This report presents experimental, analytical, and numerical results describing vibrational phenomena in a rotating machine with one loose pedestal. The loose-pedestal machine rotor vibrations represent unbalance-related excited vibrations of synchronous and fractional subsynchronous regimes. In this study the loose-pedestal machine is first simulated by a simple vibrating beam excited by a shaker mounted on it. The shaker simulates an unbalanced machine rotor. The beam occasionally enters in contact with the foundation. The excited vibrations are modified by impacting occurrences, and by periodic changes in system stiffness. A new model of the impact has been developed. The results of analytical and experimental studies stand in a good agreement. They illustrate the existence of the synchronous regime and several subsynchronous fractional regimes in various excitation frequency ranges. The analysis adequately predicts the occurrence of these regimes and determines the physical parameters affecting them. The analytical and experimental results are then compared with the responses of experimental rotor rig with one bearing pedestal looseness. They show the same qualitative pattern.

The thermal effects of rotor-to-stator rubbing resulting in rotor bowing, and subsequent changes in rotor vibrational responses are discussed in this paper. The rotor thermal bow is modeled following relationships quoted in rotordynamic literature. The rotor model takes into account its first lateral mode in which the rubbing spot differs from the modal mass location. It is shown that the rotor responds to the rub thermal effect in a “spiraling/oscillating” mode which represents a form of rotor self-exciting vibrations. A simplified model explains physical phenomena occurring in the rubbing rotor system. An example of the field data illustrates the rotor dynamic behavior.

This paper presents results of numerical simulation of the dynamic behavior of a one-lateral-mode unbalanced and radially side-loaded rotor with either loose pedestal (looseness in a stationary joint), or with one oversize bearing (looseness between a rotating and stationary joint), or with occasional rotor/stator rubbing. The nonlinearities of these systems (variable stiffness, impacting, and friction) are associated with intermittent contacts with the stationary element. The results, based on a local impact model, developed in the author’s previous publications, exhibit regular periodic, as well as chaotic vibration patterns of the rotor.

The lateral vibration response of a rotor, experiencing periodic contact with a nonrotating machine component, is considered. In the case of an inelastic impact, this causes a piecewise, step-changing stiffness of the system. Applying to the rotor model a specially developed variable transformation which smooths discontinuities, and applying then an averaging technique, a variety of imbalance-related resonant regimes of rotor lateral motion are obtained, and their stability is analyzed. The developed analytical algorithm has a high potential as a valuable research tool for investigating local nonlinear effects in rotor systems.

The paper analyzes, theoretically and experimentally, the lowest four lateral modes of an isotropic rotor/fluid-lubricated bearing system with flexible rotor and flexible bearing support. The parameters of the analytical model of the system are identified using sweep-frequency modal testing of the rotor rig. A nonsynchronous, circular-rotating-force excitation was applied sequentially at the rotor and at the fluid-lubricated bearing casing, in order to generate the response data. The approach used in this study emphasizes the dynamic features of the system which are invariant to the choice of coordinate system. The system is described using Dynamic Stiffness matrix. This provides an advantage of simplicity, allowing a comprehensive stability study for various system parameters.

The paper presents a case history of failure of a gas turbine, which was manifested in high vibrations, loud noise, and, eventually, damaged parts, such as impellers, bearings, and probes were discovered. The turbine features a bearing with floating sleeve design, originally intended to reduce lubricant relative speeds within the bearing (that is, decreasing journal to bearing speed gradient throughout the lubricant circumferential flow, breaking the flow in two sections, at both surfaces of the floating sleeve). In this turbine, the floating sleeve bearing was the major cause of the failure. It contributed to restraining the oil supply from the journal/thrust bearing assembly, which resulted in high amplitude lateral subsynchronous 1/3X vibrations. The event was accompanied by oil charring in the bearing and, due to overheating, melting of the brass thrust washer, which was in addition to mechanical deterioration. In the paper, several disadvantages of a floating sleeve bearing are discussed, such as: • Floating ring lateral instability. • Floating ring axial instability, unusual for other types of journal bearings. As a consequence, inevitable metal-to-metal surface friction occurs within the bearing in axial and lateral directions, thus increasing tendency to oil charring. The major objective for using the floating sleeve, the reduction of relative speeds within the bearing, is not achieved: The sleeve does not prevent lubricant from high speed rotation and creates further potentially severe malfunctions of the turbine.

