Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM

The ratio of bearing stiffness to the shaft stiffness has a significant impact on the lower frequencies, mode shapes and, consequently, the whirl orbits. Most works studying crack detection methods in rotating systems use bearings relatively stiff, where the shaft bending is very pronounced. This paper analyzes how the nonlinear effect of the crack in the whirl orbits and the diagnostic forces technique for detecting cracks behave for soft bearings. The results show that the extra loops, very well known in the literature, are not present for the soft bearings. On the other hand, diagnostic peaks were successful in both cases. The efficiency of these methods depends on the mathematical model of the cracked rotor. This work considers the breathing mechanism in formulating the time-varying finite element stiffness matrix of the cracked element, requiring the solution of a set of equations at each time-step. With this concern, two approaches for the solution of the dynamic response are compared: direct time integration method using Newmark’s method and solution of discrete-time state equations. The Newmark’s method requires small time-step for the accuracy of the response, however, the processing time is much smaller when compared to solution of discrete-time state equations.

This paper presents a systematic methodology to diagnose of real life problems thru a combination of traditional vibration analysis and rotordynamic modeling. Additionally, also presents a consistent approach to find reliable solutions and validate them. It addresses the diagnostic of one of four Nuclear Reactor Primary Heat Transfer Pump (PHT) that has been experiencing abnormal vibration over the years. The implemented methodology to diagnostic the high vibrations in the PHT pump is based in a hybrid between measurements and modeling. The first step has been the measurement of vibrations level in the PHT pump when the reactor was in the detention process, which was the only opportunity because the pumps are isolated from the human access when the reactor is operative. In a second step, with the obtained measurement, was developed the FEA (Finite Element Analysis) model in a healthy condition using a proprietary finite element rotordynamic tool named “Heron”. Which is rotordynamic analysis software developed to model and diagnose rotating equipment. At last step, the healthy model was used to implement different kind of failure to reproduce the vibration condition measurement in the PHT pump with high level of vibration. The match between the model with failure and measurement of the PHT pump with high vibrations allows take a diagnostic of the pump. The presented case is an excellent example for the proposed approach due to the difficulty of accessing the pump in operation for measurement and need of a high level of confidence on its solution.

This paper analyzes the performance of wavelet packet transform (WPT) and support vector machine (SVM) based fault diagnostics of induction motors (IMs) at various operating conditions. Four mechanical faults (namely, bearing fault, bowed rotor, unbalanced rotor, and misaligned rotor) and three electrical faults (namely, stator winding fault, broken rotor bar and phase unbalance) are considered for the diagnosis. In addition, two levels of severity of stator winding fault and phase unbalance are also considered. In order to develop the present fault diagnostics, firstly the vibration and current signals acquired from laboratory experiments are decomposed by the WPT via Haar wavelet. A number of useful wavelet features are then extracted from the decomposed signals of different IM faults. For estimating the correct fault type, the one-versus-one multiclass method of the SVM is finally applied by inputting the most suitable features. Here the most suitable features are chosen using the wrapper model of feature selection. The diagnostics is executed and checked for various operational conditions (i.e., the load and the speed) of IM to test the robustness of developed diagnostics. This work is of practical significance as training or testing data are not always available at all motor operational conditions.

The centrifugal pumps (CPs) are most commonly chosen fluid machines for industrial and domestic applications. They constitute vital components to sustain the process flow of the plants, and hence their failure may lead to a significant monetary loss to the plant. Failures in CPs may be due to mechanical faults and/or fluid flow anomalies. In the current work, it is attempted to build an adaptable support vector machine (SVM) based algorithm to identify critical faults, like flow restrictions (with changing severities), impeller cracks, dry run and cover plate faults. Furthermore, co-existence of mechanical and fluid flow faults is studied. Experimentally generated CP vibration data and motor current data is utilized for the fault diagnosis. The classifier parameters are chosen optimally by means of cross-validation method along with grid-search technique, and effective fault feature selection is done using the wrapper model. Furthermore, a comparative analysis on the performance of the methodology for features extracted from three domains, namely: time, frequency and wavelets (wavelet packet transform, time-frequency domain) of the raw signals is presented at a range of CP operating speeds. The analysis results presented that the developed methodology could identify fifteen CP fault conditions successfully based on features from all three domains at all CP speeds.

