Contact Interaction of Steam Turbine Inner Casing Elements During Plastic Deformation

Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Pidhornyi Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN  2709-2984 (Print), 2709-2992 (Online)
Issue Vol. 24, no. 3, 2021 (September)
Pages 34-44
Cited by J. of Mech. Eng., 2021, vol. 24, no. 3, pp. 34-44



Serhii A. Palkov, Joint-Stock Company Turboatom (199, Moskovskyi ave., Kharkiv, 61037, Ukraine), e-mail:, ORCID: 0000-0002-2215-0689

Ihor A. Palkov, Joint-Stock Company Turboatom (199, Moskovskyi ave., Kharkiv, 61037, Ukraine), e-mail:, ORCID: 0000-0002-4639-6595



A structure’s material plasticity influence on the pattern of contact interaction of its elements during operation is studied. The stress-strain state problem for the inner casing of a steam turbine high-pressure cylinder operating at supercritical steam parameters (over 240 atm and 565 °C) is solved. The problem is solved by using a finite-element software package. A model of thermoplasticity with kinematic and isotropic hardening is considered. In carrying out the study, experimental strain curves were used for the materials of the connection. The main dependencies used in solving the problem are given. The method of solving the thermal contact problem of interaction of flange connector elements in the conditions of plasticity is based on the application of a contact layer model. To be able to take into account changes in the load from the fastening in the process of combined strain of both the fastening and the casing, first proposed is a method of the three-dimensional modeling of the thermal tightening of the fastening of the horizontal casing connector by applying the linear coefficient of linear expansion of the material. The proposed approach allows modeling the stress of the initial tightening of studs by specifying a fictitious change (decrease) of the coefficient of linear expansion of a stud given as a separate body in the calculation scheme. The magnitude of the specified change in the coefficient of linear expansion is determined from the relationship between the stress of the initial tightening in the stud and the required, for its creation, elongation, which is implemented in the calculation scheme in the presence of different values of linear expansion of both the stud and the casing. To conduct the numerical experiment, an ordered finite-element grid of the casing design was constructed. A 20-node finite element was used in the construction of the casing grid and the fastening. The effect of force loads and the temperature field, in which the structural element under consideration is operated, is taken into account. An analysis of the results of distribution of equivalent stresses and contact pressure during operation is carried out. The difference between the obtained results and the results of solving the problem in the elastic formulation is noted.


Keywords: turbine, flange connector, casing, stress state, contact interaction, plasticity.


