Proceedings of the 9th IFToMM International Conference on Rotor Dynamics

A shaft train in power plants is comprised of many journal bearings supporting turbines, generator and exciter. Each single rotor may possess one or more natural frequencies below or close to the rated speed. The entire shaft train often possesses many coupled or uncoupled natural modes close to the rated speed which influence the lateral vibration behavior in the normal operation. Some modes are low damped and some highly damped. It is difficult to judge how sensitively the machine reacts to theses modes and to make an acceptance design criteria for them. ISO 21940-31 makes some recommendation about vibration sensitivity of the damped modes of simple systems with rotors having only one resonant speed over the entire service speed range or widely separated resonance speeds. But it cannot be applied to evaluate a large turbine generator shaft train with many interacting resonances. This paper proposes two methods—sum of unbalance responses and sum of modal magnification factors to analyze the vibration sensitivity of a rotor system with many frequencies in the vicinity of the service speed.

The object of this work is the application of a modal balancing approach to turbomachinery rotors. The investigation was carried out on a small commercial rotor dynamic test bench suitably modified to represent in scale a typical turbomachinery balancing problem. Software based on literature theoretical formulations was developed for both the more widespread influence coefficient method and modal balancing. The modal balancing software was coupled with a finite element rotor dynamic code in order to determine the modal shapes necessary to impose the orthogonality conditions and calculate the modal calibration sets. Results of the two approaches were compared both in terms of balancing quality and in terms of time to balance the rotor. The test results highlighted essential information for an eventual true scale industrial application of the modal method and also interesting new aspects such as the possibility of balancing modes out of the operating speed range.

Assessment of high speed balance quality of a rotor with residual modal unbalance (RMU) has many advantages over traditional residual vibration method. In addition to be practically independent from support stiffness variations, it allows utilization of full train rotordynamic analysis for setting balance limits for a single rotor. Rotordynamic calculations of a turbine-generator train identify eigenmodes that can roughly be separated into two categories: single rotor and system modes. Large units with many rotors may have over 40 modes. The challenge is to select eigenmodes relevant for each rotor in the train and generate appropriate RMU requirements for high speed balancing. The other challenge is correlating eigenmodes of a single uncoupled rotor in a balancing facility to eigenmodes of a turbine-generator train and vice versa. The paper demonstrates that unbalance response calculations for turbine-generator train using appropriate modal weight sets exciting particular modes can allow for identification of modes relevant for high speed balancing facility conditions [

1

]. These modes can then be targeted for setting appropriate RMU limits. The emphasis is given to operating speed range and modes above 2nd critical speed. The paper offers an example of setting RMU tolerance for high speed balance for a large generator rotor based on rotordynamic analysis of turbine-generator train. Field vibration data is presented to demonstrate the applicability of the approach.

This paper presents a new balancing method pertaining especially to significantly eccentric, flexible rotors. When dealing with these rotors in service facilities, standard balancing methods often require excessive runs, and vibration problems are frequently experienced upon rotor reinstallation in the field. The method presented here is based on a novel view of the unique rotordynamic behavior in these cases. The key is to fully compensate rigid modes first to bring the effective principal mass axis coincidental to the rotor’s designed geometric axis, preventing a switch of precession axes through the critical speed region. This must incorporate proper axial distribution of weights using 2N+1 balancing planes (where N is the highest operating mode). The end result is a “dynamically straight” rotor that remains balanced without distortion or bending at any speed. This method requires fewer runs, and the rotor is guaranteed not to need field balancing upon properly aligned installation.

This paper analyses the conditions required to eliminate the trial runs during the balancing of large flexible rotors. These conditions include: the identification of the principal axes of stiffness, the determination of the rotor mode shapes and modal masses, and the extraction of the modal parameters from the measured vibration data, for each critical speed considered during the balancing. The paper also discusses possible reasons why modal balancing without trial runs has not been incorporated to field balancing practice.

Tip timing blade vibration measuring systems have become nowadays common for monitoring blade vibrations, due to rather easy and non-intrusive installation of sensors. The data collected by the sensors must be heavily processed in order to get the vibration time histories of all blades at rated speed or during a run up or run down transient. In the paper a real case of tip timing measurement for a steam turbine is shown. Resonant/natural frequencies, amplitude and phase of each blade vibration with respect to the synchronous reference, are identified. The first measurement results shown are related to asynchronous vibrations of a steam turbine last stage blade row due to an instability. The second results are instead transient synchronous vibrations when passing a blade row resonance during a run up of the steam turbine. It is further shown how synchronous vibrations, although non stationary, allowed to identify damping and excitation amplitudes by means of an original approach based on modal analysis.

The nonlinear behaviour of blade rubbing has usually been investigated using complex modelling for the contact description. However, a simplified model of a 3-bladed Jeffcott rotor with nonlinear beam deformation contacting a fixed ring due to initial misalignment was used to unveil the global dynamic behaviour of the system. Chaotic regions were found at integer fraction of the natural frequency divided by the number of blades. Similarities in the global behaviour have also been observed for a model with rigid blades contacting a flexible casing. Even though the periodic and chaotic properties were observable experimentally, some difference occurred in localized frequency range due to material loss at the blade tip at higher speed. It is also difficult to accurately set all the blades with the exact same slight contact in experimental test rigs. As a result, the global properties of the rotor are also evaluated with two blades of the same length and the third one shorter. The extreme case where one or two blades are out is also investigated. The results are explored in terms of phase plots, Poincaré sections and bifurcation diagrams as function of the rotating speed. It can be seen that the inherent properties can be modified depending on the blades configuration and unbalance forces.

Considered here is the effect of multistage coupling on the dynamics of an aircraft engine rotor with eight mistuned bladed discs on a drum-disc shaft. Each disc had a different number of rotor blades. Free and forced vibrations were examined using the finite element models of single rotating blades, bladed discs, and an entire rotor. Calculations of the global rotating mode shapes of flexible mistuned bladed discs-shaft assemblies took into account the excitation of the second compressor bladed disc with 0EO, 1EO and 2EO forces. The thus obtained maximal stress values of all of the rotor blades were carefully examined and compared with a tuned system to discover resonance conditions and coupling effects. Mistuning changes the stress distribution in individual rotor blades and the level of maximum stress increases or decreases in relation to bladed discs analysed without a shaft.

Recently, DS (Directionally Solidified) and SC (Single Crystal) alloys have been widely applied for gas turbine blades instead of CC (Conventionally Casting) alloys. In this study, the mistuning analysis of the bladed disk consisting of DS blades is carried out, considering the deviations of the elastic constant and the crystal angle of the DS blade. The FMM is used to analyze the mistuned bladed disk. The maximum amplitude of the mistuned bladed disk of the DS blade is estimated by the Monte Carlo simulation combining with the response surface method, and the calculated results are compared with those of the CC blade.

The aim is to obtain simple models that can be coupled to shaft models which are used in general purpose software for analyzing its rotor-dynamic behavior. Two modal models of the blade row have been developed and introduced in the 1D beam model of the rotor, for analyzing its behavior, separately for lateral and torsion vibrations. The methodology has been applied to the last stage blade row of a steam turbine. The results of the analysis show that besides the known influence of shaft torsion vibrations on blade row vibrations, also lateral shaft vibrations can excite easily the blade row vibrations and conversely that blade row vibrations excited by the steam flow can be detected by lateral vibration measurements in the bearings of the steam turbine.

Snubbing has been proposed as a possible mechanism to reduce blade vibration of turbo machinery in resonant condition. It consists in physically limiting the vibration amplitude on the blade tip, leaving a small gap between the shrouds of adjacent blades. When the relative displacement between adjacent blades exceeds the gap, a contact occurs between the shrouds, the relative motion is restricted and energy is dissipated by friction and impact during the contact. Whilst effectiveness of snubbing has been proven in the practice on test benches and theoretical models have been developed to simulate bladed disk response in presence of snubbing, the explanation of its actual effectiveness is by intuition. In this paper, the authors propose an explanation of snubbing effectiveness to reduce blade vibrations in resonant condition, by investigating the relationship between vibration reduction and chaos onset using a suitable chaos metrics.

For safe rotor operation it is important to predict the torsional natural frequencies of the full rotor arrangement and not only of its components. The system’s natural frequencies are typically speed-dependent if rotor and blade vibrations are coupled. In this contribution we focus on the torsional rotor-blade interaction, the coupling between torsional vibrations of the shaft and bending vibrations of blade rows attached to the shaft. During the design of a turbine shaft train, rotor blades are modelled using 3D finite elements due to its complex geometry and resulting vibration modes. This kind of model incorporates typically centrifugal loading due to the rotor rotation as well as contact modelling at the rotor-blade interface. Employing the method of substructuring enables to translate any complex blade which is modelled using 3D finite elements with thousands of physical degrees of freedom into a bunch of models with a single modal degree of freedom. Natural frequencies and modal masses are assigned to each modal degree of freedom representing the blade vibrations. These single degree of freedom models are coupled via so-called modal effective moments of inertia to the rotor shaft model. The resulting model resembles the rotor-blade interaction in all its details from the rotor point of view. The efficiency of this process is two-fold. On one hand, the resulting model size of the full rotor dynamic model becomes small and simple enough to allow elaborate parametric studies and design optimisations. On the other hand, translating the complex 3D blade model into a bunch of single degrees of freedom oscillators is extracted straightforwardly from standard output of commercial finite element software packages like Abaqus or Ansys.

Modeling of impulse periodic excitation that occurs in partial arc admission of control stages in steam turbines is described and analyzed. Two different simplified approaches used by turbine manufacturers are compared to the approach proposed in this paper which is simply based on a Fourier analysis of the load diagram. Sensitivity of vibration amplitudes to small changes in the steam load time histories is analyzed by means of the proposed approach and by numerical time domain integration.

Detuning of gas turbine blades in order to avoid high cycle fatigue failure due to large resonant stresses is often unfeasible. A possible solution is to add an external source of damping, in the form of dry friction devices such as the under-platform damper. The relative movement between the blades causes possible slip between damper and blade surfaces. Due to the nonlinear nature of dry friction, dynamic analysis of structures constrained through frictional contacts is difficult, commercial finite element codes using time step integration are not suitable given the large computation times. For this reason, ad hoc numerical codes have been developed in the frequency domain. Some authors Yang and Menq (J Eng Gas Turbine Power 120:410–417, 1998) [

1

], Sanliturk et al. (J Eng Gas Turbine Power 123:919–929, 2001) [

2

], Csaba (Proceeding of ASME Gas turbine and aeroengine congress and exhibition) [

3

], Panning et al. (Int J Rotating Mach 9:219–228, 2003) [

4

] prefer a separate routine in order to compute contact forces as a function of input displacements, others Cigeroglu et al. (J Eng Gas Turbine Power 131:022505, 2009) [

5

], Firrone et al. (Modelling a friction damper: analysis of the experimental data and comparison with numerical results, 2006) [

6

], Firrone and Zucca (Numerical analysis—theory and application, 2011) [

7

] include the damper in the FE model of the bladed array. The available numerical models of dampers require a description of the contact conditions, both in the normal and in the tangential directions. The approach proposed here differs from those available in the literature in that the tangential force-displacement behaviour is described by arrays of springs in parallel, but, unlike pre-existing models, it introduces a variable sharing of normal force according to the approach along the normal. It thus modulates the tangential stick-slip capabilities according to normal force and approach and is capable to reproduce the analytical contact description as originally proposed by Cattaneo (Accademia dei Lincei 6:P I; 342–348, P II; 434–436, P III; 474–478, 1938) [

8

] and Mindlin and Deresiewicz (J Appl Mech 20:327–344, 1953) [

9

]. The paper shows how the model can be described and tuned in reference to the analytical Cattaneo and Mindlin’s benchmark for a spherical contact. It is proved that parameters tuned for a certain normal load will correctly simulate the tangential behaviour at any other lower normal load and finally that the transitions between cycles at different normal loads is correctly described. The paper further shows an application to a cylindrical contact where the tangential characteristics are derived from purposely taken experimental measurements.

A revised blade-casing rubbing model is developed and verified by experiment, and then a finite element model of rotor-disk-blade system with blade tip rubbing between the blade and casing is established in ANSYS. Complicated vibration responses are studied by analyzing spectrum cascade, displacement waveforms, bending stress waveforms, rotor orbits and normal rubbing forces under different rotating speeds. The results show that with the increase of the rotating speed, period-two motion caused by blade-casing rubbing may appear at higher rotating speeds due to larger normal rubbing forces. Amplitude enlargement phenomena may occur when the multiple frequency of rotating frequency is close to the bending natural frequency of the blade. In addition, impact resonance phenomenon can also be observed due to the effect of blade-casing gap.

Drill string vibrations are an incredible example of complexity of a rotating system due to the slenderness of the structure and coupling of flexural, axial e torsional vibrations. In this work we approach isolating the torsional vibration underlying stick-slip from the drilling itself but also including a possible second section where stick-slip originates from dry friction at rotor stator contact. The torsional test rig consisting of a horizontal very slender shaft where an electric motor drives two discs, one simulating the drill bit and the other an intermediary contact region. This work develops an experimental analysis on a full working rotor test bench. There are two separate braking systems, so that two different induced stick-slips may act. Oscillation characteristics appear in the system depending on the friction actuation point. The behavior is analyzed and it is identified the location which is responsible to cause torsional oscillations on the test rig.

The field of rotating machinery dynamic analysis has evolved over the past 60 years from the calculation of zero damped critical speeds using mechanical calculators to the computation of multi-rotor and multi-bearing damped response and stability analysis with unbelievable speed and accuracy. This capability has also required the advances in the understanding of antifriction and hydrodynamic bearings as well as both liquid and gas seals. The understanding and calculation of the aerodynamic forces from axial flow and radial flow compressors and turbines is still less than perfect and requires the application of special equations developed from practical experience. It seems then that practical experience is in fact the key to understanding the internal forces that influence the radial vibrations of the rotor shaft. That being said, it could be argued that the resolution of unwanted vibrations might require practical experience to be successful. This line of reasoning has prompted the author to document the practical experience that has allowed some very difficult machinery problems to be resolved with a combination of analytical tools, prior experience, and a dash of in-depth reasoning. The analytical tools can be purchased, the experience can be gained in a life time, but the gift of in-depth reasoning is priceless. Solving a problem that has a known cause and remedy is rewarding but when a problem from an unknown cause can be finally solved, that is the most rewarding of all. This paper will document the process of solving some very interesting problems that have occurred in the last 40+ years.

This paper presents three vibration-troubleshooting case studies of actual machinery, illustrating a practical method not only to fix or prevent similar problems but also to study how to design and operate machinery free from vibration troubles, based on unique analyses of these case studies. The analyses focus on the initiators that triggered the chain of events leading to the eventual problems and some human factors involved. Understanding only the relation between direct cause and effect won’t suffice to prevent recurrence of same or similar problems, but understanding the total process from the initiator to the final problem inclusive of human factors is much more important. Creating and building up databases consisting of similar case studies with the unique analyses incorporated will definitely contribute to giving birth to vibration-free design and operation methodology.

Torsional vibration in rotating machinery is not easily detectable, but it is very important in maintaining the rotating machinery system safety and productivity. Traditionally, the torsional vibration is detected by a phase demodulation process applied to the pulse train signal generated by a tooth wheel or an optical encoder attached to the shaft. This demodulation based method has a few unfavorable issues: the installation of the tooth wheels needs to interrupt the machinery normal operation; the installation of the optical barcode is relatively easier, however, it suffers from short term survivability in harsh industrial environments. The geometric irregularities in the tooth wheel and the end discontinuity in the optical encoder will most likely introduce overwhelming contaminations from shaft order response and its harmonics. In addition, the Hilbert Transform based phase demodulation technique has inevitable errors caused by the edge effects in FFT and IFFT analyses. Fortunately, in many industrial rotating machinery applications, the torsional vibration resonant frequency is usually low and the Keyphasor

®

and/or encoder for speed monitoring is readily available. Thus, it is feasible to use existing hardware for torsional vibration detection. In this paper, we introduce our in-house developed torsional vibration measurement tool, which used the Keyphasor/encoder data digitized by a high sampling rate and high digitization resolution analog-to-digital (A/D) convertor to evaluate the torsional vibration directly. A wavelet decomposition (WD) based method was used to separate the reference for torsional vibration extraction, which extended the analysis method to variable speed applications, such as the speed-up and coast-down operations. A few successful application cases are described in detail in the end of the paper.

This paper presents a new view of a key overlooked phenomenon when dealing with significantly eccentric rotors, namely the switch of the rotor’s axis of precession and consequent orientation in its bearings while passing through the critical speed region. This occurs in conjunction with torque effects unique to the case where a rotor’s principal mass axis and torque input axis are not coincident. This condition also governs the rotor’s phase shift process. Around the critical speed, the inertia from the eccentric mass becomes sufficiently large as to alter the mode of rotation, bringing the rotor toward a “state of least action”, where the precessional orbit rapidly decreases, and the rotor begins to rotate about its principal mass axis. The most immediate benefit of recognizing this behavior is in the development of a new balancing method pertaining especially to flexible, bowed or eccentric rotors, designed for use in balancing facilities.

This paper will discuss the unexpected high vibration seen on both the drive end and the driven end of a high-speed disc pack design coupling, in addition to the documented vibration at the coupling spacer mid-span location. The coupling was being used during the test stand mechanical verification runs of a high-speed centrifugal compressor to connect the compressor to a test gear which was driven by a test steam turbine. This paper provides the test results and the analysis procedure used to understand the vibration levels and dismiss the concerns for a journal bearing driven thermal instability at the compressor driven end bearing and at the adjacent pinion end bearing of the gearbox. A background history of coupling applications and previous relevant experience is given. Test results are given to confirm the solution of the problem, which was to reduce the length of the coupling spacer.

During full-load, full-speed string testing of a compressor train, its gearbox pinion experienced high radial vibrations at a particular frequency that was well below the gear mesh frequency, but which was excited by the pinion’s harmonics at 9× , 10× or 11× running speed. To identify the vibrations’ root cause, a coupled lateral, torsional, and axial analysis was performed on the gearbox’s two testing configurations: its no-load, uncoupled mechanical run test, and the string test. Results indicate that the vibrations likely were caused by a resonance situation involving the alignment of two highly amplified natural frequencies: the pinion’s fifth lateral mode, and a torsional-lateral mode of the pinion and its adjacent coupling. Contrary to all known published discussions of similar problems, the vibrations were not likely associated with the pinion’s heavily damped, fourth lateral mode. Modeling and analysis recommendations include aspects not typically considered in gearbox applications, such as the need for higher fidelity rotor and coupling models and the inclusion of pad/pivot radial dynamics.

The aim is to determine the extent to which the introduction of a third plane correction in a given cross-section increases the efficiency of the available low-frequency balancing on the balancer “MORION”. The project addressed the following questions:

Building a computational model of the rotor GD-40;

Determination of natural frequencies and forms of the spinning rotor;

Develop and probabilistic reasoning—a statistical model of the rotor unbalance shaft-mounted design;

Study the effectiveness of balancing systems using different corrective masses;

Use a 3-plane balancing in practice;

Analysis of influence of the correction planes.