Vibration in large turbine-generator rotor trains can be diagnosed by recognizing the specific correlated patterns visible in data presented in Bode, polar (Nyquist), shaft centerline, shaft orbit, and frequency spectrum plots, among others. Properly interpreting these data plots requires the recognition of true rotor behavior when affected by various faults. By the authors’ experience, the most prevalent faults seen in practice are the direct and indirect effects of distributed mass eccentricity within individual rotors or across an assembled rotor train. The presence of mass eccentricity leads to various effects of inertia during machine operation (often torque or load dependent), which create the principal graphical data signatures to look for and utilize in diagnostic assessment. The graphical signatures that result from the presence of imposed forces “fighting against” a rotor’s natural inertia are readily and independently recognizable, even when in combination with additional contributors of dynamic vibration such as that caused by resonant responses within critical speed regions, rubs, and bearing/fluid instability. This paper describes and presents typical data signatures in the various types of plots, including examples of shaft bows or other unresolved distributed mass eccentricity on individual rotors, plus examples of rotor misalignment on assembled multi-rotor machines caused from bent or off-square coupling faces and radially offset, misaligned bearings. Furthermore, understanding the most prevalent root causes underlying the diagnostics leads to the recognition of proactive shop strategies to prevent these faults and to substantially improve the probability of a successful startup following a turbine or generator rotor service outage.

The objective of this work is the fault diagnosis in diesel engines to assist the predictive maintenance, through the analysis of the variation of the pressure curves inside the cylinders and the torsional vibration response of the crankshaft. Hence a fault simulation model based on a zero-dimensional thermodynamic model was developed. The adopted feature vectors were chosen from the thermodynamic model and obtained from processing signals as pressure and temperature inside the cylinder, as well as, torsional vibration of the engines flywheel. These vectors are used as input of the machine learning technique in order to discriminate among several machine conditions, such as normal, pressure reduction in the intake manifold, compression ratio and amount of fuel injected reduction into the cylinders. The machine learning techniques for classification adopted in this work were the multilayer perceptron (MLP) and random forest (RF).

The research focuses on fault detection and diagnostics of cracks in a rotating shaft by using the Extended Phase Space Topology approach (EPST). EPST is based on extracting features from the constructed density profile of the system vibration responses. The extracted features are ranked and the optimal set is selected by using mutual information. Finally, an artificial neural network is used as a classifier to distinguish between the different shaft conditions. The method was implemented on a laboratory scale rotor test rig that was seeded with two damage conditions produced by a crack propagator. As will be shown, the study demonstrates that the density distribution provides rich information about the shaft structural condition. Furthermore, results show that the innovative EPST procedure has outstanding performance in shaft crack detection with minimal knowledge about the dynamic responses of the system.

Large hydrogenerators are rotating machines of vertical assembly, equipped with tilting pad journal bearings, operating at subcritical speeds (80 to 200 rpm). The nominal power of these machines may reach 700 MW, what makes vibration-based condition monitoring a compulsory task. Several international standards are applicable to vibration monitoring of hydrogenerators. However, their condition assessment criteria are grounded on measurements performed on a wide set of hydrogenerators, with power varying from 1 to 700 MW and speed in the range 60 to 1800 rpm. As result, some limits are excessively tight while others are too much permissive. Moreover, experimental observations revealed that the dynamic behavior of these machines might present significant short and long-term changes, many times with no apparent reasons. Part of this behavior is due to the lack of a defined radial static load in the journal bearings, as well as to external agents, like generator electromagnetic field or seasonal variations of bearing cooling water temperature. All these aspects make difficult the using of statistical pattern recognition. It is necessary a better understanding of the influencing mechanisms of the vibratory behavior of these machines, to differentiate normal changes from those originated by incipient faults. This paper proposes the using of a model-based approach to overcome these problems and exemplifies this using on a set of 700 MW hydrogenerators. The results obtained indicated that even simplified models might present satisfactory results, especially when models performance are improved using additional information collected by the monitoring system.

The induction motor (IM) may lose their normal efficiency and finally fail due to chronic mechanical or electrical faults or both. For the prevention of failure, the early detection of these faults is necessary. The vibration and current signals are measured and collected for varying speeds and load conditions of IMs from an experimental laboratory test rig. Experiments are conducted for four different mechanical fault conditions and five electrical fault conditions including one intact condition. The identification of fault predictions is studied by considering of all mechanical faults, electrical faults and no fault condition. The one-against-one Multiclass-Support Vector Machine Algorithms (MSVM) with radial basis function (RBF) kernel has been trained at various operating conditions of IMs and predictions performance is presented. Two MSVM algorithms, C-SVM and nu-SVM, are used for the investigation. The RBF kernel parameter (gama) and MSVM parameter (C and nu) are optimally selected by the Genetic Algorithm (GA) for better performance for each case. Prediction performances are presented for different speeds and load conditions.

