Rotordynamic Behavior Research Articles

Journal bearing differential heating evaluation with influence on rotor dynamic behaviour

The nature of differential heating across the journal of a hydrodynamically lubricated bearing has been investigated theoretically and an assessment made of the local thermal bend in the rotor at the bearing location. The energy balance for the system is time dependent and involves a stationary bearing component, an oscillating lubricant film, and a rotating, orbiting section of journal. Thermo-hydrodynamic solutions are developed which allow for temporal and spatial periodic variations of bearing, lubricant and journal temperatures. The influence of a synchronous journal orbit on the temperature distribution throughout the system is discussed. In particular, the relation between any prescribed orbit and the steady state temperature differential across the journal, resulting in steady state rotor bending, is established. The role played by such thermal bending in the onset of unstable synchronous whirl in the rotors of high-speed machines is outlined.

Development of a Set of Equations for Incorporating Disk Flexibility Effects in Rotordynamic Analyses

Rotordynamic equations that account for disk flexibility are developed. These equations employ free-free rotor modes to model the rotor system. Only transverse vibrations of the disks are considered, with the shaft/disk system considered to be torsionally rigid. Second-order elastic foreshortening effects that couple with the rotor speed to produce first-order terms in the equations of motion are included. The approach developed in this study is readily adaptable for usage in many of the codes that are currently used in rotordynamic simulations. The equations are similar to those used in standard rigid disk analyses but with additional terms that include the effects of disk flexibility. An example case is presented to demonstrate the use of the equations and to show the influence of disk flexibility on the rotor dynamic behavior of a sample system.

A Study of the Influence of Bearing Clearance on Lateral Coupled Shaft/Disk Rotordynamics

This study examines the influence of bearing clearance on the dynamic behavior of a rotating, flexible disk/shaft system. Most previous work in nonlinear rotordynamics has tended to concentrate separately on shaft vibration or on bladed disk vibration, neglecting the coupling dynamics between them. The current work examines the important rotordynamic behavior of coupled disk/shaft dynamics. A simplified nonlinear model is developed for lateral vibration of a rotor system with a bearing clearance nonlinearity. The steady-state dynamic behavior of this system is explored using numerical simulation and limit cycle analysis. It is demonstrated that bearing clearance effects can produce superharmonic vibration that may serve to excite high-amplitude disk vibration. Such vibration could lead to significantly increased bearing loads and catastrophic failure of blades and disks. In addition, multivalued responses and aperiodic behavior were observed.

A Transfer Matrix Technique for Evaluating the Natural Frequencies and Critical Speeds of a Rotor With Multiple Flexible Disks

The influence of disk flexibility on the rotordynamical behavior of turbomachinery is a topic that is of some concern to designers and analysts of such equipment. Research in this area has indicated that disk flexibility may significantly alter the dynamical behavior of a rotor system. This research effort is concerned with developing a procedure to account for disk flexibility which can readily be used for investigating how such effects might influence the natural frequencies and critical speeds of practical rotor systems. A transfer matrix procedure is developed in this work in which the disk flexibility effects are accounted for by means of additional terms included in the transfer matrix formulation. In this way the efficiency and practicality of the transfer matrix method is retained. To demonstrate this technique, a simple rotor system is studied for the effect of disk flexibility and the results discussed.

A Comparison of Analog and Digital Controls for Rotor Dynamic Vibration Reduction Through Active Magnetic Bearings

Active magnetic bearings are implemented using analog and digital controllers to achieve vibration reduction for multimass flexible rotors. Various models are developed for the rotor-bearing system, and the first three critical speeds (resonant frequencies) are shown to be unaffected by inclusion of the higher order shaft dynamics in the model. Higher order rotor-bearing models reveal the presence of “shaft modes,” the excitation of which is a function of the position of the magnetic bearing proximity probe (these modes are effectively damped by the flexible coupling employed in the test apparatus). Rotor dynamic behavior is investigated for various analog and digital controllers. Rotor response in the presence of proportional-derivative control is similar for both analog and digital control. Higher order digital control algorithms (second derivative and integral) affect the rotor response in a frequency dependent manner: Second derivative feedback is effective at reducing third mode vibration, and integral feedback, while rejecting any steady-state rotor position error, slightly accentuates the vibration at the first critical speed. Increasing the sampling rate of the digital controller has a similar effect to increasing the amount of second derivative feedback employed.