This paper presents the measured rotordynamic performance and model predictions of a 200 kW oil-free micro gas turbine simulator (MGTS). The MGTS has a single spool configuration, and a gas generator rotor (GTR) and an electric motor rotor (EMR) connected by a diaphragm coupling and supported on gas foil journal bearings (GFJBs). A couple of double acting gas foil thrust bearings (GFTB) are used inside the gas turbine. The MGTS is a full-size replica of a 200 kW micro gas turbine, with the exception of the impeller blades of the compressor and turbine. The design of the diaphragm coupling determines the first and second bending critical speeds of the MGTS. A speed-up test was conducted up to 40 krpm to evaluate the rotordynamic stability of the rotor-bearing system. The test results showed that the synchronous motion had several peaks, which were due to the rigid modes of the rotor-bearing system. The highest peak occurred at ~10 krpm and was produced by the second bending mode of the coupling. The results for 40 krpm revealed the occurrence of small amplitude synchronous motions. The predicted critical speeds of the rotor-bearing system and synchronous rotor motions were in good agreement with test data.

Failures due to the propagation of fatigue cracks in shafts are one of the most common problems in rotating machines as they can cause irreversible damage and put lives at risk. The main parameter for the study of crack propagation is the Stress Intensity Factor. When a cracked shaft rotates, the transverse crack contained in it presents the opening and closing mechanism (“breathing mechanism”). Although most of the studies on cracked shafts consider straight cracks, the real fatigue cracks have a semi-elliptical front. In this work, the numerical analysis of the Stress Intensity Factor along the entire front of a semi-elliptical crack during the rotation of the shaft has been developed taking into account the breathing mechanism.

Conducted analyses of rotors with cracked shafts show that the stability of such systems deteriorates with an increasing crack depth. Instability areas near parametric resonances enhance as a result of increasing periodic stiffness changes due to a breathing mechanism of a developing shaft crack. However, some recent studies on the dynamics of linear structures with periodically altered stiffness present an interesting phenomenon of an increase in damping. It has been demonstrated that under certain conditions a parametrically excited mechanical structure can increase its stability. When the structure falls into the parametric anti-resonant area, its vibration amplitudes quickly decay. For a long time these anti-resonant zones seemed to be not interesting, yet they can introduce additional artificial damping into the system, improving its stability and leading to further studies of their possible applications. The present paper analyzes the possibility of the appearance of such a phenomenon (the increase in damping of the parametrically excited system) in a rotor with a cracked shaft. The approach is demonstrated with a mathematical model of the machine. The breathing crack is modeled using the rigid finite element method that has previously proven its robustness and efficiency in similar applications. The stability analysis is conducted numerically by the Floquet’s technique. The conditions required for the appearance of parametric anti-resonances for different crack depths are provided. Finally, a possible application of the additional damping introduced by parametric excitation for rotor crack detection is analyzed.

Stiffness variation due to cracks in rotors is a well-known problem; plenty of studies to prevent/avoid catastrophic accidents and rotor bursts exist. FEM numerical results calculating natural modal frequencies for open cracked beams at different notch depths and slenderness ratios, are compared versus experimental laboratory measurements. Shaft beams under simply supported and free-free boundary conditions, focusing on solids and Timoshenko beam finite elements, are studied. Timoshenko beams employ the Mayes and Davies equivalent-length concept for crack modeling. Notched shafts provide useful upper bound frequency reductions values (breathing cracks display up to, and smaller decrements). Modal frequency splitting for each natural frequency are confirmed and validated by numerical simulation and tests. Modal frequencies splitting functions are given, obtained by simulation and experiments which reflect strong crack depth and slenderness ratio influences. Vibrational coupling energy of the frequency splitting reaches a maximum when the excitation is orthogonal to the crack orientation, conclusions are given.

Fatigue cracks make a rotor system susceptible to catastrophic failures. Vibration based condition monitoring of fatigue cracks is still being explored. The model-based identification using parameter estimation has been now more popular. On the contrary, very few experimental studies have been carried out on identification of fatigue cracks. An experimental crack, generated as a slot or a saw-cut, cannot simulate the open/closing behavior of a fatigue crack. By artificially generating a fatigue crack in a shaft, dynamics of a switching fatigue crack could be better studied. Such a rotor response shows a predominant 2× frequency component, and it also has higher components such as 3×, 4× and so on. In addition, these harmonics are present both in the forward and backward directions. In this paper, displacement responses were measured from a cracked rotor setup at independent spin-speeds. These responses with the help of full spectrum have been then processed and implemented in a model-based identification algorithm to estimate the crack force, the unbalance, and other system parameters.

Detection of cracks in shafts plays a critical role in maintenance. A crack can cause a catastrophic failure with costly processes of reparation. The aim of condition monitoring and fault diagnostics is to detect and to distinguish different kinds of faults. In this work vibration signals are obtained from an analytical Jeffcott rotor model and a real rotating machine during working. The aim was to identify indicators of the presence of a crack, to allow the inverse process of detecting a crack and its size for the machine tested. Signals were processed using the Wavelet Packets Transform. In signals obtained from the analytical model, the best indicators of crack were frequencies related to the first’s harmonics of the rotation speed. However, when matching the theoretical results with the experimental ones, only harmonics higher than the 2× component of the rotation speed seemed to feel that changes in practice.

This paper reviews methods and applications of fault diagnosis and state detection in centrifugal pumps. Different studies show the most common faults and their effects: Failures of mechanical seals, roller bearings, and drives as well as leakage are prevalent. Since these might lead to a stand-still of pumps, automatic fault diagnosis can improve productivity. Fault definitions, methods of fault diagnosis and state detection functionalities in centrifugal pumps as well as their categorization regarding utilized models are presented. Reviewing applications of such in centrifugal pumps shows solutions from model-free fault detection to model-based fault diagnosis. In those, impeller faults, cavitation and blockade/sedimentation receive the highest attention, while computation and sensor effort increases with method/model complexity. Two major research issues are the diagnosis of multiple fault cases and methods integrating a continuous monitoring and identification if a fault occurs.

The diagnostics of rolling element bearings is normally performed in frequency domain using suitable signal processing techniques. The simplest and most used method is the Envelope Analysis, that is based on the identification of bearing damage frequency components in the Envelope Spectrum of vibration signal. The quantification of the bearing damage is a complex task requiring a suitable damage index, robust against variations of system operating conditions and external vibration sources and also simple to be evaluated in the case of a real-time application. In the paper, an algorithm for alarm signaling is described and applied to an experimental case of failure of an industrial rolling element bearing.

In recent years there has been considerable interest in the analysis of machine vibration signals in the presence of speed variations, sometimes over wide ranges. Computed order tracking based on phase demodulation to obtain a map of phase (rotation angle) versus time is limited to a maximum speed range of 2:1. This paper shows how analysis over a much greater speed range, for example a run-up or run-down, can be achieved by dividing the signal into overlapping segments, in each of which the speed range is less than 2:1. In the order domain, the highest frequency to be retained is proportional to the speed, and so at lower speeds the required sampling frequency can be reduced accordingly, as long as higher frequency components are first removed to avoid aliasing. The paper explains how this can be done in the most efficient way.

The identification of damages in rolling element bearings is quite a simple task and is commonly performed by the application of suitable signal processing tool to vibration signals. Envelope Analysis is the most common approach for the diagnosis of rolling element bearings. It is based on the identification of bearing damage frequency components in the Envelope Spectrum of vibration signals. The main critical point of this method is the selection of a suitable frequency band for the demodulation of the vibration signal. The most used approaches are based on the value of the Kurtosis index by means of diagrams as the frequently used Fast Kurtogram or the more recent Protrugram. In the paper, an experimental case of a bearing damage is investigated and an alternative approach for the filter band selection, based on a so-called “PeaksMap” diagram, has been proposed by the authors.

Modelling the dynamics of roller element bearings has been used to explain the interactions between localized faults and their impact on the measurable quantities representing the dynamic behavior of the system e.g. acceleration. Most part of the models describes the non-linear contact of roller bearing normal forces by means of Hertz Theory. Recently, analysis of the Instantaneous Angular Speed (IAS) has been proven to effectively detect bearing mechanical faults and it has shown to be an advantageous tool for non-stationary machinery surveillance. Mechanical analysis implies that rotating speed variations are due to torque variations. However, the phenomena describing how dynamic interaction of bearing components induces tangential forces generating angular periodic disturbances to the shaft speed, have not been discussed at all. In this work an original formulation to induce tangential forces to the shaft due to the bearing components dynamics is presented. The roller bearing model is based on Hertzian contact, localized faults can be added and the analysis is suitable for simulation of non-stationary conditions.

In this paper an elasto-dynamic model of a defective sphere bearing is presented. This two-dimensional model can simulate local faults on the bearing races and rolling elements, and it is based on the non-linear Hertzian contact deformation of the rolling elements. In the model the outer race is supposed to be fixed, and the rolling elements are supposed to roll without slipping. These assumptions yield a total of

z

+ 4 Degrees of Freedom (DOF), where

z

is the number of rolling elements: three DOF come from the inner race (two displacements and one rotation), one DOF from the cage (rotation) and one DOF from each rolling element (i.e.,

z

radial displacements). Each contact between the spheres and the races is modelled by a non-linear spring (Hertz contact theory) and a damper proportional to the spring stiffness (Palmgren). The model uses a kinematic approach to calculate the trajectory of the rolling elements when passing over the defect. This trajectory is introduced into the equations of motion for the calculation of the rolling elements deformations; subsequently, the internal bearing forces are calculated. The model inputs are the bearing and defect geometry, the materials characteristics and the radial load. The model outputs the overall force transmitted to the outer race, which accurately reproduces the typical behaviour exhibited by a faulty bearing both in time and frequency domain.

Diagnostics of rolling element bearing is generally performed by suitable signal analysis tools for the vibration data. In the railway field this analysis is a complicated tasks due to variable operating conditions of the system in terms of load, speed and temperature. At present, the widely maintenance policy in railway field is based on train mileage. The natural increase of trains in the time for the same regional area is leading to more economical maintenance approaches as the condition-based one, where the maintenance activities are performed only when is economically profitable. The secondary effect of such efficient maintenance approach is the reduction of unexpected stopping failures. Besides, condition-based maintenance requires a suitable monitoring system able to analyze and track the health of the mechanical components. In the paper, the complex architecture of the monitoring system for the rolling element bearing of a regional locomotive will be shown.

The observation of the measurements in the polar domain can lead to an easier interpretation of the dynamic behavior, where the steady state and the transient behaviors could be directly distinguished. This transformation is simple and widely used in robotic. Numerical and experimental investigations are performed and presented in this paper. Experiments were performed on a test bench dedicated to the assessment of the aerodynamic behavior of a compressor impeller. The impeller is mounted at the free end of a rotor supported by two tilting pad bearings. Besides the unbalance excitations, the impeller is subject to low frequency aerodynamic perturbations. The results obtained show the effectiveness of this methodology for an easier monitoring and for the control of rotating machinery.

This work compares different digital signal processing methods for the extraction of the fundamental harmonic (1X) from noisy signals. Aim of the comparison is the identification of the best technique to measure the rotor imbalance in presence of mechanical disturbances. Four methods have been selected after the literature review: the Hilbert Vibration Decomposition (HVD), the Hilbert Huang Transform (HHT), the Wavelet Packet Decomposition (WPD) and the ordinary Fourier Transform paired with computed order tracking (COT-FT). The four methods performances were compared analyzing measurements performed in different conditions. Factorial design of experiments was used to identify the effect of the rotor size (car wheels with different diameters), of the imbalance (5, 20 and 60 g applied to the rim), of the balancing machine (two types with different mechanical characteristics) and of the type of disturbance. Globally, 216 imbalance measurements were performed. The dynamic forces measured by two piezoelectric load cells were analyzed with the four proposed methods. Results evidenced the good performances of the WPD and COT-FT. Uncertainty benefits deriving from the analysis of more than 4 revolutions are generally negligible. The possibility of merging the indications of different methods is proposed and discussed.

On-line monitoring and real-time diagnostics of rolling element bearings are complex tasks to be performed when operating conditions change continuously. In particular, real-time applications require simple and effective diagnostics tools. In the field of rolling element bearing, the most common approach is the Envelope analysis of vibration signals. The output of this analysis is the identification of bearing damage frequency components in the Envelope Spectrum of vibration signals. The degradation of bearing health could be tracked by means of suitable damage indexes. Band-Kurtosis index, that is the kurtosis value of the band-filtered signal, is often assumed. The critical point of this approach is the selection of a suitable filter band. In the paper, the use of a chaos metrics as damage indicator is described. The trend of this index is compared with the common approach of band-kurtosis indicator for an experimental case of a rolling element bearing in which the defect developed until a permanent failure .

Intelligent diagnosis of bearing knock faults in Internal Combustion Engines (IC engines) was studied in this paper. Because of previous successful application of Artificial Neural Networks (ANNs) to the condition monitoring of rotating machinery, an ANN based automated diagnosis system was proposed for the diagnosis of big-end bearing knock faults in IC engines. It consists of three separate ANNs: a fault detection network, a fault localization network, and a fault severity identification network. In order to solve the problem that ANNs need a lot of data for training, a simulation model was built to simulate various degrees of bearing knock faults. The impact forces of the bearing with different clearance were simulated first, and then the accelerations at the measurement point on the engine block were calculated. A series of experiments were also carried out, and the results were used to evaluate and update the simulation model. It was also found that the squared envelope signals, rather the raw acceleration signals, have more useful diagnostic information. The extracted/selected amplitude features were used for fault detection and severity identification, and the extracted/selected phase features were used for fault localization. It is worth pointing out that because a saturating linear function was selected as the transfer function of the ANN for the fault severity identification stage, the networks can linearly classify the fault levels and the output agrees better with the real situation. All the networks were trained using simulated data and tested using experimental data. The final results have verified that the system could efficiently diagnose bearing knock faults, especially the accurate identification of the fault levels.

This work describes shaft’s Instantaneous Angular Speed (IAS) behavior in the presence of a spall on bearing’s race at low speeds. It is shown that fault signature becomes more apparent in IAS signal when speed decreases and load increases. EEMD processing of the signal is implemented to overcome the shortcoming of IAS sensitivity at low loading conditions. IAS behaviour while passing through the spall perform three different variation stages: Speed increase (entrance moment) caused by the instantaneous loss of contact pressure, a speed sharp decrease when the rolling element hits the spall edge and finally speed recuperation phase (exit moment) and system’s dynamical response to impact. It is considered that the number of angular samples between the entrance and exit moments defines the fault size. Different fault sizes at different speeds (<60 rpm) were tested and its estimation was satisfactory which is the first step for a successful bearing prognosis.

Recently, Instantaneous Angular Speed (IAS) is becoming an interesting measurement solution for condition monitoring of rotating machines. Various researchers are studying the measurement’s limits, new signal processing methods and new industrial applications. In Spagnol et al. (Proceedings of COMADEM2013, 2003) [

1

], IAS is compared to Torsional Laser Vibrometer (TVM) and to acceleration data. IAS is less affected by noise if compared with TVM and it is very informative in respect to acceleration. The current work focuses on the estimation of the IAS through the Elapsed Time (ET) method, using a counter to measure the time elapsed between the pulses of an encoder. From the variation of the IAS during the machine loads’ cycle it is possible to identify defects and faults. The data is acquired from an experimental test rig specifically designed for IAS evaluation. The setup is composed of an asynchronous four poles electric motor driven by a 380V 50Hz line current, a bearings’ test group and a variable brake system simulating different loads’ conditions. The paper reports on the results obtained with different data processing techniques and filtering approaches. The combined effect of the errors generated by the counter and the speed variation of the machines will be analyzed and commented, showing the advantages and drawbacks of the adopted IAS measurement.

Health monitoring of bearings is very critical for satisfactory working of complex machinery. Thus, the ability to detect bearing faults and classify them based on their nature becomes very important aspect of health monitoring of machines. In the machine learning methodology for the fault taxonomy, the support vector machine (SVM) is well recognized for its generalization capabilities. In this work, the taxonomy of rolling element bearing faults has been discussed. Acceleration signatures are classified by the support vector machine (SVM) learning algorithm. The tuning of the SVM and kernel parameters is necessary for better taxonomy. The novelty of the paper is in comparing the ability to classify a set of faults by the tuned SVM and kernel parameters with the help of grid-search method (GSM), genetic algorithm (GA) and artificial bee colony algorithm (ABCA). Four fault settings along with no-fault condition were considered. Three statistical features were obtained from acceleration signatures. The fault taxonomy was performed at the identical rotational speed at which signals were captured. The taxonomy capability is observed and it depicted a very good prediction performance especially at higher speeds.

Acoustic emission (AE) refers to the elastic stress-waves produced during the release of strain energy and results from rub in rotors due to adhesion, contact and deformation of asperities and the ploughing action of wear particles. The available literature contains only a very few examples of the use of AE in detecting rub in rotating systems. The challenges to implementing AE monitoring in practice are described and discussed. There have been substantial advances in available off the shelf data acquisition systems and a relatively low cost set of equipment for carrying out such measurements is described. The technique is demonstrated on two laboratory scale rotors and the AE data showed clear indications of induced rub. The measurement results are very promising but the detectability of the AE due to rub in full scale machinery in general is an open question that can only be answered by full scale testing.

In this paper, the features of vibration signals from normal and faulty conditions of a centrifugal pump were extracted from time-domain data using the discrete wavelet transform (DWT). The DWT with Multi Resolution Analysis (MRA) was used to pre-process raw vibration signals prior to extraction of statistical features. The features obtained were used as input to Principal Component Analysis (PCA). A method based on PCA was then developed to build a framework for multi-fault diagnosis of centrifugal pumps by using historical normal conditions. The fault detection was determined using

T

2

-statistics and

Q

-statistics while fault identification was carried out through the combination of loadings and scores of principal components (PCs). The normal and faulty conditions of the centrifugal pump were collected from the Spectra Quest Machinery Fault Simulator. Various fault conditions were investigated in the experiment including cavitation, impeller fault, and combination of impeller fault and cavitation. The results showed that combined wavelet-PCA can be used to detect multi-faults in the centrifugal pump. Furthermore, the combination of loadings and scores of PCs was demonstrated which showed effective fault identification.

Impact response due to sudden changes on the contact forces is an intrinsic phenomenon at all stages of the bearing life. Even prior to the actual occurrence of surface damage, short duration impacts occur in the case of insufficient lubrication where asperities or particles interact with the surface of its mating element. As the surface condition deteriorates, the energy released by the impacts increases affecting structural modes. As soon as the system condition worsens, lower frequencies are excited and consequently increased vibration levels are displayed. The impulse response function reflects the modulation phenomena between contact forces, structural resonances and driving forces taking place in the bearing and the mechanical system that contains it. The characterization of the components of the impulse response becomes then a valuable tool for vibration monitoring. This article is framed within the research on development of advanced vibration monitoring systems, for which the authors follow a systemic approach in the definition of the monitoring requirements based on the function-failure analysis of the monitored object. The discussion focuses on the correspondence between the monitoring and monitored systems, by analyzing the impulse behavior as illustrated by the train bearings. The comparative analysis between environment and damage induced impacts highlights the different stages in bearing damage.

Local defects in races of rolling bearings generate periodic forces whose strength is largely governed by the defect size. An insight into force generation mechanism and its relationship with defect size is essential to identify the bearing health. This work presents an engineering mechanics based approach to model the forces at different events as a rolling element negotiates a fault on the race. The forcing function is modeled at entry, as a function of load, speed and curvature of defect and due to impact as a function of defect size, defect location, speed and load on the bearing. The impulse of impact force and the duration between entry and impact forces, termed as Time to Impact (TTI), are indicators of the defect size. The proposed model may provide a potential basis for implementing direct monitoring with embedded force sensor module.