In the modelling and analysis of turbine generator systems, bearing and coupling dynamic parameters are considered as the major unknowns. In the past, practitioners of rotor dynamics have modelled coupling as having speed independent stiffness and damping parameters that lead to modelling error, due to the fact that the amount of misalignment depends upon different modes of excitation. In this article, an identification algorithm has been developed for simultaneous estimation of the speed dependent bearing and coupling dynamic parameters along with residual unbalances. Lagrange’s equation is used to derive the equations of motion of the system in generalized coordinates and least squares technique is used to develop identification algorithm. The novelty of the present identification algorithm is the estimation of speed dependent coupling dynamic parameters along with speed dependent bearing dynamic parameters. Numerical experiments have been performed for a simple rotor train model to illustrate the developed algorithm. To check the robustness of the identification algorithm, measurement noise has been added in numerically simulated response. Well agreement in the estimated parameters is observed for a different level of measurement noise.

This paper proposes two modifications in a classification method for unbalancing fault severity analysis in rotating machines based on the unbalancing mass force. The unbalancing severity was categorized into three severity levels, namely High (H), Medium (M) and Low (L). The feature vectors used information from discrete-time Fourier transform (DFT), kurtosis and entropy from the vibration signals. Similarity based Model (SBM) and Kernel discriminant analysis (KDA) techniques were applied in order to evaluate the feature discrimination and reduce the input feature space. All these techniques were tested in a random forest classifier. Test results indicate that non-linear transformations to the feature space combined to random forest can further improve the classification of unbalancing severity defect, by reducing the feature space dimension from 31 to 6.

When diagnosing the vibration of a rotating machine flexibly supported by vibration isolating material, the natural frequency of the rigid body mode of the machine must be considered, in addition to the natural frequency of the rotating shaft. There are two kinds of vibration isolating materials; one has a fixed spring constant, giving it the characteristic of a linear spring, and the other has nonlinear characteristics in which the spring constant varies with the mass of the machine. When the machine is supported by a linear spring, since the natural frequency varies depending on the mass of the machine, avoiding resonance requires optimal setting of the rotation speed or selection of an appropriate vibration isolating material for the equipment to be used. Meanwhile, some nonlinear springs have constant natural frequencies even if the mass of the machine changes. As the mass of the machine increases, the spring constant also increases. Selection of such a vibration isolating material is easy, because the resonance frequency is known in advance. In this study, we analyze the vibration of a rotating machine flexibly supported by vibration isolating material. Vibration analysis was carried out on a simple model of a rotating machine supported by a linear spring or a nonlinear spring. Subsequently, the experimental equipment was manufactured and numerical calculations were performed by using the derived numerical model.

Gears are the main components of power transmissions and are subjected to high cyclic load regime which can lead to premature fracture of the gear teeth. In order to prevent such events, research on gear condition monitoring and fault diagnostics techniques have received considerable attention. Machine learning (ML) applications have been widely combined with vibration measurement and analysis techniques for fault diagnostics in gearboxes and the majority of current techniques rely on experiments to generate training data. Despite the recognized advantages of using simulated data to train ML classifiers, this approach is still not a widespread practice. This paper proposes a simulation-driven ML framework to estimate the crack size in a gear tooth using simulated vibrations signals. Firstly, a 6-degrees-of-freedom model of a one-stage gearbox was developed to simulate the dynamic behavior of a cracked pinion. Secondly, a sample with 900 simulated vibration signals was generated considering 4 different crack sizes in the pinion tooth. Thirdly, the features of the vibration signals were extracted using 20 statistical indicators and, then, the extracted features were used to train and test 4 machine learning classifiers. Several performance evaluation metrics were computed, and the performance of the ML classifiers was compared and discussed. It was shown that the Decision Tree Classifier (DTC) performed best in the identification of small crack sizes regardless of the random selection of the training subsample.

Diagnostic tasks on industrial machinery can sometimes be dealt basing only on previous experience with successful model based identification techniques. This may be required when necessary time and resources for complete diagnostic analysis are not available. Some examples of machines affected by malfunctions that have been more or less successfully analyzed, often without resorting to machine specific models, are presented. Journal ovalisation in a HP-IP steam turbine was identified in the first example, the vibration changes in a LP steam turbine could be attributed to coupling misalignment and to a loose last stage blade of the shaft in the second example. Rubs and thermal bow combined to axial shaft expansion restriction could explain the severe vibrational behavior of a steam turbine that prevented its operation in a third example. The abnormal noise of a vertical shaft generator of a hydroelectric power plant was attributed to a structural resonance excited by electromagnetic forces in a third example, where the diagnostic process was completed by validating the complex excitation mechanisms with simulations.

This paper presents the approach adopted by ISO in the ISO 13373 series for machinery diagnostics. A step-by-step flow chart approach with fault tables and examples has been adopted in the ISO 13373 series. The paper discusses the diagnosis of common faults in rotating machines including installation faults and bearing faults. Diagnosis of particular machines including gas and steam turbines, fans and blowers, hydraulic machines and electric motors are discussed. The success of this standardized diagnostic approach in field applications is illustrated through many field examples.

