The purpose of this article is to apply the wavelet transform algorithm to identify the magnetic damping and magnetic stiffness coefficients of the drive rod with which a set of 4-pole active magnetic bearing (AMB) is equipped. By taking advantage of time–frequency analysis feature, the ridge curve of rod free response after wavelet transformation can be extracted to find the natural frequency of the rod/AMB system. In other words, due to the influence of magnetized field by AMB, the stiffness of the rod dynamics is not linear any more and can be estimated from the curve of the amplitude versus frequency by wavelet transformation. On the other hand, the non-linear damping coefficients can be estimated from the derivative of amplitude versus amplitude by wavelet transformation of rod free vibration. It is found that the non-linear magnetic damping coefficients are up to second order in polynomial and the stiffness coefficient is mainly of third order, respectively. In addition, the identified second-order damping coefficient is negative and hence implies that under specific rod displacement and speed, the dynamic of rod/AMB system in axial direction is unstable.
Conical shells have advantages such as light weight, higher stiffness and strength, its stiffness ratio between axial and transverse directions can be easily adjusted by changing its apex angle. Thus conical shell can be utilized as an isolator to protect precision payloads and equipment from severe dynamic loads. In this study, vibration isolation performance of a conical shell isolator laminated with piezoelectric actuators is investigated. The conical shell isolator is manufactured from epoxy resin. The payload is at the minor of the isolator. The major end of the isolator is fixed at a flange installed on a shaker. Macro fiber composite (MFC) is used as actuator, which is laminated on the outer surface of the conical isolator. The sensing signals from sensors on the isolator is transferred to a dSPACE system and the control voltage is transferred to a power amplifier and then to the MFC actuator. The control voltage is calculated in the Matlab/Simulink environment. Both negative velocity feedback and optimal controllers are employed in the active vibration control. The payloads are simplified to be a rigid cylinder, and two payloads with different weight are investigated in the study. Experimental results show that the proposed conical shell isolator is effective for vibration isolation of payloads, and vibration amplitude of the payload can be significantly reduced.
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