This paper extends recent research on the estimation of spall size in rolling element bearings (REBs) using laboratory measurements on a bearing test rig. The prognostics of REBs remains a formidable challenge, partly because many of the classic diagnostic indicators trend non-monotonically with bearing wear, as spalls that develop on the bearing races progress from localised to distributed faults. The direct estimation of spall size from the vibration signal has recently been proposed as a potential solution to this problem. Such estimation techniques typically rely on the identification and enhancement of the events in the signal corresponding to the rolling element entry into and exit from the spall. Identification of the entry event poses the most difficulty, and for this the paper proposes a novel method, which is then applied to signals obtained from a bearing with known spall dimensions. The resulting estimates correlate well with the actual spall size.

The rotor vibrations caused by rotor unbalance and electromagnetic forces are investigated for a two-pole induction machine. Using Timoshenko beam elements, the heterogeneous assembly of the rotor is modeled and the different material properties are considered. The nonlinear simulation includes effects of rotor unbalance and the unbalanced magnetic pull (UMP). Machine parameters influencing the unbalanced magnetic pull are varied to analyze their impact on the rotor vibration.

Rotor vibrations in electrical machines depend on structural damping and stiffness properties of the laminated cores. Structural damping determines torsional and transversal vibration amplitudes at resonances. Therefore, it is very important to know the structural damping and stiffness of the laminated cores to carry out structural dynamic simulations. In this paper, a measurement set-up is presented to determine the structural damping and direction-dependent stiffness for laminated cores and stacks. The dissipated damping energy is examined as a result of harmonic excitation of different excitation amplitudes, frequencies and axial pre-stressing conditions. Thereby, the measured structural damping factor is compared to the material damping factor from tables. To allow a conclusion for the reproducibility of the evaluated damping parameters, repeated measurements are carried out and the results are statistically analyzed using the Weibull distribution.

With a less stable future electricity grid in mind, grid-induced turbo-generator vibrations are very likely to gain importance. Today there is however only limited attention paid to the interaction between electrical grid-induced excitations and mechanical vibrations of the turbo-generator shaft line. This paper describes the execution and results of a field measurement campaign that was initiated due to the appearance of subsynchronous generator vibrations in a power plant in the close vicinity of an electrical arc furnace. The measurements consist of both radial and torsional vibrations as well as of electrical parameters, in order to pinpoint their mutual interaction. A clear correlation between the electrical grid disturbances and the mechanical vibrations of the shaft line is revealed, indicating that excitations external to the power plant itself must be taken into consideration in root cause analyses of turbo-generator vibrations.

This paper investigates the rotor vibration differences among the rotor interturn short circuit fault, the static air-gap eccentricity fault, and the combined fault composed by the former two. The UMP (unbalanced magnetic pull) formulas of the three faults are firstly deduced. Then the rotor vibration characters, as well as the vibration difference comparison, are studied based on the formulas. Finally, the numerical calculation and the experiment of a non-salient fault simulating generator are taken to verify the theoretical analysis. It is shown that the rotor interturn short circuit fault mainly causes the rotor to vibrate at

f

r

(the rotating frequency of the rotor), while the static air-gap eccentricity fault primarily produces vibrations at 2

f

r

, and the combined fault generates vibrations at

f

r

, 2

f

r

, and 3

f

r

at the same time. The proposed work is available for the accuracy improvement of the generator fault diagnosis.

The power of electric motors is transmitted by mechanical drive train. The dimensions of train components are determined by steady-state and transient loads. Usually, the dimensioning torque is the electric short-circuit load. Thus, the prediction of these loads is needed in early phase of any actual project. This is challenging because the components are produced by separate manufacturers. In addition, the encountered component loads are dependent on the vibration characteristics of the torsional system. The aim of this paper is to review the main parameters affecting the ultimate coupling torque. A simple torsional model is applied for the demonstration. The main parameters of the system are the natural frequencies of the lowest modes and the inertia ratio between the motor and the driven system. Finally, the findings are compared to the standard requirements and a novel dimensioning approach is presented.

This paper considers the accelerated passing through the critical speed of an overcritical induction motor in the case of an excitation by electromagnetic forces due to a dynamic rotor eccentricity. The dynamic rotor eccentricity is caused by a magnetic eccentricity of the rotor core related to the rotor shaft. An analytical rotor model as well as a finite element rotor dynamic model are presented for rotordynamic analysis related to startup with magnetic eccentricity. Based on a finite element model, the vibrations of a 2‐pole induction motor (2 MW) are analyzed during the startup with a magnetic eccentricity of 1 % of the air gap. The FE‐calculation shows the influence of the start‐up time on the vibration amplitudes and on the critical speed for this special kind of excitation.

This paper describes a model-based fault detection method for nonlinear rotor systems based on a linearised model. The rotational system on which the faults are tested is a non-linear simulation model. The model-based fault detection procedure is developed on the basis of a linearised rotor model, in which the non-linearity is considered as unknown input. In this paper, we consider a rotor system which is supported by means of active bearings with piezoelectric actuators. For simulation purposes, the rotor is modeled with the help of finite element methods based on Timoshenko beam theory. The non-linear behavior of the piezo-actuators are described using the Preisach model. In order to reduce the complexity of the fault detection procedure, this non-linear system has been linearised. The effect of non-linearity is approximated as an unknown input in the linearised model. The linear model with the additional unknown input is intended to deliver the same system output as the non-linear rotor system, and thus can be used for the model-based fault detection and isolation (FDI). The faults which are detected in this paper are point-mass unbalances. The faults are detected on the basis of parity equations and observers. An unknown input observer (UIO) equivalent to parity equations is constructed to separate the disturbances caused due to the unknown inputs on fault detection. The results show that the methods are very effective in detecting the faults in a non-linear system.

The unbalance is one of the most common faults in rotor systems and it can cause severe damage during the rotor operation. There are many unbalance detection methods that have been proposed up to now by many researchers around the world, justifying the importance of this theme. This paper proposes a model based identification method to identify the unbalance parameters magnitude and location that avoids the usage of the complete set of rotor responses. This is an initial study that combines the Guyan reduction and the correlation analysis to generate an identification algorithm in time domain, which comes from the Lyapunov matrix equation, able to identify the unbalance parameters. It was used a Laval rotor supported by two rolling bearings whose physical characteristics, stiffness and damping, were determined by optimization using the Differential Evolution method to compare the experimental FRF with the optimized simulated one.

Shaft crack detection is a very serious problem and machines that are suspected of having a crack should be carefully and continuously monitored. The importance attributed to this problem is addressed to the serious consequences when cracks are not early identified in rotating systems. Although there are no statistical studies that account for the exact dimension of the damage caused by cracks in rotating shafts, estimations reveal that approximately $1 billion were expended in repairs, exchanges, loss of production, etc., in electrical industries, nuclear, and conventional, since the 1970s. Significant research effort has been directed in recent years to online monitoring techniques, i.e., based on vibration signals measured during rotor operation. However, most of these techniques are able to only detect deep cracks. In this context, the aim of this paper relies on the detection of incipient faults in rotating shafts by using the so-called electromechanical impedance method. Basically, this structural health monitoring technique—SHM monitors changes in the electric impedance of piezoelectric transducers bonded to (or embedded into) the host structure, through specific mathematic equations, the so-called damage metrics, to detect damage. This is possible since that the electrical impedance of the transducer is directly related to the mechanical impedance of the structure. Previously, successful experimental tests were performed in a horizontal rotor supported by roller bearings in which PZT patches were bonded along the rotor shaft. Although successful, the use of rigid PZT patches seems to be disadvantageous. Aiming at overcoming the drawbacks previously faced, in this contribution flexible transducers (MFC—macro fiber composites) are bonded along the shaft. A small mass was added on the shaft to simulate a fault condition (small structural modification). The technique was validated for the rotor under operation.

This work proposes the use of Bayesian inference to fault parameters identification taking into account the stochastic characteristic of the system. The objective is to estimate the unbalance parameters, as the unbalance moment, phase angle and axial position of the unbalance force applied to the rotor. Therefore, experimental tests with the rotor to obtain the unbalance response are performed. The statistical distribution of each parameter is obtained using a Markov Chain Monte Carlo method (MCMC), simulated with the Delayed Rejection Adaptive Metropolis algorithm (DRAM). Thus, the residual between experimental and numerical response is calculated and applied to a Bayesian inference analysis, obtaining information about the unbalance parameters, which are summarized in statistics for each parameter distributions.

The diagnosis and prediction of rotor fault is a key problem of rotor dynamics. In this investigation, a Multiple Model Estimator (MME) based method for typical rotor fault diagnosis is proposed. On a test rotor, crack and misalignment faults are produced respectively. Aiming at the test rotor, the normal, crack and misalignment rotor models are built accordingly. Based on these rotor models, a MME built with Kalman filters is setup with considering different crack and misalignment parameters. Via the estimation of the measured responses of the test rotor by MME, the rotor faults are identified successfully. It is proved that this proposed method is effective in the fault diagnosis, especially in the early stage of rotor faults.

The operators of electric power plants are interested in having at its disposal a rapid and reliable tool that provides condition monitoring as well as fault detection (unbalance, bow, cracks, etc.) and diagnostics for its rotating machinery. Monitoring machine vibrations is a major concern for any operator in order to ensure safety by preventing machine failure and scheduling any necessary maintenance. In the present paper a model based approach is used to balance a large steam turbo-generator unit experiencing high amplitude vibration levels. Such approach combines a finite element model for the shaft-bearing-support system and vibration measurement acquired on the real machine in order to identify the appropriate solution for balancing. Rotor lateral position is monitored using displacement probes mounted close to the bearings location combined to seismic transducers mounted on the bearing casing. Several vibration datasets, measured by the displacement probes and corresponding to different operating regimes of the machine, are used for fault detection. The results obtained from these analyzes are then used to balance the machine and thus reduce vibration levels.

Heavy duty gas turbine and generator are connected through rigid coupling. The bearing levels of gas turbine-generator rotor are changed relatively due to thermal expansion of casings and supports during operation, therefore bending moment is concentrated on the coupling. So the rigid coupling needs to be offset in order to be minimized the bending moment when the gas turbine and generator are assembled. In this paper an analysis method is presented to obtain the steady state dynamic response from the finite element based equations of a rotor-bearing system with initial deflection. The method is applied to analyze the dynamic response of the two-shaft rotor-bearing system with rigid coupling offset in a heavy duty gas turbine-generator. Bumps in the dynamic response of each rotor system are observed at each critical speed due to the effect of initial deflection for rigid coupling offset. Also the dynamic responses are shown to reduce for operating condition changes from cold to hot. Especially it is confirmed that the dynamic responses are sensitively affected by phase of residual mass unbalance.

According to ISO 11342 the determination of residual unbalances of flexible rotors, e.g. turbine- and generator-rotors for power plants is based on a modal approach. It delivers good estimations for the residual modal unbalance close to critical speeds. However, the majority of flexible rotors are operated at speeds out of a resonance, where ISO 11342 does not provide a procedure or a criterion to estimate the balancing quality. This is in contradiction to customer demands, who often require a proof of the balancing quality particularly at this operating speed. In this paper a procedure is presented, how to estimate the residual unbalance for the operating speed as well.

Robust control techniques have allowed engineers to create model sets which are robust to deviations from the actual system through the use of model uncertainty in the form of both additive noise and plant perturbations. To ensure the quality of the uncertain model, experimental unfalsification is employed to guarantee that the model set is able to recreate all experimental data points. In previous work, such a robust control relevant model validation technique was employed to identify the presence of damage on a rotordynamic test rig. Additionally, model-based identification was employed to model the overall change in dynamics due to the damage, as well as to provide a novel quality measure for the identified damage dynamics. In the present work, the technique is extended to include a rotordynamic model. This advancement allows for locating the damage source and to determine the local change in dynamics at the damage location. The method is demonstrated experimentally on a rotordynamic test rig through the identification of a wire EDM cut in the shaft and determination of the local change in dynamics, including axial position along the shaft.

In the present article the bearing and coupling dynamic parameters along with residual unbalances has been estimated for misalignment conditions in a flexible rotor-bearing-coupling system. These estimated parameters could be used as a measure of the misalignment. A model based approach has been experimentally tested with measured vibration data from a laboratory test rig. After estimating these parameters the reliability of estimated parameters was checked by the consistency of estimated parameters and by performing standard impact tests. It was observed that with more number of measurements consistencies of estimated parameters were very good. Moreover, the distinguishable splitting of natural frequency was observed as the amount of misalignment was increased.

This paper mainly focuses on the development of efficient three-dimensional (3D) models of TPJBs, able to contemporaneously simulate both the rotor dynamics of the system and the lubricant supply plant. The proposed modelling approach tries to obtain a good compromise between the typical accuracy of standard 3D models and the high numerical efficiency of simpler and less accurate models. In this work, the whole model has been developed and validated in collaboration with

Nuovo Pignone General Electric S.p.a.

which provided the required technical and physical data. In particular, the experimental data are referred to a suitable lube oil console system, built at the GE testing center in Massa-Carrara (MS, Italy) for the verification of plant components.

Rotordynamic predictions on machines supported by fluid film bearings typically rely on models that solve the Reynolds equation to determine the bearing dynamics. The Reynolds equation is derived from the thin film momentum equation that assumes fluid inertia terms can be totally neglected because the reduced Reynolds number is very small. This paper examines the impact of including temporal fluid inertia on tilting pad bearings that are widely used in the applications of concern. Using the small perturbation method, a new form of the perturbed equation is developed for easy application to tilting pad journal bearings. The temporal fluid inertia leads to a set of full added mass coefficients and modifications to the damping coefficients. When applied to a typical 5-pad, tilting pad bearing, it is found that the influence of temporal inertia increases with the increase of shaft whirl frequency. Its impact is also dependent on the magnitude of the added mass coefficients relative to the magnitudes of its stiffness and damping. Therefore, temporal fluid inertia effects could be important for high speed, light rotor applications, as well as applications using low viscosity fluids, such as water.

Floating ring bearings are commonly applied in automotive turbocharger machinery because they are inexpensive and are able to reduce unbalance-induced vibrations. This type of bearings, however, can become a source of noise due to oil whirl-induced sub-synchronous vibrations. This study examined whether the concept of a floating ring bearing with a lobed clearance might be a solution to diminish oil whirl induced vibrations. A numerical model is developed to evaluate the dynamic behavior of the coupled rotor-bearing system. The resulting run-up simulations have been validated with experimental results of turbocharger run-up measurements. The results of the plain floating ring design and the multilobe floating ring design are compared, showing that the multilobe floating ring bearing design is superior in suppressing both synchronous and sub-synchronous vibrations at the cost of a slight increase in friction losses. Hence, multilobe floating ring bearings are an attractive alternative to plain floating ring bearings for automotive turbocharger applications.

This paper deals with the simulation of turbochargers run-up behaviour. To predict the main design criterions for turbocharger applications like vibrations, friction power loss, minimal gap etc. a detailed and efficient computation is needed. The rotor dynamic simulation of the turbocharger is, due to the nonlinearities resulting from the oil-film, interacting with rotor shaft bending, done within an appropriate multibody simulation. By reason of turbines high rotational speed full-floating-rings are used to reduce the oil velocity gradient in the fluid-films. The bearings are modeled based on a transient numerical solution of Reynolds’ equation at each step of time integration. The pressure distribution can be affected by geometrical modifications like annular grooves in the full-floating-rings. The effect of these changes on the run-up behaviour of an automotive turbocharger is being studied. In addition the cause of jumps between subsynchronous vibrations will be shown for an explicit turbocharger.

Semi-floating ring bearings are preferred to be incorporated in high-speed rotor systems since they usually provide a better vibration and damping behavior than full-floating ring bearings. Nevertheless, such rotor bearing systems can show whirl/whip instabilities as well which lead to subsynchronous oscillations in addition to synchronous oscillations due to unbalance. Moreover, a critical bifurcation can take place into a regime of subsynchronous oscillations with extremely high amplitudes which resembles Total Instability known from investigations of full-floating ring bearings. To illustrate the various types of subsynchronous oscillations, different rotor models are investigated under the influence of semi-floating ring bearings. First, transient run-up simulations are performed to outline the nonlinear phenomena. Then, the stability and bifurcation behavior is analyzed in detail by using the methods of numerical continuation.

Squeeze Film Dampers (SFDs) are effective means to reduce shaft vibration and eliminate instabilities in high performance rotating machinery. Presently there is a need to characterize the performance of ultra-short length SFDs for aero jet engines where overall weight and space are at a premium. The paper presents force coefficients and dynamic film pressures measured in an open ends SFD with slenderness ratio

L/D

= 0.2 and for two film clearances

c

A

= 0.129 mm and

c

B

= 0.254 mm. The film land length

L

= 25.4 mm and diameter

D

= 125.7 mm. ISO VG2 lubricant flows into the axial mid-plane of the film land through three orifices spaced 120

o

. The journal has end grooves (width and depth = 2.5 × 3.8 mm) for the installation of piston rings, and hence the total wetted length

L

tot

= 36.8 mm. A static loader pulls the bearing cartridge (BC) to a set static eccentricity (

e

s

), and two shakers, orthogonally positioned, exert dynamic loads on the BC to create circular orbits of amplitude (

r

) over a range of whirl frequencies (

ω

). In the current tests, the end seals are not in place. Comparing the dynamic forced performance of the open ends SFDs, the small clearance damper generates about four times more damping than the one with a larger clearance, whereas the inertia coefficients are approximately twice as large. The test results modestly agree with the theoretical ratios, where damping scales with ~1/

c

3

and inertia with ~1/

c

. The measurements also evidence significant dynamic pressures at the end grooves, which amplify the test elements’ inertia coefficients. The test results continue to demonstrate the paramount effect of grooves on enhancing the dynamic forced response of SFDs.

Analyzing of the spring-damper-mass system model and rotor dynamic Characteristics, a simple and easy identification method for stiffness and damping coefficient of rotor-sliding bearing system based on system lag angle is developed in this paper. The function relationship between system lag angle and rotor system parameters including speed, vibration mass, stiffness and damping is deduced. The system lag angle at different speeds can be gotten from the finite element model of rotor sliding bearing system. For most type of sliding bearing, the oil film dynamic characteristics coefficients usually are almost stable in the range of working speed and the vibration fluctuation is small. The stiffness and damping coefficients of rotor sliding bearing system, doesn’t need to take artificially excitation, can be obtained by the lag angle equation and fitted by using the least square method. Finally, the rotor testing rig with single disk and plain cylindrical journal bearing was taken as an example to validate the proposed method. Compared with the identification results of operational modal analysis, it is shown that the proposed method has some advantages: high precision, easy to achieve, and capable of rapid identification.

Dynamic characteristics of journal bearings with uniform square dimples on the whole bearing surface are numerically calculated considering the inertia effect and the energy loss based on the oil film discontinuity at the edge of dimples. The comparison of the results with a smooth bearing without dimples shows that all the stiffness and damping coefficients for the textured bearings are smaller than those for the smooth bearing over a wide range of eccentricity ratio. The effects of the number of dimples are investigated under a constant total area of dimples, and the cross-coupled stiffness coefficients decrease significantly at lower eccentricity ratio for the large number of dimples due to the inertia effect and energy loss at the discontinuous dimple edge. The linear stability threshold shaft speeds of a symmetrical rigid rotor increase with the number of dimples, which is attributable to the reduction of the cross-coupled stiffness coefficients.

