NONLINEAR VIBRATION ANALYSIS OF CYLINDRICAL ROLLING CONTACT BEARING

Abstract

newlineBearings are used extensively in all rotating machinery in the industry to support load. Their performance is utmost important in chemical, petrochemical, automotive, power generation, and aerospace turbo machinery and process industries in the entire world. newlineRolling element bearings are one of the most widely used components in the industrial 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. These 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. The importance of a clear understanding of vibrations associated with rolling element bearings is therefore obvious. This work attempts to analyze the non-linear vibration response of high-speed rotor supported by 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 defects and sources of parametric excitation, which are the varying compliance of rolling element bearings. newlineThe 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 stiffness is obtained on the basis of the Hertzian elastic contact deformation theory. The system equations of motion have non-analytic stiffness terms, which are found to be numerically stiff. The implicit type numerical integration technique Newmark- and#946; with Newton-Raphson method has been used for the solution of these system equations. Various techniques like Poincare maps, bifurcation diagram, phase trajectories, and Fast Fourier Transformations (FFT) are newline newlineused to study the nature of the response. Theoretical analysis for the balanced 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 distributed defects. newlineThe experimental study has been carried out to study the vibration response under different conditions and to validate the theoretical results; the same operating parameters and conditions have been chosen for carrying out the experimental study. Three different types of fault (outer race, inner race) have been taken up for the present experimental study of rolling element bearings. Rotor speed is varied up to 3000 RPM. It is also investigated that the defect frequencies from the experimental results is in the better agreement with the frequencies obtained by the numerical results. newlineA very little work has been reported in the literature on the effect of balanced rotor conditions with non-linear stiffness and non-linear damping and defective bearings on the dynamic behavior of high speed cylindr ical roller bearings, which are analyzed in detail in the present investigation. Hence, this study will give the basic input to design/maintenance engineers about the faults detection and their effects on system responses. Local defect is modeled on inner race and outer race of the bearing surfaces as well as combined defects are also modeled in this work. The results were obtained in the form of time series, frequency responses and phase trajectories. The validity of the proposed Model verified by comparison of frequency components of the system response with those obtained from experiments. newline newline