The paper describes a synchronous vibration instability problem encountered on a centrifugal compressor with oil-lubricated bearings. The problem was solved by modification of the compressor rotor; however, the root cause was not completely understood at that time. A possible explanation was based on a theory that suggested differential heating of the bearing journals. It was decided to verify this theory by experiments. Therefore a test rotor was designed with identical rotor dynamic characteristics to those of the compressor rotor. To fill a gap in the published research on bearing thermohydrodynamics, an experimental technique was devised to measure the surface temperature variations around one of the journals of this rotor. The dependence of significant temperature differentials across the journal upon its orbit was confirmed.

The Synchronous Instability of a Compressor Rotor Due to Bearing Journal Differential Heating

The thermal effects of rotor-to-stator rub, and their influence on the rotor vibrational response, are discussed in this paper. Based on machinery observations, it is assumed in the analysis that velocities of transient thermal effects are considerably lower than that of rotor vibrations, and thermal effects affect only rotor steady-state vibrational responses. These responses would change due to thermally induced bow of the rotor, which can be considered slowly varying in time for the purposes of rotor vibration calculation. Thus uncoupled from the thermal problem, the rotor vibration is analyzed. The major consideration is given to the rotor, which experiences intermittent contact with the stator due to predetermined thermal bow of the rotor, unbalance force, and radial constant load force. In the case of an inelastic impact, this causes an on/off step-change in the stiffness of the system. A specially developed transformation is applied to the system model which contains discontinuities, and an averaging technique is then used to analyze stability of the different resonance regimes of rotor motion that were obtained. These regimes are further used to calculate the heat generated during rotor-to-stator contact stages, as a function of thermal conditions and rotor thermal bow modal parameters. The calculated heat input is used as a boundary condition for the rotor heat transfer problem. The latter is treated as quasi-static, which allows the application of an asymptotic method to the problem. The solution at its first approximation is used to adjust the rotor thermal bow value. As a result of this calculation, an ordinary differential equation with complex variables is obtained for the thermal bow, and it is investigated from the stability standpoint.

/pdf/rotor-to-stator-rub-related-thermal-mechanical-effects-in-389yn4ln54.pdf

Rotor-to-stator, rub-related, thermal/mechanical effects in rotating machinery

A theoretical model has been developed for a synchronous thermal instability that is caused by differential viscous shearing in bearings of overhung rotors. This model employs an unbalance threshold criterion for instability instead of utilizing a traditional frequency-domain stability analysis. The current model will be used to investigate several case studies for both plain and tilting pad journal bearing rotors in the second part of this article.

/pdf/part-i-theoretical-model-for-a-synchronous-thermal-28ovek0hi4.pdf

Part I—Theoretical Model for a Synchronous Thermal Instability Operating in Overhung Rotors

The rotor–stator rubbing in rotating machinery generated as a consequence of rotor imbalance, shaft misalignment, and casing deformation is a potential threat to the machinery that seriously affects its performance. Timely prediction and correction of the rubbing are essential for the prolonged life of the machinery and its overall performance. A complete understanding of the system behavior during interaction is a great challenge for researchers working in the field of rotor dynamics. Rubbing phenomena involve complex contact nonlinearities and associated thermal effects, which makes the analysis very difficult. Research works in this field are started with the analysis of simple two degree-of-freedom models and now dealing with extensive three-dimensional finite element models. This paper provides a comprehensive review of different numerical models of rotor–stator rubbing with respect to their ability in simulating the actual response characteristics. A detailed description of contact modeling is also presented with the advantages and disadvantages of each model. Different methods for solving the numerical models are briefly explained. In addition, a commentary on different emerging techniques of rub identification is also reported. Finally, some informed recommendations on future directions are made by stating what lacks in the current research activities.

The numerical modeling of rotor–stator rubbing in rotating machinery: a comprehensive review

This article presents an analytical study of the dynamics and stability of rotors subjected to rubbing due to contact with seals, taking account of associated thermal effects. The seal interaction force acting on the shaft gives rise to a friction force, which is a source of heating and can induce so-called spiral vibrations. A mathematical model that has been developed couples the heat-conduction equation with the equations for motion of the rotor. Numerical simulations have been conducted that show the thermomechanical behavior of the rotor at various operating conditions. A procedure for analyzing the stability of multibearing rotors based on the system eigenvalue analysis and the state-space approach has been proposed. Finally, the experimental data related to full annular rub have been presented.

https://downloads.hindawi.com/journals/ijrm/2003/414915.pdf

Thermomechanical Behavior of Rotor with Rubbing

The Newkirk Effect is the vibration change due to thermal distortion of a rotor caused by rubbing on stationary components. B. Newkirk first noticed this phenomenon in 1924 and gave a qualitative explanation for it. The effect is not yet well enough understood. This and the importance of it in designing high-speed turbine rotors demand further work in this area. In this work an analytic study was undertaken. The static bow due to an arbitrary heat input can be found from a convolution integral of a source bow function and a heat function. Utilizing the dynamic response of the system, the resulting dynamic bow was computed. This dynamic bow controls the generated heat and the associated heat function. The resulting model can be described by a complex integral equation which can be transformed into two nonlinear differential equations. The stability and the modes of these equations have been studied. The equations themselves were solved with numerical methods. Three modes of the Newkirk Effect were discovered: spiralling, oscillating, and constant modes. It was found that critical speeds only indirectly influence the modes. The important factor is still the dynamic characteristics of the system in the form of a phase angle. It is believed that this analysis can be used for the design of rotors free of rubbing at wide ranges of speeds.Copyright © 1973 by ASME

/pdf/newkirk-effect-thermally-induced-dynamic-instability-of-high-3jcysjinln.pdf

A. D. Dimarogonas

Papers

Newkirk Effect: Thermally Induced Dynamic Instability of High-Speed Rotors