During the operation of rotating machines, especially during starts and stops, hydrodynamic bearings can be progressively worn down. In order to prevent an irreversible failure condition of the entire rotating system, it is necessary to precisely detect wear, without disconnect or disassemble the system. The wear can cause significant geometric changes in the bearing wall, changing the nominal radial clearance. Therefore, the discontinuities can influence the dynamic characteristics of the bearing. In this context, the main objective of this paper is to present a numerical model that represents both the hydrodynamic bearing and the geometric discontinuities to be identified. The parameters of depth, angular span and angular position, according to the wear model, are adjusted by the comparison of the numerical and experimental unbalance response of the system considering the rising of the backward component due to the bearing anisotropy increasing.

Oil free microturbomachinery relies on gas bearings, in particular bump type foil bearings (BFBs), to make nearly frictionless systems with improved efficiency, long life and extended maintenance intervals. Rotors supported on generation I BFBs often show large amplitude sub synchronous whirl motions that limit their application into high speed conditions. Mechanically preloading a BFB through shimming is a common practice that improves rotordynamic performance. This paper quantifies the effectiveness of shimming on the forced performance of a BFB (

L

= 38.1 mm,

D

= 36.5 mm) that comprises of a single top foil and bump foil strip. The dry-friction torque (

T

) during startup is proportional to the applied load and increases with shim thickness. The bearing lift-off shaft speed, establishing operation with a gas film, also increases with load. The friction factor

f

=

T/

(

RW

) during dry friction operation at start up increases with shim thickness albeit decreasing with applied load. Once the bearing is airborne, the bearing–shimmed or not–shows approximately the same low friction factor,

f

~ 0.05 under a specific load

W/

(

LD

) ~ 20 kPa. Dynamic loads spanning 200–450 Hz excite the BFB in a rotordynamics rig operating at 50 krpm (833 Hz). A static vertical load,

W/

(

LD

) acts on the bearing. The bearing direct stiffnesses increase with increasing excitation frequency while the damping coefficients decrease slightly. The stiffnesses for the various BFB configurations offer unremarkable differences. The direct damping coefficients of the shimmed BFB are up to 30 % larger than the coefficients of the original bearing. The frequency averaged material loss factor for BFB with 50 µm shims

$$(\bar{\gamma }\sim 0. 6 2)$$

(

γ

¯

∼

0.62

)

is 25 % larger than that for the original bearing

$$(\bar{\gamma }\sim 0. 4 7 )$$

(

γ

¯

∼

0.47

)

. As expected, a shimmed BFB dissipates more mechanical energy than a BFB without shims.

Tilting-pad journal bearings (TPJBs), owing to their inherent dynamic stability characteristics, have been widely used to support the rotors of high rotating machinery such as steam and gas turbines. TPJBs offer better stability than fixed geometry bearings due to their lower cross-coupled stiffness coefficients. Because of the merit, a large of theoretical and experimental studies have been executed to reveal important characteristics of the TPJBs such as fluid-film thickness, pad–pivot friction, load capacity, temperature, stiffness and damping coefficients and so on. However, the theoretical evaluation of these coefficients for TPJBs is difficult because of their complex geometry, boundary and thermal conditions and turbulent flow. Therefore it is very essential to design and build a suitable test rig for performing experiments. This paper describes a test rig with unusual configuration compared to test rigs which are available in literature for the experimental characterization of TPJBs. The bearings could be installed in the load-on-pad (LOP) or load-between-pad (LBP) configurations. In particular, Sommerfeld number, steady-state and transient temperatures, pad pressure, dynamic stiffness and damping coefficients in different operation conditions could be estimated.

The investigation of steady state and dynamic effects is essential in the field of rotor dynamics to evaluate the behavior of hydrodynamic bearings. This paper describes an experimental study which was conducted on a test rig to determine dynamic performance characteristics of a tilting-pad journal bearing (TPJB). The tests have been carried out on five-pad TPJBs with a nominal diameter of 100 mm, a length-to-diameter L/D of 0.7 and load-on-pad (LOP) and load-between-pad (LBP) configuration. The stiffness and damping coefficients are evaluated from multiple frequency excitations (25–50 Hz) exerted on the bearing housing by a pair of hydraulic actuators, varying load direction and unit load using experimental data considering the linearized expression of the oil-film forces. The results show that the dynamic damping force coefficients are not strong functions of the frequency of excitation, unit load or load direction. However direct stiffness coefficients seem to be affected by frequency of excitation, unit load or load direction, in which unit load has a strong effect on direct stiffness coefficients.

A journal bearing with variable geometry (VGJB) was proposed and its operating principle was investigated theoretically in previous works showing a promising impact on the vibration quenching of simple and more complicated rotor bearing system during the passage through the first critical speed. The journal bearing with variable geometry is presented in this paper in its final form with the detailed design and manufacturing procedure. The current journal bearing was constructed in order to be applied in a simple experimental rotor bearing system composed by a Jeffcott rotor mounted on one plain cylindrical journal bearing and one VGJB. The inspiration for the current idea is based on the fact that the alteration of the fluid film characteristics of stiffness and damping during the passage through resonance results in vibration quenching [

1

]. This alteration of the bearing characteristics is achieved by the introduction of an additional fluid film thickness using the passive displacement of the lower half-bearing part. The influence of the additional fluid film to the characteristics of journal bearings has been investigated because of wear phenomena that appear often in plain journal bearings [

2

–

4

]. The applicability of the current journal bearing can contribute towards the vibration amplitude reduction of high scale rotor bearing systems where the resonance amplitude during the passage through resonance is a matter of consideration because of its influence in the foundation and the surrounding environment of the rotational system [

5

]. In the presented experimental application, the developed resonance amplitude is reduced at about 40 % compared to the system with normal journal bearings. The diagrams of amplitude with respect to the rotational speed during the start up of the system prove the reduction of the vibration amplitude while diagrams of the operational characteristics of the journal bearing are also presented. The VGJB is a totally passively activated subsystem that has to be tuned with respect to the fluid film pressure that is developed in the journal bearings during the passage through resonance. The damping and spring elements that consists of the operational mechanism of the journal bearing with variable geometry are presented in detail. In contrast to the many suggested damping mechanisms for the vibration quenching of rotor bearing systems, the present journal bearing does not add damping properties in the system but it alters the stiffness and damping properties of the fluid film in the specific time duration during the passage through resonance.

The trend in the last years in industrial applications of tilting-pad thrust bearings is the replacement of the traditional white metal of the pads with a polymeric material such as PTFE or PEEK, improving the bearing performances and extending its operating conditions. The main cause on the improved performances of the bearing is the compliance of the pad layer that leads to a more uniform pressure distribution over the pad and a reduction of its maximum value with respect to Babbitt metal pads. The effect of this improvement is the possibility of the reduction of the bearing overall dimensions because of the load capacity increase. The secondary benefits concern the very low friction coefficient of the polymeric material as well as the high resistance to chemical attacks as in sea-water applications. The improvement of the bearing performances have been investigated in the paper by means of thermoelastohydrodynamic (TEHD) analyses using a multiphysics software.

The dynamic behavior of rotor systems is influenced by thrust bearings. Therefore, a time-efficient model of oil-lubricated thrust bearings is introduced within this contribution. The areas of application for this bearing model are multibody simulations and more specifically high-speed rotordynamic systems. The Reynolds equation is solved at each pad of the bearing for the calculation of the fluid-film forces and moments, where the effect of misalignment of the shaft is also considered. For the solution of Reynolds equation the weak formulation is used, i.e. the Galerkin approach. This optimized bearing model results in heavily reduced simulation times especially if they are compared to the relatively large simulation times needed in co-simulations. The applied procedure can be easily implemented into commercial software and is flexible for investigating any bearing geometry and number of pads. Finally, the effect of the thrust bearing is studied in run-up simulations on an example rotor-bearing system.

Electrical discharges in rotating machines may interest every kind of bearings, both roller, oil-film thrust or journal, when an electrical machine is installed in the shaft-line. The consequence of this phenomenon is a reduction of the performances of the bearing such as its load capacity, leading to possible failures of the bearing pads mainly due to overheating. In this paper, a case history of electro discharge machining of the thrust bearing of a small steam turbine is presented. A detailed model, able to take into account the effect of electrical pitting and loading capacity decreasing as a consequence of the damage of the Babbitt metal, is also proposed in the paper. Simulations show that the phenomenon causes the irreversible failure of the thrust bearing.

Oil whirl/whip phenomena have been observed for some lightly loaded or unloaded rotor-hydrodynamic bearing systems. To describe and analyze this type of unstable motion, nonlinear hydrodynamic bearing models have been used as well as numerical-integration approaches that eventually converge to limit-cycle orbits. However, if a system includes a large number of bearings, a numerical approach can be time consuming and slow to converge. This paper presents a new way to solve for the limit-cycle orbits of oil whirl/whip. A flexible lumped rotor is modeled as supported by two massless hydrodynamic bearings. Oil film force expressions in terms of the frequency and amplitude of the oil whirl/whip limit cycle are developed for both cavitating and non-cavitating bearings. Free-body analysis is conducted for the rotor and bearing, and then the Newton-Raphson Method (NRM) is adopted to obtain the stable oil whirl/whip response. The stability of NRM solutions is checked. Another approach using conventional nonlinear hydrodynamic bearing model and Runge-Kutta method is employed to confirm the reliability of the new approach. The effects of bearing cavitation, external damping, and imbalance are studied.

In the dynamic analysis of rotors supported on journal bearings, Reynolds equation is solved at each time step. In the present work, Reynolds equation is solved using pseudospectral method to estimate fluid film forces. Fluid pressure is approximated by a finite number of Chebyshev polynomials along the bearing length and Fourier series along the bearing circumference. Fluid domain is reduced to a finite set of algebraic equations with pressure at specific grid points as variables using collocation method. Unlike in finite element method (FEM), spectral method uses higher order global basis functions which guarantee high accuracy and lower computational time. A comparison study of fluid film forces for a bearing geometry with an L/D ratio of 0.25 with short bearing theory, solution of Reynolds equation using FEM and pseudospectral method (PSM) is presented. Two different elements are studied in FEM: 3 node triangular element and 9 node quadrilateral element. Computational time taken for one time pressure calculation is also compared. Pseudospectral method is found to be efficient than FEM for a converged solution.

Unbalance is the main cause of increase of time varying forces transmitted between the rotor and its frame. A flexible suspension with added damping devices is a frequently used technological solution making it possible to reduce their magnitudes. To achieve optimum performance of the damping elements, their damping effect must be controllable. This is offered by magnetorheological squeeze film dampers. Magnetorheological oils are suspensions that under influence of magnetic field behave as liquids with a yielding shear stress. This is caused by forming a chain structure of particles dispersed in carrying liquid induced by magnetic field. Even if this process is rapid, it is not instantaneous. To investigate this phenomenon and its influence on performance of the damping devices a new enhanced mathematical model of a short magnetorheological squeeze film damper has been established. The magnetorheological oil is represented by Bingham material. The steady state yielding shear stress of the magnetorheological liquid is approximated by a power function of magnetic induction. Its dependence on time is described by a differential equation of the first order. The developed mathematical model has been implemented in the computational model of a flexibly supported rigid rotor. In accordance with the theory predictions, the results of the computational simulations showed a strong influence of the delayed yielding effect on performance of the studied damping devices.

Tilting pad journal bearings counteract the occurrence of possible unstable vibrations of rotating machines. However, lightly loaded shoes can be the source of subsynchronous oil-film forces that, in turn, cause subsynchronous vibrations of some pads. This pad-fluttering phenomenon can cause high level vibrations of the shaft, especially when the subsynchronous oil-film forces excite a flexural normal mode of the rotor system. Some basic measures can be implemented to prevent this serious phenomenon. The experimental findings detected during the performance tests of two identical centrifugal compressors that have been affected by pad-fluttering onsets are shown and analysed. Besides, the satisfactory results obtained with a suitable corrective action are shown and discussed.

This work aims to evaluate the influence of the thermal effects of tilting pad bearings in the stability conditions, through the simulation of a rotating system with cylindrical fluid seal and tilting pad journal bearing. Mathematical models obtained by Finite Element Method are used to represent this rotating system, in which the seals and bearings are considered through dynamic coefficients. The dynamic coefficients of the tilting pad journal bearing are obtained through the thermohydrodynamic and hydrodynamic analysis. Two different approaches are also considered when evaluating the mathematical models of the rotating system: the first considering the full matrices of the tilting pad journal bearing, while the second considers the synchronously reduced model of the coefficients. The stability analysis is carried considering the log-dec of the complete rotating system, allowing the discussion of the influence of the thermal effects on the rotating machines’ dynamic behavior.

The scope of this work is to mathematically optimize the choice of geometrical parameters of a hydrodynamic journal bearing to maximize its performance. Despite the fact that several works have investigated methods to predict the optimal shape of this family of sliding bearings, significant opportunities remain to improve the efficiency of the algorithm through the use of validated computational fluid dynamics and intelligent stochastic algorithms to find the function’s maximum and minimum. This work presents a set of experiments carried out to validate simulations of fluid film bearings. These virtual models are used to determine the temperatures inside the bearing film. A series of objective functions were built and minimized in order to maximize the performance of the bearing and obtain the optimal combination of geometrical parameters for the design. The paper shows the capabilities of the algorithm to improve an existing journal bearing design as well as the validation data of the CFD simulations.

The quantitative impact of pivot position, pivot support stiffness, and deformation on frequency dependency of a stiffness (K) and damping (C) KC matrix model for tilting-pad journal bearings is investigated. A theoretical model for prediction of frequency influences is introduced neglecting inertia effects. Predictions based on this model are validated with test data taken from literature. The results achieve good agreement with experimental data. A sensitivity analysis is performed providing the following key results: (i) all three investigated parameters possibly exhibit non negligible frequency influences, (ii) significant misinterpretations are possible if single influencing parameters on the operation conditions are disregarded or only roughly estimated, (iii) a frequency independent KCM model is suitable for off-center pivot position and sub-synchronous frequency ratios, (iv) a state-space model separating rotor and pad movement is necessary to model all theoretical possible effects by a linear model with frequency independent coefficients for a certain rotor speed.

The research reported in this paper is based on a nonlinear two degree of freedom model of an unbalanced rigid rotor bearing system. The nonlinearity is introduced into the model through closed form expressions of the short bearing hydrodynamic forces. The model in its nondimensional form depends on three nondimensional parameters: the bearing modulus, the rotor rotating speed and unbalance. For the balanced system, numerical continuation is applied to predict the branch of equilibrium positions of the journal and its bifurcation into stable or unstable limit cycles at the linear stability threshold speed. For the unbalanced system, however, numerical integration is used to find the bifurcation diagrams using the rotor speed as a bifurcation parameter. Poincaré sections are used to characterize the journal motion. The investigation is carried out for three bearing parameters covering a large domain of rotor bearing conditions. The effect of unbalance on the journal motion is investigated in each case. Compared to the balanced system, it has been found that unbalance may introduce, at different speed ranges, periodic oscillations at multiple periods of rotation, quasi-periodic oscillations and chaotic motion. The effect of unbalance on journal motion is highlighted and closely related to the bifurcation diagram of the balanced rotor.

This work aims to analyse the influence of the temperature and the viscosity variation of the lubricant fluid on the behavior of fixed-geometry thrust bearings. For this purpose, a numerical thermohydrodynamic (THD) model, based on the solution of the Generalized Reynolds’ Equation and of the Energy Equation, was developed, enabling the calculation of both pressure and temperature distribution along the fluid film. The influence of heat exchange in the radial direction is analysed by comparing the results of two different THD models: one considering heat exchanges in all directions; another considering heat exchanges only in two directions (circumferential direction and across the film). The results of load capacity of the bearing and its dynamic coefficients are compared to the obtained by a purely hydrodynamic (HD) model. The influence of speed and minimum film thickness on the behavior of the system is also evaluated.

The asymmetric flexible rotor turbocharger supported by floating ring bearings is studied. We use the model of flexible asymmetric rotor and the nonlinear bearing forces have been calculated by using the numerical solution of the Reynolds equation for both fluid films. It is shown that at this rotor speed range the rotor performs direct nonsynchronous regular precession, which corresponds to the conical shape of the rotor motion. The rotor speed at which the shape of the rotor precession abruptly changes from conical to cylindrical has been revealed. It is established that the cylindrical shape of the precession corresponds to the unacceptable increase of bearing loads. Thus, the maximum rotational speed above which the turbocharger rotor under study shuts has been found. The implications can be applied to the turbocharger rotors supported by two bearings with floating ring bearings and console location of the compressor and turbine wheels.

The article focuses on active rotor supports based on the fluid-film bearings. Several approaches to design of such bearings are shown, a more detailed design of an active hybrid bearing with controllable lubricant supply pressure is presented. A certain approach to mathematical modeling of a rotor system with an active radial hybrid bearing is reviewed. Corresponding results of mathematical modeling are shown. A conclusion on efficiency, as well as prospects of further research in this field, of such bearings is made. Moreover, peculiarities of active fluid-film bearings are studied. Prospects of intellectualization of rotor motion control systems are reviewed. A structural diagram of a rotor motion control system, where methods commonly referred to as artificial intelligence are used, is presented.

It’s known that a rotating machine, when in operation, is susceptible to vibrations, which occurs due to external excitations or to vibrations inherent from the machine operation, as the residual mass unbalanced excitations. If the rotating machine is supported by bearings with hydrodynamic lubrication, those are, consequently, susceptible to sub-syncronous vibrations due to a fluid-induced instability. The sub-syncronous vibrations, known as oil whirl/whip, can cause critical failures in the system, and consequent sudden stops and irreversible damages in the bearings. Through characterization of the oil film, by linearized stiffness and damping coefficients, it is possible to obtain an approximation to the threshold of instability. The hydrodynamic lubrication’s classical theory applies the constant viscosity condition to calculate the dynamic coefficients. Nevertheless, when the bearing is under operation, viscous fluid shear occurs, resulting in the increasing of the lubricant temperature, influencing the dynamic behavior of the entire rotational system. This paper presents a comparative analysis of the dynamic behavior, regarding the threshold of instability, considering the Lund critical mass and the logarithmic decrement theories for the classical hydrodynamic model and the thermohydrodynamic model.

Active control of vibrations is an important capability of bearings using magnetorheological fluids as lubricants. Magnetorheological fluids are a suspension of micron sized iron particles in a carrier fluid, usually a mineral oil. These particles, polarized under the influence of a magnetic field, form chains inside the lubricant volume, they hinder the flow of the fluid, change its apparent viscosity and offer active control on the available damping of the bearing. Magnetorheological fluid’s apparent viscosity relies heavily on the viscosity of the base fluid. The base fluid’s viscosity depends on temperature. On the other hand the existence of particles is a factor that may influence the lubricant’s temperature. In this paper the dynamic characteristics of a journal bearing lubricated with magnetorheological fluids are investigated for a range of temperature and load conditions.

