Mathematical modeling of the rotor dynamics of a turbomachine on gas foil bearings subjected to vibration

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Abstract

BACKGROUND: The use of gas foil bearings is a promising development in the field of turbomachinery due to their economy, autonomous operation capability, and durability. However, gas foil bearings have lower load capacities than other types of bearings. However, turbomachines are complicated, dynamic systems that must meet high standards of safety, sustainability, and durability against external mechanical factors like vibration, shock, etc.

AIM: Development of a mathematical model of rotor dynamics to predict the displacement of the rotor in foil bearings for maintaining separation between the rotor and the housing while being subjected to vibration.

METHODS: A mathematical model of the dynamics of a stiff rotor on gas foil bearings was built and analyzed, taking into account the flexibility of the bearing bushing supports and the housing of the turbomachine. Stationary and transient modes of operation, including the transient modes combined with random vibration, are simulated. The system of ordinary derivatives equations describing the mathematical model was solved by the Rado IIA method. Random vibration was modeled using digital Fourier transformation. The modeling results were analyzed by discrete Fourier transformation and short-time Fourier transformation.

RESULTS AND CONCLUSIONS: Rotor movement trajectories were obtained and the results were compared with author’s previous experimental data. Upper bound of maximal displacements was obtained. The maximum values of rotor displacement can be used to set the optimal values of blade tip gaps.

About the authors

Vitaly S. Nikolaev

Bauman Moscow State Technical University; PJSC NPO Nauka

Author for correspondence.
Email: vs.nikolaev.bmstu@gmail.com
ORCID iD: 0000-0002-5360-9368
SPIN-code: 5847-3632

Postgraduate Student

Russian Federation, Moscow; Moscow

Igor V. Tishchenko

Bauman Moscow State Technical University; PJSC NPO Nauka

Email: iv.tischenko@bmstu.ru
ORCID iD: 0000-0001-6094-8723
SPIN-code: 5630-4301

Cand. Sci. (Tech.), Associate Professor

Russian Federation, Moscow; Moscow

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Supplementary files

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2. Fig. 1. Rotor–gas foil bearings–bearings bushings system.

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3. Fig. 2. Physical model of a radial bearing.

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4. Fig. 3. Air cycle machine with the test fixture for attachment to a shaker, and the dynamic scheme of housing.

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5. Fig. 4. Scheme diagram of the axial bearings. Axial bearings are presented as nonfixed equivalent springs to prevent axial movement and rotation.

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6. Fig. 5. Trajectory of rotor side A motion without any outside impact: a) rotor rotation = 20 krpm, b) rotor rotation = 30 krpm.

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7. Fig. 6. Trajectory of rotor side B motion without any outside impact a) rotor rotation = 20 krpm, b) Rotor rotation = 30 krpm.

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8. Fig. 7. Rotor side B response to the influence of a sinusoidal vibration of scanning frequency with vibroacceleration amplitude of 0.5 g. Rotor rotation = 26 krpm. Top: experimental data, bottom: computed data.

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9. Fig. 8. Trajectory of rotor motion under the combined effect of sinusoidal and random vibration, 25% of the nominal regime. Left – computed data, right – experimental data. Top – side of support A, bottom – side of support B.

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Copyright (c) 2022 Nikolaev V.S., Tishchenko I.V.

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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