Measured and simulated orbits of the rotor deflection and bearing forces are applied to understand and separate the effects of multiple, simultaneous errors. Hereto, the paper firstly defines a clear terminology which is mandatory when dealing with multiple errors. The physics and mathematical descriptions of several errors are summarized and illustrated for the Jeffcott rotor model. Furthermore, a short introduction to orbit dynamics is given including force orbits.Based on these fundamentals, the authors present the theoretics of an online roundness error identification method. This method uses a Fourier decomposition for reconstruction the different components. One example recorded at an academic rotor test rig proves these methods.

Rotating machines are widely used in industry. Unforeseen machine failures affect production schedules, product quality, and production costs. Therefore, condition monitoring of rotating machine can play an important role in machine availability. There is a growing number of methods for Machine Condition Monitoring (MCM). Yet, the performance of these methods is limited by the massive amounts of data need to be collected for MCM. This work proposes a computational method which can greatly reduce the high dimensional vibration dataset to a set of compressively-sampled measurements using Compressive Sampling (CS). Then, to learn fewer features from these compressively-sampled measurements we propose an effective multi-step feature learning algorithm that combines the advantages of Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Canonical Correlation Analysis (CCA). Finally, with these learned features, we use multi-class Support Vector Machine (SVM) to classify machine health conditions. Experiments on a roller element bearing fault classification task based on vibration signals are used to evaluate the efficiency of the proposed method. The most obvious finding to emerge from this study is that we are able to achieve high classification accuracy even from highly reduced vibration signal measurements. Moreover, the efficiency of our proposed method outperforms some recently published results. The proposed method offers better accuracy and has lower costs in time and storage requirements.

The rubbing between rotor and stator often occurs in rotating machinery at position with small clearances and can cause unexpected machine downtime. Therefore, it is important to develop trustworthy tools for rub detection. As the rubbing process is nonlinear this paper beside conventional Fourier transform and Hilbert Huang Transform (HHT) also considers potential of Teager-Huang transform (THT). This approach is based on, empirical mode decomposition (EMD) and Teager Kaiser energy operator (TKEO) technique. First, the original vibration signal is decomposed into Intrinsic Mode Function (IMF) components by using Empirical Mode Decomposition (EMD), and then Teager energy operator is applied to estimate the instantaneous amplitude and instantaneous frequency of each IMF component, so the time-frequency distribution of the analyzed signal is obtained.Diagnostic tool is tested on laboratory test rig at two different rotor operating conditions i.e. without rotor–stator rubbing and with partial rotor–stator rub. Measurements of rotor lateral displacements are made using non-contact eddy current displacement sensors.

Bearing failures not only increase the cost due to production loss and need for repair or replacement, but also threaten the personnel safety. Manufacturers of rotating machinery tend to adopt new health monitoring services, using regular inspections or embedding sensors for health monitoring systems within each unit. Early failure signs of a bearing defect are usually weak compared to other sources of excitation. Furthermore, fault detection of bearings appears to be more complicated in the case of planetary gearboxes. As a result, a plethora of signal processing tools have been proposed, focusing towards fault detection and diagnosis of rolling element bearings, such as Envelope Analysis through the selection of the filtering band with Kurtogram. Recently, Cyclic Spectral Correlation/Coherence have been presented as powerful tools for condition monitoring of rolling element bearings, exploiting their cyclostationary behaviour. The aforementioned tools perform well under steady speed operating conditions but their effectiveness drops in the case of speed varying operating conditions, which is quite common in applications such as wind turbines and helicopter drive trains. In order to overcome this difficulty, a new diagnostic tool is introduced based on the integration of the Order-Frequency Cyclic Spectral Coherence along a frequency band that contains the diagnostic information. A special procedure is proposed in order to automatically select the filtering band, maximizing the corresponding fault indicators. The effectiveness of the methodology is validated using experimental and real data captured on planetary gearboxes, including various faults with different levels of diagnostic complexity.

This paper presents the results of transmission error (TE) analysis of spur planetary gearboxes using finite element methods. Two subsystem models were established to study changes in the transmission error caused by planet gear tooth root cracks and spalls. The simulation results reveal that a tooth crack gives changes twice in a planet revolution (crack opening and closing against the sun and ring gears, respectively) while a tooth spall only gives a change once per planet revolution (since the spalled flank only contacts either the sun or the ring). Moreover, the effect of a tooth crack has a duration independent of the size of the crack, and varies with the load. The results of this paper could be used directly as a potential approach to diagnose the type of planet gear fault if the TE can be measured directly, or used in simulations of dynamic responses to develop signal processing methods to extract the information from vibration responses.