This paper discusses the development of a novel bearing the Smart Electro-Magnetic Actuator Journal Integrated Bearing (SEMAJIB). The SEMAJIB is essentially a journal bearing with an electro-magnetic actuator all flooded in oil. The basic principle is that the rotor is carried on the journal bearing, and the electro-magnetic actuator is used to control the journal bearing instability. The paper discusses the design of the SEMAJIB and the design of a test rig including a multi-mode rotor. System identification of the test rig including the rotor and the bearings is discussed in detail. This includes the free-free rotor identification, and the identification of the rotor supported on the SEMAJIB bearings as well as the magnetic actuator testing. The effect of misalignment on the system characteristics is illustrated. The test rig is then used to study the dynamics of the controlled SEMAJIB. The rotor system is essentially running on the journal bearing until the instability occurs, the electro-magnetic actuator is then applied by PD control to eliminate the instability, basically adding damping. The rotor can then transgress the instability threshold and operate smoothly at higher speeds.

In this paper, the effects of rough bearing surface on the stochastic responses and the vibration characteristics of a rotor-bearing system subject to random fluid-induced forces are investigated. Based on Stokes theory, the stochastic Reynolds-type equation for the bearing taking into account the influences of rough surfaces is deduced, where roughness heights of bearing surface is considered as an uncertain-but-bounded parameter, which is modeled by a bounded random variable with approximates the Gaussian distribution. The stochastic modeling on uncertainties of bearing surface and fluid-induced forces is then developed. Finally, the dynamic behaviors and response statistics of the stochastic rotor-bearing system are demonstrated by rotor orbit and its mean amplitude of the vibration (MAV for short). The results show that the dynamic responses depend upon the structure type of surface roughness. Generally, the longitudinal roughness tends to decrease the mean size of rotor orbit at critical or sub-critical speed, but it may results in a larger radius of curvature in some position of orbit especially at critical or super-critical speed, while effects of transverse bearing roughness on the mean size of rotor orbit is not significant when frequencies are away from critical speed as compared to the smooth-bearing case.

A reduced Reynolds equation for an ideal gas, with a Winkler-type housing compliance is coupled with a rigid rotor model and solved simultaneously. By means of a Galerkin approach the dimension of the instationary bearing problem is reduced, without simplifications by neglecting individual terms. An evident reduction of calculation time is achieved, and consequently a direct time integration of the coupled problem without resorting to look-up tables is possible. Using this coupled model, the effects of the compliancy on the stationary solutions and during rotor run-up and run-down simulations are investigated.

The article presents the study of thermal phenomena that accompany the foil bearings operation. Tests were carried out on a specially designed high speed test rig, using a multi-channel measurement system and a thermal imaging camera. The object of the study was a 2nd generation gas foil bearing. In order to reduce the sliding friction, the top foil was covered with specially selected plastic and was operating with the journal covered by a layer of ceramic. The study was conducted at different speeds in which the temperature of the top foil was measured at several points spaced around the circumference of the bearing. In addition, the temperature distribution was analyzed on the outer surfaces of the bearing by means of the infrared camera. On the basis of the results, it was examined how rotational speed affects the temperature of foil bearing elements. The maximum temperature that can occur at steady operational conditions was also determined.

We performed a dynamic analysis of a foil structure under a range of loads using commercial FE software and actual tests. A dynamic load of between 2 and 8 N was applied by an electromagnetic shaker. The frequency range was from 100 to 600 Hz. A static force of between 40 and 140 N was applied by using a tension wire attached to the housing. To facilitate the analysis, the FE model assumed a fully circular geometry and a 2D wire mesh when describing the actual gas foil journal bearing. The excitation direction was assumed to have a single degree of freedom. The dynamic analysis permitted the evaluation of the stiffness and the damping coefficient of the 1D characteristic with the circular geometry. The dynamic coefficient was calculated using the relationship between the displacement and excitation force within the defined frequency range.

This work presents the numerical model of an experimental set-up where it was made an evaluation on the static characteristics of the shaft and the identification of the dynamic characteristics for an aerostatic radial porous bearing. The use of ceramic porous as journal for aerostatic bearings can improve its perform related to the wear, thermal stability, stiffness and load capacity allowing that spindles work with precision at speed above 20,000 rpm with small clearances (40 μ). In order to investigate these bearings were developed static analyses to obtain the deflection and stiffness of the support shaft, stiffness of the aerostatic porous bearing and dynamic identification for experimental set-up. The static analysis indicated stiffness of shaft and aerostatic porous bearing of 20.1 and 2.6 kN/mm, respectively. The dynamic analysis indicated that the first natural frequency of the rotor is close to 1365.9 Hz, which is much higher than the first natural frequency of the aerostatic ceramic porous bearing whose value is 775.0 Hz. One can concluded that geometrical configuration and support conditions choosen allow a robust condition to proceed the experimental tests in order to obtain dynamic characteristic of the aerostatic porous bearing.

This study aims to analyze the flow characteristics and the thermal features of foil thrust bearing. The flow in the gas film is modeled with 2D compressible Reynolds equation including effects of centrifugal forces in the gas film. The Couette Approximation is adopted for the analysis of temperature distribution in the gas film, and the small perturbations method is used to calculate its dynamic force coefficients. The results show that the Couette Approximation can be used to calculate the temperature distribution in foil thrust bearing with reasonable accuracy and the analysis of the fluid flow reveals that most of the side-leakage occurs in the low-temperature converging region removing less than 5 % of the heat generated in the gas film. Furthermore, with the proper control of cooling flow rate through the bump foils, more than 70 % of the heat generated in the gas film can be removed.

The paper presents a fragment of the investigations on the gas foil bearings modeling, which were made out in the Institute of Fluid Flow Machinery (IMP PAN). The calculations are carried out in the S-MESWIR system of computer codes, originally invented in the IMP PAN and with the use of commercial software. A two-bearings laboratory rotor of about 3.5 kg weight is proposed. It is modeled in the S-MESWIR system with the use of beam finite elements. It is dynamically forced with the unbalance. The properties of the bearings are defined with the FE model of foil set. The air was assumed as a lubricating gas. For low speeds the gas layer may be not developed because the aerodynamic effects between the bearing journal and the top-foil are too weak. Thus the rotor is supported on the foils only. For higher values of rotational speed a gas film was fully developed and it takes part in the carrying of the load. The paper presents the example how the modification of the structural layer properties (especially stiffness) can change the dynamic characteristics of the rotating system.

Numerical and experimental investigation of dynamics for simulator of compact gas turbine rotor in foil gasdynamic bearings is carried out. For definition of influence on rotor-simulator—gas bearings—casing system dynamics from main parameters such as rotor imbalance and structural damping, the series of rotor, casing, foil bearings and gas lubrication finite-element models are developed. Influence of gas foil bearing design and temperature state is considered. In experimental part of work the rotor floating up in bearings conditions are determined for operation in normal conditions and at 420 °C heat. Estimation of coatings in support durability was carried out at cyclic start-stops. For calculated and experimentally obtained rotor orbits the system main frequency characteristics were determined using spectrum analysis. Rotor system sensitivity for changing main parameters is shown. Numerical simulation and experimental results provided additional tools for analysis of effects observed in experiment and for numerical model verification.

Gas foil bearings (GFBs) have been successfully introduced in the field of high speed turbo machineries. A combination of low power loss, high speed operation and the omission of an oil system heighten the importance for small and medium sized turbo machineries, e.g. turbochargers or range extenders. However, experimental and numerical investigations have shown subsynchronous vibrations, which affect the rotor dynamic behaviour. Structural damping generated by friction contacts inside the compliant structure may reduce vibrations up to a certain level. In addition, several proved methods and devices, e.g. side feed pressurerisation, pre-loading due to shims and viscoelastic foil bearings are common techniques to decrease non synchronous vibrations. However, far too little attention has been paid to the causes of these non-linear effects. Understanding the causes may results in a higher knowledge of the overall GFB dynamic behaviour. Thus, the aim of this paper is to analyse the causes of these non-linear vibrations. A hypothesis is stated, that the non-linear vibrations are influenced by a self excitation and a forced non-linearity. The non-linear compressible transient Reynolds equation is discretised by a hybrid finite difference scheme with an implicit time discretisation while the pressure field is coupled with a 2D plate model. This plate model is linked to a spring-damper configuration. The time domain analysis shows, that the subsynchronous frequencies may excite the system eigenfrequency. In addition, good correlations between the onset speed of sub synchronous vibrations of the time domain simulations and the linearised frequency domain analysis are shown. In the second part of this paper, the effects of different bump foil configurations (bump-type GFB, shimmed GFB and a lobed GFB) on the dynamic performance are considered. It is shown, that an effective reduction of sub synchronous vibrations due to a non-uniform circumferential stiffness distribution and the use of shims is possible. Especially, the low loaded case (5 N) has an increase of onset speed of subsynchronous vibration of ≈173 %, compared to the same bearing setup without shims.

This paper studies foil gas bearings for the small-size high-speed turbomachinery applications. The main part of the work is devoted to the modeling of the foil gas bearings using computational fluid dynamics (CFD). Deformation of compliant elements is incorporated directly into the CFD model by means of analytical expressions and moving mesh technique. The CFD model is used to predict load capacity and rotordynamic stiffness coefficients of the foil bearing. The studied bearing is a multi-leaf foil bearing with four foils mounted on the elastic layer. The radial deflection of the elastic layer depends on the gauge pressure in the gas film. Results are presented for the rigid bearing and the foil bearing for the eccentricity ratios of 0.75, 1.0, 1.5. Information on computational costs, usability, and validity of the presented CFD-based approach is given. Application of an alternative model of foil bearing based on the Reynolds equation is also discussed.

Externally pressurized gas journal bearings with an asymmetric gas supply mechanism have been developed by authors. This bearing has a large load capacity compared with conventional symmetric gas supply bearings because low and high pressurized gases are supplied to loaded and counter-loaded side bearing surfaces, respectively. It has been proposed that this type of bearing has advantageous characteristics applicable for use in a general purpose X-ray computed tomography scanner gantries. The adaptation of this gas bearing to the device can conceivably contribute to an improved performance by increasing the rotational speed and decreasing the operating noise. This is effective for higher precision scanning and for reduction of the level of stress on a patient. Numerical calculations of this bearing were conducted and the resulting characteristics were compared with those of a conventional symmetric supply gas journal bearing. The effectiveness of the bearing for this application was demonstrated by conducting rotation tests using a small size test rig. The rotor generates centrifugal force by the rotation. The bearing diameter and length were 60 and 120 mm, respectively. The test bearing was operated under several supply gas pressure controlled conditions. The rotor vibration amplitude can be decreased by supply pressure control under generating the centrifugal force condition. The amplitude increased under conventional symmetric gas supply conditions with an increase in rotational frequency. Therefore, effectiveness and safeness of the bearing was experimentally verified. The gas flow rate decreased under controlled supply pressure conditions compared with conventional supply pressure conditions.

In this paper a 12 DOF gear dynamic model was developed and the equations of motions were derived. A one-stage reduction gear was modelled with gyroscopic effect of the gear disc, and both cases of symmetric and asymmetric disc were studied. Gear mesh stiffness was calculated for different crack sizes, and dynamic response was simulated. Time domain scalar indicators (the RMS, kurtosis and the crest factor) were applied for fault detection analysis. In the case of asymmetric disc the simulation shows results that are different from those obtained in the symmetric case. The coupling terms have an effect on the obtained pinion’s displacement which is studied for fault detection analysis. Therefore, for simulating the pinion’s displacement, this model can be considered for more accurate modelling in case of asymmetric disc.

In the study on the dynamic characteristics of spline rotor system, the spline stiffness is simplified as the constant related with single tooth stiffness. Based on spline single tooth stiffness calculation, according to spline deformation, stress and torque, spline transverse meshing stiffness model is established, and the numerical simulation analysis is managed. The results show that: under the small deformation condition, spline lateral stiffness is a constant related with single tooth stiffness, number of teeth and pressure angle; under the large deformation, there is complex nonlinear relationship between the lateral stiffness and torque, lateral force. The results provide more accurate theoretical model for nonlinear dynamic characteristics analysis of spline rotor system.

The modeling and dynamics of the coupled planetary gear and rotor system is studied. The dynamic model of planetary gear system connected with the input shaft and output shaft is established. A concept of micro-relative displacement is introduced to describe the relative motion between each part of the planetary gear system, thus the positive semidefinite gear system is transformed into positive definite system. Considering the time-varying characteristic of gear mesh stiffness, the incremental harmonic balance method is adopted to analyze the response of the coupled rotor and planetary gear system. The analysis results are compared with that of the single planetary gear system. It shows that the nonlinear response behaviors of the planetary gear-rotor system are significantly different from the single planetary gear set, so the influence of rotors on both ends cannot be ignored, especially when the rotors are large.

The wind turbine drive train dynamic analysis is carried out with and without existence of gear tooth breakage. The loads acting on the wind turbine are considered based on Danish Standard DS472 which is a simplified method of taking loads in wind turbine. A broken gear tooth is modelled by the change in the gear tooth thickness. The gear mesh stiffness of broken tooth is evaluated by the change in cross sectional area and area moment of inertia due to change in tooth geometry. From the frequency representation of vibration data, the fault information is not clearly observed due to the insensitiveness of the dynamic system to the stochastic loads. However, by further analysis, fault information is obtained with the use of the gear tooth contact force from which a clear sub harmonics are observed at the defective pinion tooth frequency.

Bearings play a pivotal role in the rotating machine scenario, due to their ubiquity and importance. A crowd of signal processing procedures have been developed in order to extract information about incipient localised faults in bearings from the measured acceleration signals. In the case of bearings for planetary gear applications, additional complexities are introduced. First, transducers may only be placed on the exterior of the gearbox, usually rather far from bearings. Second, the rotational axes of the planet gears are not fixed, i.e. they move with respect to the gearbox housing and thus to the transducers. As a result, the vibration signature of the planet gear bearings can be altered by the variable transfer path. In this condition, the standard signal processing techniques fail, and the characteristic bearing fault frequencies cannot be determined. On the other hand, global indicators of the bearing health may be used, but they are not able to specify where the fault is located. In this paper, a pre-processing technique is applied to the vibration signals of a planetary gearbox in order to highlight the planet gear bearing signatures. This technique is based on the McFaddens time synchronous averaging method to extract the vibration data relative to each planet. Then, cyclostationary techniques such as the Cyclic Power has be applied to extract the bearing signature.

The gearbox is one of the key subsystems in a typical wind turbine. It has the task to transfer power from the low speed shaft connected to the rotor to the high speed shaft connected to the generator. Larger wind turbines require more power and gearboxes with higher load capacity need to be designed and a deep knowledge into gearbox dynamics becomes of fundamental importance. When dealing with a machine in operating conditions with several rotating components, components are introduced in the signal that make the application of standard techniques such as Operational Modal Analysis very difficult and in some cases almost impossible. For this reason, new techniques to tackle with these conditions were investigated in the past, such as Order Based Modal Analysis. This method represents an extension of standard OMA to extract a modal model from measurement on a machine during run-up (or run-down) conditions. The applicability limits of standard OMA are here demonstrated on the data acquired on a 13.2 MW wind turbine gearbox testing facility during controlled run-up conditions. The advantages of the proposed methodology will be demonstrated by firstly applying it on data simulated using a validated model of the testing facility. The additional challenges that need to be faced when applying the method to real data will also be presented.

This paper presents the results of torsional stiffness analysis of involute spur planetary gears in mesh using finite element methods. A planetary gear model with 3 planet gears and its subsystem models have been developed to study the relationship between the overall torsional stiffness and the subsystem torsional stiffness. The subsystem models include one isolated sun-planet-ring pair, one isolated sun-planet external pair and one isolated planet-ring internal pair. A strategy utilising a small preload step via a weak spring was first applied to eliminate the gap between the teeth and then different torque levels were applied to calculate the transmission error due to the resulting elastic deformations. This calculation was repeated at multiple positions covering two tooth mesh cycles in the overall and subsystem models. The theoretical gear contact position was determined using an ANSYS APDL program and the gear rolling range was digitized into equidistant rolling angles. The sun-planet torsional stiffness variation has been shown to dominate the combined torsional stiffness and, based on the subsystem torsional stiffness, an analytical method for predicting the overall torsional stiffness is presented.

The efficacy of the planetary gear transmissions is strongly conditioned by the leveling of the load sharing achieved among the different planet paths. There are two main causes accepted as the most important sources of uneven load sharing, which are the errors in the positioning of the planets and the eccentricity of the gears. Several solutions have been implemented in these mechanical systems in order to improve the load sharing among planets, such as configurations with a floating member or the use of a flexible ring. In this work a dynamic planetary transmission model is presented, which has been developed by the authors and successfully used to simulate the effect of cracking and pitting on various variables in ordinary gear transmissions. This model has been extended in order to allow internal gearing, extending the simulating platform to include the static modeling capability of the planetary transmission behavior, including the presence of defects in gear positioning. The planetary transmission model presented in this work is an evolution of the previous one, and it allows now for the study of the planetary transmission behavior in dynamic regime. This model has been applied to the study of the load sharing in the presence of eccentricity errors in the planets. An assessment of the results is performed, and a comparison between the positioning and eccentricity errors in terms of their effects is also presented.

Dynamic characteristics of a tilting pad bearing strongly depend on the direction of applying load as well as the magnitude. As the bearing load of geared compressor are determined by aerodynamic forces of impellers and mesh forces of helical gears in accordance with operating speed, dynamic coefficient of each bearing also varies with respect to rotor speed. Hence, in order to ensure rotordynamic stability of geared compressor, accurate estimations of bearing loads and corresponding dynamic characteristics of tilting pad bearings in accordance with operating speeds are highly requested. In this study, bearing dynamic test rig was developed based on floating bearing housing design, with speed range from 3000 to 32,000 rpm. In order to precisely estimate lateral critical speeds and the stability of pinion rotor of integrally geared compressor, the experimental investigation has been carried out on five pads tilting-pad journal bearings of 45 mm in diameter. Static eccentricities of the tilting pad bearings were investigated with various load directions and corresponding dynamic characteristics were also obtained. Multi-frequency excitations have been used to evaluate the nature of frequency dependency of the bearing dynamic coefficients. Using experimentally identified dynamic coefficients of rocker-back type tilting pad bearing with respect to rotating speed, rotordynamic analysis of gear-driven pinion rotor was carried out and compared with shaft vibration measurement. The predicted rotor behavior showed good agreement with measured one.

A novel topology based on active magnetic bearing coupling for reducing synchronous vibration in rotors at critical speeds is outlined. The topology consists of a hollow rotor with a flexible concentric secondary shaft running along its length. Between the two shafts are one or more actively managed couplings. A design of a test rig to illustrate the effectiveness of the concept is presented, and results of finite element modelling on the rig are provided. It is shown that for the specific topology modelled, peak vibration amplitudes are around an order of magnitude lower than those of a decoupled rotor.

Applicability of electro-magnetic actuator for active vibration control of long rotors, commonly found in power-plant turbines is addressed in this work through simulations. Appreciable vibration reduction with the Proportional-Derivative (PD) control law applied on the difference between nominal and instantaneous air-gap between rotor surface and actuator poles is reported in literature. This paper investigates and finds that the Proportional and high frequency band limited Derivative control action (abbreviated as PD

hfbl

) is much more efficient than the former in terms of unbalanced response reduction and increment of Stability Limit Speeds (SLS) of long rotor-shaft systems. This paper also establishes a philosophical link between the PD

hfbl

control action and a multi-element mechanical suspension model, or viscoelastic suspension model, reported to reduce response and increase stability limit speed of rotors in literature. Examples of simulations are presented in support of the conclusions.

