization to nonlocalization in strongly nonlinear damped oscillators. Chaos, Solitons and Fractals, 2000; 11(10): 1535–1542. https://doi.org/10.1016/S0960-0779(99)00076-4.
• 17. Cveticanin L., Pogany T. Oscillator with a sum of noninteger–order nonlinearities. Journal of Applied Mathematics, 2012, 649050. https://doi.org/10.1155/2012/649050.
• 18. Pukach P.Ya., Kuzio I.V. Resonance phenomena in quasi-zero stiffness vibration isolation systems. Naukovyi Visnyk Nationalnogo Hirnychoho Universytetu, 2015; 3: 62–67.
• 19. Pukach P. Investigation of bending vibrations Voigt-Kelvin bars with regard for nonlinear resistance force. Journal of Mathematical Sciences, 2016; 215(1): 71–78. https://doi.org/10.1007/s10958-016-2823-0.
• 20. Olshanskyi V.P., Olshanskyi S.V. Ateb-synus u rozviazku zadachi Hertsa pry udari. Visnyk NTU ‘KhPI’ Ser. Matematychne modeliuvannia v tekhnitsi ta tekhnolohiiakh. Kharkiv, 2018; 3(1279): 98–193.
• 21. Olshanskii V., Spolnik O., Slipchenko M., Znaidiuk V. Modeling the elastic imact of a body with a special point at its surface. Eastern-European Journal of Enterprise Technologies, 2019; 1/7(97): 25–32. https://doi.org/10.15587/1729-4061.2019.155854.
• 22. Havrylenko Y., Kholodniak Y., Halko S., Vershkov O., Bondarenko L., Suprun O., Miroshnyk O., Shchur T., Śrutek M., Gackowska M. Interpolation with specified error of a point series belonging to a monotone curve. Entropy. 2021; 23(5): 493. https://doi.org/10.3390/e23050493.
• 23. Olshanskyi V.P. Pro rukh ostsyliatora zi stepenevoiu kharakterystykoiu pruzhnosti. Vibratsii i Tekhnitsi ta Tekhnolohiiakh, 2017; 3(68): 34–40.
• 24. Olshanskyi V.P., Bohomolov O.V., Bohomolov O.O. Pro peretvorennia udarom zadempfovanoi mekhanichnoi systemy v ostsyliator. Suchasni napriamy tekhnolohii ta mekhanizatsii protsesiv pererobnykh ta kharchovykh vyrobnytstv. Visnyk KhNTUSH, 2018; 194: 18–31.
• 25. Yang B. Machine learning-based evolution model and the simulation of a profit model of agricultural products logistics financing. Neural Computing and Applications, 2019; 31(9), 4733–4759. https://doi.org/10.1007/s00521-019-04072-5.
• 26. Setooden A., Azizi A. Bending and free vibration analyses of rectangular laminated composite plates resting on elastic foundation using a refined shear deformation theory. Iranian Journal of Materials Forming, 2015; 2(2): 1–13. https://doi.org/10.22099/ijmf.2015.3236.
• 27. Du J., Wang S., He C., Zhou B., Ruan Y.-L., Shou H. Identification of regulatory networks and hub genes controlling soybean seed set and size using RNA sequencing analysis. Journal of Experimental Botany, 2017; 68(8): 1955–1972. https://doi.org/10.1093/jxb/erw460.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).