Eric J. Hahn

Vibration Control of Rotor by Squeeze Film Damper with Magnetorheological Fluid

Using magnetorheological (MR) fluid in place of lubricating oil in a traditional squeeze film damper (SFD) can build a variable-damping SFD controlled by an magnetic field, and can be used to control the vibration of rotor systems. The structure of an MR fluid SFD is introduced. The Reynolds equation of the MR fluid squeeze film is derived and solved based on the Bingham model, and the formulas for flowing velocity, pressure distribution, film force, and the magnetic pull force of the damper are presented. The mechanical properties of the squeeze film and the unbalance response characteristics of the MR fluid damper-rigid rotor system are analyzed theoretically.

A rig for testing lateral misalignment effects in a flexible rotor supported on three or more hydrodynamic journal bearings

The vibration behaviour of statically indeterminate rotor-bearing systems with hydrodynamic journal bearings is predicted to be significantly dependent on the relative lateral alignment of the bearing housings (i.e. system configurations). To validate this, a rig wherein the rotor is supported on four bearings is being designed. This paper describes the salient features of the rig which is shown to be capable of traversing several critical speeds over its operating range, to be capable of whirl instability, and to be capable of a wide range of lateral misalignment combinations which result in significant vibration amplitude changes. Appropriate instrumentation will enable bearing reaction forces and rotor motions to be measured for various speeds, unbalance and system configurations. Theoretical results suggest that the rig is well suited for misalignment identification experiments though the predicted ability of different system configurations to yield virtually identical vibration response emphasises the need for careful experimental design.

Motion patterns at rotor stator contact

The present paper discusses the various movement patterns during rotor stator contact. Both rotor and stator are assumed to be flexible damped single degree of freedom systems. The contact is described by a flexible viscoelastic model. Dry friction between rotor and stator is taken into account. Despite strong non-linearity due to contact, rotor unbalance causes purely synchronous motions. However, in some circumstances, the synchronous motion may become unstable and the rotor motion turns into a non-synchronous state, which can be very destructive. Non-synchronous motions include backward whirl, sub- and super-harmonic vibration and chaotic motion. The influence of various system parameters on the different types of motion is investigated by numerical simulation. The transients between synchronous to non-synchronous motions are exemplarily demonstrated by run-up and run-down processes. It is shown that different motion types may co-exist. Even in speed regions where the synchronous whirl is stable, non-synchronous motions with rotor stator contact are possible.Copyright

Nonlinear Dynamics of a Cracked Rotor in a Maneuvering Aircraft

The nonlinear dynamics of a cracked rotor system in an aircraft maneuvering with constant velocity or acceleration was investigated. The influence of the aircraft climbing angle on the cracked rotor system response is of particular interest and the results show that the climbing angle can markedly affect the parameter range for bifurcation, for quasiperiodic response and for chaotic response as well as for system stability. Aircraft acceleration is also shown to significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for on-line rotor crack fault diagnosis.

Experimental Study on Vibration Properties and Control of Squeeze Mode MR Fluid Damper-Flexible Rotor System

A squeeze mode MR fluid damper used for rotor vibration control is designed and manufactured, and the unbalance response properties and control method of a single-disk flexible rotor system supported by the damper are studied experimentally. It is found from the study that the magnetic pull force can decrease both the first critical speed and the critical amplitude; the oil film reaction force can decrease the amplitude at the undamped critical speeds, but increase the amplitude in a speed range between two undamped critical speeds. For the rotor system supported by a journal bearing and an MR fluid damper, it is possible to appear oil film instability as the increasing of the control current. The damper may have the best effect to make the vibration minimize within the range of all working speed by using on-off control method. The research show that the squeeze mode MR fluid damper has the advantages such as simple structure, clearly effectiveness, quick response, etc., and this kind of damper has a promising potential future in vibration control of flexible rotor systems.Copyright

Recent Developments in Turbomachinery Modeling for Improved Balancing and Vibration Response Analysis

Present day turbogenerator installations are statically indeterminate rotor-bearing-foundation systems utilizing nonlinear hydrodynamic bearings. For optimal balancing and diagnostic purposes it is important to be able to correctly predict the system vibration behavior over the operating speed range. Essential aspects of this involve identifying the unbalance state, identifying appropriate dynamic foundation parameters, and identifying the system configuration state (relative location of the support bearings). This paper shows that, provided the system response is periodic at some speeds over the operating range and appropriate rotor and bearing housing motion measurements are made, it is possible, in principle, to satisfactorily achieve the above identifications without relying on the Reynolds equation for evaluating bearing forces. Preliminary results indicate that the identifications achieved promise to be superior to identification approaches that use the Reynolds equation.