Light rubs between shaft and stationary parts are one of the most common faults in rotating machines. Sometimes, deposits of carbonized oil may form in the area close to oil-film journal bearings, especially in steam turbines. These deposits may cause the blockage of the available radial clearance between shaft and oil deflectors. In this case light rubs can be generated even starting from rather low vibration levels of the shaft. The friction forces generated by the rubs usually cause a shaft thermal bow and additional synchronous vibrations. Because of the continuous increase of vibration levels and rub-induced contact forces the blocking material can be quickly abraded. This causes a continuous decrease of the shaft thermal bow and vibration amplitudes. Therefore, intermittent onsets of high vibration levels may occur in the operating condition. These fault symptoms are ambiguous and they can make it difficult to diagnose the root cause of the malfunction. This paper shows a case history in which deposits of carbonized oil caused rubbing phenomena, in the area close to oil deflectors, and recurrent temporary peaks of the 1X vibration levels of a steam turbine. A diagnostic method that has allowed identifying the cause of the fault is described. Besides, comparisons between experimental data and numerical results obtained with a diagnostic model-based method are also shown.

The occurrence of spiral vibrations in large rotating machines is not a very common phenomenon. However, this kind of shaft vibration, usually caused by rubs between rotating and stationary parts, may give rise to a rather quick and considerable change of the vibration amplitudes. Some well-known methods can be used to study and simulate spiral vibrations, however, further unconventional techniques have been developed by the authors to analyse experimental vibration data of rotating machines that are affected by this phenomenon. The results provided by these innovative techniques can allow the models used by common investigation methods to be developed and optimized. Moreover, they can also be useful to conceive effective corrective actions that can eliminate spiral vibrations. In the paper, the results obtained by applying unconventional techniques to the analysis of stable and unstable spiral vibrations that affected the dynamic behaviour of a large rotating machine, on which brush seals were mounted, are shown and discussed.

The application of Prognostics and Health Monitoring (PHM) concepts in rail vehicles is a rapidly growing field of research, and extensive efforts are being spent with the aim of improving the reliability and availability of railway systems and of substantially reducing maintenance costs by switching from time-based to event-driven maintenance policies. This paper is aimed at proving that effective PHM can be applied also on already existing rolling stocks. To do this, and focusing on bearings of the traction system, a prototype monitoring system, described in the paper, was developed and installed on a E464 locomotive. This regional train locomotive class, despite being recent since they were built between 1999 and 2015, is not equipped by any monitoring system for the bearings. The bearings have been monitored for about three years of service, during which the locomotive has undergone to a major maintenance and all the bearings of the traction system has been replaced. This allowed to examine them and to assess if damage indexes corresponded to actual faults. A huge amount of vibration data has been collected and it was possible to assess that the overall system cannot be considered as in stationary operation, neither when the train speed is constant nor when the same track is travelled. Many different techniques have been developed and tested with the aim of detecting bearing damages, considering that fault signals are heavily masked noise. The results are here described and it is shown that the introduced fault indexes are able to monitor the damage evolution in non-stationary conditions.

The optimal filtering of cyclic transients is a major issue in machine diagnostic. As these components are typically associated with incipient faults, their enhancement improves fault detectability and identification. This paper proposes an optimal linear-time-invariant filtering that enhances cyclic transients in the general scenario of a non-steady operating regime. The proposed solution is based on an angle-time cyclostationary modeling of the signal and the noise, contrary to the widely adopted “spectral kurtosis” which assumes the stationarity of the noise. The proposed approach is investigated and compared with the spectral kurtosis on synthetic and real-world vibration signals captured from a helicopter engine operating under nonstationary regime.

Sensor detachment are very common in aeronautic applications wherein equipment operate under very high power and severe environmental conditions. The effect of such defects is detrimental for health monitoring which requires an accurate vibration measure and, therefore, their detection is of high practical importance. This paper investigates the effect of accelerometer faults on the measured vibrations and proposes a two-step methodology to detect their presence using the signal itself. The first step consists of a prewhitening step which has for aim to remove the deterministic part of the signal. The second designs a relevant asymmetry indicator, namely the outlier counter indicator, able to detect the presence of an attachment fault. The efficiency of the proposed methodology is demonstrated on real vibration signals acquired from an aircraft engine gearbox in healthy and faulty sensor cases.

During the commissioning of a diesel hydrotreating unit, high frequency vibration was detected on the Hydrogen makeup compressor, causing machine shutdown and alarming levels of vibration on the piping system. The high frequency components – concentrated between 11× and 15× the compressor speed – were present even during no-load operation and reached values around 3 to 4 times the fundamental frequency amplitude. The high frequency made impossible the improvement of the piping by inclusion of supports. Pressure pulsations, initially believed to be the most likely root cause, were measured and did not show any abnormal values. The measurements ultimately showed that the compressor itself seemed to be the main source of the high frequency. The crankshaft’s second torsional frequency and flywheel’s first bending mode were changed by redesign of these elements, which also showed no positive result. Several further tests were carried out in order to assess the main cause of the vibration. Spectrum analysis during startup and shutdown, PxV diagram evaluation and bump tests finally revealed that a complex interaction between two crankshaft torsional natural frequencies and two structural natural frequencies were the cause of the problem.

