Local faults, like spalls in rolling element bearings, give rise to periodic impulsive excitation to the supporting structure. So, an impact based force evaluation, the resulting response analysis of the structure, and experiments are reported in this paper to identify local bearing fault as well as its size. Magnitude and duration of such excitation force are functions of bearing geometry, load, speed, and size of defect. An approach based on the principles of engineering mechanics is followed to obtain a time function of the impact force which is used next to simulate the response of the bearing housing. This response is analyzed in time and frequency domains to get an idea about the bearing fault and its size. Experiments conducted on deep groove ball bearing for different defect sizes and different speeds show acceptable correlation with the theoretical simulation. Hence, the impact based model has laid a theoretical platform to gain insight into the physical phenomena, which is not measured in practice, through impact excitation mechanism and may hold sufficient potential for bearing fault identification.

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This paper presents a theoretical model for the forcing function generated on the structure as a rolling element negotiates a spall-like defect on the inner race, considered to be a moving race. The negotiation of defect has been seen as a sequence of events for the purpose of understanding the physics behind this negotiation. Such an analysis has not been attempted in the literature and thus forms the basic contribution in this work. Defects are assumed to generate two events; one at the leading edge and other at the trailing edge. The entry event at the leading edge is modeled using contact mechanics and is a function of load, speed, and curvature of defect edge whereas impact event, modeled using the principles of mechanics, is a function of load, speed, size of defect, and curvature of defect edge. The vibratory response of the nonlinear rotor bearing system subject to such excitation is simulated numerically using fourth-order Runge Kutta method and analyzed in both time and frequency domains. The modeling results provide insight into the physical mechanism which is not measured in practice and highlight the weakness of entry pulse in comparison to the impact pulse, also observed by several other researchers in their experimental tests. Defects of varying severity were simulated and tested to validate the proposed model and the acceptable correlation of amplitudes at the characteristic defect frequency provides a preliminary multi-event theoretical model. The developed model has therefore laid a theoretical platform to monitor the size of the defect on inner race which may be considered not only to identify but also to quantify the defect.

Vibration analysis has been widely accepted as a common and reliable method for bearing fault identification, however, the presence of noise in the measured signal poses the maximum amount of difficulty. Therefore, for the clearer detection of defect frequencies related to bearing faults, a denoising technique based on the Kalman filtering algorithm is presented in this paper. The Kalman filter yields a linear, unbiased, and minimum mean error variance recursive algorithm to optimally estimate the unknown states of a dynamic system from noisy data taken at discrete real time intervals. The dynamics of a rotor bearing system is presented through a linear model, where displacement and velocity vectors are chosen as states of the system. Process noise and measurement noise in the equations of motion take into account the modeling inaccuracies and vibration from other sources, respectively. The covariance matrix of the process noise has been obtained through the transfer function approach. The efficiency of the proposed technique is validated through experiments. Periodic noise and random noises obeying the white Gaussian, colored Gaussian and non-Gaussian distribution have been simulated and mixed with a clean experimental signal in order to study the efficiency of the standard Kalman filter under various noisy environments. Additionally, external vibrations to the test rig have been imparted through an electromechanical shaker. The results indicate an improvement in the signal to noise ratio, resulting in the clear identification of characteristic defect frequencies after passing the signal through the Kalman filter. The authors find that there is sufficient potential in using the Kalman filter as an effective tool to denoise the bearing vibration signal.

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