The dynamic response of bearing under load and speed often determine the performance limitations of the machines and it is necessary to be able to predict bearing dynamic performance as an integral part of machine design analysis. In this paper, a mathematical model has been developed to investigate a nonlinear dynamic behavior of a rotor-bearing system due to localized defects of inner race and outer race. In the mathematical formulation, the contacts between rolling elements and inner/outer race is considered as nonlinear springs whose stiffness is obtaining using Hertz contact stress theory. Here nonlinear damping is also taken into consideration for cylindrical roller bearing. The governing equations of motion are formulated by using energy approach. Contact force and contact stiffness having nonlinearity and is calculated by using Newton-Raphson method for n-unknown nonlinear simultaneous equation. The new mark implicit integration technique is coupled with the Newton-Raphson method to solve the differential equations. A computer program is developed to simulate the defect on inner race and outer race and all the results are represented in the time and frequency domain. Equations of motions are solved by using Newmark-b method for phase plot/Poincare map. The proposed mathematical model is also compared with experimental results having radial and axial load condition. From the results obtained from the predicted model for frequency spectrum and phase plot at various speeds, the mathematical modeling and experimental results are found quite similar.

In this paper, an analytical model is proposed to study the behavior of defective bearing and rotor system. An overhung rotor system and defective roller bearing are considered for the study. Rotor is considered with unbalanced mass and bearing is taken as the cylindrical roller bearing having localized surface defect. To analyze all the system components' effect at one node, finite element method is used to predict exact system vibrations. Euler-Bernoulli's beam element is used to discretize the shaft. Gyroscopic effect of overhung rotor is also taken into account and governing equations of motion have been modified according to our system. Hertz contact stress theory is used for every roller-race contact to calculate the overall nonlinear bearing force. Governing differential equation is solved by Newmark-b time integration method. Nonlinear matrix equation, which is generated at each time-step in Newmark's method, is solved by Broyden's method. Results for defective bearing are obtained and plotted in the time and frequency domain. Poincare map has been plotted to view the system's minimum stability time. An experiment has been carried out to validate the proposed analysis work. In this paper, it has been shown how rotor dynamic analysis can be achieved numerically with minimum calculations.

Frequently it is found in the industry that unbalances of the rotating components generate vibration due to centrifugal force. Here an attempt has been made to reduce vibrations caused by unbalance in the impeller of the Air Blower. The Dynamic Vibration Absorber (DVA) device is designed in such a way that optimal tuning damping factor and mass ratio were found as same as that obtained by using higher order of perturbation method. The designed DVA brings Vrms values within the limit set by ISO 10816-3 for Unlimited Long-Term Operation Allowable. More than 50% appreciable vibration reduction was measured in radial horizontal and vertical direction both at the motor drive and non-drive end.

This paper presents a mathematical model to investigate the vibration behavior of a rotor-bearing system due to localized defects of inner race and outer race for cylindrical roller bearing. In the formulation, the contacts between rolling elements and inner/outer races are considered as nonlinear springs as well as nonlinear damping. The governing equations of motion are formulated using energy approach,