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Symbolic dynamics is a current interest in the area of anomaly detection, especially in mechanical systems.  Symbolic dynamics reduces the overall dimensionality of system responses while maintaining a high level of robustness to noise.  Rolling element bearings are particularly common mechanical components where anomaly detection is of high importance.  Harsh operating conditions and manufacturing imperfections increase vibration innately reducing component life and increasing downtime and costly repairs.  This thesis presents a novel way to detect bearing vibrational anomalies through Symbolic Aggregate Approximation (SAX) in the two-dimensional time-frequency domain.  SAX reduces computational requirements by partitioning high-dimensional sensor data into discrete states.  This analysis specifically suits bearing vibration data in the time-frequency domain, as the distribution of data does not greatly change between normal and faulty conditions. Under ground truth synthetically-generated experiments, two-dimensional SAX in conjunction with Markov model feature extraction is successful in detecting anomalies (> 99%) using short time spans (< 0.1 seconds) of data in the time-frequency domain with low false alarms (< 8%).  Analysis of real-world datasets validates the performance over the commonly used one-dimensional symbolic analysis by detecting 100% of experimental anomalous vibration with 0 false alarms in all fault types using less than 1 second of data for the basis of 'normality'. Two-dimensional SAX also demonstrates the ability to detect anomalies in predicative monitoring environments earlier than previous methods, even in low Signal-to-Noise ratios. / Master of Science

<p>Lubrication and friction of modern rolling element bearings were investigated to develop a physics-based bearing friction model. A test rig was designed and developed to measure the frictional torque of radially loaded rolling element bearings with oil bath lubrication. Deep groove ball bearings and radial needle roller bearings were studied at various loads, speeds and lubrication conditions. Experimental results indicate that bearing friction models currently used in industry can be inaccurate, especially when predicting bearing fluid drag losses. A separate test rig was designed and developed to investigate the lubrication and friction of rolling element bearing cage pockets, as new cage pocket designs could improve bearing efficiency. Cage pocket oil starvation was observed for certain operating conditions, and the starvation was found to correlate strongly with cage pocket friction. In order to better understand friction and lubrication characteristics of bearings, computational fluid dynamics (CFD) models were developed to compare with the experimental results. Fluid motion inside the rolling element bearings was investigated using CFD to determine fluid drag torque of bearing components. Fluid drag torque obtained from CFD and experimental measurements are in good agreement. Results from the CFD models also included pressure distributions over bearing surfaces and fluid velocity near rolling elements, but were limited to global length scales. At the micro-scale, rolling element bearing lubrication and friction is dictated by elastohydrodynamic lubrication (EHL). The radial needle roller bearings and deep groove ball bearings used in this investigation are characterized by line and elliptical contacts, respectively. EHL modeling was therefore developed for line contacts with a strongly coupled fluid solid interaction (FSI) solver. Solid bodies were modeled with finite element (FE) software to incorporate inhomogeneities such as inclusions and surface features which affect EHL pressure, film thickness and friction. Results were used to investigate lubricant film thickness at lubricated line contacts under various operating conditions. This work was further extended to model EHL circular contacts with an FSI approach, combining CFD and FE software. The newly developed FSI EHL model provided critical insights regarding fluid behavior in and around EHL point contacts and fluid properties within the lubricant film. Given the modeling results at the micro and macro scale within the rolling element bearings, a better understanding of bearing friction and lubrication is developed, and supported by experimental data.</p>

Thesis. (M. Tech. (Mechanical Engineering))--Vaal University of Technology / Bearing condition monitoring and fault diagnosis have been studied for many years. Popular techniques are applied through advanced signal processing and pattern recognition technologies. The subject of the research was vibration condition monitoring of incipient damage in rolling element bearings. The research was confined to deep-groove ball bearings because of their common applications in industry. The aim of the research was to apply neural networks to vibration condition monitoring of rolling element bearings. Kohonen's Self-Organising Feature Map is the neural network that was used to enable an automatic condition monitoring system. Bearing vibration is induced during bearing operation and the main cause is bearing friction, which ultimately causes wear and incipient spalling in a rolling element bearing. To obtain rolling element bearing vibrations a condition monitoring test rig for rolling element bearings had to be designed and built. A digital vibration measurement acquisition environment was created in Labview and Matlab. Data from the bearing test rig was recorded with a piezoelectric accelerometer, and an S-type load cell connected to dynamic signal analysis cards. The vibration measurement instrumentation was cost-effective and yielded accurate and repeatable measurements. Defects on rolling element bearings were artificially inflicted so that a pattern of bearing defects could be established. An input data format of vibration statistical parameters was created using the time and frequency domain signals. Kohonen's Self-Organising Feature Maps were trained in the input data, utilising an unsupervised, competitive learning algorithm and vector quantisation to cluster the bearing defects on a two-dimensional topographical map. A new practical dimension to condition monitoring of rolling element bearings was developed. The use of time domain and frequency domain analysis of bearing vibration has been combined with a visual and classification analysis of distinct bearing defects through the application of the Self-Organising Feature Map. This is a suitable technique for rolling element bearing defect detection, remaining bearing life estimation and to assist in planning maintenance schedules. / National Research Foundation; Council for Scientific and Industrial Research

