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The subject of this thesis is about the balancing of large flexible rotors which exhibit mixed modal characteristics. The objective of the research was to develop a balancing procedure to determine correction masses without trial runs. This required the determination of(a) the modal vibration vectors for each resonance, (b) the modal damping ratios,(c) the mode shapes and(d) the equivalent mass of the rotor for each mode. It was made clear from the beginning that trial runs are unavoidable either, when the mode shapes cannot be determined using an analytical or numerical method, or when there is dual vibration at normal operating speed, produced by the influence of higher unbalanced modes, is too high to allow continuous operation of the machine. Therefore, the scope of the project was limited to the possible determination of correction masses without trial runs for the vibration modes included within the normal operating range. Some studies about the minimisation or complete elimination of trial runs have been published by several authors, but a literature search revealed no reports of systematic application of these procedures to field balancing of large turbo generators. This suggested that some practical difficulties had still to be overcome, opening the possibility for further research on this area. Analysis of the rotor response demonstrated the necessity of considering the angular position of the transducers when registering the rotor vibration. It was shown that measuring in a direction other than those of the principal axes of stiffness introduces errors when determining the magnitude and phase of the correction masses. That is to say, failing to consider the effects of the transducer angular position eliminates the possibility of balancing the rotor without trial runs. This is the first time that this problem has been recognised. The procedure developed was verified using an experimental rotor rig. The successful application of the procedure to the balancing of this rotor demonstrates that balancing withouttrialrunsisnotonlyatheoreticalbutalsoapracticalpossibility. The dynamic characteristics of the rotor rig, however, were some what limited and did not cover all the possibilities considered during the project. Therefore, a more complete numerical example was also successfully solved using the computer model of a rotor with characteristics similar to those of a real turbine, and whose unbalanced distribution was not initially known by this author.

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2007. / Thesis presented in partial fulfilment of the requirements for the degree of Master of Engineering Science (Mechanical) at the University of Stellenbosch. / ENGLISH ABSTRACT: This thesis examines the development of a specialized, high-speed bearing in order to reduce vibration levels, reduce cutting times and increase blade stability during diamond sawing. The sawing process is required to be smooth, straight and unhindered – a task which is made difficult by the extreme hardness of the diamond as well as unseen grains which could potentially ruin the cut by deflecting the blade. This has an adverse effect on the quality of the cut and the yield obtained from the stone. The current equipment used for diamond sawing is very basic and a significant improvement can be made in terms of quality and sawing speed with the addition of an improved bearing. An aerostatic bearing was designed in order to achieve lower vibration levels and increased spindle speeds. A speed of 18 500 rpm was achieved with this bearing. A numerical model of the bearing was built with the aim of predicting the bearing’s dynamic behaviour. A finite element method (FEM) analysis was done to confirm the rigid body assumption made. Experimental modal analysis (EMA) was done to determine the frequencies and damping ratios of the natural modes of the rotor. The model was seen to predict the frequencies of the modes to within 6%. This model would be used for future design work to ensure that the frequencies of these modes are designed outside of the operating speed range of the aerostatic bearing. Tests were done to compare the vibration levels between the conventional machine and the aerostatic machine during sawing. The overall RMS acceleration was reduced by 70% on the housing of the aerostatic machine and by 50% on the diamond clamp. / AFRIKAANSE OPSOMMING: Hierdie tesis ondersoek die ontwikkeling van ‘n gespesialeerde, hoë-spoed laer om vibrasie en sny tye te verminder, asook om lem stabilitiet te verhoog in die diamant sny proses. Die sny proses moet glad, reguit en akkuraat wees, maar dit is nie altyd moontlik nie as gevolg van die variasie in hardheid van die diamant asook die naat in die daimant wat die lem maklik kan laat afwyk. Hierdie het ‘n negative effek op die kwalitiet van die snit. Die konvensionele diamant saag masjien is baie eenvoudig en ‘n groot verbetering in die snit kwalitiet en lemspoed is moontlik as ‘n nuwe laer ontwerp en implementeer kan word. ‘n Aerostatiese laer en rotor is ontwikkel om die vibrasie te verminder en die lemspoed to verhoog. ‘n Lemspoed van 18 500 rpm was verkry met die nuwe laer. ‘n Numeriese model is ontiwkkel om die beweging van die rotor dinamies te bereken. Die Eindige Element Metode (EEM) is gebruik om te bepaal of die aanname dat die rotor rigied is, wel aanvaarbaar is. Eksperimentele Modale Analise (EMA) is gebuik om die natuurlike frekwensies en die dempingsverhoudings vir die rotor te bepaal. Die model het die frekwensies tot binne 6% van die werklike waardes bereken. Hierdie model sal in die toekoms gebruik kan word vir die ontwerp van aerostatiese laers om te verseker dat die natuurlike frekwensies buite die spoedbereik van die aerostatiese masjien val. Toetse is gedoen om die vibrasievlakke van die huidige en die aerostatise masjien te meet tydens die snyproses. Die totale WGK versnelling het met 70% op die huls van die aerostatiese masjien, en met 50% op die diamant dop, verminder.

