Purpose Minimization of energy losses and wear in support elements belongs to the key requirements in the design and operation of high-speed rotating machines. This objective can be achieved through the use of contactless support elements. According to Earnshaw’s theorem, permanent magnetic bearings are inherently unstable. Active magnetic bearings are technologically complex and require a sophisticated and costly control system, which reduces the reliability and safety of rotor support elements. An alternative solution is provided by superconducting bearings, whose operation is based on stable magnetic levitation. The aim of the conducted research was to develop a computational model of a horizontal rotor supported by superconducting bearings, applicable for the analysis of rotor vibrations induced by unbalance and for the investigation of possible vibration attenuation strategies. Methods In the developed computational model, the horizontal rotor is considered an absolutely rigid body. The superconducting bearings are represented by force couplings. The magnetic forces and moments exerted by the superconducting material on the permanent magnets attached to the rotor shaft are determined using the frozen mirror image method. Rotor vibration attenuation is achieved by an electrodynamic damper operating on the principle of eddy currents. Slight damping caused by the surrounding environment is assumed to be linear. The rotor device is symmetrical. Owing to the symmetry of the rotor system, its vibration is governed by a set of two nonlinear equations of motion. After their transformation into the state space, the equations are solved using the Euler method. Applicability of the developed computational model was verified by experimental research. Results The study performed led to the development of a computational procedure for the vibration analysis of horizontal rotors supported by superconducting bearings. Computational simulations yielded several important results. The superconducting bearings have sufficient load-carrying capacity in both the axial and radial directions. The electrodynamic damper proved to be particularly effective in the vicinity of the critical speed of the rotor. Moreover, switching the damper off does not lead to the occurrence of undesirable transient phenomena, such as a sudden increase in vibration amplitude or forces transmitted to the rotor supports. The results obtained by simulations are consistent with the experimental ones. Conclusion The research work resulted in the development of an efficient tool for vibration analysis of horizontal rotors mounted in superconducting bearings. The established procedure enables the analysis of various operational regimes and delivers information on vibration amplitudes, spectral characteristics, and system critical speeds. The results contribute to an improved understanding of the complex multiphysical interactions between the superconducting material and the permanent magnets attached to the rotor shaft.

Vibration Analysis of Unbalanced Horizontal Rotors Mounted in Superconducting Bearings

期刊论文
发表日期：

2026年6月19日

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Jaroslav Zapoměl,
Jan Kozánek,
Petr Šulc

摘要

Purpose

Minimization of energy losses and wear in support elements belongs to the key requirements in the design and operation of high-speed rotating machines. This objective can be achieved through the use of contactless support elements. According to Earnshaw’s theorem, permanent magnetic bearings are inherently unstable. Active magnetic bearings are technologically complex and require a sophisticated and costly control system, which reduces the reliability and safety of rotor support elements. An alternative solution is provided by superconducting bearings, whose operation is based on stable magnetic levitation. The aim of the conducted research was to develop a computational model of a horizontal rotor supported by superconducting bearings, applicable for the analysis of rotor vibrations induced by unbalance and for the investigation of possible vibration attenuation strategies.

Methods

In the developed computational model, the horizontal rotor is considered an absolutely rigid body. The superconducting bearings are represented by force couplings. The magnetic forces and moments exerted by the superconducting material on the permanent magnets attached to the rotor shaft are determined using the frozen mirror image method. Rotor vibration attenuation is achieved by an electrodynamic damper operating on the principle of eddy currents. Slight damping caused by the surrounding environment is assumed to be linear. The rotor device is symmetrical. Owing to the symmetry of the rotor system, its vibration is governed by a set of two nonlinear equations of motion. After their transformation into the state space, the equations are solved using the Euler method. Applicability of the developed computational model was verified by experimental research.

Results

The study performed led to the development of a computational procedure for the vibration analysis of horizontal rotors supported by superconducting bearings. Computational simulations yielded several important results. The superconducting bearings have sufficient load-carrying capacity in both the axial and radial directions. The electrodynamic damper proved to be particularly effective in the vicinity of the critical speed of the rotor. Moreover, switching the damper off does not lead to the occurrence of undesirable transient phenomena, such as a sudden increase in vibration amplitude or forces transmitted to the rotor supports. The results obtained by simulations are consistent with the experimental ones.

Conclusion

The research work resulted in the development of an efficient tool for vibration analysis of horizontal rotors mounted in superconducting bearings. The established procedure enables the analysis of various operational regimes and delivers information on vibration amplitudes, spectral characteristics, and system critical speeds. The results contribute to an improved understanding of the complex multiphysical interactions between the superconducting material and the permanent magnets attached to the rotor shaft.