This paper is a continuation of the series of papers on application of the improved fluid force model for lightly loaded shafts rotating in a fluid environment. The fluid force model is based on the strength of the circumferential flow. The considered two–mode rotor is supported in two fluid–lubricated bearings, thus it contains two potential sources of instability. The eigenvalue solution predicts thresholds of stability and provide natural frequencies and modes of the system, including the flow–induced modes The nonlinear model of the rotor/bearing system allows for evaluation of parameters of after instability onset self–excited vibrations (whirl and whip). Experimental data illustrate the dynamic phenomena predicted by the model. In particular, they show an undocumented new phenomenon, the simultaneous existence of two whip vibrations with frequencies corresponding to two modes of the rotor. A radial preload of the rotor results in specific changes of the fluid forces (an increase of radial stiffness and reduction of circumferential velocity) providing better stability of the rotor. This effect predicted by the model is illustrated by the experimental data.

This paper outlines the sweep frequency rotating force perturbation method for identifying the dynamic stiffness characteristics of rotor/bearing/seal systems. Emphasis is placed on nonsynchronous perturbation of rotating shafts in a sequence of constant rotative speeds. In particular, results of the identification of flexible rotor multi–mode parameters and identification of fluid forces in seals and bearings are given. These results, presented in the direct and quadrature dynamic stiffness formats, permit the separation of components for easy identification. Another example of the perturbation method application is the identification of the lateral–torsional coupling due to shaft anisotropy. Results of laboratory rig experiments, the identification algorithm, and data processing techniques are discussed.

This paper discusses one of the problems associated with establishing acceptable vibration levels for rotating machinery related to non collocation of critical vibration and available measurement locations. A critical vibration location is any point along the rotor which has a reduced clearance or a high potential for rubbing, such as seal locations. Non collocation occurs because the physical and/or environmental conditions at the critical locations prohibit the installation of suitable measurement transducers at those points. This leads to the dilemma of correlating the critical and measured vibration responses so the machine can be protected at the critical locations using the known responses at the measurement positions. This paper presents a method for estimating the vibration amplitudes and phases, either synchronous or nonsynchronous, at the critical locations using the known vibration responses at the measurement points, the current operating speed, the machine configuration data, and optimization techniques. A computer program has been developed for a personal computer running Windows 3.1 under DOS 5.0 which uses finite element modeling of the rotor to create a calculated rotor response and a data acquisition system to get the actual measured responses. A local convergence algorithm is then implemented to minimize the error between the calculated and measured vibration responses at the measured locations. The calculated responses at the critical locations then become the estimated vibration response for these points. To evaluate the accuracy of the technique, experiments were conducted using a rotor rig in which the vibration responses at both the critical and measurement locations were measured. The computer program was then used to estimate the vibration responses at the critical locations. The estimated vibration responses were then compared with the measured responses at the same location to evaluate the effectiveness of the technique. The results of these experiments are also included in this paper.

This paper outlines the dynamic behavior of externally excited rotor/stator systems with occasional, partial rubbing conditions. The observed phenomenon have one major source of a strong nonlinearity: transition from no contact to contact state between mechanical elements, one of which is rotating. This results in variable stiffness and damping, impacting, and intermittent involvement of friction. A new model for such a transition (impact) is developed. In case of the contact between rotating and stationary elements, it correlates the local radial and tangential (“super ball”) effects with global behavior of the system. The results of numerical simulations of a simple rotor/stator system based on that model are presented in the form of bifurcation diagrams, rotor lateral vibration time–base waves, and orbits. The vibrational behavior of the considered system is characterized by orderly harmonic and subharmonic responses, as well as by chaotic vibrations. A new result (additional subharmonic regime of vibration) is obtained for the case of heavy rub of an anisotropically supported rotor. The correspondence between numerical simulation and previously obtained experimental data supports the adequacy of the new model of impact.

Nonsynchronous perturbation techniques developed over the last few years have proven to be a very powerful tool for parameter identification of rotating systems. In order to obtain interpretable results, some limitations have had to be imposed on the analytical models and rotor systems used in the process, such as applied forces, and measurement transducers had to be located near major masses on the rotor. In the laboratory environment these limitations can usually be accommodated, but not always, while in the field, compliance is almost impossible. This paper explores the use of finite element modeling, measured vibration response data, and optimization techniques to extend the applicability of parameter identification through nonsynchronous perturbation techniques to those systems in which the perturbation forces and/or resultant response measurements cannot be conveniently located at the mass centers. In this technique, a finite element model of the rotor system is constructed, and all known information about the system parameters input to a computer program designed to operate on a personal computer. The program then computes the theoretical response of the system, by processing user-supplied initial conditions for the unknown system parameters, and compares these results with the vibration responses measured on the machine, and collected by the data acquisition system. The unknown parameters are then modified using local convergence optimization techniques until the error between the theoretical and measured responses is acceptably small. If the system parameters under investigation coincide with the unknown parameters in the computer program, they are identified in the process. This technique was applied to an experimental rotor system constructed such that the parameters under investigation, the direct and quadrature dynamic stiffness components for a plain oil-lubricated journal bearing operating at low eccentricity, could be determined by both this technique and conventional unbalance force testing. The results of the nonsynchronous tests are presented in the paper.