The failure of rolling element bearings is one of the foremost causes of breakdown in rotary machinery. So far, a variety of vibration-based techniques have been developed to monitor the condition of bearings; however, the role of vibration behavior is rarely considered in the proposed techniques. This thesis presents an analytical study of a healthy rotor-bearing system to gain an understanding of the different categories of bearing vibration. In this study, a two degree-of-freedom model is employed, where the contacts between the rolling elements and races are considered to be nonlinear springs. The analytical investigations confirm that the nature of the inner ring oscillation depends on the internal clearance. A fault-free bearing with a small backlash exhibits periodic behavior; however, bearings categorized as having normal clearance oscillate chaotically. The results from the numerical simulations agree with those from the experiments confirming bearing’s chaotic response at various rotational speeds. Bearing faults generate periodic impacts which affect the chaotic behavior. This effect manifests itself in the phase plane, Poincare map, and chaotic quantifiers such as the Lyapunov exponent, correlation dimension, and information entropy. These quantifiers serve as useful indices for detecting bearing defects. To compare the sensitivity and robustness of chaotic indices with those of well-accepted fault detection techniques, a comprehensive investigation is conducted. The test results demonstrate that the Correlation Dimension (CD), Normalized Information Entropy (NIE), and a proposed time-frequency index, the Maximum Approximate Coefficient of Wavelet transform (MACW), are the most reliable fault indicators. A neuro-fuzzy diagnosis system is then developed, where the strength of the aforementioned indices are integrated to provide a more robust assessment of a bearing’s health condition. Moreover, a prognosis scheme, based on the Adaptive Neuro Fuzzy Inference System (ANFIS), in combination with a set of logical rules, is proposed for estimating the next state of a bearing’s condition. Experimental results confirm the viability of forecasting health condition under different speeds and loads.

The failure of rolling element bearings is one of the foremost causes of breakdown in rotary machinery. So far, a variety of vibration-based techniques have been developed to monitor the condition of bearings; however, the role of vibration behavior is rarely considered in the proposed techniques. This thesis presents an analytical study of a healthy rotor-bearing system to gain an understanding of the different categories of bearing vibration. In this study, a two degree-of-freedom model is employed, where the contacts between the rolling elements and races are considered to be nonlinear springs. The analytical investigations confirm that the nature of the inner ring oscillation depends on the internal clearance. A fault-free bearing with a small backlash exhibits periodic behavior; however, bearings categorized as having normal clearance oscillate chaotically. The results from the numerical simulations agree with those from the experiments confirming bearing’s chaotic response at various rotational speeds. Bearing faults generate periodic impacts which affect the chaotic behavior. This effect manifests itself in the phase plane, Poincare map, and chaotic quantifiers such as the Lyapunov exponent, correlation dimension, and information entropy. These quantifiers serve as useful indices for detecting bearing defects. To compare the sensitivity and robustness of chaotic indices with those of well-accepted fault detection techniques, a comprehensive investigation is conducted. The test results demonstrate that the Correlation Dimension (CD), Normalized Information Entropy (NIE), and a proposed time-frequency index, the Maximum Approximate Coefficient of Wavelet transform (MACW), are the most reliable fault indicators. A neuro-fuzzy diagnosis system is then developed, where the strength of the aforementioned indices are integrated to provide a more robust assessment of a bearing’s health condition. Moreover, a prognosis scheme, based on the Adaptive Neuro Fuzzy Inference System (ANFIS), in combination with a set of logical rules, is proposed for estimating the next state of a bearing’s condition. Experimental results confirm the viability of forecasting health condition under different speeds and loads.

This thesis is focus at diagnostics of processing machines by diagnostics of vibration with the OCTAVIS system. There is mentioned a view of the present vibration monitoring methods, description of developed diagnosis bench, measuring in this bench and measuring of the chosen production machine.

Rotating blades are considered to be the one of the most common cause of failures in rotating machinery. Blade failure modes normally occur as a result of cracks due to unexpected operating conditions, which are normally caused by accidents of foreign objects damage, high cycle fatigue, blade rubbing, blade root looseness, and degradation from erosion and corrosion. Thus, detection of blade faults has an important role in reducing blade related failures and allowing repairs to be scheduled for the machinery. This in turn will lead to reduction in maintenance costs and thus raise productivity and safety aspects of operation. To maintain vital components of rotating machines, such as blades, shafts, bearings and gear boxes, at optimal levels, detection of failures in such components is important, because this will prevent any serious damage that could affect performance. This research study involves laboratory tests on a small rig with a bladed disc rotor that applied vibration measurements and analysis for blade fault detection. Three measurements: shaft torsional vibration, on-bearing vibration (OBV) and on-casing vibration (OCV), are used. A small test rig of a single stage bladed disc holding 8-blades was designed and manufactured, to carry out this research study to assess the usefulness and capability of each vibration technique in detection of incipient defects within machine blades. A series of tests was conducted on a test rig for three different cases of blade health conditions: (a) healthy blade(s) with mistuned effects, (b) blade root looseness and (c) cracks in a blade on two different blade sizes (long and short blades) in order to discover changes in blades' dynamic behaviour during the machine running-up operation. The data were collected using the three measurements during machine run-up and then recorded. The measured vibration data were analysed by computing the blades' resonance at different engine orders (EOs) related to the blade(s) resonance frequencies and their higher harmonics, to understand the blade(s) dynamics behaviour for the cases of healthy and faulty blade(s). Data have been further processed using a polar plot presentation method which provides clear results that can be used for monitoring blade integrity. To validate the obtained experimental results, a simplified mathematical model was also developed. Finally, a comparative study between three methods was undertaken to understand the relative advantages and limitations in the blade heath monitoring.