Rigid-body resonances used to be the only known vibration phenomena to occur in washing machines. However, lately there have been unexpected incidences of excessive, self-destructive vibrations. It is not clear how these incidents can be explained and reliably prevented. It is presumed that design changes evoke or shift vibrational phenomena which did not occur in the operating speed range of previous machines. Rotordynamic theories might be a suitable explanatory approach for these effects. However, since these effects have yet not been an issue, rotordynamic theories have never been applied to washing machines, even though they are obviously a rotor system and effects are well known for other applications. This paper investigates and highlights rotordynamic effects in frontloaders with a horizontal axis of rotation. To do so, a numerical multi-body model is utilized for dynamical analysis. Potential causes for rotordynamic effects in washing machines are discussed and included in the model. Numerical analyses of eigenvalues and transient displacements show several rotordynamic effects, their rough speeds and their dependency of different parameters. It is discussed how likely each effect is to shift into the operating speed range because of design changes, and thus how likely it is to become a threat. This gives a supplemented overview of the dynamic behavior of washing machines.

Rotors are crucial components of machinery, widely used in different areas of industry, as compressors, automotive transmissions, wind turbines and others. The development of accurate computational models able to aid the project phase of rotating machines is essential to drop tests and prototypes costs and to reduce processing time consumption, with good performance in predicting the dynamic behaviors of rotor-bearing systems. The present work studies the Laval Rotor modeled with a five-degrees-of-freedom decentered disc subject to rotating unbalanced force and combining radial and thrust loads. The rotor is supported on two ball bearings with angular contact under elastohydrodynamic (EHD) lubrication. Although these bearings are identical, they are under different loads due to forces distribution, being, consequently, characterized separately. In order to obtain stiffness and damping equivalent parameters for each bearing, in axial and radial directions, an optimization is carried out, integrating the dynamic equilibrium of the bearings’ spheres with the transient multi-level algorithm solution of EHD equations. Further on, a lumped parameter model of the rotor is analyzed. The shaft inertia is assumed negligible, and its stiffness matrix is obtained using influence coefficients. The dissipative forces approach considers proportional structural damping. As consequence of the disc decentered position, a gyroscopic component is present in the system. The nonlinear bearings reaction forces are included in the model as external forces and the complete system of equations is solved in time domain, enabling the analysis of rotor and bearing responses. Finally, the fundamental frequencies of the complete system are obtained.

Rotating systems operating in different foundations structures can present distinct dynamic response. In case of a compliant foundation, interaction between machine and its supports leads to a more complex system with additional degrees of freedom. These degrees of freedom introduce new natural frequencies and vibration modes for the system. When these foundation-induced modes are in the rotor operating range of frequency, a serious problem may arise, since a machine cannot be tested for every different foundation type expected in industry environment, especially in preliminary design phase. Furthermore, foundation replacement or adaptation are costly operations. A significant improvement in machine-foundation compatibility is possible by the introduction of some compensation in machine to change these additional critical frequencies. Therefore, this paper proposes a compensation method for foundation effects through finite element analysis and shape optimization. An optimization is used to find a compromise between minimum mass increase and manufacturing time to ensure a low cost shape, as a result the cost of machine adjustments is reduced. The algorithm is designed to be simple enough to run on cheap micro-controllers. Consequently, the complete system can be embedded in the machine for a negligible amount of its total cost. Simulations’ results show the method as effective in compensating the influence of foundations with minor loss of precision due to simplifications required to make the algorithm less computational intensive than a full-fledged solution designed to run in workstations. In this way, the method is promising for future applications in rotating machines present in industrial plants.

This work deals with the nonlinear analysis of a nonsmooth rotordynamic system subjected to friction during contact between rotor and stator. The system consists of a Jeffcott rotor surrounded by a stator, both modeled as linear oscillators with two degrees of freedom each. Impact between rotor and stator is modeled as an elastic interaction, subjected to Coulomb friction. Numerical simulations are carried out using the fourth-order Runge-Kutta method to integrate the differential equations of motion. The contact possibility ensures a nonlinear behavior, which motivates investigations concerning parameters variation, such as: rotating speed, contact stiffness and friction coefficient. Initially, a qualitative space parameter analysis involving these quantities is performed, in order to identify the contact nature (no contact, intermittent contact and permanent contact). Then, bifurcation diagrams are used to characterize the system response dynamical complexity, as a function of the friction coefficient. For some specific parameters sets of special interest, trajectories in state subspaces and Poincare sections reveal a vast dynamical behavior richness, mainly associated to intermittent contact conditions, including the possibility of chaos.

