Abstract
The active magnetic bearings system plays a vital role in high-speed rotors technology, where many research articles have discussed the nonlinear dynamics of different categories of this system such as the four-pole, six-pole, eight-pole, and sixteen-pole systems. Although the twelve-pole system has many advantages over the eight-pole one (such as a negligible cross-coupling effect, low power consumption, better suspension behaviors, and high dynamic stiffness), the twelve-pole system oscillatory behaviors have not been studied before. Therefore, this article is assigned to explore the effect of the magneto-electro-mechanical nonlinearities on the oscillatory motion of the twelve-pole system controlled via a proportional derivative controller for the first time. The normalized equations of motion that govern the system vibrations are established by means of classical mechanics. Then, the averaging equations are extracted utilizing the asymptotic analysis. The influence of all system parameters on the steady-state oscillation amplitudes is explored. Stability charts in a two-dimensional space are constructed. The stable margin of both the system and control parameters is determined. The obtained investigations reveal that proportional gain plays a dominant role in reshaping the dynamics and motion bifurcation of the twelve-pole systems. In addition, it is found that stability charts of the system can be controlled by simply utilizing both the proportional and derivative gains. Moreover, the numerical simulations showed that the twelve-poles system can exhibit both quasiperiodic and chaotic oscillations besides the periodic motion depending on the control parameters’ magnitude.
Highlights
An active magnetic bearings system (AMBS) is a mechanism that supports rotating shafts applying a controllable magnetic force without any physical contact
The AMBS is works as follows: (1) the proximity sensors measure the instantaneous vibrations x(t) and y(t) of the rotor; (2) the measured signals x(t) and y(t) are sent to the digital controller to manipulate them according to the provided control algorithm; (3) the manipulated signals are fed back again to the power amplifiers, which in turn apply controlled electrical currents to the electromagnetic poles; and (4) the electromagnetic poles generate a corresponding attractive magnetic force that allows the rotor system to rotate without lateral oscillations in X and Y directions
The twelve-pole AMBS system vibrational behaviors are extensively analyzed within this article
Summary
An active magnetic bearings system (AMBS) is a mechanism that supports rotating shafts applying a controllable magnetic force without any physical contact. Saeed et al [17,18] introduced a detailed investigation for the sixteen-pole system with constant stiffness coefficients They studied the influence of Cartesian and radial control methodologies on both the bifurcation characteristics and vibration reduction of the AMBS system. The authors reported that the rotor system has quartic stable periodic motions in the case of Cartesian control, while the system behaves like a Duffing oscillator with a hardening spring characteristic at the radial control case Zhang and his team introduced a detailed investigation for the sixteen-pole AMBS’ having time-varying stiffness coefficients [19,20,21,22,23]. The obtained stability charts confirmed the possibility of controlling both the motion bifurcation and vibration amplitudes of the studied system using the control gains
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