Topic
Critical speed
About: Critical speed is a research topic. Over the lifetime, 2764 publications have been published within this topic receiving 31365 citations.
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30 Apr 2009
TL;DR: In this article, an exact method is employed to evaluate free vibration of the moving web in sub-and super-critical speeds, and the free vibration eigenvalues are extracted for a range of axial speeds.
Abstract: Moving webs can be found in a wide range of industrial applications such as paper handling, textile manufacturing, and magnetic tape recording. The moving web in these applications, which is generally orthotropic, may experience speeds more than critical speed. Critical speed is defined as that axial speed where the system vibration has a vanishing eigenvalue and is subject to a buckling instability. At a supercritical speed, the web may experience types of instabilities and subsequently sever out of plane vibrations.
In this paper, based on thin plate theory, the equation of out-of-plane motion is derived for an orthotropic web. Then an exact method is employed to evaluate free vibration of the web in sub- and super-critical speeds. This method is in fact the Levy-type solution of the equation of motion in a stiffness matrix form. The exact vibration eigenvalues which are generally complex values, are the roots of stiffness matrix determinant. Since the terms of the determinant are complex transcendental functions of eigenvalues, classical eigenvalue solver can not be used. So a suitable algorithm is used here to extract eigenvalues in the two-dimensional plane of complex numbers.
Using a numerical example, the reliability of the formulation and the solution procedure is shown. The free vibration eigenvalues is extracted for a range of axial speeds. Based on the results, flutter and divergence instabilities of the moving web are studied at supercritical speeds.
10 citations
01 Jan 2015
TL;DR: In this article, it is shown that the backward whirl can be observed when the rotor is coasting down to rest from above the critical speed corresponding to the backward Whirl.
Abstract: The determination of whirling frequencies of high speed turbines is always challenging in rotor dynamics. The natural frequencies of a Jeffcott rotor are split in the presence of gyroscopic effect. It is quite well known that the lower branch corresponds to the backward whirl and the upper branch corresponds to forward whirl. The forward whirl mode of the rotor has been observed experimentally, however, the backward whirl has not been observed. In this study it is shown that the backward whirl can be observed when the rotor is coasting down to rest from above the critical speed corresponding to the backward whirl. In order to illustrate the forward and the backward critical speeds of a simple Jeffcott rotor, the natural frequencies are obtained analytically for the second natural frequency of the system because of the large gyroscopic effect present in that mode. An experimental set up was used to verify the presence of backward whirl while the rotor is coasting down to rest. The rotor is also simulated using finite element method by ANSYS, and Campbell diagram is plotted. The analytical, experimental and ANSYS simulations confirm the existence of the backward whirl when the rotor is coasting down.
10 citations
TL;DR: In this article, the authors dealt with a synchronous vibration instability that occurred in a two-stage overhung centrifugal compressor supported by magnetic bearings, where the concentration of iron loss and thermal bending due to heat have been identified as the causes of the phenomenon, because the vibration stopped increasing when unbalance force rejection control was applied.
10 citations
TL;DR: In this article , a two-layer model of the railway track is analyzed with focus on the critical velocity and instability of moving masses, where the model is assumed to be infinite with no changes in properties in the longitudinal direction.
10 citations
TL;DR: In this paper, two different numerical methods are presented for the dynamic response of Euler-Bernoulli and Timoshenko beam under the impact of 10-DOF high-speed train (HST).
Abstract: In this paper, two different numerical methods are presented for the dynamic response of Euler–Bernoulli and Timoshenko beam under the impact of 10-DOF high-speed train (HST). Bridge beam is modeled in simply supported and uniform structure. The train traveling at high and constant speed on the bridge is modeled by taking into consideration primary and secondary suspension systems. The motion equation of the system was obtained using the Hamilton principle. These differential equations have been solved in the time domain using the fourth-order Runge–Kutta algorithm. The motion equations of the system have been converted to finite element format using Galerkin’s weak-form formulation. The finite element solution of the system was solved using the Newmark-β algorithm, and both algorithms were compared. In addition, Timoshenko beam theory and Euler–Bernoulli beam theory presented in the study were compared in terms of both bridge dynamics and train dynamics. As a result, although the speed difference between the two theories is significant at the critical speed values of HST, this difference in certain speed values decreases considerably.
10 citations