The reaction of a radial flexible ring with flanges in the supports of machine rotors to radial displacement has been studied. Two models of deformation and contact interaction of an elastic element with two rigid bodies positioned inside and outside of the ring have been developed. These models are based on variational statements with respect to the unknown forces and displacements. The options of gap and offset on both sides of the contact between the ring and the rigid bodies have been considered. A substantially nonlinear static reaction of the ring to radial displacement has been established. Radial reaction curves have been obtained across a wide range of design parameters, enabling a well-justified choice of an elastic damper with the desired stiffness properties.
Similar content being viewed by others
References
K. Vasizu, Variational Methods in the Theory of Elasticity and Plasticity [in Russian], Mir, Moscow (1987).
A. S. Kravchuk and V. A. Sursyakov, “Numerical solution of geometrically nonlinear contact problems,” Dokl. AN SSSR, 259, No. 6, 1327–1329 (1981).
K. V. Avramov and Y. V. Mikhlin, “Review of applications of nonlinear normal modes for vibrating mechanical systems,” Appl. Mech. Rev., 65, No. 2, 020801 (2013).
K. Avramov, M. Shulzhenko, O. Borysiuk, and C. Pierre, “Influence of periodic excitation on selfsustained vibrations of one disk rotors in arbitrary length journals bearings,” Int. J. Nonlin. Mech., 77, 274–280 (2015).
M. Cha, and S. Glavatskih, “Nonlinear dynamic behaviour of vertical and horizontal rotors in compliant liner tilting pad journal bearings: Some design considerations,” Tribology Int., 82, 142–152 (2015).
I. Hlavacek, J. Haslinger, J. Necas, and J. Lovisek, Solution of Variational Inequalities in Mechanics, Springer–Verlag, New York (1988).
C. Hua, G. Cao, Z. Rao, et al., “Coupled bending and torsional vibration of a rotor system with nonlinear friction,” J. Mech. Sci. Technol., 31, 2679–2689 (2017).
J. J. Kalker, “Variational and non-variational theory of frictionless adhesive contact between elastic bodies,” Wear, 119, No. 1, 63–76 (1987).
A. S. Kelson, H. P. Cymanskii, and B. H. Yakovlev, Dynamics of Rotor-Bearing Systems, Nauka, Moscow (1982).
N. Kikuchi, and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, (1986).
G. Martynenko, “Application of nonlinear models for a well-defined description of the dynamics of rotors in magnetic bearings,” Eureka Phys. Eng., No. 3, 3–12 (2016).
G. Martynenko, “Resonance mode detuning in rotor systems employing active and passive magnetic bearings with controlled stiffness,” Int. J. Automot. Mech. Eng., 13, No. 2, 3293–3308 (2016).
P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions, Birkhäuser, Boston (1985).
M. L. Shi, D. Z. Wang, and J. G. Zhang, “Nonlinear dynamic analysis of a vertical rotor-bearing system,” J. Mech. Sci. Technol., 27, 9–19 (2013).
M. M. Tkachuk, A. Grabovskyi, M. A. Tkachuk, M. Saverska, and I. Hrechka, “A semi-analytical method for analys of contact interaction between structural elements along aligned surfaces,” East.-Eur. J. Enterp. Technol., 1, No. 7 (103), 16–25 (2020).
M. M. Tkachuk, A. Grabovskyi, M. A. Tkachuk, and O. Shut, “Computational-experimental evaluation of stiffness response in elastic supports of rotor systems,” in: H. Altenbach, M. Amabili, and Y. V. Mikhlin (eds.), Nonlinear Mechanics of Complex Structures (Advanced Structured Materials), 157, 353–366 (2021).
M. Tkachuk, A. Grabovskyi, and A. Tkachuk, “Numerical and analytical analysis methods for radial response of flexible ring dampers,” in: M. Rackov, R. Mitroviã, and M. Caviã (eds.), Machine and Industrial Design in Mechanical Engineering: Proceedings of KOD 2021, Mechanisms and Machine Science, 109, 499–506 (2022).
M. M. Tkachuk, A. Grabovskyi, M. A. Tkachuk, A. Zarubina, and A. Lipeyko, “Analysis of elastic supports and rotor flexibility for dynamics of a cantilever impeller,” J. Phys.: Conf. Ser., 1741, 012043 (2021).
M. Tkachuk, O. Shut, A. Marchenko, A. Grabovskyi, et al., “Strength and stability criteria limiting geometrical dimensions of a cantilever impeller,” SAE Technical Paper, 2021-01-5056 (2021).
Y. Zhang, L. He, J. Yang, F. Wan, and J. Gao, “Vibration control of an unbalanced single-side cantilevered rotor system with a novel integral squeeze film bearing damper,” Appl. Sci., 20, No. 9, 4371 (2019).
O. C. Zienkiewicz, R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, Butterworth–Heinemann, Oxford (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prykladna Mekhanika, Vol. 60, No. 2, pp. 126–134, March–April 2024.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Tkachuk, M.M., Tkachuk, A.M., Grabovskyi, A.V. et al. Nonlinear Static Reaction of Elastic Ring with Flanges in Rotor Supports. Int Appl Mech 60, 235–242 (2024). https://doi.org/10.1007/s10778-024-01277-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-024-01277-7