Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 21, no. 3, 2018 (September)
Pages 53-58
Cited by J. of Mech. Eng., 2018, vol. 21, no. 3, pp. 53-58



Aleksey Kairov, Admiral Makarov National University of Shipbuilding (9, Heroyiv Ukrayiny ave, Mykolaiv, 54025, Ukraine), ORCID: 0000-0003-3051-9690

Sergey Morgun, Admiral Makarov National University of Shipbuilding (9, Heroyiv Ukrayiny ave, Mykolaiv, 54025, Ukraine), e-mail:, ORCID: 0000-0003-2881-7541



A refined mathematical model of gas turbine engine rotors using three-dimensional finite elements of a curvilinear form is developed. All the calculations were performed for rotors, which are widely used in power machine building and shipbuilding. The fact is that such components have a constructive heterogeneity that can hardly be correctly explained using well-known finite elements and their shape functions. On the other hand, the mathematical model should be as simple as possible with a view to its wide use in the process of designing a rotor. Therefore, a new refined finite-element mathematical model was developed, consisting of three-dimensional curvilinear hexahedral finite elements. It was used to calculate the displacement field caused by the complex action of the heat flux and contact load at the junction of rotor elements. This approach makes it possible to describe the entire rotor as a superposition of the developed curvilinear finite element models and make the calculation process more correct and compact. To solve this problem, a system of matrix equations was compiled. It is based on the use of energy balance dependences in the mechanical contact interaction of rotor elements, as well as the heat balance under the influence of non-stationary heat flow. When creating a numerical algorithm for solving the problem, the direct decomposition of Cholesky was used. To make the solution more compact, the Sherman scheme was used. All the calculations of displacement and temperature fields were carried out for two widely used types of joints, which are used to create such rotors, namely: joints with clearance and interference.


Keywords: three-dimensional finite elements, gas turbine rotors, displacement and temperature fields, contact thermoelasticity problem, clearance, interference


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Received 01 June 2018

Published 30 September 2018