Modern high-speed and high-power flexible rotors are increasingly supported on active magnetic bearings (AMBs). Apart from supporting/attenuating rotors now AMBs have been utilized for obtaining fault conditions of such rotating machineries. For this accurate characterization of AMB rotordynamic parameters is very important apart from accurate modeling of rotors. The latter could be performed by finite element methods quite accurately. The present paper proposes a model based identification algorithm that concurrently estimates the speed-dependent AMB rotordynamic parameters and residual unbalances present in a flexible rotor system that is fully levitated on AMBs. To test this algorithm, an experiment on a flexible rotor system fully levitated on active magnetic bearings (AMBs) by PID controllers, was conducted. The rotor was given the run-up and run-down within certain duration of time for the fast, medium and slow runs. For each run displacements at all disc locations and currents at AMB locations were collected. By using these responses, simultaneously the speed-dependent bearing parameters and residual unbalances were estimated using the developed identification algorithm. The estimates were consistent for different runs and compare well with theoretical values.

Active Magnetic Bearings (AMBs) suspend rotor systems and also facilitate active rotor vibration control through feedback control law for appropriate contactless electromagnetic force. However for rotors on moving bases e.g. ships, airplanes, the equations of rotor motion become parametrically excited and so a feedback control methodology, e.g. with Proportional Derivative (PD) control law needs assessment of stability. It is observed that the equations of motion of a rigid rotor with respect to base, translating and pitching in one plane, under the action of linearized electromagnetic forces from AMBs at ends, take the form of forced damped Mathieu equations. This paper first attempts the stability analysis to tune controller parameters and then uses the Active Disturbance Rejection Control (ADRC) with Extended State Observers (ESO) to reject disturbances. Simulated results show considerable rotor vibration suppression and thus prove AMBs as effective suspensions for vibration control of rotor-shaft systems on moving platforms.

Conventional centralized proportional-integral-derivative (PID) control methods manipulate the feedback gains in prescribed forms until they achieve the desired control performance, but they have often failed to stabilize the lightly-damped and unstable conical modes, among the rigid body modes, of the rigid rotor-AMB system with large gyroscopic effect over high rotational speed range. In this study, an eigenvalue assignment for decoupled translational and conical modes is proposed in the complex domain to yield a unique PID controller in a closed form, preserving isotropic bearing characteristics. The eigenvalue assignment necessitates the constraints required for decoupling of two modal equations related to translational and conical whirl motions from the complex equation of motion written in the center of gravity coordinates of the rigid rotor. A flywheel energy storage system is taken as a simulation example in order to demonstrate the validity and effectiveness of the proposed eigenvalue assignment. The simulation results show that the eigenvalue assignment algorithm is superior to conventional control methods at systematically ensuring sufficient stability margins for the lightly-damped and unstable conical modes with unique, explicit gain-scheduled PID controller with respect to the rotational speed.

This paper presents a state space model validation and means of vibration suppression for a rigid rotor supported by hybrid foil-magnetic bearings (HFMBs), using an additional PD controller. The main difficulty related to reducing the vibration of a rigid rotor using an HFMB is the realization of a controller that can minimize resonance without rigid modes. To solve this problem, we developed a state space scheme for system modeling and controller design. First, a rigid rotor supported by air foil bearings is linearized with a magnetic bearing and PD controller, to give a new stable rotor-bearing system. Then, we propose a model validation procedure that uses analytical open-loop imbalance responses to obtain an accurate model of the HFMB rigid-rotor system. After that, a rotor behavior simulation with a PD controller under a range of conditions was designed so as to suppress the rigid mode of the stable rotor-bearing system. A comparison of the measured and simulated results revealed poor controllability and vibration control in the rigid modes. Simulation with step-by-step disturbances, as well as the measured results for the imbalance up to 10,000 rpm, verified the efficacy of the HFMB scheme.

The construction of passive magnetic bearings is shown in the paper. Advantages and disadvantages a passive magnetic bearing with magnets, superconductors and electro-dynamic bearing are presented by Authors. They discus influence such parameters as load, speed of rotor, temperature and cost design and exploitation of bearing. Here are presented construction of the passive magnetic suspension designed for jet engines and linear bearing for UAV’s launchers.

In the paper comparative rotor-dynamic analyses are carried out for various rotor-shaft systems supported on the classical journal-, rolling element- and on the passive magnetic bearings. The investigations are performed by means of the advanced 3D finite element model of the electrodynamic passive magnetic bearing and of the structural model of the rotor-shaft—bearing systems, using which proper Campbell diagrams, amplitude—frequency characteristics and complex eigenvalues have been determined as well as numerical simulations of rotor-shaft transient dynamic responses were carried out. The presented study is focused on the lateral vibration damping abilities realized by the mentioned above bearing types. In this way, advantages of the prospective passive magnetic bearing have been emphasized.

Active Magnetic Bearings (AMBs) have many advantages such as allowing near frictionless rotation and high rotational speeds. Touchdown bearings (TDBs) are a requirement in AMBs to prevent system damage under certain conditions, such as high loads, transient faults, or external disturbances. These conditions may lead to rotor/TDB contact. The AMBs may have the capability to restore contact-free levitation of the rotor, though this will require an understanding of the TDB contact dynamics, together with appropriate control strategies. The experimental evaluation of a TDB dynamic contact force measurement system, in which strain gauge sensors are employed, is described in this paper. The relationships between TDB contact force dynamics and induced AMB forces are derived. Assessment of contact forces under varying amplitudes and frequencies applied by an AMB is presented. The data generated can be used to validate dynamic system models, and aid the design of control action to minimise or eliminate contact forces.

Active magnetic bearings (AMBs) offer considerable benefits compared to conventional bearings. On the other hand, AMBs require backup bearings to avoid damage resulting from a failure in the component itself, in the power system, or in the control system. During a rotor-bearing contact event, the structure of the backup bearings has an impact on the dynamic actions of the rotor. In this paper, the dynamics of an AMB-supported rotor during contact with backup bearings is studied with a simulation model. Modeling of the backup bearings is done using a comprehensive cageless ball bearing model, which includes the effect of misalignment. The elasticity of the rotor is described using the finite element method. Verification of the model for misaligned cageless ball bearings is done by comparing the simulated results to measurements. The verified model of the backup bearings is found to correspond to the features of a real system.

The use of rotor-mounted sensors and actuators in active vibration control of rotating machinery has the potential to overcome certain limitations of conventional stator-mounted components. A test system has been constructed to evaluate internal sensing and actuation strategies, where components are mounted within a hollow-shaft rotor. MEMS accelerometers are used to measure the vibration-induced acceleration of the rotor centre in the rotating frame of reference. With appropriate calibration and processing, this data can be used as a substitute for rotor displacement measurements. The results presented show how measurement accuracy tends to increase with rotational speed. As the accelerometers are located within the rotating reference frame, identification of the magnitude and phase of the rotor unbalance can be performed directly without the need for correlating fixed frame measurements with timing marks. Experimental results for sub-critical operation of the test system and comparison with theoretical predictions show the effectiveness of the system.

Rotating machines have to meet rigorous requirements in order to prevent instability during its operation. In the context of stability analysis, experimental tests such as stepped sine are widely used to determine the modal parameters of rotating systems: forward and backward natural frequencies and damping factors. Nevertheless, classical modal analysis techniques require prior knowledge of the system behavior, so that rotational speed and external excitation frequencies can be defined for the experimental tests. This work aims the assessment of model based numerical calculations to reduce or even stave off the preliminary tests. Validation starts with the evaluation of lubricated bearings model by shaft center locus. Afterwards, mass unbalance response is evaluated, and then, the stability analysis is conducted based on the logarithmic decrement. Finally, the numerical evaluation is compared to an experimental procedure regarding the precision of predicted critical frequencies for the tests and the evaluation of stability threshold.

A better understanding of the characteristic features of different faults associated with rotating machines is very vital, so that appropriate and timely maintenance interventions can be recommended prior to the occurrence of catastrophic failures. Rotor orbit analysis of machine vibration data collected using proximity probes has been observed to be useful for faults diagnosis in rotating machines. Although this analysis is extensively applied for rotating machines’ faults diagnosis in several industries, however, very limited experimental results are still available in literatures. In the current study, rotor orbit analysis has been conducted on an experimental rig of 1500 mm rotor length, supported by four flexibly mounted anti-friction ball bearings. A number of faults have also been experimentally simulated on the rig for the purpose of this study. Hence, the paper presents the experiments conducted, the rotor orbit analysis and observations, which may further enhance the understanding of rotating machines’ behaviors under different faults.

The spline joint is widely used in rotor system. The stiffness of joint is always smaller than the geometry nominally same structure without interface, meanwhile the dynamic characteristics are complicated because of existing of contact surface which affects rotor’s stiffness and dynamics further. In this paper, experimental studies of spline joint specimen are completed by two methods which include dynamic sinusoidal excitation experiment, and acoustic emission propagation experiment. The results indicate that the joint behaves nonlinearly, and the energy dissipation varies with nut’s torque and contact tolerance, meanwhile the contact status changes with the load. At last, the static stiffness test of a rotor with spline joint is completed, the influence of the key parameters are analyzed. The stiffness of rotor with spline joint varies with external loads and geometry structures. The technology in controlling the mechanical and dynamic properties of the rotor with joints by careful adjusting of geometry, load and assembly during designing should be attached great importance.

The paper presents first a description of the methods used for the analysis of global dynamics of rotating systems like jet engines, gas and steam turbines. The growing necessity to simulate not just the rotating parts, but the global assembly of rotors, stators and linking devices leads to new design methodologies allowing to capture more accurately global but also local phenomena as well as the impact of more and more demanding features like highly nonlinear bearings, the effect of gaps and clearances, etc. The fact a machine is not one single piece but an assembly of parts connected by semi-rigid joints has an influence on the global and local dynamics of the system. More importantly, novel methods are described with the goal to calculate very accurately both global (bending, torsion…) but also local (blade) modes related to multistage compressors. The use of inertial and rotating frame approaches is discussed when the goal is to describe rotors and stators in a full 3D way so to take into account not just 3D geometrical details but also, for example, centrifuge stiffening. Different applications related to jet engines, gas and steam turbines, turbochargers are described and discussed.

Flexural and lateral coupled vibrations usually exist in rotordynamics applications, as it is caused by common malfunction conditions and complex distributed inertial elements connected to the shaft may determine the coupling as well. In the paper, the authors present an accurate, innovative and fully coupled finite element (FE) rotordynamics formulation with 6 DOFS for each node for the evaluation of the dynamic behaviour of multi-rotor systems that has been conceived with the goal of investigating the flexural-torsional interaction. The model is able to model long rotors of complex topology, such as rotor with distributed inertias or connected simultaneously in several points, couplings and gear-boxes and it uses coupled shape-functions. The model proposed represents a systematic and practical approach to the rotordynamics modeling issue and its main contribution to the research topic of coupled flexural-torsional vibration in rotors is due to its general topology. The effectiveness of the model in predicting the critical behaviour of the a flywheel masses test bench has been preliminary tested by means of experimental data of vibration tests campaign, performed in collaboration with Politecnico di Milano.

The magnetic field within electrical machines causes an electromechanical interaction between the electrical and mechanical dynamics of the system. A relatively small asymmetry of flux distribution in the air gap creates an unbalanced magnetic force which tends to pull the rotor towards the stator in the direction of the highest flux density. This unbalanced magnetic force (or pull) in an electrical machine is exploited in so-called self-bearing or bearing-less electrical machine where, as well as functioning as a motor or generator, the machine can also produce transverse forces perpendicular to the rotation axis. The presence of magnetic field of pole pair

p

is due to the main supply of the motor and the presence of magnetic field of pole pair

$$ p \pm 1 $$

p

±

1

is due to the asymmetry present in the magnetic field or due to the eccentric rotor motion. So, the presence of magnetic field of pole pair

$$ p \pm 1 $$

p

±

1

will produce an unbalanced magnetic force in the air gap. This paper addresses a special type of stator winding scheme having parallel branches and a novel Wheatstone-bridge type connection in order to achieve direct control on the unbalanced components of stator magnetomotive force (MMF) whilst having no effect on the torque-producing components of the stator MMF. An Finite Element code has been developed in MATLAB and used as the basic tool for this investigation. It has been demonstrated in case of an induction motor that a controllable force in the air gap can be produced. The results from numerical model have been verified by experimental results.

A system for automatic model-based monitoring of multiple coexistent errors is being developed. Within this publication, the unsteady bow curve of a test rig rotor is examined. For simulating this rotor, the bow model of the Jeffcott rotor is expanded to a MDOF rotor. The application of the Ritz approach enriched with problem-specific shape functions leads to an accurate simulation with low numerical effort. The bow model and the monitoring scheme are successfully tested. Bow, unbalance and roundness error can be identified separately during normal operation of the rotor.

A correct prediction of the dynamic behaviour of rotors represents a critical issue in the rotating machines field. A large amount of research work dealing with rotor-dynamics modelling can be found in literature and nowadays both traditional simple and complex models may be adopted to investigate the vibration behaviour of rotating equipments. In this paper, the authors introduce an accurate and general-purpose model for the evaluation of the dynamic behaviour of multi-rotor systems, that has been conceived with the purpose of modelling complex rotors through a systematic and practical approach. The model, which aims at overcoming the modelling limitations characterising commercial dedicated softwares and which is based on a finite element rotor-dynamics formulation, is able to deal with long rotors characterised by complex topology, such as rotor with distributed inertias or connected simultaneously in several points. The investigated rotor test case is a flywheel masses test bench for railway brakes that is formed of several rotors with complex topology (distributed inertias). The model has been validated in a preliminary step by means of experimental data coming from a test campaign for the vibration assessment, performed in collaboration with Politecnico di Milano.

Vertical turbines installed in hydroelectric dams and guided by hydrodynamic cylindrical journal bearings may suffer from sub-synchronous vibrations. This is especially true when the rotor, the bearings and the seals are perfectly aligned. When present, the sub-synchronous vibrations have large amplitudes and generally limit the rotation speed of the machine to values lower than its operating regime. Nevertheless, machining and assembly defects lead to the misalignment of the rotor and its bearings and seals therefore strongly affecting its vibration signature. The present work is based on a numerical non-linear model of a vertical turbine able to take into account all its components and the most often encountered defects. The rotor is modeled by using 1-D Timoshenko beam finite elements and the presence of a rigid coupling is taken into account. The non-linear forces in the tilting pad thrust bearing and the journal bearings are obtained from the solution of Reynolds equation. The numerical results show how the radial misalignment of the journal bearings eliminates the sub-synchronous vibrations.

Ensuring the operating safety of electrical power plants is a major issue for operators. Regarding turbine generator sets, a risk was identified due to the potential loss of one or more low pressure last stage blades of the turbine which could lead to a large unbalance, and then to an accident. This kind of accident is generally avoided using several means among which robust design, condition monitoring and periodic non destructive inspections. Nevertheless, safety studies must be undertaken. This led researchers to develop realistic numerical methods to predict the effects of such an accident. In this framework, EDF R&D has developed its own method to describe the most accurately the dynamic behavior of a shaft-line in an accidental situation caused by a blade loss. The objective is to evaluate the loads on the bearings in these conditions and compare them to the maximum design loads provided by the manufacturers. This methodology is composed of two phases. The first one focuses on the study of the shaft-line behavior before the blade loss considering the linear behavior of the bearings oil film: a preliminary static computation is made under gravity loads considering the altimetry of the bearings. Loads on the bearings resulting of this calculation are used by a bearing code in order to compute the dynamic coefficients associated with the oil film. Then, the harmonic response to unbalance is calculated for different unbalance positions. The objective is to find the critical positions, critical rotational speeds and the most loaded bearings, for which a nonlinear modeling of the oil film is to be considered. The second phase starts at the instant which follows the blade loss and simulates the shutdown of the turbine. The simulation of the transient response under unbalance is performed taking into account the nonlinear behavior of the most loaded bearings oil films. The aim is to estimate the maximum loads that the bearings have to support, especially when the rotor to stator contact occurs. In this paper, the steps described above are detailed and applied on an industrial study. Results and performances are presented as well.

In present study, the non-linear dynamic behavior of a rigid-unbalanced rotor supported on cylindrical roller bearing is analyzed. An analytical model of the rotor-bearing system is developed for the investigation. The Hertzian contact between the bearing components and the clearance are considered as source of nonlinearities in the study. The contact between the rolling elements and races is model using nonlinear spring-mass system. Stiffness of nonlinear spring is calculated by Hertzian elastic contact deformation theory. Responses show system behavior as periodic, sub-harmonic and chaotic at different rotor speed. All the results are presented in form of fast Fourier transforms and Poincarè maps. Presence of instability and chaos in the dynamic response has been observed as the speed of the rotor-bearing system is changed. The study shows that the interaction of varying compliance (

VC

) frequency due to parametric excitation and rotational frequency (

X

) due to the unbalanced rotor force.

The present paper focuses on the dynamic behavior of fiber reinforced composite discs. Rotating discs are an important sub-component of any rotor dynamic system. Variation of natural frequencies for different fiber reinforcement configurations against rotational speed due to stress stiffening effect has been studied in detail. Critical Speed of various configurations has been examined. Tsai-Wu failure criterion has been applied to examine the bursting speed of composite disc. Useful results are obtained for rectilinear orthotropic reinforcement of rotating disc.

The nonlinear behavior of a rotating system with large elastic deformation subjected to harmonically varying ground disturbance has been investigated numerically. The Euler-Bernoulli beam theorem has been adopted in order to derive the partial differential equation governing the dynamics characteristics of the rotating system using extended Hamilton’s principle. Method of multiple scales has been selected in approximately finding the nonlinear dynamic characteristics of the system for possible resonance conditions. The effect of nonlinearities and other variations in the values of different parameters like amplitude of external excitation, position of disk along the span, and mass of the disk on the system performance has been investigated. The outcome from the present work will furnish a proper guidance to the designers in the vicinity of the limitation and safe range of operational speed of rotor shaft under the variation of other control parameters.

This work illustrates the application of general-purpose multibody formulations to the analysis of rotating systems dynamics. Various benchmark problems encompassing multiple deformable components are presented and analyzed. The suitability of the approach is assessed and conclusions are drawn on the basis of correlating the numerical simulations with analogous examples from the open literature.

Dynamic absorbers are simple passive devices installed on mechanical systems to absorb and dissipate kinetic energy, thus reducing the amplitude of vibrations/oscillations. The most widely spread typologies of dynamic absorbers belong either to the family of the Tuned Mass Dampers (TMD) and Tuneable Liquid Column Dampers (TLCD). They are both based on an inertial element, represented by a rigid body (TMD) or a water volume (TLCD) and an elastic-damping element, which consists of the same water volume in the TLCD case. Dynamic absorbers are almost exclusively applied in large civil structures, such as tall buildings and electricity transmission cables. The scope of this paper is to investigate the possibility to use TMDs and TLCDs for the reduction of vibrations on rotating machines. The study, based on numerical simulations and on experimental tests on specifically designed test-rigs. This study will provide design guidelines, specific for the application of TMD and TLCD on rotating machines, and investigate the effectiveness and limits of the two families of dynamic absorbers. Optimal tuning parameters will be identified for the specific application either analytically or numerically, in order to maximize the effectiveness of the two devices for rotating machines. A comparison between the two absorbers will also be provided, in order to identify the most effective choice or combination of TMD and TLCD.

