{"id":2265,"date":"2021-01-18T19:41:45","date_gmt":"2021-01-18T17:41:45","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=2265"},"modified":"2021-02-16T13:56:52","modified_gmt":"2021-02-16T11:56:52","slug":"%d1%80%d0%be%d0%b7%d0%b2%d1%8f%d0%b7%d0%b0%d0%bd%d0%bd%d1%8f-%d1%80%d1%96%d0%b2%d0%bd%d1%8f%d0%bd%d0%bd%d1%8f-%d1%84%d1%80%d0%b5%d0%b4%d0%b3%d0%be%d0%bb%d1%8c%d0%bc%d0%b0-%d0%b4%d0%bb%d1%8f","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=2265","title":{"rendered":"\u0420\u043e\u0437\u0432\u2019\u044f\u0437\u0430\u043d\u043d\u044f \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f \u0444\u0440\u0435\u0434\u0433\u043e\u043b\u044c\u043c\u0430 \u0434\u043b\u044f \u0440\u0443\u0445\u0443 \u043d\u0435\u0437\u0440\u0456\u0432\u043d\u043e\u0432\u0430\u0436\u0435\u043d\u043e\u0433\u043e \u0440\u043e\u0442\u043e\u0440\u0430 \u0437 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0438\u043c\u0438 \u043c\u0430\u0441\u0430\u043c\u0438"},"content":{"rendered":"

<\/p>\n

\u0420\u041e\u0417\u0412\u2019\u042f\u0417\u0410\u041d\u041d\u042f \u0420\u0406\u0412\u041d\u042f\u041d\u041d\u042f \u0424\u0420\u0415\u0414\u0413\u041e\u041b\u042c\u041c\u0410 \u0414\u041b\u042f \u0420\u0423\u0425\u0423 \u041d\u0415\u0417\u0420\u0406\u0412\u041d\u041e\u0412\u0410\u0416\u0415\u041d\u041e\u0413\u041e \u0420\u041e\u0422\u041e\u0420\u0410 \u0417 \u0414\u0418\u0421\u041a\u0420\u0415\u0422\u041d\u0418\u041c\u0418 \u041c\u0410\u0421\u0410\u041c\u0418<\/p>\n

SOLUTION OF THE FREDHOLM EQUATION FOR MOTION UNBALANCED LUMPED ROTOR<\/p>\n

 
\n<\/a>
\n\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 107-111. \u041d\u043e\u043c\u0435\u0440: \u21164, 2020 (287)<\/strong><\/p>\n

\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u0412.\u041f.\u00a0\u0420\u041e\u0419\u0417\u041c\u0410\u041d, \u0410.\u0412.\u00a0\u0413\u041e\u0420\u041e\u0428\u041a\u041e, \u0421.\u0410. \u041f\u0415\u0422\u0420\u0410\u0429\u0423\u041a
\n\u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442<\/p>\n

V.P.\u00a0ROYZMAN, A.V.\u00a0GOROSHKO, S.A. PETRASCHUK
\nKhmelnytskyi National University<\/p>\n

 
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2020-287-4-107-111<\/a><\/p>\n

 <\/p>\n

\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review : <\/strong>16.10.2020 \u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed : <\/strong>04.11.2020 \u0440.<\/p>\n

 <\/p>\n

\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u043c\u043e\u0432\u043e\u044e \u043e\u0440\u0438\u0433\u0456\u043d\u0430\u043b\u0443<\/strong><\/p>\n

