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Abstract:
New technologies are being developed to elaborate cutting-edge electrical jet engines to replace classical constructions. These new concepts consider the possibility of using electrical machines both as starters and generators, as well as suspension systems for the turbine shafts of aircraft engines. The paper will present mathematical analysis regarding active magnetic bearing (AMB) implementation for rotor–shaft support. This technology allows the elimination of friction forces between cooperating kinematic pairs (stator and rotor), reduces the adverse effects of classic bearings, and increases operating speed range and an operational susceptibility. The mathematical and numerical analysis of active magnetic suspension systems are presented. Next, a comparison of the theoretical studies using Comsol Multiphysics software and its experimental verification are described. A discussion regarding the mathematical analysis and experimental effects is also provided. The conclusion summarizes the theoretical and experimental features of heteropolar radial active magnetic bearings in new electric aircraft engines.

Keywords:
active magnetic bearings,electric jet engine,current stiffness coefficient,displacement stiffness coefficient

Abstract:
This paper deals with research on the magnetic bearing control systems for a high-speed rotating machine. Theoretical and experimental characteristics of the control systems with the model algorithmic control (MAC) algorithm and the proportional-derivative (PD) algorithm are presented. The MAC algorithm is the non-parametric predictive control method that uses an impulse response model. A laboratory model of the rotor-bearing unit under study consists of two active radial magnetic bearings and one active axial (thrust) magnetic bearing. The control system of the rotor position in air gaps consists of the fast prototyping control unit with a signal processor, the input and output modules, power amplifiers, contactless eddy current sensors and the host PC with dedicated software. Rotor displacement and control current signals were registered during investigations using a data acquisition (DAQ) system. In addition, measurements were performed for various rotor speeds, control algorithms and disturbance signals generated by the control system. Finally, the obtained time histories were presented, analyzed and discussed in this paper.

Keywords:
magnetic bearing; predictive algorithm; high speed rotating machine

Abstract:
The purpose of this study is to create a concept for what would be a structurally simple and perationally robust support for the automotive turbocharger rotor in electrodynamic passive magnetic bearings. Because this kind of magnetic suspension-in its fundamental version-is dynamically unstable, to avoid the disadvantages contained therein, what is being proposed is the addition of external damping through the employment of the newly designed combined self-stabilizing electrodynamic passive magnetic bearing. The electromagnetic stiffness and damping characteristics of combined electrodynamic passive magnetic bearings have been determined for various shaft rotational speeds by means of the advanced 3D finite element method. In this study, a dynamic interaction between the turbocharger rotor shaft and the passive magnetic suspension is proposed as a support for both the fundamental electrodynamic passive magnetic bearings and the suggested combined self-stabilizing passive magnetic bearings. Here, the main attention is focused on the asymptotic stability of both the rotor shaft suspension variants. The additional damping magnitudes required to stabilize the most sensitive lateral eigenmodes of the object under consideration have been determined by means of the Routh-Hurwitz stability criterion.

Keywords:
rotor dynamics, combined electrodynamic passive magnetic bearings, turbocharger flexible rotor shaft, stability analysis, stabilizing damping magnitude

Abstract:
Electro-dynamic passive magnetic bearings are now viewed as a feasible option when looking for support for high-speed rotors. Nevertheless, because of the skew-symmetrical visco-elastic properties of such bearings, they are prone to operational instability. In order to avoid this, the paper proposes the addition of external damping into the newly designed vibrating laboratory rotor-shaft system. This may be achieved by means of using simple passive dampers that would be found among the components of the electro-dynamic bearing housings along with magnetic dampers, which satisfy the operational principles of active magnetic bearings. Theoretical investigations are going to be conducted by means of a structural computer model of the rotor-shaft under construction, which will take into consideration its actual dimensions and material properties. The additional damping magnitudes required to stabilize the most sensitive lateral eigenmodes of the object under consideration have been determined by means of the Routh-Hurwitz stability criterion.

