Please use this identifier to cite or link to this item: http://localhost:8081/xmlui/handle/123456789/6686
Authors: Kankar, Pavan Kumar
Issue Date: 2011
Abstract: Rolling element bearings are extensively used in most of the rotating machines to support static/dynamic loads. Their performance is utmost important in power stations, chemical plants, automotive industries, aerospace turbo machinery and process industries that require precise and efficient performance. These bearings can take up both radial and axial loads for most of the applications. They have a great influence on the dynamic behavior of the rotating machines and act as a source of vibration and noise in these systems. There is a critical need to increase reliability and performance of rolling element bearings to prevent catastrophic failure of the machinery. Rolling element bearings generate vibrations during operation even if they are geometrically and elastically perfect. This is because of the use of a finite number of rolling elements to carry the load. The number of rolling elements and their position in the load zone change with bearing rotation, giving rise to a periodical variation of the total stiffness of the bearing assembly. This variation of stiffness generates vibrations commonly known as Varying Compliance vibrations. The other possible sources of vibrations are due to radial internal clearance, the unbalanced rotor force and the defective bearing elements of a rotor bearing system. This work attempts to analyze the non-linear vibration response of a high-speed rotor supported on rolling element bearings under the balance and unbalanced rotor conditions and due to defective rolling element bearings. A mathematical model has been developed, which takes into account the sources of non-linearity such as Hertzian contact (non-linear contact stiffness), radial internal clearance, non-linear damping, distributed and localized defects and sources of parametric excitation, which are the varying compliance of rolling element bearings. The mathematical formulation accounts for tangential and radial motions of rolling elements, as well as of the rotor, the inner and the outer races. The contacts between the rolling elements and the races are treated as non-linear springs, whose stiffnesses are obtained on the basis of the Hertzian elastic contact deformation theory. The governing equations of motion for the rotor bearing system have non-analytic stiffness terms, which are found to be numerically stiff. The implicit type numerical integration technique Newmark- 1 with Newton-Raphson method has been used for the solution of these system equations. Various techniques like Poincare maps, bifurcation diagram, phase trajectories, non-autonomous shooting technique, orbit plots and Fast Fourier Transformations (FFT) are used to study the ii nature of the response. Theoretical analysis for the balance and the unbalanced rotor over a wide range of rotor speed has revealed several regions of instability and deterministic chaotic response. An important finding from the present analysis is the existence of unstable and chaotic response region at very high speeds, primarily due to the bearing clearance and defects in components of rolling element bearing. The model also predicts discrete spectrum with specific frequency components for each order of waviness under distributed defects class. For outer race waviness, the spectrum has components at outer race defect frequency (cob,) and its harmonics. In case of inner race waviness, the waviness order to number of rolling elements and its multiples give rise to spectral components at the inner race defect frequency (6),,,, ) and its multiples. Other orders of waviness generate side band at multiples of rotor frequency about these peaks. In the case of ball waviness, a ball with wavy surface in the set will cause vibrations at two frequencies i.e. at the (cocage ) and at the wave passage frequency of the ball (a)wp = N w° roll ),In the case of off-size rolling element; the model predicts discrete spectra having significant components at multiples of cage frequency. Under localized defects class as spall on outer race, the spectrum has components at the ball passage frequency ( cobpfi, ) and its sub harmonics. In case of spall on inner race, the spectrum has components at ball passage frequency ( cobpfi ) and its harmonics. The severe vibrations are found to be associated with the two frequency interactions as ball passage frequency ( cobpfi ) and rotational frequency of inner race. For bearing with spall on ball, the spectrum has components at the twice of ball spin frequency and its harmonics. The effect of unbalanced rotor has been clearly observed from the vibration spectra as the system is bio-periodically excited. From the analysis of the spectrum plots, it is inferred that the system is excited at rotational frequency ( X ) mainly due to unbalanced rotor force and varying compliance frequency (VC) induced due to radial internal clearance. Other peaks are appeared in the spectra at the interaction of two exciting frequencies as (VC ± nX) . The effects of the parameters like the rotor speed, the radial internal clearance, the unbalanced rotor force and the bearing defects on dynamic response are analyzed theoretically and these results are found to match fairly well with the published results. In the present investigation, an experimental study has been conducted on healthy and defective ball bearings. Fault diagnosis of ball bearings is carried out using various machine learning techniques and response surface method. Design of experiment (DOE) and response surface methodology (RSM) procedures are used to conduct several trials for investigating iii combined effect of defects with varying rotor speed on the system vibration response. Severe vibration (Max. peak of vibration excitation) occurs in case of bearing with ball defect and inner race defect at rotor speed of 5000 rpm for horizontal and vertical acceleration responses. Inner race defect and rotor speed have significant effect on vibration response as compared to outer race defect and ball defect. A wavelet based fault diagnosis methodology using various machine learning methods like support vector machine (SVM), artificial neural network (ANN) and self-organizing maps (SOM), is also presented in this study. This methodology incorporates most appropriate features, which are extracted from wavelet coefficients of raw vibration signals. Two wavelet selection criteria Maximum Energy to Shannon Entropy Ratio and Maximum Relative Wavelet Energy are used and compared to select an appropriate wavelet for feature extraction. The wavelet selected using Maximum Energy to Shannon Entropy Ratio criterion (Meyer wavelet) gives better classification efficiency. The performance of SVM (classification efficiency 98.667 %) is found to be best due to its inherent generalization capability. By using proposed methodology, useful features can be extracted from the original data and dimension of original data can be reduced by removing irrelevant features, so that the classifier can achieve a higher accuracy. The results show the potential application of proposed methodology with machine learning techniques for the development of on-line fault diagnosis systems for machine condition. The current study also gives designers a diagnostic tool for prediction the trends of instability in a rotor bearing system for healthy and defective bearings.
Other Identifiers: Ph.D
Research Supervisor/ Guide: Harsha, S. P.
Shaema, Satish C.
metadata.dc.type: Doctoral Thesis
Appears in Collections:DOCTORAL THESES (MIED)

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