Determining the frequency of transverse oscillations of an elastically fixed disk of a circular saw

Authors

DOI:

https://doi.org/10.15587/1729-4061.2023.285516

Keywords:

circular saw, transverse oscillations, ring plate, natural frequency, elastic fastening

Abstract

The object of the study is a circular saw blade. An annular plate of constant thickness with a free outer contour and a fixed inner contour was taken as the calculation scheme of the saw blade. The real conditions for fixing the internal circuit correspond to the elastic fixing of the saw blade with clamping flanges on the shaft of the machine. For the accepted calculation scheme of the circular saw, the dynamic model was a fourth-order nonlinear differential equation of the transverse oscillations of the annular plate with the corresponding boundary conditions. The rotation of the circular saw was taken into account in the dynamic model due to the radial force in the middle surface of the ring plate. This force arises as a result of the action of centrifugal forces during the rotation of the saw blade. The solution to the fourth-order nonlinear differential equation was constructed using the Bubnov-Galyorkin numerical method. The boundary conditions for constructing the solution were as follows: the outer contour of the saw disk was considered free; the inner contour of the saw disk – elastically fixed with a certain stiffness coefficient.

The solution was implemented in the Maple 15 mathematical environment in the form of a developed program. According to the obtained frequency equation, the values of cyclic and natural frequencies of transverse oscillations of circular saw disks of different thicknesses with the same radius of the inner contour and three values of the radii of the outer contour were determined: 150 mm, 200 m, and 250 mm. The effect of the rigidity of the internal contour fixing and the angular speed of rotation of the saw blade on the natural frequencies of transverse oscillations was studied. The study was performed for saw disks in the case of oscillations with one, two, and three nodal diameters. It was established that the rigidity of the internal contour of the saw blade has the greatest influence on the natural frequency of transverse oscillations with one nodal diameter

Author Biographies

Lidiia Dziuba, Lviv State University of Life Safety

Doctor of Technical Sciences, Associate Professor

Department of Applied Mathematics and Mechanics

Oksana Chmyr, Lviv State University of Life Safety

PhD, Associate Professor

Department of Applied Mathematics and Mechanics

Olha Menshykova, Lviv State University of Life Safety

PhD, Associate Professor

Institute of Civil Protection

Khrystyna Lishchynska, Hetman Petro Sahaidachnyi National Army Academy

PhD, Associate Professor

Department of Engineering Mechanics (Weapons and Equipment of Military Engineering Forces)