Keywords:
rotor-dynamics, electrodynamic passive magnetic bearings, flexible rotor-shaft, active magnetic damper, stability analysis

Abstract:
The purpose of this paper is to create a concept of the structurally simple and operationally robust support of high-speed rotors in the electrodynamic passive magnetic bearings (EDPMB). Since this kind of a magnetic suspension in its fundamental version is dynamically unstable, in order to avoid such an essential disadvantage there is proposed the addition of external damping by the use of the newly designed combined, self-stabilizing electrodynamic passive magnetic bearing. The electromagnetic stiffness- and damping characteristics of the combined EDPMB have been determined for various shaft rotational speeds by means of the advanced 3D finite element method. The dynamic investigations are performed for a single-span, high-speed flexible rotor-shaft. In the computational part a dynamic interaction between the rotor-shaft and the passive magnetic suspension is carried out for a support in the fundamental EDPMBs and in the proposed combined, self-stabilizing passive magnetic bearings. Here, the main attention is focused on asymptotic stability of the both rotor-shaft suspension variants. In addition, for the considered rotor-shaft-bearing system amplitude-frequency characteristics of forced steady-state bending vibrations have been determined. By means of this investigation there is demonstrated a resonance suppression ability using the external damping generated by the proposed combined EDPMBs.

Keywords:
magnetic bearing, electrodynamic passive magnetic bearings, EDPMB, rotor-shaft suspension, high-speed rotors

Abstract:
The electrodynamic passive magnetic bearings became now a very promising kind of support for high-speed rotors. Nevertheless, because of skew-symmetrical visco-elastic properties of such bearings, they are sensitive to operational instability. In order to avoid this disadvantage, in the paper there are proposed stabilization concepts reducing to an introduction of a sufficient magnitude of additional external damping into the vibrating rotor-shaft system. This purpose is going to be realized by means of simple and effective passive dampers built in the electrodynamic bearing housings as well as using heteropolar magnetic dampers which realize operational principles of the active magnetic bearing. The theoretical investigations are going to be carried out by means of a structural computer model of the rotor-shaft system, taking into consideration its full geometry and material properties.

Abstract:
In recent years, magnetic bearing technology has been implemented in many practical applications. In
comparison with mechanical bearings, the magnetic ones have decreased stiffness coefficients and increased
damping coefficients of radial bearings reducing the critical rotor speeds, [1]. These features are given the
magnetic bearings a considerable potential to become a key element in rotating machines, like jet engines,
turbo-compressors, generators and many others, [2]. Active magnetic bearings allow precise control of a
rotor position and enable “online” monitoring, diagnosing, and identifying high-speed machines, [3].
The magnetic bearings are structurally unstable. Namely, an effective control system with a proper controller
ought to be designed to ensure defined control quality indicators. In general, control systems of magnetic
bearings are mostly restricted for using proportional-integral-derivative (PID) controllers. However, robust
and slide control methods are also used in similar systems, [4]. Some predictive control algorithms were
implemented in the analyzed AMB control loop [1].
The paper presents the research results of a parametric predictive control algorithm implemented in a highspeed
rotor machine’s magnetic bearing support system. The theoretical and experimental analyses of the
control system with the Extended Horizon Adaptive Control (EHAC) algorithm are presented using an
AutoRegressive with eXogenous input (ARX) model. A laboratory model of the magnetic suspension system
consists of two active radial magnetic bearings and one axial (thrust) active magnetic bearing. The levitated
rotor displacement in air-gaps and control current signals in control loops were measured for various rotor
speeds and several parameters of the control algorithm, and they were presented in the form of time histories.
Moreover, the power consumption of the magnetic bearing system with the predictive control algorithms was
analysed, and the influence of a tuning factor and control horizon on rotor dynamic properties were
determined. The theoretical studies were carried out using Matlab and Simulink software, whereas the
experimental studies were performed using an appropriately dedicated test rig.
References
[1] Kurnyta-Mazurek P., Szolc T., Henzel M., Falkowski K.: „Control system with nonparametric predictive algorithm
for the high-speed rotating machine with magnetic bearings”, Bulletin of the Polish Academy of Sciences: Technical
Science, 2021
[2] Brusa: “Semi-active and active magnetic stabilisation of supercritical rotor dynamics by contra-rotating damping”,
Mechatronics 24, 2014, pp. 500–510, //doi.org/10.1016/j.mechatronics.2014.06.001.
[3] R. Siva Srinivas, R. Tiwari, Ch. Kannababu: “Application of active magnetic bearings in flexible rotordynamic
systems – A state-of-the-art review”, Mechanical Systems and Signal Processing, 106, 2018, pp. 537-572
[4] A. Tonoli, A. Bonfitto, M. Silvagni, and L. D. Suarez, “Rotors on Active Magnetic Bearings: Modeling and Control
Techniques”, in Advances in Vibration Engineering and Structural Dynamics. London, United Kingdom:
IntechOpen, 2012 [Online]. Available: https://www.intechopen.com/chapters/41670 doi: 10.5772/51298

Keywords:
active magnetic bearings, pramaetric predictive control, high-speed machines