Smart Search 

Title of the article



Ishin N.N., Candidate of Technical Sciences, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus

Goman A.M., Candidate of Technical Sciences, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

Skorohodov A.S., Candidate of Technical Sciences, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus

Year 2010 Issue 3 Pages 33-39
Type of article RAR Index UDK 621.833 Index BBK  

Methods of analytical calculation of resonance conditions of the gearings stipulated by two major factors - periodic change of rigidity of teeth on a phase of engagement and an impact teeth input in engagement in connection with inaccuracy of manufacture and mounting of gears, and also an elastic strain of teeth under loading are considered. Researches were carried out on the dynamic model considering only torsional oscillations of gears. Influence of damping on the resonance phenomena in gearings is studied.


resonance conditions, periodic change of rigidity, elastic strain of teeth, dynamic model, torsional oscillations of gears

  • GOST 21354-87. Peredachi zubchatye cilindricheskie jevol'ventnye vneshnego zaceplenija. Raschet na prochnost' [State Standard 21354-87. Cylindrical gears involute of external engagement. Strength analysis]. Moscow, Izd-vo standartov, 1988. 93 p.
  • Vysockij M.S., Gileles L.H. Gruzovye avtomobili: Proektirovanie i osnovy konstruirovanija [Trucks: designing and design principles]. Moscow, Mashinostroenie, 1995. 256 p.
  • Algin V.B. Dinamika, nadezhnost' i resursnoe proektirovanie transmissij mobil'nyh mashin [Dynamics, reliability and resource designing of transmissions of mobile machines]. Minsk, Navuka i tjehnika, 1995. 256 p.
  • Berestnev O.V., Goman A.M., Ishin N.N. Analiticheskie metody mehaniki v dinamike privodov [Analytical methods of mechanics in dynamics of drives]. Minsk, Navuka i tjehnika, 1992. 238 p.
  • Berestnev O.V. [et al.]. Jeksperimental'nye issledovanija dinamicheskih nagruzok i vibroakusticheskih harakteristik peredach s samoustanavlivajushhimisja zubchatymi kolesami [Experimental investigation of dynamic loads and vibro-acoustic characteristics of transmission with spherical gears]. Minsk, IMINMASh AN BSSR, 1987. 98 p.
  • Calculation of load capacity of spur and helical gears: ISO 6336-1:2006. Part 1: Basic principles, introduction and general factors of influence. Available at:
  • Fundamental Rating Factor and Calculation Methods for Involute Spur and Helical Gear Teeth: ANSI / AGMA 2001 C95 // American Gear Manufacturers Association, 1995. 70 p. Available at:
  • Astashev V.K. [et al.]. Vibracii v tehnike [Vibration in technique]. Moscow, Mashinostroenie, vol. 6, 1995. 460 p.
  • Grinkevich V.K. Vynuzhdennye kolebanija zubchatyh koles odnostupenchatogo reduktora [Forced oscillations of gears of single-stage reducer]. Vibroakusticheskaja aktivnost' mehanizmov s zubchatymi peredachami [Vibroakustic activity of mechanisms with gears]. Moscow, Nauka, 1971, pp. 107-113.
  • Borisov D.S. O rezonansnyh javlenijah v sisteme s periodicheski izmenjajushhejsja zhestkost'ju pri nalichii periodicheskoj vozmushhajushhej siloj [Resonance phenomena in system with periodically varying stiffness in presence of periodic disturbing force]. Vibroizoljacija mashin i vibrozashhita cheloveka operatora [Vibration isolation of machines and vibration protection of human operator]. Moscow, Nauka, 1973, pp. 93-94.
  • Petrovskij I.G. Lekcii po teorii obyknovennyh differencial'nyh uravnenij [Lectures on the theory of ordinary differential equations]. Moscow, 2009. 240 p.
  • Bogoljubov N.N., Mitropol'skij Ju.A. Asimptoticheskie metody v teorii nelinejnyh kolebanij [Asymptotic methods in theory of nonlinear oscillations]. Moscow, Nauka, 2005. 605 p.
  • Panovko Ja.G. Vvedenie v teoriju mehanicheskih kolebanij [Introduction to mechanical vibrations theory]. Moscow, Nauka, 1991. 272 p.
  • Biderman V.L. Teorija mehanicheskih kolebanij [Theory of mechanical vibrations]. Moscow, Vyssh. shk., 1980. 408 p.