References

  1. Dzyuba, L. F., Chmyr, O. Y., Menshykova, O. V., LishchynskaK. І. (2022). Simulation of transverse oscillations of the cutting mechanism of the circular saw machine. Scientific Bulletin of UNFU, 32 (4), 55–59. doi: https://doi.org/10.36930/40320409
  2. Pylypchuk, M. I., Andrievskij, P. V. (2009). Directions of perfection of constructions of machine-tools forsawing of logs by round saws. Scientific Bulletin of UNFU, 19.9, 111–118. Available at: https://nv.nltu.edu.ua/Archive/2009/19_9/111_Pylypczuk_19_9.pdf
  3. Taras, V. I., Pylypchuk, M. I., Salovsky, S. A., Lisak, A. V. (2018). Substantiation of designing parameters of the round saw with combined crown gear. Scientific Bulletin of UNFU, 28 (10), 101–107. doi: https://doi.org/10.15421/40281021
  4. Yan, X., Cui, Y., Qiu, H., Ding, T., Zhu, N., Wang, B. (2023). The Transverse Vibration Characteristics of Circular Saw Blade on Mobile Cantilever-Type CNC Sawing Machine. Machines, 11 (5), 549. doi: https://doi.org/10.3390/machines11050549
  5. Pohl, M., Rose, M. (2016). Piezoelectric shunt damping of a circular saw blade with autonomous power supply for noise and vibration reduction. Journal of Sound and Vibration, 361, 20–31. doi: https://doi.org/10.1016/j.jsv.2015.09.021
  6. Svoreň, J., Javorek, L., Droba, A., Krajčovičová, M. (2015). Determination of critical rotational speed of saw blades by using various methods. Pro Ligno, 11 (4), 478–486. Available at: http://www.proligno.ro/en/articles/2015/4/Svoren_final.pdf
  7. Gospodarič, B., Bučar, B., Fajdiga, G. (2014). Active vibration control of circular saw blades. European Journal of Wood and Wood Products, 73 (2), 151–158. doi: https://doi.org/10.1007/s00107-014-0874-9
  8. Cristóvão, L., Ekevad, M., Grönlund, A. (2012). Natural frequencies of roll-tensioned circular sawblades: effects of roller loads, number of grooves, and groove positions. BioResources, 7 (2). doi: https://doi.org/10.15376/biores.7.2.2209-2219
  9. Merhar, M., Gornik Bučar, D. (2017). The Influence of Radial Slots on Dynamic Stability of Thermally Stressed Circular Saw Blade. Drvna Industrija, 68 (4), 341–349. doi: https://doi.org/10.5552/drind.2017.1739
  10. Feng, W., Zhang, J., Zhou, H., Di, H. (2020). Investigation on the vibration characteristics of circular saw blade with different slots. Journal of Physics: Conference Series, 1633 (1), 012006. doi: https://doi.org/10.1088/1742-6596/1633/1/012006
  11. Anđelić, N., Braut, S., Pavlović, A. (2018). Variation of Natural Frequencies by Circular Saw Blade Rotation. Technical Gazette, 25 (1), 10–17. doi: https://doi.org/10.17559/tv-20160210110559
  12. Skoblar, A., Andjelic, N., Zigulic, R. (2016). Determination of critical rotational speed of circular saws from natural frequencies of annular plate with analogous dimensions. International Journal of Quality Research, 10 (1), 177–192. doi: https://doi.org/10.18421/IJQR10.01-09
  13. Chemeris, O. (2013). Vibration of the circular annular plate with. Visnyk NTUU «KPI». Seriya: mashynobuduvannia, 3 (69), 98–105. Available at: https://ela.kpi.ua/handle/123456789/15643
  14. Trapezon, K., Trapezon, A. (2020). Construction of an algorithm to analytically solve a problem on the free vibrations of a composite plate of variable thickness. Eastern-European Journal of Enterprise Technologies, 1 (7 (103)), 26–33. doi: https://doi.org/10.15587/1729-4061.2020.191123
  15. Trapezon, K., Trapezon, A., Orlov, A. (2020). Analysis of free oscillations of round thin plates of variable thickness with a point support. Eastern-European Journal of Enterprise Technologies, 3 (7 (105)), 6–12. doi: https://doi.org/10.15587/1729-4061.2020.197463
  16. Dziuba, L. F., Menshykova, O. V., Rebezniuk, I. T. (2012). Vilni kolyvannia dyska kruhloi pylky. Visnyk SevNTU, 133, 75–78. Available at: http://virt.ldubgd.edu.ua/pluginfile.php/14588/mod_folder/content/0/Year-2012/Дзюба%20Л.Ф/St_8.pdf?forcedownload=1
  17. Babenko, A. Ye., Boronko, O. O., Lavrenko, Ya. I., Trubachev, S. I. (2022). Kolyvannia sterzhniv, plastyn ta obolonok. Kyiv: KPI im. Ihoria Sikorskoho, 252. Available at: https://ela.kpi.ua/bitstream/123456789/48522/1/Kolyvannia.pdf
Determining the frequency of transverse oscillations of an elastically fixed disk of a circular saw

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Published

2023-08-31

How to Cite

Dziuba, L., Chmyr, O., Menshykova, O., & Lishchynska, K. (2023). Determining the frequency of transverse oscillations of an elastically fixed disk of a circular saw. Eastern-European Journal of Enterprise Technologies, 4(7 (124), 13–20. https://doi.org/10.15587/1729-4061.2023.285516

Issue

Vol. 4 No. 7 (124) (2023): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2023 Lidiia Dziuba, Oksana Chmyr, Olha Menshykova, Khrystyna Lishchynska

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