Analytical Model of Wear-Out Failures in Spur Gears of External Gearing

  • Alexander V. Antsupov
  • M. G. SlobodianskiiEmail author
  • V. P. Antsupov
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The paper presents the failures of spur gears by the wear resistance criterion of abraded surfaces as one of the main reduction reasons of technical and economic indicators of mechanical equipment. High wear rates of gears lead to an increase in the share of unplanned downtime of metallurgical machines and an increase in labor intensity of repair operations. Therefore, in order to solve the problem of increasing the gear’s wear resistance and durability and to search for appropriate structural and technological solutions in this work, an analytical model of the forming process of their gradual wear failures has been built. The model is based on a basic relationship for estimating the rate of wear-out conjugation elements, obtained as a result of the joint-equation solution of molecular mechanical and structural energy friction theory. The equation for predicting the technical resource of gears is obtained from the condition of getting critical energy density of defects in the structure of the material in the wear products. Based on the solution of this equation system, taking into account the dependencies describing the initial and boundary conditions of the interaction of gearing elements, the algorithm calculating their average expected resource is formulated. It can be used to analyze the effectiveness of various structural and technological methods of increasing the durability of gears and selecting the most appropriate ones. A distinctive feature of the proposed model implementation is the fact that it does not require experimental characteristics of similar linear wear rates, coefficients, or wear factors.


Spur gear Durability Model Criterion Prediction Lifetime Life Failure 


  1. 1.
    GOST 21354-87 Transmission toothed cylindrical involute external gearing. Calculation of strengthGoogle Scholar
  2. 2.
    ISO 6336-2:2006 Calculation of load capacity of spur and helical gears. Part 2: Calculation of surface durability (pitting)Google Scholar
  3. 3.
    ISO 6336-3:2006 Calculation of load capacity of spur and helical gears. Part 3: Calculation of tooth bending strengthGoogle Scholar
  4. 4.
    Klebanov B, Barlam D, Nystrom F (2008) Machine elements: life and design. CRC Press, New YorkCrossRefGoogle Scholar
  5. 5.
    Budynas R, Nisbett K (2015) Shigley’s mechanical engineering design, tenth edition. McGraw-Hill EducationGoogle Scholar
  6. 6.
    Timofeev G, Krasavin S, Silchenko P et al (2017) Calculation of durability of gear mechanisms of electromechanical drives. News of higher educational institutions. Eng. Ind 9:12–21Google Scholar
  7. 7.
    Drozdov Yu, Frolov K (1982) Theoretical-invariant method for calculating the intensity of surface destruction of solids under friction. Surface Phys Chem Mech 5:138–146Google Scholar
  8. 8.
    Drozdov Yu, Yugin E, Belov A (2010) Applied tribology (friction, wear, lubrication). Eco-Press, MoscowGoogle Scholar
  9. 9.
    Pronikov A (2002) Parametric reliability of machines. Publishing House of Bauman Moscow State Technical University, MoscowGoogle Scholar
  10. 10.
    Antsupov A, Antsupov A, Antsupov V (2017) Analytical method for project resource estimation of metallurgical machinery parts. Izvestiya Vysshikh Uchebnykh Zavedenij. Chernaya Metallurgiya, pp 62–66. Scholar
  11. 11.
    Antsupov A, Antsupov V, Antsupov A (2016) Estimation and assurance of machine component design lifetime. Proc Eng 150:726–733. Scholar
  12. 12.
    Fleischer G, Gröger H (1972) Methode zur Bestimmung des Verschleißes auf der Grundlage der Energiehypothese. Berich im Rahmen der wiss. technischen Zusammenarbeit auf dem Gebiet Reibung, Schmierung und Verschleiß zwischen dem IMASCH, Moskau und den Forschungsinstitutionen der DDR. TH Magdeburg, pp 285–296Google Scholar
  13. 13.
    Fedorov V (2014) Fundamentals of ergodynamics and synergetics of deformable bodies. Publishing house FGBOU VPO KSTU, KaliningradGoogle Scholar
  14. 14.
    Antsupov A Jr, Slobodiansky M, Antsupov V et al (2018) Assessment of the life of parts and components of metallurgical machines at the stage of their design and operation. Publishing House. Nosov Magnitogorsk state tech. un. MagnitogorskGoogle Scholar
  15. 15.
    Kragelsky I, Dobychin M, Kombalov V (1977) Fundamentals of calculations for friction and wear. Mashinostroenie, MoscowGoogle Scholar
  16. 16.
    Antsupov A, Antsupov V, Slobodianskii M et al (2016) Energy-mechanical concept of the durability prediction of friction units on the wear resistance criterion of elements. J Friction Wear 37(5):494–499. Scholar
  17. 17.
    Protasov B (1979) Energy relations in tribocoupling and prediction of its durability. Saratov University, SaratovGoogle Scholar
  18. 18.
    GOST 16532-70 Transmission spur involute external gearing. Geometry calculationGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Alexander V. Antsupov
    • 1
  • M. G. Slobodianskii
    • 2
    Email author
  • V. P. Antsupov
    • 2
  1. 1.Ural Federal University Named After the First President of Russia B.N. YeltsinEkaterinburgRussia
  2. 2.Nosov Magnitogorsk State Technical UniversityMagnitogorsk CityRussia

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