On strength analysis of a Z-shape metal seal with incising elements, being elastic-plastically deformed


Shishkin S. V.1, Boikov A. A.1*, Kolpakov A. M.2**

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. ,

*e-mail: a.boickov@yandex.ru
**e-mail: a.kolpakov@mai.ru


Flange joints with metal deformable seals are used in piping systems of aviation and space engineering. The article presents the joint with non-contacting flanges, sealed-off by the Z-shaped sealing installing in the unit. As the result of the threaded joint tightening, the flanges close in, squeezing the seal, which elasto-plasticaly deforms herewith. The problem of obtaining a technique for calculating the seal stiffness and its strength analysis is being set. The seal is considered as a profiled axisymmetric ring, subjected to power factors being axisymmetric as well. Theoretical study was conducted, within which framework the K.B. Bitseno theory of rings axisymmetric deformation and I.A. Birger method of variable elasticity parameters were considered with the view of their combining.

Since the seal in the presented problem is subjected to the pure bending, the authors consider its bend stiffness only. The article presents derivation of basic relationships of the design procedure of the Z-shaped seal, elasto-plastically deformed while the joint tightening. It presents the basic assumptions, which allow simplify the technique, making it fully applied. Similar to any other calculation, performed by the I.A. Birger method of variable elasticity parameters, the technique obtained in the article is iterative as well. It can be applied in strength analysis of flange joints while calculating stress-strain state of the Z-shaped seal.

Finally, encompassing rather narrow spectrum of structures types, the research problem solution possesses utterly high potential for further application in similar tasks, where computing of the stress-strain state of the profiled ring being elasto-plastically deformed is required. The main advantage herewith of the obtained design procedure is its relative simplicity due to the fact that elasto-plastical problem is solved completely by the theory of elasticity methods, which is inherited from the above mentioned method of variable elasticity parameters.


Z-shape seal, elastic-plastic problem, method of various parameters of elasticity


  1. Babkin V.T., Zaichenko A.A., Aleksandrov V.V. Germetichnost’ nepodvizhnykh soedinenii i gidravlicheskikh system (Tightness of immovable connections and hydraulic systems), Moscow, Mashinostroenie, 1977, 173 p.

  2. Khill R. Matematicheskaya teoriya plastichnosti (Mathematical theory of plasticity), Moscow, Gostekhizdat, 1956, 407 p.

  3. Malinin N.N. Prikladnaya teoriya plastichnosti i polzuchesti (Engineering theory of plasticity and creeping), Moscow, Mashinostroenie, 1975, 400 p.

  4. Loginov V.N. Materialy VI Regional’noi nauchno-prakticheskoi konferentsii “Pevznerovskie chteniya”, Komsomol’sk-na-Amure, 2018, pp. 83 – 87.

  5. Birger I.A. Sterzhni, plastinki, obolochki (Rods, plates, shells), Moscow, Fizmatlit, 1992, 392 p.

  6. Pisarenko G.S., Mozharovskii N.S. Uravneniya i kraevye zadachi teorii plastichnosti i polzuchesti (Equations and edge problems of theory of plasticity and creeping), Kiev, Naukova dumka, 1981, 496 p.

  7. Boyarshinov S.V. Osnovy stroitel’noi mekhaniki mashin (Fundamentals of structural mechanics of the machines), Moscow, Mashinostroenie, 1973, 456 p.

  8. Khavinson S.Ya. Lektsii po integral’nomu ischisleniyu (Lectures on integral calculus), Moscow, Vysshaya shkola, 1976, 198 p.

  9. Ivanova Zh.V., Surin T.L., Sheregov S.V. Matematicheskii analiz. Differentsial’noe i integral’noe ischislenie funktsii mnogikh peremennykh (Mathematical analysis. Differential and integral calculus of multivariable function), Vitebsk, Izd-vo VGU im. P.M. Masherova, 2010, 90 p.

  10. Grazhdantseva E.Yu. Integral’noe ischislenie funktsii odnoi peremennoi (Integral calculus of one-variable function), Irkutsk, Izd-vo IGU, 2012, 114 p.

  11. Berezin I.S., Zhidkov N.P. Metody vychislenii (Methods of calculations), Moscow, Gosudarstvennoe izdatel’stvo fiziko-matematicheskoi literatury, 1962, 464 p.

  12. Pis’mennyi D.T. Konspekt lektsii po vysshei matematike (Lecture conspectus on higher mathematics), Moscow, AIRIS press, 2019, 603 p.

  13. Shakirzyanova O.G., Zhuravleva E.G. Matematicheskii analiz: differentsial’noe i integral’noe ischislenie funktsii odnoi peremennoi (Mathematical analysis. Differential and integral calculus of one-variable function), Penza, Izd-vo PGU, 2015, 137 p.

  14. Davydov D.V., Myasnyankin Yu.M. Vestnik Voronezhskogo gosudarstvennogo universiteta: Fizika. Matematika, 2009, no. 1, pp. 94 – 100.

  15. Martin H. Sadd. Elasticity. Theory, applications and numerics, Burlington, USA, 2009, Elsevier Inc, 536 p.

  16. Birger I.A., Iosilevich G.B. Rez’bovye i flantsevye soedineniya (Thread and flange connections), Moscow, Mashinostroenie, 1990, 368 p.

  17. Ivlev D.D. Izvestiya AN SSSR, 1957, no 10, pp. 89 – 93.

  18. Ivlev D.D., Maksimova L.A. Izvestiya RAN. Mekhanika tverdogo tela, 2000, no. 3, pp. 131 – 136.

  19. Sokolovskii V.V. Teoriya plastichnosti (Theory of plasticity), Moscow, Vysshaya shkola, 1969, 608 p.

  20. Kachanov L.M. Osnovy teorii plastichnosti (Fundamentals of plasticity theory), Moscow, Nauka, 1969, 420 p.

  21. Birger I.A. Mavlyutov R.R. Soprotivlenie materialov (Strength of materials), Moscow, Nauka, 1986, 560 p.

  22. Ruslantsev A.N., Dumanskii A.M., Alimov M.A. Trudy MAI, 2017, no. 96, available at: http://trudymai.ru/eng/published.php?ID=85659

  23. Gnezdilov V.A., Grishanina T.V., Nagornov A.Yu. Trudy MAI, 2017, no. 95, available at: http://trudymai.ru/eng/published.php?ID=84435

  24. Anosov Yu.V., Danilin A.N., Kurdyumov N.N. Trudy MAI, 2015, no. 80, available at: http://trudymai.ru/eng/published.php?ID=56958


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