Ningsheng Feng

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.

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.

Numerical evaluation of an identification technique for flexibly supported rigid turbomachinery foundations

Abstract Appropriate modelling of turbomachinery foundations of existing installations is essential for determining the vibration behaviour of the machine. Earlier work had shown that provided one has an accurate rotor model and provided the system response is periodic, a practically feasible approach for identifying the relevant foundation parameters was possible in just two rundowns (one rundown only if the unbalance distribution is known) when the foundation consisted of simple pedestals. This paper generalises the approach to identifying all rigid body modes of a flexibly supported rigid foundation, allowing for the possibility of coupling or cross talk between the bearing supports. Numerical experiments show that the proposed approach is theoretically sound and practically realisable, in that identification is possible with 2 digit measurement accuracy, and potential problems of bearing force evaluations are circumvented.

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.

The Effect of Cavitation on the Vibration Behaviour of Nonlinear Rotor Bearing Systems

Rotor bearing systems frequently utilise hydrodynamic bearings whose dynamic properties are generally influenced by the bearing reaction forces (which determine the bearing stiffness and damping coefficients). These reaction forces are frequently unknown and are generally determined from the solution of the Reynolds equation using rotor motion measurements as input. Of interest is the attainable accuracy of such bearing force determinations, and for experimental evaluation, a test rig was fabricated, the design specification of which required that the rotor system run stably over its operating speed range. This paper describes the commissioning of this rig for stability purposes with the aid of natural frequency analyses, noting the required design modifications to ensure stable operation. Stability was found to be significantly influenced by the extent of the continuous fluid film in the hydrodynamic circumferentially grooved bearings. It was concluded that the assumption of a 180 degree film extent was totally inappropriate even though the bearing ends were open to the atmosphere, whereas the assumption of fluid film break up at the lubricant saturation vapour pressure proved appropriate for stability predictions provided one ensured that the bearings were flooded. Preliminary bearing force evaluations proved inconclusive, primarily because the self aligning bearings nevertheless experienced angular misalignment; and because there was uncertainty as to how much air was entrained in the bearings, in spite of attempts to prevent air ingress.Copyright

On Uncertainty Propagation in Mass, Damping and Stiffness Matrices Identification of Mechanical Systems

The accuracy in estimating the mass, damping and stiffness matrices for mechanical systems depends on the error propagation through the stages involved in the parameter identification, i.e. excitation and response measurements, signal processing and modeling stages. Robust algorithms are available to estimate the system’s parameters in the presence of “noisy” measurements. However, uncertainties in the identified parameters of mechanical systems have not been usually reported or have simply been overlooked in the identification strategy. An overall uncertainty occurs for each identified parameter, and it may be defined in terms of error propagation. The recognition of relevant error contributions is the key to accomplishing parameter error estimation in the identification process, a task that may imply subtle aspects. An approach is proposed for uncertainty estimation in mass, stiffness and damping matrices for linearized mechanical systems. This approach is formulated as an extension of the accepted practice for evaluating experimental uncertainty for a scalar measurand. Typical error sources throughout the identification stages are also discussed. The suggested approach may be applied to identify mechanical systems in the frequency domain, and is independent of the algorithm used to estimate the system parameters. Practical limitations of the suggested approach are also discussed.Copyright

Practical Applications of Vibration Analysis Software for Diagnosis and Condition Monitoring of Turbomachinery

The benefits of modelling turbomachinery for diagnostic and condition monitoring purposes have not been fully appreciated by the power generation industry or the consultants who service the industry. This paper describes the capabilities and practical application of vibration analysis software for analysing rotor bearing systems of rigidly coupled rotors supported on several hydrodynamic bearings of various bearing profiles. The software has two distinct components — the measurement component and the modelling component. The combination of the two provides access to existing rotating machinery and machinery in the commissioning stage in order to identify the cause of vibration problems and the corrective action required. The modelling software evaluates the effects of bearing alignment changes and operating parameter changes on system stability and vibration response. The data collection analysis software that links with the modelling results provides valuable information about the measured shaft performance at the bearings. The combination of the two components provides an efficient and valuable tool that yields significant cost benefits. The application of the software to a 360Mw and 450Mw unit is evaluated.Copyright