The purpose of this study is to investigate the optimal design of rotors with respect to different objective functions. The dynamic behavior of a rotating system is strongly influenced by various parameters such as mass and stiffness distribution, rigid disk inertial properties, bearing locations and coefficients. To a greater or lesser extent, all bearings are flexible and all bearings absorb energy. Moreover, load deflection relationships are often a function of shaft speed. An optimal design can be achieved by minimizing a selected target function subjected to specific constraints within a set of reasonable bounds for inner and outer diameters of the different stations, stiffness and damping coefficients of the support bearings and their positions. Optimal design of rotors has been reported by many authors in the literature. However, all of these optimization analyses considered beam elements instead of solid elements to the best knowledge of the authors. Nowadays three-dimensional models of rotors are common practice in the industry. Therefore solid models of rotating systems are considered in the current work. Stability criteria, critical speeds, weight, real and complex eigenfrequencies, and unbalance responses may be defined as a set of objective functions and constraints. In order to judge the stability, the equivalent damping ratio is evaluated. The determination of the damped critical speeds is accomplished using a Campbell diagram, a plot of damped natural whirl frequencies versus spin speeds, which is generated by determining the natural frequencies over a range of rotational speeds. A mode-tracking procedure is implemented in order to sort the complex eigenvalues. The complete finite element analysis including the complex design optimization problem of the rotor system at hand is conducted in PERMAS. For this purpose several optimization algorithms are available. Furthermore gradient-based and derivative free methods can be used. A combined shape and sizing optimization is used to illustrate the procedure by means of an example taken from the literature.

This contribution deals with active vibration isolation of unbalance induced vibrations of a rotating shaft using

$${\mathcal{H}}_{\infty }$$

H

∞

-optimal control and piezoelectric actuators. Controller design for the considered system is challenging and requires a high demand in robustness due to speed-dependent system behavior in consequence of the gyroscopic effect. Recent studies in the field of active control of rotor systems, especially at the Institute for Mechatronic Systems in Mechanical Engineering at TU Darmstadt, mainly focus on the attenuation of rotor displacements. For many applications, like aircraft engines, not only the rotor’s deformation itself is of high interest, but also its interaction with the environment. Former works on active vibration attenuation show that active reduction of rotor displacements can be attended by an undesirable increase of bearing forces. In addition to these works, this article deals with the decoupling of a rotating shaft from the surrounding structure, which is also known as vibration isolation. The investigations are based on a rotor test rig with a statically determined bearing configuration. One of the two bearing supports is active and consists of two piezoelectric stack actuators as well as two collocated piezoelectric load washers. The operating range of the test rig includes two unbalance induced resonances. Since the control performance strongly depends on the accuracy of the description of the system dynamics, a finite element model of the rotor is determined and extended by discrete piezoelectric elements. The obtained parametric model is capable of capturing the system’s speed-dependent dynamics. The

$${\mathcal{H}}_{\infty }$$

H

∞

-optimal controller will be derived using the parametric finite element model. Finally, the feasibility of the described approach will be validated by testing the control performance by means of vibration isolation in simulation and experiment.

The objective of this work is the study of the dynamic of angular contact ball element bearings considering the elastohydrodynamic lubrication. A computational model was built to foresee the dynamic behavior influence on the lubrication condition of those components. The model of EHD lubrication is taken into account in the bearing dynamic model, to obtain coefficients of stiffness, damping and subsequent characterization of the bearing, for different loading condition. The dynamic model has five degrees of freedom. The model considers, in its development, centripetal force and gyroscopic effects, and static equilibrium analysis are accomplished to find the force distribution in each sphere. With the force distribution, the dimensionless Moes parameters of lubrication and load are calculated, as well as the contact elliptic ratio, which are used in the EHD model. Therefore, it is possible to calculate the contact pressure, film thickness, as well as the contact force parameters and corresponding stiffness and damping coefficients.

Active Vibration Control has proven to be a good opportunity for attenuation of lateral vibration of rotating shafts in literature. Besides the choice of suitable sensors and actuators, the controller itself has a particularly strong influence on the performance of an Active Vibration Control system since it generates the control signal from sensor signals. There are numerous controller types available for the purpose of active vibration control. These controllers include simple feedback approaches but also more sophisticated model based feedback and feedforward approaches. In this part I of a two-part article three feedback controllers from different fields of research and a feedforward controller are designed for active control of lateral synchronous vibration of a rotor test rig. In particular, PDT1-Control, H

∞

-Optimal Control, LQG-Control and feedforward control using the FxLMS algorithm are introduced.

In part I of this two-part article, three feedback controllers from different fields of research and a feedforward controller have been discussed. In this part II, feedback controllers are optimized to identify the optimum performance which is not necessary for the feedforward controller since it is self-adapting. The four controllers are compared against each other on the basis of their optimal control performance. Results are validated experimentally.

In this contribution, the effect of impulsive parametric excitation to the modal energy content of torsional systems is investigated. First, it is shown analytically that impulsive parametric excitation allows to transfer vibration energy between sets of modes of vibration. Transferring vibration energy from lower to higher modes allows to utilize the damping properties inherent in a mechanical structure much more effectively. This leads to a faster decrease of the overall energy content, and hence, of the vibrations of a mechanical system, compared to the case where no impulsive parametric excitation is present, as it is demonstrated with some numerical investigations.

The rotor of a 3-stage axial turbine designed for an ORC plant, supported by two axial/radial lubricated roller bearings, has some axial clearance in between the outer bearing ring shoulder in the casing to allow for thermal expansion. The rotor can move freely within the clearance before the bearings on both sides are able to apply a restoring force. In order to avoid axial vibrations excited by possible operating fluid pressure fluctuations, an unilateral axial squeeze film damper has been designed. CFD calculations have allowed to characterize the damper, which is highly non-linear. The damper has been introduced in the model of the machine and its performance has been analyzed by comparing the behavior of the damped rotor to the un-damped rotor, at the different exciting frequencies. The comparison has been performed necessarily in the time domain due to the presence of two non-linearity: unsymmetrical damper and non-linear elastic restoring force. The results of the comparison have shown the efficiency of the damper especially in conditions close to resonance.

Synchronous generators form the main part of a turbo generator set, yet their rotor dynamic behavior is not as common as the turbines in the system. This paper addresses the rotor dynamics of synchronous generators. The generator is modeled as a beam for the shaft and rotor core, as lumped masses and transverse inertias for flywheels, fan, and exciter. Bearing oil film is modeled using speed dependent stiffness and damping coefficients in both direct and cross-coupled directions. Direct stiffness coefficients are modeled for the bearing housing and supporting structure. The unbalance response is also determined as a function of the speed. The analysis is repeated replacing the beam model of the shaft as a solid model.

A primary problem in the turbine industry is associated with the mitigation of bending vibration modes of high-speed rotating shafts. This is especially pertinent at speeds approaching the critical frequencies. Here, a shaft, complete with eccentric sleeves at the free ends, is designed and developed, with a view to passively control critical speeds and vibration induced bending. In this article, using the Extended Hamilton’s principle, the equations of motion (axial, torsional, in-plane and out-of-plane bending) for a rotating flexible shaft are derived; considering non-constant rotating speed, Coriolis and centrifugal forces, with the associated boundary conditions due to the eccentric sleeves and torsional springs in angular deformations of lateral vibrations in bending. The numerical dynamic analysis showed that considering the sleeves as flexible only had a small effect upon the first critical speed of the shaft. Therefore, rigid body modelling of the sleeves is sufficient to capture the essential dynamics of the system. The derived equations of motion with the associated boundary conditions show that in the case of constant rotating speed, the eccentric sleeves are coupling xy-bending with xz-bending and also torsion. Also the derived equations of motion and the associated boundary conditions in the case of non-constant rotating speed are essentially nonlinear due to inertia terms. This work is essential to the advance of linear and nonlinear dynamic analysis of the system by means of determination of normal modes and critical speeds of the shaft.

Studying the dynamic behaviour of continuum using discretization through Finite Element is common place. This paper attempts to apply the concept of rigid multibodies connected with proper kinematic pairs to approximate the kinematic behaviour of a flexible body; the system of interconnected rigid multibodies is then used to simulate the deformation pattern of a flexible body under dynamic loading. With this aim, this paper simulates, to begin with, the dynamic behaviour of a simple Cantilevered beam by considering several bar-like rigid multibodies connected by revolute pairs having properly design torsional stiffness to simulate the static deformation pattern under different loading conditions. Later this system is used to find out the dynamic deformation pattern with the help of the software, called ReDySim (Shah et al. in CSTAM Theor Appl Mech Lett 2:063011, 2012 [

2

]), a multibody dynamic simulation package based on Decoupled Natural Orthogonal Complement (DeNOC) (Saha et al. in Mech Sci 4:1–20, 2013 [

1

]) concept, in the form of mode shapes and natural frequencies of the system. Next the same model is extended to simulate the dynamic behaviour of a Cantilevered overhung rotor-shaft. The results obtained from ReDySim are compared with those obtained from a MATLAB code written for simulating a formulation based on FEM; a close match between these two dynamics behaviors is obtained to prove the validity of the approach. Thus the rigid multi-body equivalent of a continuum (a structure or a rotor) is built and this is supposed to be useful in simulating dynamic behaviour of continua under generic dynamic conditions.

This paper aims to study the influence of varying number of balls on nonlinear dynamic behavior of an unbalanced rotor supported by ball bearings. Centrifugal force due to rotation of balls is included in the model. An oscillating spring-mass-damper is considered to formulate the contact between races and rolling elements. Stiffness for the spring-mass-damper system is calculated using Hertzian elastic contact deformation theory. The results show appearance of regions of periodic, sub-harmonic and chaotic behavior on response of the system. Invariably, the route to chaos is seen to be intermittency mechanism by period doubling behavior. Poincare maps and frequency responses are used to explain and to study the system behavior.

Taking a 1000 MW turbo-generator rotor as an example, the sensitivities to thermal effect in temperature range of 20–570 °C, both for lateral and torsional vibration, are analyzed. In addition, for lateral vibration, the sensitivities of the critical speeds are analyzed by changing bearing stiffness. The results show that increasing bearing-support stiffness leads to natural frequencies increased gradually but not linear. The first order is much more sensitive than the others. When stiffness of bearing is large enough, the natural frequencies almost do not change. For torsional vibration, the sensitivities of natural frequencies are analyzed by changing some mechanical parameters. With changing the stiffness and inertia of the rotor, their influences to the characteristics of the torsional vibration are obtained. The frequency can be modulated by changing the sectional structure of the shafting to avoid torsional vibration resonant. The results are also shown that torsional frequency and mode shape are much more sensitive to mechanical parameter than to thermal effect.

The progress towards a whole-engine design philosophy and the development of new technologies like open rotors, where coupled behaviour due to Coriolis and gyroscopic effects could be more pronounced, calls for an assessment of the prediction capabilities currently available in commercial FE software packages. Finite element models including these rotational effects are rarely used in simulations of bladed disc-shaft assemblies, and the confidence in FE codes to provide reliable frequency and mode shape data can therefore be improved. Different models were used as benchmark test cases in the evaluation, including the classic Stodola-Green rotor, and a blade-disc-shaft assembly, and the resulting Campbell diagrams were compared to analytical solutions from the literature. The ability of the codes to exploit the cyclic symmetry of bladed discs for computational efficiency was also assessed. The results show that all investigated codes are able to capture the Coriolis-induced frequency splits, but discrepancies arise at high speeds and in the vicinity of instabilities.

To simulate the behavior of large rotors it is necessary to model them using adequate FE-models. The simulation time for such models could be quite long. The models of rotors are challenging for model order reduction (MOR) techniques. The models depend on rotational speed, because the gyroscopic effect is not negligible. Therefore a new parameter preserving model order reduction algorithm—called Ω preserving MOR (ΩP-MOR)—is presented in this work. If the ΩP-MOR algorithm is used with the Krylov subspace method, an arbitrary number of moments could be matched for every value of the parameter. With this work, moment matching is proven for the first time. To demonstrate the efficiency of the algorithm, the reduction and simulation of a real rotor model is shown. With the ΩP-MOR algorithm more than 99.9 % of simulation time could be saved with an error factor smaller than 0.1 %.

This paper presents theoretical analysis of non-synchronous vibration in rotor systems. A finite element method on the basis of the Timoshenko beam formulation implemented in the in-house code is applied as a standard tool to perform transient rotordynamic analysis using the Newmark algorithm for the direct numerical integration of the equations of motion. The analysis is demonstrated for a free power turbine rotor system of a small-size turboprop engine. Different sources of non-synchronous excitation are studied including squeeze film damper and rotor-to-stator contact interaction.

In recent years, the use of rolling bearings in high-speed rotating machinery has become increasingly frequent. Applications where hydrodynamic bearings were traditionally employed are now switching to rolling element bearings. The compressor industry is a notable example. Compared to hydrodynamic bearings, rolling bearings offer the important advantage of reduced friction. However, their use in high speed applications must be carefully evaluated. In fact, the system rotor-dynamics depends heavily on the bearing stiffness and this can change greatly depending on the operating conditions. In this paper, the rolling bearing impact on the stiffness of a high rotating speed shaft system is examined. Bearing stiffness is studied as a function of three important design parameters: load, rotational speed and bearing internal clearance. Although these results are, in principle, applicable to all turbo-machineries, a selected case study will be presented that is best suited for centrifugal compressor applications.

Since Spherical Roller Bearings (SRBs) have high load capacity and are self-aligning, they are seeing increasing use in the rotating machinery. Typical applications are paper machines, steel rolling, marine equipment, geared transmissions and modern high power wind turbines. Therefore, it is becoming increasingly important to study the dynamic behavior of SRBs and know the excitations caused by internal imperfections. Extensive research has been conducted to study the dynamics of ball bearings, while studies related to spherical roller bearings are short-shrifted. In this paper a three degree of freedom dynamic model of spherical roller bearing that takes into account the inner and outer race surface defects is introduced. In the model, bearing forces and deflections are calculated as a function of contact deformation and bearing geometry parameters according to nonlinear Hertzian contact theory; taking radial clearance into account. Two defect cases are simulated: an elliptical surface concavity on the inner race, and an elliptical surface concavity on the outer race. In case of elliptical surface concavity, it is assumed that the contact between the roller and inner and outer races is continuous as each bearing roller passes over the defect, and contact stiffness in the defect area varies as a function of the defect’s contact geometry. The equations of motion were solved numerically. Simulation results demonstrate that the SRB model is sufficiently accurate for typical rotor bearing systems. Numerical results also show that each local defect excites vibration at a frequencies corresponding to the bearing defect frequencies, and thus, makes it possible to identify the location of the defect (i.e. inner or outer race) from the simulated frequency spectrum. Numerical simulation is carried out successfully for a full rotor-bearing system to demonstrate the application of developed SRB model in a real world analysis. Finally, simulation results are verified and compared to measured data obtained from an equivalent rotor bearing system with a predefined local defect. Comparison shows a good agreement between the simulated and measured results.

Investigation of rotor dynamic defects is often instigated following machinery protection panel trips due to high vibration. Initial investigations often identify the location of the problem and the rotor dynamic characteristics causing the problem. However, underlying causes may be better appreciated by examination of process or auxiliary data. Combining this data into the rotor dynamic interpretation can lead to faster and more accurate diagnosis of machinery defects. Three cases studies are presented from export compressors operating on UKCS installations process and rotor dynamic data was combined to determine the cause of machine trip and to recommend maintenance intervention actions. In all these cases, additional process data was logged from the platform instrumentation or control systems along with proximity probe displacement, allowing diagnosis of the machine condition. The importance of collecting and analyzing process and auxiliary data provides invaluable assistance in recognizing defects, minimizing maintenance intervention time and maintaining reliability of production critical machinery.

This paper made an experimental investigation of cage instability in respect to cage pocket designs, ball-pocket clearances, and flow rate in cryogenic environment. Test bearing bore size is 70 mm deep groove ball bearing. Cage pocket designs are circular and elliptical, and ball-pocket clearances are 0.6, 1.2, 1.8 mm. Test is operating at 6000 rpm during 1500 s in liquid nitrogen. As a several criterions of wear and stability for cryogenic ball bearing, we measured a friction coefficient of bearing and sound vibration FFT were measured and analyzed to predict failure mechanism of bearing elements. From these results, predicted and diagnosed with sound properties of cage, inner/outer race and balls. These works will be assessed more stable with optimum ball-pocket clearance and elliptical pocket design bearing in sufficient coolant.

The dynamics of a multi disk rotor contacting a non-rotating stator with many degrees of freedom is analyzed experimentally. For this task a test rig is built up and described in the paper. Experimental results for slow run-ups and run-downs as well as orbits and frequency spectra are presented showing synchronous motion as well as backward whirl motion. The results validate the applicability of models with many degrees of freedom for rotor and for stator. A forced modal decoupling method is applied to the MDOF system and demonstrates that in a limited rotation speed regime simple SDOF models for rotor-stator contact are able to sufficiently describe the experimentally observed dynamics.

Rotor–stator rubbing is occasional problem faced by rotating machines especially during startups and shut downs when passing through their critical speeds. The rubbing often occurs in rotating machinery at position with small clearances and can sometimes cause catastrophic breakdown of machine. So it is important to develop reliable tools for rub diagnosis. This paper investigates partial rub occurrence during constant and slightly variable speed operation and try to define vibration diagnosis patterns for its detection with Hilbert Huang Transform (HHT). The HHT is relatively new method which includes Empirical Mode Decomposition (EMD) and the Hilbert Transform. Diagnostic tool is tested on laboratory test rig for rotor to stator contact dynamics research at two different rotor operating conditions i.e. without rotor–stator contact and with partial rotor–stator rub. Measurements were performed with non-contact eddy current displacement sensors. Results are presented in the shape of HHT spectra of Intrinsic Mode Functions (IMF) and are compared to classical FFT spectra and spectrograms based on Short Time Fourier Transform (STFT). Rotor orbits are also presented to additionally verify rubbing condition.

Multi-component extraction is an available method for fault vibration signal analysis of rotary machinery, so a new method for rubbing fault diagnosis based on variational mode decomposition (VMD) is proposed. VMD is a newly developed technique for adaptive signal decomposition, which can non-recursively decompose a multi-component signal into a number of quasi-orthogonal intrinsic mode functions. VMD is then first applied to detect multiple rubbing-caused signatures for rotor-stator fault diagnosis via numerical simulated response. A comparison has also been conducted to investigate the effectiveness of monitoring the rubbing-caused signatures by using VMD, empirical wavelet transform (EWT), EEMD and EMD. The analysis results of the rubbing signals show that the multiple features of these signals can be efficiently extracted with the VMD.

In turbo-engines the sudden increase of mass unbalance, due for example to a blade-loss, can generate rotor-stator contacts in different zones of the motor architecture: turbine blade/flange, centrifugal compressor wheel/shroud, seals, stop-end bearing. The aim of this paper is to analyse the influence of such rotor-stator interactions on the dynamic behaviour of two types of academic rotors. Several contact laws combined with smoothing methods are investigated in order to implement them in rotor dynamics models. The full annular rub and a finite impact series in forward whirl are exhibited.