High speed rotating machines usually include such components as rotors, bearings, casings, foundations and are widely used in many industries. However their rotors may all face foundation external excitation problems during machine operation and service. Therefore design engineers are interested in accurate rotor response prediction when support structure is subjected to sudden impact excitation in order to set sufficient clearances and ensure machine safe operation. The problem is relevant for marine engines (gas and steam turbines) for evaluation of their reliable operation for the case when a hull of the ship is exposed to impact from giant sea waves. The paper describes methodology for creation of rotor-bearing-support system for HP steam turbine rotor of a transport marine engine whose support structure was subjected to impact excitation. The impact phenomenon was further studied on the base of developed experimental test rig with a simplified rotor structure mounted on foundation with a flexible suspension system. Two numerical models were used for verification of the experimental results: the model with a simplified rotor representation (massless shaft) on a lumped mass foundation structure and a model with beam type rotor on a lumped mass foundation. Proposed numerical models showed adequate results for rotor response prediction, what was confirmed by similarity of obtained curves for impact excitation coefficients and comparability of rotor disk orbits for experiment and simulation. Experimental testing confirmed that external foundation impact excitation may significantly influence on maximum deviations of rotor disk orbits in comparison with the case of rotor normal operation without excitation. Simulation and experiment results revealed that impact excitation coefficients within the tested range of amplitudes and rotor speeds increased almost linear and were proportional to maximum displacement amplitude measured on foundation. For subcritical and supercritical speeds impact excitation coefficients were close in values and increased faster in comparison with excitation performed for the speeds close to rotor critical speed. Proposed method for model creation and analysis could be further used for rotordynamic simulations of more complicated machines e.g. marine power engines.

Challenging applications, such as re-injection of natural gas and carbon dioxide for the oil and gas upstream market, continue to push centrifugal compressor original equipment manufacturers (OEM) to the edge of their experience working with ultra-high density fluids. Given the uncertainties associated with the machinery design with regards to rotor stability, an increasing number of end-users are requiring stability verification tests to validate the rotordynamic models to reduce the risk of rotor instability issues during operation, as well as the risk of critical speeds with low damping inside the operational speed range at full or partial load conditions. The method of choice for stability tests has been the experimental modal analysis (EMA) techniques. These techniques generally require the temporary installation of an electromagnetic shaker on the compressor’s non-drive end (NDE) to non-synchronously excite the mode(s) of interest. While such EMA techniques have advantages for verification testing, the need for an external exciter does create additional costs and complications that must be managed. A possible alternative to these traditional EMA techniques is to adopt operational modal analysis (OMA) methods, where no external device is needed and the excitation comes solely from the ambient. The use of a OMA technique in a very low density gas (hydrogen) is the focus of this present work, in order to demonstrate the limitation, advantages and applicability of the proposed method.

The dynamics of helicopter main rotor is described by a highly nonlinear equations, and it is responsible to provide the sustentation of the rotorcraft. The representative frequency to this dynamics are associated to different regimes: unstable, periodic, and even chaotic behavior. The system responses are investigate performing several simulations under a set of numerical values of frequency. One important subject is to evaluate the goodness of the prediction of the simulated dynamics. The dynamical analysis is performed by bred vector approach. The breeding technique executes the model with a perturbed initial condition. The difference between the reference and the perturbed dynamics is called bred vector. The procedure can be employed systematically, producing a time series of bred vector. The bred vector magnitude is applied for addressing the predictability of the model, i.e., the degree of confidence from the simulation.

Reciprocating compressors are used in several types of applications, such as gas distribution and refrigeration systems. One of the main causes of failure of these machines are high loads, which leads to large stresses in the crankshaft. In order to study effects of these loads, the dynamic model of a two-stage reciprocating compressor driven by asynchronous and synchronous electric motor was developed. This model is described by a rigid system composed of piston, rod, crosshead, connecting rod and crankshaft. Based on the Newton and Euler equations, the resistive loads acting on the crankshaft are calculated. The mass and the inertia of these components as well as the thermodynamic cycle are parameters for this model. The thermodynamic cycle assumed ideal gas for an isotropic system, a thermal insulation between the gas and cylinder and an instant behavior of the valves. These assumptions are reasonable because the simulated reciprocating compressor operates with compression ratio below two, resulting in the absence of large temperature rates and gradients. Since the resistive forces are cyclic, the torque applied by the drive will also oscillate cyclically, resulting in an oscillation of the angular velocity. The simulation results show that there are great amplitudes of torque due to the high pressure of the compressed gas. In the permanent regime, the loads had a good agreement with experimental data. The study proved to be important in the design and operation of the reciprocating compressor, in order to prevent failure of the crankshaft.

