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The prediction of critical speeds of a rotating shaft is a crucial issue in a variety of industrial applications ranging from turbomachinery to disk storage systems. The modeling and analysis of rotordynamic systems is subject to a number of complications, but perhaps the most important characteristic is to pass through a critical speed under spin-up conditions. This is associated with classical resonance phenomena and high amplitudes, and is often a highly undesirable situation. However, given uncertainties in the modeling of such systems, it can be very difficult to predict critical speeds based on purely theoretical considerations. Thus, it is clearly useful to gain knowledge of the critical speeds of rotordynamic systems under in situ conditions. The present study describes a relatively simple method to predict the first critical speed using data from low rotational speeds. The method is shown to work well for two standard rotordynamic models, and with data from experiments conducted during this study.

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An approximate solution technique for tilting pad journal bearings is presented. The method makes use of approximations to the axial pressure profile and the temperature profiles and includes heat transfer between the film and its boundaries. A second order profile is assumed to represent the temperature distribution across the film. The classical Reynolds equation is applied, using the viscosity based on the cross-film average of temperature. The transfer of heat in the pads is modeled as purely radial conduction, and the journal surface temperature is given by a circumferential average of the film temperatures. Results of calculations are presented for a sample case representative of an industrial compressor or turbine bearing and are compared to isothermal results. The dynamic characteristics in this case are found to vary by 10 to 35 percent for a change in lubricant inlet temperature of 28°C. Temperature distributions in the lubricant and on the surfaces of the pads are given.

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.