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Analytical Methods for Determining the Static and Dynamic Behavior of Thin-Walled Structures During Machining

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Mathematical Modeling and Simulation of Systems (MODS'2020) (MODS 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1265))

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Abstract

The flexibility of thin-walled component and presence of a low natural vibrations frequency significantly affects the efficiency and accuracy of the milling, so inevitably arise the problem of determining the details of influence of the deformation of the cutting tool and the natural vibration frequencies. In this paper we construct analytical solutions for these problems for a plate, two opposite edges of which are simply supported, and the other two may be supported by the beam and the plates. Action of the milling cutter modeled by the concentrated force. The results were compared with results obtained by finite element method. The influence of the stiffness of the reinforcing plates on the magnitude of deflection of the loaded plate is studied, and the variation of the deflection depending on the point of application of force is shown. The obtained analytical solutions can be easily used in the software of CNC machines for selecting milling regimes and adjusting of the cutting tool path.

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References

  1. Herranz, S., Campa, F.J., De Lacalle, L.L., et al.: The milling of airframe components with low rigidity: a general approach to avoid static and dynamic problems. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 219(11), 789–801 (2005). https://doi.org/10.1243/095440505X32742

    Article  Google Scholar 

  2. Del Sol, I., Rivero, A., López de Lacalle, L.N., Gamez, A.J.: Thin-wall machining of light alloys: a review of models and industrial approaches. Materials 12(12), 2012 (2019). https://doi.org/10.3390/ma12122012

    Article  Google Scholar 

  3. Aksonov, Y., Kombarov, V., Fojtů, O., et al.: Investigation of processes in high-speed equipment using CNC capabilities. MM Sci. J. 2019(04), 3271–3276 (2019). https://doi.org/10.17973/MMSJ.2019_11_2019081

    Article  Google Scholar 

  4. Arnaud, L., Gonzalo, O., Seguy, S., et al.: Simulation of low rigidity part machining applied to thin-walled structures. Int. J. Adv. Manuf. Technol. 54(5–8), 479–488 (2011). https://doi.org/10.1007/s00170-010-2976-9

    Article  Google Scholar 

  5. Kononenko, S., Dobrotvorskiy, S., Basova, Y., et al.: Deflections and frequency analysis in the milling of thin-walled parts with variable low stiffness. Acta Polytech. 59(3), 283–291 (2019). https://doi.org/10.14311/AP.2019.59.0283

    Article  Google Scholar 

  6. Korzhyk, V., Khaskin, V., Voitenko, O., et al.: Welding technology in additive manufacturing processes of 3D objects. Mater. Sci. Forum 906, 121–130 (2017). https://doi.org/10.4028/www.scientific.net/MSF.906.121

  7. Grzesik, W.: Hybrid additive and subtractive manufacturing processes and systems: a review. J. Mach. Eng. 18(4), 5–24 (2018). https://doi.org/10.5604/01.3001.0012.7629

    Article  MathSciNet  Google Scholar 

  8. Ivanov, V., Dehtiarov, I., Pavlenko, I., et al.: Parametric optimization of fixtures for multiaxis machining of parts. In: Hamrol, A., et al. (eds.) Advances in Manufacturing II. MANUFACTURING 2019. LNME, pp. 335–347. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-18789-7_28

    Chapter  Google Scholar 

  9. Jáuregui, J.C., Reséndiz, J.R., Thenozhi, S., et al.: Frequency and time-frequency analysis of cutting force and vibration signals for tool condition monitoring. IEEE Access 6, 6400–6410 (2018). https://doi.org/10.1109/ACCESS.2018.2797003

    Article  Google Scholar 

  10. Kombarov, V., Sorokin, V., Fojtů, O., et al.: S-curve algorithm of acceleration/deceleration with smoothly-limited jerk in high-speed equipment control tasks. MM Sci. J. 2019(04), 3264–3270 (2019). https://doi.org/10.17973/MMSJ.2019_11_2019080

    Article  Google Scholar 

  11. Kolar, P., Sulitka, M., Matyska, V., Fojtu, P.: Optimization of five-axis finish milling using a virtualmachine tool. MM Sci. J. 2019(05), 3534–3543 (2019). https://doi.org/10.17973/MMSJ.2019_12_2019037