Les roulements soumis à des mouvements oscillatoires et des charges élevées sont nécessaires pour le fonctionnement de nombreux mécanismes industriels (actionneurs, commandes d’avions, machines pour l’usinage, robots, chaînes d’assemblages, …). Ces roulements sont soumis à des pressions de contact locales extrêmement élevées avec des vitesses de roulement faibles qui ne permettent pas une lubrification adéquate des interfaces des premiers corps avec de l’huile. Les essais d’endurance sur les roulements ont permis la reconstitution des courbes de dégradation pendant la vie du roulement. Des analyses des surfaces, effectués à chaque phase de la vie du roulement ont permis aussi bien de suivre l’évolution de la topographie à l’interface entre les pistes et les éléments roulants. D’autre parte, des analyses numériques par éléments finis ont permis d’obtenir des informations sur les distributions des contraintes et des déformations. Le croisement des résultats expérimentaux et numériques a donc permis la reconstruction des mécanismes locaux d’accommodation. Dans le cas d’un roulement oscillant non graissé, les déplacements relatifs et les contraintes sont principalement accommodés aux interfaces des premiers corps en contact, ce qui accélère l’endommagement final du roulement. Dans le cas d’un roulement oscillant graissé, une partie des déplacements relatifs et contraintes est accommodée dans une sous couche qui se forme dans la peau des éléments roulants. Cette accommodation se manifeste par l’accumulation de déformations plastiques qui s’avèrent être aussi à l’origine de l’endommagement final du roulement. L’analyse des surfaces de contact des roulements oscillants graissés montre qu’il se forme, en présence de la graisse et très tôt dans la vie du roulement, une couche (troisième corps graisse/particule et TTS en surface de la piste) qui protège les surfaces en contact. D’autre part, une expertise de roulement ayant fonctionné sur un avion de de type A340 révèle une forte similarité entre ses faciès d’usure et ceux obtenus lors des essais d’endurance, et valide ainsi les mécanismes d’accommodation reconstitués. Enfin, des questions portant sur les effets de la quantité de graisse, du glissement des éléments roulants, et des pauses sur un essai donné sont aussi traitées. / Bearings subjected to oscillatory motions and high loads are necessary for the operation of several industrial mechanisms (actuators, aircraft controls, machining, robots, assembly lines, ...). These bearings are subjected to extremely high local contact pressures with low running speeds, which do not permit adequate lubrication of the interfaces of the first bodies with oil. Endurance tests perfomed on commercial bearings allowed at reconstructing the evolution of the degradation curves during the bearing life. Surface analyses carried out at each phase of the bearing life also allowed at following the evolution of the topography at the interface between the bearing raceways and the rolling elements. On the other hand, numerical analyses, by finite element method, have led to obtain information on the distributions of stresses and deformations. The dialogue between experimental and numerical results allowed the reconstruction of the local accomodation mechanisms. In the case of ungreased oscillating bearings, the relative displacements are mainly accommodated at the surfaces of the first bodies in contact, which accelerates the damage of the bearing. In the case of greased oscillating bearings, part of the relative displacements and stresses are accommodated at the subsurface of the rolling elements. This accommodation mechanism is manifested by the accumulation of plastic deformations which are at the origin of the final degradation of the bearing. The analysis of the contact surfaces of the raceways of the greased oscillating bearings shows as well that, in the presence of grease, a layer (third body mixture of grease and particles, and TTS on the track surface) protects the surfaces of the raceway and thus accommodates the other part of the displacements and stresses. On the other hand, the analysis of an airelon bearing, dismounted from an A340 type aircraft, revealed a strong similarity between its topographies and those obtained during the performed endurance tests, validateing the reconstructed accommodation mechanisms. Finally, questions about the effects of the amount of grease, sliding of the rolling elements, and pauses on a given test heve been discussed too.

