The article deals with the computational study of the rigid rotor coupled with squeeze film dampers. Various techniques such as the method of computation of the synchronous response with a circular centred orbit, the harmonic balance method, and the direct time integration method are used to analyse the nonlinear behaviour of the rotor system. The results indicate that the rotor system can exhibit both a synchronous circular response with a large orbit radius and a nonsynchronous response with a quasiperiodic character. However, both responses are undesirable in rotating machinery and should be avoided. The new results are presented to provide insight into the impact of initial conditions on the vibration response via basins of attraction. The simulations show that: (i) the basins of attraction are more sensitive to the choice of the initial velocities than displacements, (ii) the basins of attraction are noticeably dependent on the rotor speed in the region of a nonsynchronous response, and (iii) the border between the basins of attraction can be smooth or without a clear structure. The research brings clear conditions defined by parameters such as the dimensionless SFD constant, unbalance, and rotational speed for the suppression of undesirable nonlinear phenomena. The results suggest that the damper can effectively improve the vibration response of high-speed rotating machinery, but its design must be chosen appropriately.
The aim of this paper is to demonstrate capabilities of the created numerical procedure, which is based on harmonic balance method. Furthermore, the procedure incorporates the alternating frequency-time domain technique and the arc-length parameterization to solve the steady-state response of nonlinear systems in efficient manner, including unstable branches. The stability of the motion was assessed by two methods: the 2n-pass method and Hill's method. The procedure was verified on an example from literature to prove its sufficient accuracy and subsequently, the procedure was applied on the finite element model of the rotor system mounted on the squeeze film dampers. The carried out computational simulations confirmed that the created procedure is efficient for the strongly nonlinear response and it gives similar results as the time integration.
Rotors are often coupled with a stationary part by rolling element bearings. To suppress their excessive vibration, the bearings are inserted in squeeze film dampers. The control of damping in the support elements offers the possibility to minimize the oscillation amplitude of accelerating or decelerating rotors, passing the regions of critical speeds. The controllable damping effect can be achieved if the squeeze film dampers are lubricated with magnetorheological oil. The change in the applied current feeding the electric coil changes magnetic induction in the damper gap, which changes the oil damping properties. The minimum vibration amplitude of the rotor running up or down through the resonance area is accomplished if the current increase or decrease is not sudden, but if it is distributed in some time interval. This article concentrates on determination of the optimum parameters of this manipulation. The developed procedure leads to solving an unconstrained optimization problem with the implicit objective function. The evolution method was used for its solving. In the investigated case, the proposed procedure made it possible to reduce maximum vibration amplitude by about 40% compared with the uncontrolled current decrease. The main contribution of the conducted research work is presentation of a new and original procedure for controlling the damping effect in the rotor supports. It provides a new idea to the designers and engineers regarding how to minimize amplitude of the rotor vibration when passing the critical speed. In addition, the article points to a new area of utilization of controllable magnetorheological squeeze film dampers.
Nowadays, to reduce vibrations of machines, damping devices utilize the eddy current damping effect being increasingly investigated for its advantages of no mechanical contact, no viscous liquid required, high reliability, and good damping capacity. This article studied the main principle of the eddy current damping effect for a moving permanent magnet in a stationary and electrically conductive nonmagnetic cylindrical tube. The magnetic damping coefficient is investigated experimentally, analytically, and by numerical simulations in a steady-state. The numerical simulation is performed in the ANSYS Maxwell programme. The obtained results indicate that the damping force affecting the moving magnet has a viscous form. The experimentally measured and computed results are in good agreement. The effect of varying tube diameter and the tube wall thickness on the magnetic damping coefficient is shown. The contribution of this article consists in the development and a comparison of the obtained results of three approaches for determining the magnetic damping coefficient for a moving magnet in a cylindrical tube.
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