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To represent the support characteristic of active magnetic bearings (AMB), the commonly used parameters are the equivalent stiffness and the equivalent damping, which inherit the parameters of the stiffness and the damping from traditional mechanical bearings. First, by analyzing the diversity and the similarity between traditional mechanical bearing and AMB, the prior condition for applying the parametric representation of equivalent stiffness and equivalent damping to AMB is illuminated. Then, a method for measuring the equivalent stiffness and the equivalent damping of AMB-rotor system is proposed with multi-frequency excitation. One of its outstanding features is that the proposed method is based on the multi-degree of freedom (DOF) rotor model, not the single- DOF model, because the single DOF model cannot be suitably applied to the multi-DOF AMB-rotor systems. Otherwise, in order to decrease the identification error, the multi-frequency excitation can achieve the lowest peak value by means of appropriate selection for the relative phasing of each component, so that the possibility of the rotor displacement exceeding clearances of AMB and the magnetic force reaching saturation is minimized. Finally, the experiments, which are carried out on an AMB-rotor test rig with a vertical shaft, indicate that the proposed method can efficiently reduce the peak value for the superimposed multi-frequency excitation and correctly identify the equivalent stiffness and equivalent damping of AMB-rotor system. [ABSTRACT FROM AUTHOR]

Abstract: A method for multi-frequency periodic vibration suppressing in active magnetic bearing (AMB)-rotor systems is proposed, which is based on an adaptive finite-duration impulse response (FIR) filter in time domain. Firstly, the theoretic feasibility of the method is proved. However, two problems would be unavoidable, if the conventional adaptive FIR filter is adopted in practical application. One is that the convergence rate of the different frequency components may be highly disparate in multi-frequency vibration control. The other is that the computational complexity is significantly increased because the long memory FIR filter is required to match the transient response time of the AMB-rotor system. To overcome the problems above, the Fast Block Least Mean Square (FBLMS) algorithm is adopted to efficiently implement the computation in frequency domain at a computational cost far less than that of the conventional FIR filter. By the FBLMS algorithm, regardless of the number of the considered frequency components in vibration disturbance, the computational complexity would be invariable. Moreover, filter’s weights in the FBLMS algorithm have the intuitional relation with signal’s frequency. As a result, the convergence rate of each frequency component can be adjusted by assigning the individual step size parameter for each weight. Experiments with the reciprocating simulating disturbance test and the rotating harmonic vibration test were carried out on an AMB-rigid rotor test rig with a vertical shaft. The experiment results indicate that the proposed method with the FBLMS algorithm can achieve the good effectiveness for suppressing the multi-frequency vibration. The convergence property of each frequency component can be adjusted conveniently. Each harmonic component of the vibration can be addressed, respectively, by reconfiguring the frequency components of the reference input signal. [Copyright &y& Elsevier]

Abstract: For a flexible rotor system under seismic excitation, H 2, H ∞ and mixed H 2/H ∞ control strategies were formulated by means of linear matrix inequality (LMI) to attenuate the transient vibration of the flexible rotor system under a nonstationary seismic excitation and to improve robust performance of the flexible rotor system. A double-disc cantilever flexible rotor system was used as an example to verify the feasibility and the validity of the H 2, H ∞ and mixed H 2/H ∞ control strategies in active vibration control for a rotor system subjected to nonstationary El Centro seismic excitation. The performances of the rotor system in both frequency and time domains were analysed based on numerical optimization technique, which bases on an efficient convex optimization software. The feasibility and the effectiveness of the control strategies presented in active vibration control for a rotor system were verified. It is shown that for the H ∞ control, the displacement responses of the rotor system are effectively suppressed in the frequency domain, but transient-response performances are not so good. For the H 2 control, the transient responses of the rotor system attenuate quickly, but the frequency-response performances are not so good. The effectiveness of the mixed H 2/H ∞ control to suppress the displacement responses of the rotor system in the frequency domain and the transient response in time domain greatly depends on the H ∞ performance index. If the H ∞ performance index in the mixed H 2/H ∞ control is properly chosen, the mixed H 2/H ∞ control can effectively suppress both the displacement responses of the rotor system in the frequency domain and the transient response in time domain. [Copyright &y& Elsevier]

Abstract: Based on the particular characteristic of a magneto-rheological (MR) fluid, i.e., a rapid, reversible and dramatic change in its rheological properties produced by the application of an external magnetic field, a simple disk-type MR fluid damper operating in shear flow mode is presented in this paper. The magnetic field of the disk-type MR fluid damper is analyzed by the finite element method in order to show if the design is reasonable. The effect of excitation current in the coil on the magnetic flux density in the axial gaps filled with the MR fluid is studied both theoretically and experimentally. Finally, the effectiveness of the disk-type MR fluid damper for attenuating the vibration of rotor systems and of a simple open-loop on-off control based on the feedback of rotational speed for controlling vibration of rotor systems are experimentally studied in a flexible rotor system. It is shown that the dynamic characteristics of the disk-type MR fluid damper can be easily controlled by a steady magnetic field produced by a simple electrical magnetic coil with a low DC current (less than 1A) and that the disk-type MR fluid damper is very effective for attenuating and controlling the vibration of the rotor systems. It is possible to supply the optimum supporting damping for every vibration mode in the rotor system by using the disk-type MR damper, if the location of the disk-type MR fluid damper in the rotor is properly chosen. [Copyright &y& Elsevier]

The dynamic characteristics of a cracked rotor with an active magnetic bearing (AMB) are theoretically analyzed in this paper. The effects of using optimal controller parameters on the dynamic characteristics of the cracked rotor and the effect of a crack on the stability of the active control system are discussed. It is shown that the dynamic characteristics of the cracked rotor with AMBs are clearly more complex than that of the traditional cracked rotor system. Adaptive control with AMBs may hide the fault characteristics of the cracked rotor, rather than helping to diagnose a crack; this will depend on the controller strategy used. It is very difficult to detect a crack in the rotor with an AMB support system when the vibration of the rotor system is fully controlled. Monitoring the super-harmonic components of 2× and 3× revolution in the sub-critical speed region can be used as an index to detect a crack in the rotor with an AMB system. If the effect of the crack is not taken into account at the design stage of the controller, then the rotor–AMB system will lose its stability in some cases when cracks appear. [Copyright &y& Elsevier]