Modeling, fault assessment, and diagnostics of rolling element bearings and induction motors were studied. Dynamic model of rolling element bearings with faults were developed using vector bond graphs. The model incorporates gyroscopic and centrifugal effects, contact deflections and forces, contact slip and separations, and localized faults. Dents and pits on inner race, outer race and balls were modeled through surface profile changes. Experiments with healthy and faulty bearings validated the model. Bearing load zones under various radial loads and clearances were simulated. The model was used to study dynamics of faulty bearings. Effects of type, size and shape of faults on the vibration response and on dynamics of contacts in presence of localized faults were studied. A signal processing algorithm, called feature plot, based on variable window averaging and time feature extraction was proposed for diagnostics of rolling element bearings. Conducting experiments, faults such as dents, pits, and rough surfaces on inner race, balls, and outer race were detected and isolated using the feature plot technique. Time features such as shape factor, skewness, Kurtosis, peak value, crest factor, impulse factor and mean absolute deviation were used in feature plots. Performance of feature plots in bearing fault detection when finite numbers of samples are available was shown. Results suggest that the feature plot technique can detect and isolate localized faults and rough surface defects in rolling element bearings. The proposed diagnostic algorithm has the potential for other applications such as gearbox. A model-based diagnostic framework consisting of modeling, non-linear observability analysis, and parameter tuning was developed for three-phase induction motors. A bond graph model was developed and verified with experiments. Nonlinear observability based on Lie derivatives identified the most observable configuration of sensors and parameters. Continuous-discrete Extended Kalman Filter (EKF) technique was used for parameter tuning to detect stator and rotor faults, bearing friction, and mechanical loads from currents and speed signals. A dynamic process noise technique based on the validation index was implemented for EKF. Complex step Jacobian technique improved computational performance of EKF and observability analysis. Results suggest that motor faults, bearing rotational friction, and mechanical load of induction motors can be detected using model-based diagnostics as long as the configuration of sensors and parameters is observable. / text

Condition monitoring of critical machinery has many economic benefits. The primary objective is to detect faults, for example on rolling element bearings, at an early stage to take corrective action prior to the catastrophic failure of a component. In this context, it is important to be able to discriminate between stable and deteriorating fault conditions. A number of conventional vibration analysis techniques exist by which certain faults in rotating machinery may be identified. However, under circumstances involving multiple fault conditions conventional condition monitoring techniques may fail, e.g. by indicating deteriorating fault conditions for stable fault situations or vice versa. Condition monitoring of rotating machinery that may have multiple, possibly simultaneous, fault conditions is investigated in this thesis. Different combinations of interacting fault conditions are studied both through experimental methods and simulated models. Novel signal processing techniques (such as cepstral analysis and equidistant Fourier transforms) and pattern recognition techniques (based on the nearest neighbour algorithm) are applied to vibration problems of this nature. A set of signal processing and pattern recognition techniques is developed for the detection of small incipient mechanical faults in the presence of noise and dynamic load (imbalance). In the case investigated the dynamic loading consisted of varying degrees of imbalance. It is demonstrated that the proposed techniques may be applied successfully to the detection of multiple fault conditions. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2004.

Condition monitoring of critical machinery has many economic benefits. The primary objective is to detect faults, for example on rolling element bearings, at an early stage to take corrective action prior to the catastrophic failure of a component. In this context, it is important to be able to discriminate between stable and deteriorating fault conditions. A number of conventional vibration analysis techniques exist by which certain faults in rotating machinery may be identified. However, under circumstances involving multiple fault conditions conventional condition monitoring techniques may fail, e.g. by indicating deteriorating fault conditions for stable fault situations or vice versa. Condition monitoring of rotating machinery that may have multiple, possibly simultaneous, fault conditions is investigated in this thesis. Different combinations of interacting fault conditions are studied both through experimental methods and simulated models. Novel signal processing techniques (such as cepstral analysis and equidistant Fourier transforms) and pattern recognition techniques (based on the nearest neighbour algorithm) are applied to vibration problems of this nature. A set of signal processing and pattern recognition techniques is developed for the detection of small incipient mechanical faults in the presence of noise and dynamic load (imbalance). In the case investigated the dynamic loading consisted of varying degrees of imbalance. It is demonstrated that the proposed techniques may be applied successfully to the detection of multiple fault conditions. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2004.