A comparison of techniques for identifying the configuration state of statically indeterminate rotor bearing systems

Abstract Turbomachinery rotors are frequently supported on several hydrodynamic bearings and so are statically indeterminate. In such cases, the relative locations of the bearing centres (viz. the system configuration state) affect the bearing reaction forces and hence their stiffness and damping properties, thereby significantly influencing the vibration behaviour of the rotor bearing system. Since this configuration state may differ from its value at time of installation, due to thermal effects and/or foundation settlement, it would be useful to identify its value under operating conditions. This paper illustrates how this can be done in principle, regardless of the unbalance, by measuring the locations of the rotor journals relative to their respective bearing housings at any speed at which the system has reached steady state operating conditions, provided one has good models of the rotor and the foundation. Two identification procedures are compared. Both methods rely, to varying degrees, on using the Reynolds equation for hydrodynamic lubrication to obtain the bearing reaction forces. The first procedure uses the Reynolds equation to evaluate both the magnitudes and directions of the forces (the ‘magnitude and direction’ or MAD method), whereas the second procedure uses the Reynolds equation to evaluate only the directions of the forces (the ‘direction only’ or DO method). Numerical experiments on a flexibly supported statically indeterminate four bearing flexible rotor prove that both the MAD and DO identification procedures are sound in principle, being able to identify the locations of the two inboard bearings relative to the two outboard bearings to within 0.1 μm assuming seven-digit accuracy in journal orbit eccentricity measurements. On the other hand, three-digit measurement accuracy, felt to be the best accuracy practically achievable, restricts identification of the bearing locations to within 10 μm, with somewhat better identification being achieved with the MAD procedure. Such identification accuracy presupposes that the Reynolds equation correctly predicts the bearing reaction forces and could be in error owing to the temperature dependence of the bearing clearance, the assumption of a mean lubricant viscosity and the uncertainty of the cavitation boundaries. It is shown that error in lubricant viscosity may introduce significant errors into the identification achievable with the MAD procedure, but has no effect on that achievable with the DO procedure; and error in clearance introduces more error into the identification achievable with the MAD procedure than the DO procedure. Identification errors due to assumed cavitation conditions still need to be addressed.

Experimental Evaluation of a Modal Parameter Based Foundation Identification Procedure

One approach to model foundations of existing turbomachinery installations uses motion measurements at bearing supports and at select points on the foundation to identify the modal parameters of an equivalent foundation. This paper describes an experimental evaluation of this approach. Discussed are the experimental rig, its commissioning, the procedure for obtaining the required measurements and preliminary identification results. The proposed approach could identify reasonably accurately foundation natural frequencies, but identification of damping ratios, modal masses and mode shapes was significantly influenced by input data errors. The resulting equivalent foundation could predict only approximately the frequency response of the rig. Further investigations are needed to improve these predictions prior to field applications.

On the Identification of the Modal Parameters for a Flexible Turbomachinery Foundation

The evaluation of the vibration behaviour of turbomachinery installations, where the model of the rotor support structure (foundation or casing) is unknown and the foundation has natural frequencies in or near the operating speed range, is still problematic. An attractive approach for identifying the foundation uses motion measurements of the rotor and the foundation at the bearing supports to indentify the parameters of an equivalent foundation, i.e. one which reproduces similar vibration responses over the operating speed range. Earlier work identified perfectly the modal parameters of a flexibly supported rigid foundation block, a situation involving only the six rigid body modes of the foundation, so that the equations of motion of the foundation could be written with a diagonal mass matrix. However, in practice, foundations such as gas turbine casings have flexural modes in or near the operating speed range, in which case it is unlikely that the foundation mass can be adequately represented by a diagonal mass matrix. Hence, this paper further develops the above identification technique to enable identification of a flexibly supported foundation block which has seven vibration modes in or near the operating speed range. It is shown by numerical experiments that the assumption of a diagonal mass matrix for the foundation does not result in a satisfactory equivalent foundation. On the other hand, when the identification procedure is enhanced to cater for a full symmetric foundation mass matrix, it is possible to identify the modal parameters of an equivalent foundation which, when substituted for the actual foundation of an unbalanced rotor bearing system, satisfactorily reproduces the system unbalance response. This is so even when the ‘measurement’ data used to identify the modal parameters is truncated to two digit accuracy to better represent practical measurement accuracy. It is concluded that the proposed foundation identification technique is likely to be applicable to practical field installations.Copyright

Identification of foundations in rotating machinery using modal parameters

An attractive approach for identifying the dynamic stiffness of a rotating machinery foundation is to identify the relevant modal parameters of an equivalent foundation, using for the identification the motion measurements of the rotor and the foundation at the bearing supports. Earlier procedures required the identification of all assumed vibrating modes, even if the highest assumed mode frequency turned out to be well outside the operating speed range of interest. This paper overcomes such problems by enhancing the earlier identification technique to solve accurately for fewer modes than actually assumed; essentially by generalising the technique to be able to handle rectangular modal matrices. Numerical experiments show that this enhanced technique allows one to assume more degrees of freedom than actually necessary, yet still identify all the relevant vibration modes while ignoring unnecessary ones. The new identification procedure is robust in that good equivalent foundations are identified even when the measurement data is truncated to two digits and is therefore likely to be applicable in the field.