A Finite-Element Perturbation Approach to Fluid/Rotor Interaction in Turbomachinery Elements. Part 2: Application

A newly devised perturbation model for the fluid-induced vibration of turbomachinery rotating elements is used to compute the rotordynamic coefficients of an annular seal. First, the finite element-based solution of the flow field in the centered-rotor operation mode is verified and its grid dependency tested for different seal configurations. The rotordynamic behavior of a hydraulic seal with a clearance gap depth/length ratio of 0.01, as a representative case, is then analyzed under a cylindrical type of rotor whirl and several running speeds. The direct and cross-coupled rotordynamic coefficients dictating the rotor instability mechanism in this case are compared to experimental and analytical data, and the outcome is favorable. The numerical results are also used to discuss the validity of a common assumption in existing computational models in regard to the circumferential distribution of the perturbed flow variables in the eccentric rotor operation mode.

Rotor Dynamics of Centrifugal Pumps "a Matter of Fluid Forces"

In the industrial application of centrifugal pumps, power densities and operating speeds have increased continuously in the last decade. Operating experience at these increased speeds and power densities has shown the tremendous impact of rotor dynamics on the reliability of these pumps. This has resulted in a considerable research and development (R&D) effort world wide towards the phenomena that affect pump rotor dynamic behavior. This paper reviews the available methods and the specific R&D conducted towards effective prediction of pump rotor dynamic behavior

Some Observations of Chaotic Vibration Phenomena in High-Speed Rotordynamics

Subharmonic response in rotordynamics may be encountered when a rotor is operated with its rotational centerline eccentric to that of a close clearance static part, so that local contact can take place during each orbit when the rotor is excited by residual unbalance. The rotor will tend to bounce at or near its fundamental frequency when the rotor is operated at or near a speed which is a whole number [n] times that frequency. Using a simple numerical model of a Jeffcott rotor mounted on a nonlinear spring, it is found that the vibratory response in the transition zone midway between adjacent zones of subharmonic response has all the characteristics of chaotic behavior. The transition from subharmonic to chaotic response has a complex substructure which involves a sequence of bifurcations of the orbit with variations in speed. This class of rotordynamic behavior was confirmed and illustrated by experimental observations of the vibratory response of a high-speed turbomachine, operating at a speed between 8 and 9 times its fundamental rotor frequency when in local contact across a clearance in the support system. A narrow region between zones of 8th order and 9th order subharmonic response was identified where the response had all the characteristics of the chaotic motion identified in the numerical model.

Rotordynamic Analysis of Multistage Centrifugal Pumps.

This paper describes the stability analysis of a multistage centrifugal pump in boiler feed. The individual contribution of hydraulic impeller forces, noncontact seals and bearings to rotordynamic behavior are evaluated according to logarithmic decrements. The influence of bearing and seal shapes on the rotor stability is investigated. Also, the vibration of actual multistage pumps is measured corresponding to the analysis. Theoretical stability threshold speeds are compared with experiments and are found to be compatible. As a result, it was confirmed that the rotor stability is strongly affected by the characteristics of the seal type.

Fast Response Tip Clearance Measurements in Axial Flow Compressors—Techniques and Results

As part of an investigation of the effects of tip clearance performance of development axial flow compressors, a system for detecting rotor blade tip rubs has been developed and a tip clearance measuring system modified to detect clearance changes at a bandwidth of 500 Hz. Mean clearance changes have been measured as well as changes during surge. Rotor orbit has also been investigated and the system has become an important means of monitoring rotordynamic behaviour. Subharmonic components of rotor orbit have been discovered.

Whirl and whipȁRotor/bearing stability problems

A mathematical model of an unloaded symmetric rotor supported by one rigid and one fluid lubricated bearing is proposed. The rotor model is represented by generalized (modal) parameters of its first bending mode. The rotational character of the bearing fluid force is taken into account. The model yields synchronous vibrations due to rotor unbalance as a particular solution of the equations of motion, rotor/bearing system natural frequencies and corresponding self-excited vibrations known as “oil whirl” and “oil whip”. The stability analysis yields rotative speed threshold of stability. The model also gives the evaluation of stability of the rotor synchronous vibrations. In the first balance resonance speed region two more thresholds of stability are encountered. The width of this stability region is directly related to the amount of rotor unbalance. The results of the analysis based on this model stand with very good agreement with field observations of rotor dynamic behavior and the experimental data.