A rotor system with two orthogonal lateral and two angular (torsional) degrees of freedom is considered. The rotor has asymmetry of the lateral stiffness and is laterally loaded with a constant radial force and a rotating unbalance. Constant driving and load torques are applied to the rotor. The important part of the research includes an analysis of “snapping” action, when, during rotation, the rotor experiences a peak of torsional acceleration. This occurs when the “strong stiffness” axis of the anisotropic rotor passes under the axis of the sideload. The numerical simulation of the analytical model exhibits a “snapping” (accelerated) torsional response of the rotor at twice synchronous frequency (2 ×), and it is especially pronounced at 1 × and 2 × torsional resonances. The “snapping” response can initiate a rotor crack in the area of stress concentration, can stimulate existing crack propagation, and can be a cause of the coupling failure. The analytical results are obtained by the Averaging Method application. They confirm the numerical results and show the possibility of combination resonance occurrences. The synchronous dynamic stiffness for the frequency range around 1 × lateral resonance is analytically obtained. The specific shape of the quadrature dynamic stiffness component can serve as a shaft crack indicator and can be used for early detection of a lateral crack on the rotor.

The paper contains the study of the lubricant fluid forces applied to the journal in a cylindrical, externally-pressurized bearing. The analytical expressions take into account the appearance of fluid cavitation at high eccentricity level. The obtained expressions for fluid forces and torque are used for numerical simulation of a simple, one-mode rotor system. The system exhibits typical fluid whirl/whip instability which results in high fluid resistance torque values. The latter is considered as one of the causes of turbomachinery efficiency deterioration due to fluid-induced instabilities. This paper is a continuation of the study undertaken by Bently et al. (1985), Muszynska (1986), and Petchenev et al. (1995).

Focused on rotor lateral modes, the paper discusses specifics of damping evaluation in rotating machines. Rotors force the fluid trapped in small rotor-to-stator radial clearances to rotate in circumferential fashion. The fluid in circumferential motion generates a tangential force acting in feedback on the rotor. This force direction is opposite to that of damping force. The “effective damping” is, therefore, reduced or even nullified by the fluid interaction effects. The classical measures of damping in mechanical structures, such as Logarithmic Decrement and Amplification Factor, which are used to evaluate machine susceptibility to instability based on documented vibration data, have to be adjusted to include the fluid interaction effects. These measures now represent the measures of Quadrature Dynamic Stiffness ( QDS ). It is shown that they contain the expression defined as Stability Margin (or Nondimensional Stability Margin), derived from the stability condition of the rotor system. A simple model of isotropic rotor lateral vibrations is used to obtain the QDS measures.

This paper documents analytical and experimental research of the lateral and torsional responses of a cracked rotor to different types of excitation. The experimental research has been performed on a rotor rig, which emulate a turbogenerator. It includes driving motor coupled to the main rotor, a lateral nonsynchronous perturbation device, and a generator with an electrical field consisting of a constant component (constant torsional load) and a sinusoidal component, provided by a signal generator. The generator was used as a torsional nonsynchronous perturbation device. The midspan of the rotor was modified so that a section could be changed starting with a circular cross-section (undamaged rotor) to the cross-section with transverse crack. The lateral and torsional responses have been measured at two axial locations. The obtained lateral data was processed using directional filtering into forward and reverse components of the corresponding filtered elliptical orbits. The forward component of the lateral response to nonsynchronous perturbation allows to identify overall stiffness reduction and rotating stiffness asymmetry introduced by the change in midspan rotor cross-section, while the reverse component largly depends on the support asymmetry. The nonsynchronous torsional excitation allows identify of the system torsional dynamic stiffness and it’s reduction due to the crack. The ratio of the filtered to 1× or to the perturbation frequency rotor responses at two axial locations was considered as an indicator of a lateral mode shape change due to the crack. The experimental results are compared with the analytical model of the rotor response, which was obtained by the application of a perturbation method of small parameter to the system of nonlinear equations. The equations describe the rotor system with four lateral (two displacements and two inclination angles) and two torsional degrees of freedom.