Structure vibration response of rotor-bearing-case-installation section system caused by sudden unbalance load due to blade out of the high-speed flexible rotor has been the focus in the field of aero-engine development. This paper deals with the sudden unbalance response characteristics of a high-speed flexible rotor during a blade out event. To reveal the unbalance response influence of blade released mass and rotating speed, a flexible rotor-damping support-protection support system is constructed using LS-DYNA. This model consists of rotor, disk, single blade, protection support and damping support. The diameter of the disk is designed to be 196 mm and the mass of a released blade is 33 or 66 g with two different widths. It can be seen from the shearing stress results that the rotor shaft is twisted off at a weak key point. After single blade out, rubbing between rotor and protection support is classified as the following two stages. It is observed that as single blade released out, higher rotating speed and larger unbalance mass lead to more violent vibration and cause more severe impact force transmitted to bearing and installation section. They can also lead to less stay time during the first stage mentioned above. To verify the results of simulation, blade out tests are carried out on a high speed spin tester. Severe vibration happens on the support base in the course of shutting down, but rotor has no apparent damage in single blade out test with small mass and low speed. However single blade out event with larger mass and higher speed can cause more danger. Large and long-term unbalance on protection support-support base-protection ring-hanger makes the system vibrate severely and these can lead to break of the support base and twist of the rotor shaft. It can be concluded that the results of tests turn out to be agreed well with those of simulation analysis.

One option to increase efficiency of turbomachines is the reduction of leakage losses by using and improving sealing concepts with minimized clearance, accepting the risk of rub of rotors to the seals under operational conditions. Beside wear and subsequently increased leakage losses, rub affects rotordynamics of turbomachines with reaction to fluid dynamics again. Brush seals consider these issues and combine excellent leakage characteristics with compliant behaviour under rub conditions. While brush seal related topics like leakage characteristics, fluid dynamics, design issues and wear were investigated in detail during the last decades; publications concerning impact of brush seals on rotordynamics are more or less rare. The following paper deals with the influence of light rub of rotors to brush seals on rotordynamics. Light rub implies frictional heat, partly entering the shaft and leading to thermal expansion. A not uniform heat distribution of the shaft through eccentric rub can lead to thermal bending of the shaft causing further growth of shaft deflection. This phenomenon is known as Newkirk-Effect also referred to as spiral vibrations because of the spirally shaped shaft orbit in rotating coordinates. Depending on thermal parameters and damping in particular, stable and unstable operating areas can be identified. In extension to existing steady state descriptions this paper pursues a transient consideration of spiral vibrations due to rub to brush seals. The objective is a better understanding of the magnitude and implications of spiral vibration and its possible prediction during run-up and rundown. For that purpose the power loss due to rub is taken into account and a rotordynamic analysis is conducted for a simple rotor model consisting of a bulky shaft rubbing to a brush seal supported by rigid bearings. In a first step a run-up with a constant low drive torque is considered with focus on behaviour at stability limit near first eigenfrequency.

Floating ring annular seals represent one of the solutions for controlling leakage in high speed rotating machinery. Low leakage is ensured by the small radial clearance. Under normal operating conditions, the ring must be able to “float” on the rotor in order to accommodate its vibration. Impacts between the carbon ring and the rotor are prohibited. The present paper introduces a non-linear numerical model of gradually increasing complexity. A first version of the model has two translation degrees of freedom and describes planar trajectories of the floating ring. It uses transient hydrodynamic and Coulomb forces. The next step is including impacts between the rotor and the carbon ring and between anti-rotation pins and the ring casing. A rotation degree of freedom must be also added. The results show that for a given rotation speed and with increasing amplitude of the rotor whirl, the trajectory of the floating ring seal changes from uniform whirl to quasi-periodic before triggering contacts in the main seal. The impacts of the anti-rotation pins with the ring casing completely modify the dynamic response.

To analysis the effects of clearance on labyrinth brush seal in a gas turbine, the leakage flow characteristics and distribution on rotor surface, bristle pack free height and fence height were numerically analyzed using Reynolds-averaged Navier-Stokes (RANS) solutions coupling with a non-Darcian porous medium model. The reliability of the present numerical method was proved, which were in agreement with the experimental and numerical results from literatures. Five sizes of bristle pack tip clearances (0, 0.1, 0.2, 0.3, and 0.4 mm) under different pressure ratios, and other operating conditions were utilized to investigate the clearance modification on the labyrinth brush seal dynamic behaviors which were compared with the corresponding labyrinth seal. The results indicate that at the same pressure ratio the increase of clearance size between the bristle pack and rotor surface will lead to leakage rate rise. More over, at the same clearance and pressure ratio the flow fields in labyrinth brush seal are more complex than labyrinth seal, and the leakage rate of labyrinth brush seal is significantly less than labyrinth seal. The leakage flow pattern, static pressure, and velocity in the labyrinth brush seal and labyrinth seal was also illustrated.

The aerodynamic analysis of a non-contacting finger seal is performed on the basis of an equivalent 2-DOF model of a padded finger. Gas loads acting on flexible fingers are nonlinearly dependent on the radial clearance and are evaluated by calculations based on the 2D Reynolds equation for a thin gas layer. The computations are conducted by using of the in-house nonlinear FEA program. Finger stiffness coefficients are calculated by using the previously developed finger “beam” model. The dynamic response of the fingers to rotor’s radial excursions of model type is evaluated. The stability of the fingers in the gas flow is also assessed. The obtained results allow us to conclude that the radial adjustment of the seal to the rotor’s radial excursion is possible in case of a circumferentially convergent operating gap under the pads. Otherwise the developing suction force can drop the fingers towards the rotor surface and cause an undesired contact between the seal and the rotor.

One of the causes of rotor instability is the damping of the rotating parts of the system. Its de-stabilizing effect can be counteracted only by introducing a suitable non rotating damping, with the instability threshold increasing with increasing ratio between non rotating and rotating damping. The aim of the present paper is showing that support anisotropy tends to increase the stability of the system, an effect here shown to take place in both cases of viscous and hysteretic damping. A heuristic explanation of the stability increase due to support anisotropy can be given considering that anisotropic supports usually cause the orbits to be elliptical, which increases energy dissipation due to rotating damping. Actually, no increase of the instability threshold was observed in a case in which the orbits remain circular in spite of the anisotropy of the supports.

This work presents the evaluation of periodic stability of rotating machinery and its sensitivity analysis. The stability criterion is based on the characteristic exponents or more generally the eigenvalues of the monodromy matrix of the periodic system following Floquet’s Theory. Parametric sensitivity of the stability is formulated to provide a methodology for robustness in rotating machinery analysis and design. The problem is formulated for a generic rotating dynamical system having periodic coefficients and demonstrated on a helicopter blade in forward flight and on a cracked rotating shaft.

The finite element method with a nonlinear film force model is applied to investigate the dynamic response and instability of a steam turbine rotor-bearing system. The nonlinear governing equations of motion with a large number DOF are solved by employing the Newmark method. The Budiansky-Roth criterion is developed to determine the threshold speed of the instability of rotor-bearing system during run-up and run down. The simulations manifest there are two different threshold speeds of the instability during run-up and run-down, which is referred to as hysteresis phenomenon associated with the instability of rotor-bearing system. The effects rotor damping on the dynamic response and instability of the steam turbine rotor-bearing system are numerically examined. It is shown that the location and width of the hysteresis loop are greatly influenced by rotor damping.

Stability of lateral rotordynamic modes is an essential consideration during design and acceptance testing of rotating machinery. Experimental modal analysis (EMA) can be used for assessment but is in practice very difficult in actual operating conditions, principally due to the challenges of quantifying the excitation force. Operational modal analysis (OMA) does not require measurement of excitation forces and therefore presents significant logistical advantages over EMA. The background and theoretical concepts of OMA are presented and its use is demonstrated on a 500 kW centrifugal compressor. Measurements performed during commissioning at first raised suspicion that the stability was marginal. However OMA was used to confirm that the first forward mode of the compressor was actually stable and the measurements were reconciled with the predicted behavior. The results show that the assessment of stability margins of rotating machinery can be measured with OMA using only proximity probe data acquired during normal operation.

This paper deals with the motion of a gyroscopic exercise tool called as the ‘Power Ball’. This gyroscopic exercise tool, which is used to train the hand muscles utilizes a gyroscopic effect caused by a whirling motion of a high speed rotating body. When the input motion is applied to the outer casing, the internal rotor spins at thousands of rpm whirling with a slow precession motion. This paper shows the dynamic model of this tool considering the contact/separation conditions and the sliding motion between the rotor and the case. Two kinds of motion are observed in a numerical simulation. In this paper, stability analysis of motion of the tool is carried out based on the energy balance between the input and output energy in the tool.

This work focuses on the effects of the flexible supporting structures and on the bearing interaction caused by their elastic deflection on the whole rotor-substructures system [

1

]. More particularly, a careful theoretical and experimental analysis is performed to understand how the supporting structures influence the rotors behaviour [

2

,

3

] through the actions of the machine bearings. To this end, this study considers a model of the whole rotating machine [

4

], taking into account the coupling of the dynamic behaviour of the different system components. The whole FEM model has been implemented in the ANSYS [

5

] simulation environment. The main goal of this research, is to offer an optimal balance between efficiency and accuracy allowing the modelling of the real physical complex system and simultaneously the reduction of calculation times. The whole analysis has been developed and validated in cooperation with General Electric S.p.A. which provided the technical and experimental data related to some tests recently performed in Massa-Carrara (Italy) on a benchmark turbocompressor machine.

The dynamic behaviour of the supporting structure of rotating machines can significantly affect the shaft-train vibration. When a foundation natural frequency is close to the machine operating speed, the forces caused by even almost negligible malfunctions can cause very high vibration levels. This paper shows a case history in which a natural frequency of a generator case, and that of an auxiliary shaft, significantly affected the dynamic behaviour of a power unit. The existence of these critical natural frequencies has been confirmed through specific experimental tests, the results of which are shown in the paper.

The accurate modelling of the complicated dynamic phenomena characterizing rotors and support structures represents a critical issue in rotor dynamics field. A correct prediction of the whole system behavior is fundamental to identify safe operating conditions and to avoid instabilities that may lead to erroneous project solutions or possible unwanted consequences for the plant. Although a generic rotating machine is mainly composed by four components (rotors, bearings, stators and supporting structures), many research activities are often more focused on single components rather than on the whole system. The importance of a combined analysis of rotors and elastic supporting structures arises with the continuous development of turbo machinery applications, in particular in the Oil and Gas field where a wide variety of structurally optimized solutions with reduced weight on off-shore installations or modularized turbo-compression and turbo-generator trains, requires a more complete analysis not only limited to the rotor-bearing system. Complex elastic systems, in some cases, strongly affect the entire shaft line rotor dynamic response such as mode shapes, resonance frequencies, unbalance response and critical speeds. The aim of the study is a development of a new efficient methodology based on FEM approach to model the complete rotating machinery systems (rotors, bearings, stators and supporting structures), by means of appropriate transfer functions matrix. Taking advantage from the matrix of transfer functions H(ω) obtained through PSD analysis, the baseplate dynamic behavior can be timely and CPU efficiently computed, avoiding computationally expensive harmonic sweeps. The appropriate usage of undocumented ANSYS command ‘TFUN’ has been pursued in order to extract the required components of the transfer functions matrix at the bearing location. With such a solution the full dynamic interaction between the system components was accurately accounted. The outcome of the new methodology was successfully tested in a real field issue where evidences of structure to rotor interaction emerged at the proximity probe measurement during machine start-up.

This paper is intended to present potential considerations for engineers and scientists to assess bearing pedestal degradation for a category of Low Pressure (LP) steam turbines. Structural degradation is assessed primarily comparing measured rotor frequencies of the nominal and the degraded configurations because pedestal stiffness plays an important role in the determination of rotor system natural frequencies. An electrical shaker was applied to obtain frequencies for the components tested. The results indicated that among the two rotor modes (U and S modes that are defined in Sect.

2

) tested, S-mode frequency corresponding to the conical mode consistently indicated strong correlation to pedestal degradation. Additionally, measured pedestal stiffness data corresponding to the S-mode complemented these findings. 72 shaker tests were performed to date on LP bearing steel pedestal designs of different manufacturers and the conclusions derived for pedestal degradation are the same regardless.

This paper illustrates a method of modeling and experimental characterization of resilient supports for turbomolecular pumps at component level. A dedicated test bench has been designed and realized. The modeling approach (Kelvin’s and Wiechert’s model) along with the characterization procedure aimed to evaluate the stiffness and damping introduced by the support at varying of pump spin speed are illustrated.

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.

This paper presents a numerical model of how a visco-elastic support affects the dynamical response of a 42 MW Kaplan turbine that is experiencing resonance problems. The supports are placed between the bearing bracket and the supporting concrete structure. Since the supports are nonlinear, the nodal displacements are solved using a Runge-Kutta time integration method where the visco-elastic supports are implemented as a nonlinear force. To reduce calculation time the number of degrees of freedom of the rotor model is reduced using the Improved Reduction System. Excitation of the system is implemented as a stationary force in the runner with varying frequency. The resulting nodal displacement from the transient simulation is then compared to the system simulated without the supports to show how the machine dynamics are affected. The simulations show that the visco-elastic supports efficiently reduces the displacements in the lower vibration modes. The reduced vibration levels should decrease the probability of resonance problems occurring when running at operating speed.

Modeling for rotor-bearing-foundation systems is one of the key bases for efficient dynamic analysis in the field of turbomachinery. However it should be noted that the term foundation structure should be interpreted depending on the purpose of the rotating machine. Thus in heavy power machinery it is usually a massive fixed base structure made of steel frames and concrete e.g. for power generating turbine units, but in aerospace it is relatively light and flexible beam type wing for aircraft engines. Since rotating machinery such as modern aircraft engines usually designed, marketed and sold for the most part based on analytical and numerical predictions, methods to incorporate the foundation influence effect in rotordynamic calculations are very important. The aim of the current paper is to observe recent efficient approaches for foundation structure modeling and to point out contemporary methods used by engineers for foundation structure parameters identification. Further in the simulation section of the paper simplified models were created in modern FEM software packages in order to demonstrate foundation structure influence on the dynamics of rotor-bearing system and their interaction.

This paper investigates the dynamic behavior of a rotor—bearing system supported by elastic springs. The system itself is made of several Belleville washer springs located circumferentially around the bearing. The standard accepted design criteria for such system are based on the estimation of the stiffness from analytical formulas developed in 1930s under the assumption of radial deformation only on the springs. Theoretically this system should generate low stiffness in comparison to bearing and pedestal stiffness. However the author experience showed that secondary stiffness effects become dominant and introduce additional non-linear stiffness component, what changes significantly lateral response of the system. First, a classic approach based on an analytical 1D solution for radial stiffness is demonstrated with comparison to simulations including also elasto–plastic material behavior. Then the 3D model is introduced to estimate combined radial and shear stiffness. Here the most important finding is that up to now neglected shear stiffness is much higher than the radial one. Also FEA simulations showed high variability of the actual value of the spring stiffness suggesting overall non-linearity and possible hysteresis under cyclic loading. A linearization procedure is outlined in the paper and presented for an example spring configuration from a gas turbine installation. Eventually the combined radial and shear stiffness is implemented in a PGT25 gas turbine model. The real rotor testing in the bunker revealed that the usually neglected shear stiffness of the Belleville washer springs has significantly more influence on vibration profile, than compared to simulation assuming only radial stiffness.

Turbine generator sets (gas and/or steam turbine plus generator) operating at their rated speed under non-steady-state conditions normally show transient changes of shaft and bearing vibration. These vibration changes are generally associated with thermal variations of the rotor support structure or thermal effects within the rotor shaft line. For the turbogenerator rotor the changes of shaft and bearing vibrations may be due to the increase of rotor field current during initial loading or due to a change of rotor field current during load changes. To achieve that on-site vibration behaviour of the generator rotor is acceptable Alstom has introduced the so-called heat run test in the mid 1960s. As part of the internal factory acceptance tests in the spin pit, the heat run test is carried out after the balancing of the rotor by injecting direct current into the rotor field winding at rated speed and monitoring of the winding temperature and the first order shaft and bearing vibrations.

A new model for analyzing the Morton effect is presented. Previous studies of the Morton effect were either simplified or rigorously detailed requiring huge computational effort. The present work describes the new model which tries to combine accuracy of the model and computational efficiency. Perturbation method was used for the governing equations of the lubrication theory. The averaging method was applied to the equations of motion, facilitating large time steps for the numerical integration process, thus, greatly reducing the computational effort. The estimation of the spectral radius of transition operator was proposed as a convenient indicator for the rotordynamic system’s stability threshold. As a concrete example a double overhung turboexpander supported on 5-pad tilting-pad bearings was considered, which has been previously studied experimentally and analytically by Schmied and others in 2008.

Laborelec is responsible for the follow-up of the vibration behavior of a fleet of more than 100 shaft lines within the power generation division of GDF SUEZ. Vector vibration monitoring of such a large number of units permits to develop a detailed comparison of the vibration behavior of units of a similar type. Nowadays, an important part of that fleet consists of combined-cycle single shaft units. Spiral vibrations, as described already in extensive reference papers (Schmied, Proceedings of the ASME conference on rotating machinery dynamics, 1987; Pennacchi et al. Proceedings of the ISMA conference noise and vibration engineering, 2010; Eckert et al. 7th IFToMM conference on rotor dynamics, 2006; Eckert and Schmied, J Eng Gas Turbines Power 130:012509, 2008) have been measured on a large part of this single shaft fleet, for some even already since commissioning. Due to continuous vector vibration monitoring and extensive measurement campaigns in order to better understand the driving influences behind this phenomenon, a large reference database is available to describe the observed differences of this hot spot behavior (period, modal deformation, limit cycle,…). Although these shaft lines can be considered as identical from a macro-scale point of view, quite various dynamic responses have been measured over the years. In this way, an alternative and interesting image can be sketched of this spiral vibration behavior on large turbomachinery equipment from an operational point of view. This paper will therefore describe the similarities, differences and learning points from specific vibration analysis together with recent field experiences on spiral vibrations measured on single shaft units within the GDF SUEZ fleet.

The phenomenon of vibration vector rotation caused by thermally induced unbalance changes, referred to as the “spiral vibration” (SV), is frequently observed in large rotating machinery. Since the SV is a consequence of an interaction between mechanical and thermal unbalance of the rotor, a set of standard rotordynamic equations must be extended by the additional thermal equation. For the case of rotor deformation caused by a hot spot on a slip ring of turbo-generator a new thermo-elastic model has been formulated. A solution for the thermal mode response of a simplified system has been derived analytically using the non-dimensional form of the thermal equation. This paper provides formulae for stability threshold and spiral period corresponding to the newly developed model of thermal excitation. The presented theoretical results have been adopted in more detailed numerical models and used to effectively extend stability margin of the SV in turbo-generator shaft trains.

Considered here are Nonlinear Auto-Regressive neural networks with eXogenous inputs (NARX) as a mathematical model of a steam turbine rotor for controlling steam turbine stress on-line. In order to obtain neural networks that locate critical stress and temperature points in the steam turbine during transient states, an FE rotor model was built. This model was used to train the neural networks on the basis of steam turbine transient operating data. The training included nonlinearity related to steam turbine expansion, heat exchange and rotor material properties during transients. Simultaneous neural networks are algorithms which can be implemented on PLC controllers. This allows for the application neural networks to control steam turbine stress in industrial power plants.