\u00a0 \u00a0 \u041e\u0441\u043d\u043e\u0432\u043d\u0438\u043c\u0438 \u043c\u0435\u0442\u043e\u0434\u0430\u043c\u0438 \u0431\u0430\u043b\u0430\u043d\u0441\u0443\u0432\u0430\u043d\u043d\u044f \u0440\u043e\u0442\u043e\u0440\u0456\u0432 \u0454 \u0431\u0430\u043b\u0430\u043d\u0441\u0443\u0432\u0430\u043d\u043d\u044f \u0437\u0430 \u0432\u043b\u0430\u0441\u043d\u0438\u043c\u0438 \u0444\u043e\u0440\u043c\u0430\u043c\u0438 \u0456 \u0431\u0430\u043b\u0430\u043d\u0441\u0443\u0432\u0430\u043d\u043d\u044f \u0437\u0430 \u0441\u0442\u0430\u0442\u0438\u0447\u043d\u0438\u043c\u0438 \u0430\u0431\u043e \u0434\u0438\u043d\u0430\u043c\u0456\u0447\u043d\u0438\u043c\u0438 \u043a\u043e\u0435\u0444\u0456\u0446\u0456\u0454\u043d\u0442\u0430\u043c \u0432\u043f\u043b\u0438\u0432\u0443. \u0423 \u043f\u0440\u043e\u0446\u0435\u0441\u0456 \u0437\u0440\u0456\u0432\u043d\u043e\u0432\u0430\u0436\u0435\u043d\u043d\u044f \u0433\u043d\u0443\u0447\u043a\u043e\u0433\u043e \u0440\u043e\u0442\u043e\u0440\u0430 \u0437\u0430 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430\u043c\u0438 \u0432\u0438\u043c\u0456\u0440\u044e\u0432\u0430\u043d\u044c \u043f\u0440\u043e\u0433\u0438\u043d\u0456\u0432 \u0443 \u0440\u0456\u0437\u043d\u0438\u0445 \u043f\u0435\u0440\u0435\u0440\u0456\u0437\u0430\u0445 \u0440\u043e\u0442\u043e\u0440\u0430 \u0456\u0434\u0435\u043d\u0442\u0438\u0444\u0456\u043a\u0443\u044e\u0442\u044c \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0456 \u043c\u0456\u0441\u0446\u044f \u0440\u043e\u0437\u0442\u0430\u0448\u0443\u0432\u0430\u043d\u043d\u044f \u0435\u043a\u0441\u0446\u0435\u043d\u0442\u0440\u0438\u0441\u0438\u0442\u0435\u0442\u0456\u0432 (\u0434\u0438\u0441\u0431\u0430\u043b\u0430\u043d\u0441\u0456\u0432) \u043a\u043e\u0436\u043d\u043e\u0457 \u0437 \u043c\u0430\u0441 \u0434\u043b\u044f \u043f\u043e\u0434\u0430\u043b\u044c\u0448\u043e\u0457 \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438 \u043a\u043e\u043c\u043f\u0435\u043d\u0441\u0443\u0432\u0430\u043b\u044c\u043d\u0438\u0445 \u0432\u0430\u043d\u0442\u0430\u0436\u0456\u0432, \u0449\u043e \u0457\u0445 \u0437\u0440\u0456\u0432\u043d\u043e\u0432\u0430\u0436\u0443\u044e\u0442\u044c. \u0414\u043b\u044f \u0446\u044c\u043e\u0433\u043e \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043e \u0430\u043d\u0430\u043b\u0456\u0437 \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u043a\u0456\u0432 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f \u0424\u0440\u0435\u0434\u0433\u043e\u043b\u044c\u043c\u0430 \u0406\u0406 \u0440\u043e\u0434\u0443, \u0449\u043e \u043e\u043f\u0438\u0441\u0443\u0454 \u0440\u0443\u0445 \u043d\u0435\u0437\u0440\u0456\u0432\u043d\u043e\u0432\u0430\u0436\u0435\u043d\u043e\u0433\u043e \u0440\u043e\u0442\u043e\u0440\u0430. \u041f\u0440\u043e\u0430\u043d\u0430\u043b\u0456\u0437\u043e\u0432\u0430\u043d\u0456 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f, \u043a\u0440\u0438\u0442\u0438\u0447\u043d\u0456 \u0447\u0430\u0441\u0442\u043e\u0442\u0438, \u043f\u0440\u043e\u0433\u0438\u043d\u0438 \u0456 \u0444\u043e\u0440\u043c\u0438 \u043a\u043e\u043b\u0438\u0432\u0430\u043d\u044c \u043e\u0434\u043d\u043e\u043c\u0430\u0441\u043e\u0432\u043e\u0433\u043e \u0456 \u0434\u0432\u043e\u043c\u0430\u0441\u043e\u0432\u043e\u0433\u043e \u0440\u043e\u0442\u043e\u0440\u0430 \u0431\u0435\u0437 \u0443\u0440\u0430\u0445\u0443\u0432\u0430\u043d\u043d\u044f \u0433\u0456\u0440\u043e\u0441\u043a\u043e\u043f\u0456\u0447\u043d\u0438\u0445 \u043c\u043e\u043c\u0435\u043d\u0442\u0456\u0432. \u041e\u0431\u0491\u0440\u0443\u043d\u0442\u043e\u0432\u0430\u043d\u0430 \u043c\u043e\u0436\u043b\u0438\u0432\u0456\u0441\u0442\u044c \u0443\u0441\u0443\u043d\u0435\u043d\u043d\u044f \u0434\u0438\u0441\u0431\u0430\u043b\u0430\u043d\u0441\u0443, \u043f\u043e \u043a\u043e\u0436\u043d\u0456\u0439 \u0437 \u0444\u043e\u0440\u043c \u0437\u0433\u0438\u043d\u0443 \u0440\u043e\u0442\u043e\u0440\u0430, \u0432\u0438\u044f\u0432\u043b\u044f\u044e\u0447\u0438 \u0439\u043e\u0433\u043e \u0432 \u043f\u0440\u043e\u0433\u0438\u043d\u0430\u0445 \u043d\u0430 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u043d\u0438\u0445 \u043a\u0440\u0438\u0442\u0438\u0447\u043d\u0438\u0445 \u0447\u0430\u0441\u0442\u043e\u0442\u0430\u0445 \u043e\u0431\u0435\u0440\u0442\u0430\u043d\u043d\u044f.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0433\u043d\u0443\u0447\u043a\u0438\u0439 \u0440\u043e\u0442\u043e\u0440, \u0432\u0456\u0431\u0440\u0430\u0446\u0456\u0457, \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f \u0424\u0440\u0435\u0434\u0433\u043e\u043b\u044c\u043c\u0430, \u0435\u043a\u0441\u0446\u0435\u043d\u0442\u0440\u0438\u0441\u0438\u0442\u0435\u0442, \u043f\u0440\u043e\u0433\u0438\u043d\u0438, \u0432\u043b\u0430\u0441\u043d\u0456 \u0444\u043e\u0440\u043c\u0438.<\/p>\n

