Russian Engineering Research

, Volume 38, Issue 12, pp 916–920 | Cite as

Mill Eigenfrequency in Thermal Fitting

  • M. M. ErmolaevEmail author
  • S. K. Rudnev
  • P. A. Bykov


A method is proposed for the analytical calculation of the elastic displacement of a shaft relative to a bush in joints with interference under the action of radial force and a bending torque. Those displacements are associated with elastic deformation of the shaft, the bush, and the contact layer formed by their rough surfaces. On the basis of that approach, a method is proposed for estimating the lower eigenfrequency of the shaft–bush system. As an example, the thermal fitting of an axial tool in a mandrel is considered.


joints interference contact layer contact pliability contact interaction thermal fitting 



Financial support was provided by the Russian Ministry of Education and Science (contract 14.577.21.0128, identifier RFMEFI 57714X0128).


  1. 1.
    Zakharov, M.N., Prochnostnaya nadezhnost’ oborudovaniya: uchebnoe posobie (Strength Reliability of Equipment: Manual), Moscow: Mosk. Gos. Tekh. Univ. im. N.E. Baumana, 2011.Google Scholar
  2. 2.
    Chernyanskii, P.M., Osnovy proektirovaniya tochnykh stankov. Teoriya i raschet: uchebnoe posobie dlya vuzov (Fundamentals of Design of Precise Machines. Theory and Calculations: Manual for Higher Education Institutions), Moscow: Knorus, 2010.Google Scholar
  3. 3.
    Birger, I.A. and Mavlyutov, M.M., Soprotivlenie materialov (Strength of Materials), Moscow: Nauka, 1986.Google Scholar
  4. 4.
    Ivanov, A.S., Contact rigidity of fixed joints of machine parts, Extended Abstract of Doctoral (Eng.) Dissertation, Moscow, 2006.Google Scholar
  5. 5.
    Levina, Z.M., Issledovanie i raschet kontaktnoi zhestkosti: Metodicheskie ukazaniya (Research and Calculation of Contact Rigidity: Methodological Guide), Moscow: ENIMS, 1969.Google Scholar
  6. 6.
    Reshetov, D.N. and Levina, Z.M., Calculation of contact rigidity in machine engineering, in Voprosy prochnosti materialov i konstruktsii (Strength of Materials and Constructions), Moscow: Akad. Nauk SSSR, 1959, pp. 375–392.Google Scholar
  7. 7.
    Häusler, N., Zum Mechanismus der Biegemomentubertragung in Schrumpfverbindungen, Konstruktion, 1976, vol. 28, no. 3, pp. 103–108.Google Scholar
  8. 8.
    Ermolaev, M.M., Calculation of fixed joints of machine parts taking into account the contact compliance layer, Extended Abstract of Cand. Sci. (Eng.) Dissertation, Moscow, 2015.Google Scholar
  9. 9.
    Ivanov, A.S. and Popov, B.A., Calculation of the connection with interference taking into account the contact rigidity of the conjugating surfaces, Vestn. Mashinostr., 2005, no. 4, pp. 31–36.Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Bauman Moscow State Technical UniversityMoscowRussia

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