Accommodating inevitable misalignment is one of the couplings main functions and, in order to predict theoretically the effects of this malfunction on machine behavior, it is essential to introduce the flexible coupling model in the system’s equation of motion. Structural analysis of metallic disc coupling is conducted by means of finite element method, in which the flexible disc component is modeled using thin shell formulation, yielding linear coefficients of stiffness due to misalignment. Afterwards, cyclic forces and moments due to restoring effects of the coupling are considered in rotating system steady state response. Couplings reactions inserted in misaligned shafts are assumed to behavior as a composition of harmonic components with frequencies of 1x up to 4x the rotor spin speed. The effect of the disc geometry in the transverse vibrations is investigated for angular and parallel misalignment, based on orbit shapes and full spectrum information.

The vibration of flexible rotating structures has been extensively investigated by the rotordynamics community. The analysis is usually performed via the finite element method using normal mode superposition. However, some interesting features of these structures may be hidden using a modal approach. In this paper, a wave-based approach is used to study the dynamic behavior of flexible rotating structures. Using a wave description, it is straightforward to show that the gyroscopic effect inherent to flexible rotating structures breaks the time-reversal symmetry. This corresponds to an asymmetric wave propagation, i.e., a forward-going wave and its corresponding backward-going pair travel with different wave speeds. In this paper, we show that this feature of flexible rotating structures makes them a natural mechanical circulator. On the other hand, we show that in the case of inhomogeneous flexible rotating structures designed as spectral gap elastic materials, i.e., phononic crystals or locally resonant metamaterials, the rotational speed has a strong influence in the location and width of the band gaps. The mathematical formulation of these problems have been presented by the authors elsewhere. Here, the conceptual aspects of these investigations are discussed under the light of original numerical simulation results.

In some electrical machines, the symmetrical ventilation system design allows airflow axially from the two end sides to the rotor core. Once the rotor core plates are mounted on shaft is necessary to weld ribs, steel beams radially disposed on shaft, to create channels for the airflow to come in between the shaft and rotor plates. In case of shaft material with a poor weldability, instead of welded ribs, it must be used a type of shaft runner mounted with interference on the shaft. Lately, this shaft runner would support the rotating electric machine rotor core. On this concept, the airflow goes through the welded beams on the shaft runner, considering the design and manufacturing with a steel that has good weldability. The interference with which the shaft runner was mounted, affects its dynamic behavior, because when the rotating electric machine runs, the centrifugal forces on its rotor tends to relieve the pressure in the fit between the runner and the shaft. This relief may generates areas in which there will not be contact, which consequently changes the rotor dynamic behavior. This paper proposes a specific calculation routine, based on finite element analysis via ANSYS®, to study the influence of interference fit for the shaft runner on the rotordynamic behavior of the machine.

Complex space missions involving large angle maneuvers and fast attitude control require nonlinear control methods to design the Satellite Controller System (SCS) in order to satisfy robustness and performance requirements. One candidate method for a nonlinear SCS control law is the State-Dependent Riccati Equation (SDRE). SDRE provides an effective algorithm for synthesizing nonlinear feedback control by allowing nonlinearities in the system states while offering great design flexibility through state-dependent weighting matrices. In that context, analysis by simulation of nonlinear control methods can save money and time. Although, commercial 3D simulators exist that can accommodate various satellites components including the controllers, in this paper, we present a 3D simulator and the investigation of a SDRE control law performance by simulations. The simulator is implemented based on Java and related open-source software libraries (Hipparchus - linear algebra library, and Orekit - flight dynamics library), therefore, it can run in a variety of platforms and it has low cost. These open-source libraries were extended in order to solve the optimization problem that is the cornerstone of the SDRE method, a major contribution of the simulator. The simulator is evaluated taking into account a typical mission of the Brazilian National Institute for Space Research (INPE), in which the SCS must stabilize a satellite in three-axis using reaction wheels so that the optical payload can point to the desired target. Two SCS control laws (a linear and a SDRE based) were simulated for an attitude maneuver in the launch and early orbit phase (LEOP), the upside-down maneuver. The results of simulations shown that SDRE-based controller provides better performance.

The present paper is devoted to the modeling of systems comprising a flexible rotor mounted onto an elastic base, undergoing arbitrary rotations. By using a Lagrangian approach, the equations of motion are derived for the coupled rotor-base system, considering finite element discretization for both the base and the rotor. Numerical simulations are performed for a specific configuration of the rotor-bearing system and attitude motion. Results are interpreted to evaluate, both qualitatively and quantitatively, the influence of the base motion and flexibility on the dynamic behavior of the rotor, in terms of unbalance responses. Based on the results, conclusions are drawn, especially in terms of the conditions under which the flexibility of the base is indispensable for accurate prediction of the rotor behavior.