 <\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

\u00a0 \u00a0 The main methods of balancing rotors are balancing according to their own forms and balancing according to static or dynamic coefficients of influence. In the process of balancing a flexible rotor, according to the results of measurements of deflections in various sections of the rotor, the magnitude and location of eccentricities (imbalances) of each of the masses are identified for further installation of compensating balancing weights. For this, the analysis of solutions of the Fredholm equation of the second kind, describing the motion of an unbalanced rotor, is carried out. The equations, critical frequencies, deflections and vibration modes of a single-mass and dual-mass rotor are analyzed without taking into account gyroscopic moments. The possibility of eliminating the imbalance for each of the rotor bending forms is substantiated by measuring it in deflections at the corresponding critical rotation frequencies.<\/p>\n

Keywords:<\/strong> flexible rotor, vibrations, Fredholm equation, eccentricity, deflections, natural forms.<\/p>\n

 <\/p>\n

References<\/strong><\/p>\n

    \n
  1. Kumenko A. Balansirovka gibkih rotorov i valoprovodov na osnove sistem KOMPAKS\u00ae s primeneniem datchikov vala \/ A. Kumenko \/\/ Delovoj zhurnal Neftegaz. RU. \u2013 2015. \u2013 \u2116 3. \u2013 S. 58\u201361<\/li>\n
  2. Sidorov I.N. Iteracionnyj algoritm identifikacii koefficientov zhestkosti i dempfirovaniya opor razgonnobalansirovochnogo stenda pri balansirovke gibkih rotorov \/ I.N. Sidorov, V.V. Tuktarova \/\/ Nauchno-tehnicheskij vestnik Povolzhya. \u2013 2014. \u2013 \u2116 6. \u2013 S. 329\u2013332.<\/li>\n
  3. Dimarogonas A. D., Paipetis S. A., Chondros T. G. Analytical methods in rotor dynamics. Berlin\u2013Heidelberg\u2013New York\u2013Springer Verlag, 2013, Darlow M. S. Balancing of high-speed machinery. Springer Science & Business Media. 2012.<\/li>\n
  4. Galyaka V.G. Osobennosti prakticheskoj balansirovki rotorov turbokompressornyh agregatov, osnovannye na eksperimentalnom utochnenii ih dinamicheskih modelej \/ V. G. Galyaka, V.I. Simonovskij \/\/ Problemy mashinostroeniya 10. \u2013 2007. \u2013 1. \u2013 S. 75\u201379.<\/li>\n
  5. E. Levit et al. Manual balancing. Moscow: Mashinostroenie, 1992. 464 p.<\/li>\n
  6. Darlow M. S. 2012. Balancing of high-speed machinery, Springer Science & Business Media.<\/li>\n
  7. Zhou S., Shi J. 2001. Active balancing and vibration control of rotating machinery: a survey. Shock and Vibration Digest, T. 33, \u2116 5. R. 361\u2013371.<\/li>\n
  8. Rojzman V.P. Identifikaciya i balansirovka gibkih rotornyh sistem : monografiya \/ V.P. Rojzman. \u2013 Hmelnickij : HNU, 2017. \u2013 186 s.<\/li>\n<\/ol>\n

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