ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Fedotov P. E., Sokolov N. V. Solving a nonlinear problem for a one-sided dynamically loaded sliding thrust bearing. Izvestiya VUZ. Applied Nonlinear Dynamics, 2024, vol. 32, iss. 2, pp. 180-196. DOI: 10.18500/0869-6632-003097, EDN: REYSBQ

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
519.63; 621.822.2
DOI: 
10.18500/0869-6632-003097
EDN: 
REYSBQ

Solving a nonlinear problem for a one-sided dynamically loaded sliding thrust bearing

Autors: 
Fedotov Pavel Evgenevich,
Sokolov Nikolay Victorovich, Kazan State Technological University named after Kirov
Abstract: 

The purpose of this study is to propose an efficient numerical method for solving the inverse nonlinear problem of the movement of the compressor rotor collar in a fluid film thrust bearing.

Methods. A periodic thermoelastohydrodynamic (PTEHD) mathematical model of hydrodynamic and thermal processes in a bearing is constructed under the condition of the rotor collar motion. Within the framework of the model, an inverse nonlinear problem of determining the position of the collar under a given external load is formulated. An iterative solution method is proposed, which utilizes the solution of the direct problem. To reduce computational costs, a modified Dekker–Brent method is employed in conjunction with a modified Newton’s method.

Results. Numerical experiments have been conducted, demonstrating the effectiveness of the proposed approaches. The suggested methods significantly reduce the required computational resources by minimizing the number of calls to the target function in the optimization problem. A software suite has been developed that allows for the calculation of the nonlinear system of rotor motion under various physical and geometric parameters.

Conclusion. An efficient set of numerical methods for solving the inverse nonlinear problem of the motion of the rotor collar in the compressor fluid film thrust bearing is proposed. The method’s effectiveness lies in substantial savings of computational resources. The method’s efficiency has been demonstrated in numerical experiments.

Key words: 
fluid film thrust bearing
differential equations
inverse nonlinear problem
zeroin
Dekker–Brent method
Newton’s method
Acknowledgments: 
This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program (“PRIORITY– 2030”)
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Received: 
10.10.2023
Accepted: 
06.02.2024
Available online: 
01.03.2024
Published: 
29.03.2024
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