Full text: Download in PDF



  1. Mohamed, O., Khalil, A., & Wang, J. (2020). Modeling and control of supercritical and ultra-supercritical power plants: A review. Energies, vol. 13, pp. 2935.
  2. Di Gianfrancesco, A. (2017). Materials for ultra-supercritical and advanced ultra-supercritical power plants. Woodhead Publishing, 900 p.
  3. Arkadyev, B. A. (2015). Features of steam turbine cooling by the example of an SKR-100 turbine for supercritical steam parameters. Thermal Engineering, vol. 62, pp. 728–734.
  4. Shulzhenko, N. G., Gontarovskiy, P. P., & Zaytsev, B. F. (2011). Zadachi termoprochnosti, vibrodiagnostiki i resursa energoagregatov (modeli, metody, rezultaty issledovaniy) [Problems of thermal strength, vibration diagnostics and resource of power units (models, methods, research results)]. Saarbrücken, Germany: LAP LAMBERT Academic Publishing GmbH & Co.KG, 370 p. (in Russian).
  5. Breslavs’kyi, D. V., Korytko, Y. M., & Morachkovs’kyi, O. K. (2011). Cyclic thermal creep model for the bodies of revolution. Strength of Materials, vol. 43, iss. 2, article 134.
  6. Lvov, G., Lysenko, S., & Gorash, Ye. (2008). Creep and creep-rupture strength of gas turbine components in view of nonuniform temperature distribution. Strength of Materials, vol. 40, iss. 5, pp. 525–530.
  7. Chernousenko, O., Rindyuk, D., Peshko, V., & Goryazhenko, V. (2018). Development of a technological approach to the control of turbine casings resource for supercritical steam parameters. Eastern-European Journal of Enterprise Technologies, vol. 2, no. 1 (92), pp. 51–56.
  8. Palkov, I. & Palkov, S. (2020). Napruzheno-deformovanyi stan elementiv parovykh turbin v umovakh plastychnoho deformuvannia [Stress-strain state of elements of steam turbines under conditions of plastic deformation]. Yaderna ta radiatsiina bezpekaNuclear and Radiation Safety, no. 4 (88), pp. 14–17 (in Ukrainian).
  9. Palkov, S. & Shulzhenko, M. (2019). Elastic stress-strain state of elements of the internal high-pressure casing for steam turbines. Journal of Mechanical Engineering – Problemy mashynobuduvannia, vol. 22, no. 4, pp. 32–40.
  10. Laxminarayan, K., Reddy, B., & Kumar, O. (2014). Optimization of steam turbine casing for static loading condition. International Journal of Materials Science and Engineering, vol. 35, pp. 28–37.
  11. Bagaviev, A. (2011). Integrity assessment of high pressure steam turbine casing. Materials at High Temperatures, vol. 28, iss. 3, pp. 205–211.
  12. Dhananjaya Rao, P., Sarkar, A. & Sastri, V. M. K. (1993). Finite element analysis of the three-dimensional transient temperature field in steam turbine casings. International Journal of Mechanical Sciences, vol. 35, iss. 7, pp. 587–595.
  13. Rout, I., Gaikwad, A., Verma, V., & Tariq, M. (2013). Thermal analysis of steam turbine power plants. Journal of Mechanical and Civil Engineering, vol. 7, iss. 2, pp. 28–36.
  14. McFarlane, B. (2017). Autodesk inventor exercises: For autodesk® inventor® and other feature-based modelling software. London: Routledge, 434 p.
  15. Zienkiewicz, O. C, Taylor, R. L., & Fox, D. D. (2014). The finite element method for solid and structural mechanics. Butterworth-Heinemann, Oxford, 415 p.
  16. Kostikov, A. & Palkov, S. (2020). Contact deformation of the pipeline sealing unit. Journal of Mechanical Engineering – Problemy mashynobuduvannia, vol. 23, no. 4, pp. 52–62.
  17. Benkhira, El-H., Fakhar, R., & Mandyly, Y. (2019). Numerical approximation of a frictional contact problem in elasto-plasticity based on the penalty approach. ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik, vol. 99, iss. 12, e201800300.
  18. Stein, E. (2005). Adaptive finite elements in linear and nonlinear solid and structural mechanics. In CISM International Centre for Mechanical Sciences. Springer, 363 p.
  19. Jaszak, P. & Adamek, K. (2019). Design and analysis of the flange-bolted joint with respect to required tightness and strength. Open Engineering, vol. 9, iss. 1, pp. 338–349.
  20. Hwang, D. & Stallings, J. (1994). Finite element analysis of bolted flange connections. Computers & Structures, vol. 51, iss. 5, pp. 521–533.
  21. Wegst, M. & Wegst, C. (2019). Stahlschlüssel – Key to Steel 2019: Nachschlagewerk Dt./Engl./Franz; Stahlschlüssel-Verlag: Marbach, Germany, 1058 p.
  22. Chaboche, J. L. (1991). On some modification of kinematic hardening to improve the description of ratcheting effects. International Journal of Plasticity, vol. 7, iss. 7, pp. 661–678.
  23. Pei, X., Dong, P., & Mei, J. (2021). The effects of kinematic hardening on thermal ratcheting and Bree diagram boundaries. Thin-Walled Structures, vol. 159, Article 107235.


Received 04 August 2021

Published 30 September 2021