    Article  Google Scholar 

  12. Rai, J.K., Xirouchakis, P.: Finite element method based machining simulation environment for analyzing part errors induced during milling of thin-walled components. Int. J. Mach. Tools Manuf. 48(6), 629–643 (2008). https://doi.org/10.1016/j.ijmachtools.2007.11.004

    Article  Google Scholar 

  13. Wan, M., Zhang, W.H., Qin, G.H., Wang, Z.P.: Strategies for error prediction and error control in peripheral milling of thin-walled workpiece. Int. J. Mach. Tools Manuf. 48(12–13), 1366–1374 (2008). https://doi.org/10.1016/j.ijmachtools.2008.05.005

    Article  Google Scholar 

  14. Chen, W., Xue, J., Tang, D., et al.: Deformation prediction and error compensation in multilayer milling processes for thin-walled parts. Int. J. Mach. Tools Manuf. 49(11), 859–864 (2009). https://doi.org/10.1016/j.ijmachtools.2009.05.006

    Article  Google Scholar 

  15. Yan, Q., Luo, M., Tang, K.: Multi-axis variable depth-of-cut machining of thin-walled workpieces based on the workpiece deflection constraint. Comput. Aided Des. 100, 14–29 (2018). https://doi.org/10.1016/j.cad.2018.02.007

    Article  Google Scholar 

  16. Dobrotvorskiy, S., Basova, Y., Kononenko, S., et al.: Numerical deflections analysis of variable low stiffness of thin-walled parts during milling. In: Ivanov, V., et al. (eds.) Advances in Design, Simulation and Manufacturing II. DSMIE 2019. LNME, pp. 43–53. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-22365-6_5

    Chapter  Google Scholar 

  17. Timoshenko, S., Woinowsky-Krieger, S.: Theory of Plates and Shells, 2nd edn. McGraw-Hill Education, New Delhi (2015)

    MATH  Google Scholar 

  18. Aijun, T., Zhanqiang, L.: Deformations of thin-walled plate due to static end milling force. J. Mater. Process. Technol. 206(1–3), 345–351 (2008). https://doi.org/10.1016/j.jmatprotec.2007.12.089

    Article  Google Scholar 

  19. Khalilov, S.A., Myntiuk, V.B.: Postbuckling analysis of flexible elastic frames. J. Appl. Ind. Math. 12(1), 28–39 (2018). https://doi.org/10.1134/S1990478918010040

    Article  MathSciNet  Google Scholar 

  20. Myntiuk, V.B.: Postbuckling of a uniformly compressed simply supported plate with free in-plane translating edges. J. Appl. Ind. Math. 14(1), 176–185 (2020). https://doi.org/10.1134/S1990478920010160

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. National Aerospace University “Kharkiv Aviation Institute”, 17 Chkalova Street, Kharkiv, 61070, Ukraine

    Sergiy Plankovskyy, Vitalii Myntiuk, Yevgen Tsegelnyk & Volodymyr Kombarov

  2. Kharkiv State Aircraft Manufacturing Company, 134 Sumska Street, Kharkiv, 61023, Ukraine

    Sergiy Zadorozhniy

Authors
  1. Sergiy Plankovskyy
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  2. Vitalii Myntiuk
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  3. Yevgen Tsegelnyk
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  4. Sergiy Zadorozhniy
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  5. Volodymyr Kombarov
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Corresponding author

Correspondence to Yevgen Tsegelnyk .

Editor information

Editors and Affiliations

  1. Ministerstvo Education and Science, Chernihiv National University of Technology, Chernihiv, Ukraine

    Serhiy Shkarlet

  2. Institute of Mathematical Machines and Systems, Ukraine National Academy of Science, Kyiv, Ukraine

    Anatoliy Morozov

  3. VM Glushkov Institute of Cybernetics of NAS of Ukraine, Ukraine National Academy of Science, Kyiv, Ukraine

    Alexander Palagin

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Plankovskyy, S., Myntiuk, V., Tsegelnyk, Y., Zadorozhniy, S., Kombarov, V. (2021). Analytical Methods for Determining the Static and Dynamic Behavior of Thin-Walled Structures During Machining. In: Shkarlet, S., Morozov, A., Palagin, A. (eds) Mathematical Modeling and Simulation of Systems (MODS'2020). MODS 2020. Advances in Intelligent Systems and Computing, vol 1265. Springer, Cham. https://doi.org/10.1007/978-3-030-58124-4_8

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