N. Tandon

A Dynamic Model for Vibration Studies of Deep Groove Ball Bearings Considering Single and Multiple Defects in Races

A dynamic model is reported herein for the study of vibrations of deep groove ball bearings having single and multiple defects on surfaces of inner and outer races. Masses of shaft, housing, races, and balls are considered in the modeling. The coupled solution of governing equations of motions is obtained using Runge―Kutta method. The model provides the vibrations of shaft, balls, and housing in time and frequency domains. Computed results from the model are validated with experimental results, which are generated using healthy and defective deep groove ball bearings. Characteristic defect frequencies and its harmonics are broadly investigated using both theoretical and experimental results. Comparison of vibration spectra for the cases having single and two defects on races reveals relatively higher velocity amplitudes with two defects. Good correlations between theoretical and experimental results are observed. Authors believe that this dynamic model can be used with confidence for the study and prediction of vibrations of healthy and defective deep groove ball bearings.

Vibration Modeling of a Rigid Rotor Supported on the Lubricated Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races

Nonlinear vibration analysis of angular contact ball bearings supporting a rigid rotor ispresented herein considering the frictional moments (load dependent and load independ-ent components of frictional moments) in the bearings. Six degrees of freedom (DOF) ofrigid rotor is considered in the dynamic modeling of the rotor-bearings system. More-over, waviness on surfaces of inner race, outer race, and ball are considered in the modelby representing it as sinusoidal functions with waviness orders of 6, 15, and 25. Twoamplitudes of waviness, 0.05 and 0.2lm, are considered in the investigation looking forthe practical aspects. The proposed model is validated with the experimental results byperforming the experiments. Moreover, the present model has also been validated withpublished results of researchers by incorporating needful changes in the DOF in the pro-posed model. Based on the computed results, it is observed that load dependent frictionalmoment (LDFM) significantly enhances the amplitudes of vibrations in comparison toload independent frictional moment (LIFM) irrespective to values of waviness amplitudeand waviness order. The influence of inner race waviness is relatively more on the vibra-tions in comparison to waviness of outer race and ball. Moreover, vibrations of systemenhance considerably at high amplitude of waviness, increase in the order of waviness,and at elevated operating parameters. [DOI: 10.1115/1.4005140]

Fault identification of rolling element bearings from vibration signals: an application of Kalman and H∞ Filters

Application and comparison of performance of two filtering techniques, Kalman and H ∞ Filters, for bearing fault identification, under various types of noise are reported herein. Kalman and H ∞ Filters are optimal state estimators; Kalman is the minimum variance estimator while H ∞ minimizes the worst case estimation error. Existing state equations of a rotor bearing system has been taken and non-linearity along with a number of unmodelled effects is blended with the process noise. Experimental investigations have also been carried out to study the application of these filters for bearing signal de-noising.

A system dynamic approach to bearing fault identification with the application of Kalman and H∞ filters

This work attempts to examine the scope of applying Kalman filter and H∞ filter individually on the vibration signal acquired for identifying local defects in a rolling element bearing. This is essentially a system dynamic approach, which is another choice, examined to be a better one in comparison with few other signal analysis approaches reported in the literature. Kalman and H∞ filters are optimal state estimators; Kalman filter is the minimum variance estimator while H∞ filter minimizes the worst case estimation error. States, displacement and velocity, of a rotor shaft system are obtained from its equations of motion, which are written by including the process noise and measurement noise to take into account modeling inaccuracies and vibration from other sources. Experiments have been carried out to investigate the performance of Kalman and H∞ filters each with the Envelope Analysis technique, a popular one for identification of bearing faults, in a noisy environment. Envelope Analysis is performed by taking a Hilbert transform of the band pass filtered signal, whose centre frequency and bandwidth are to be properly selected for satisfactory performance of the algorithm. Signals from test bearings running nearly at constant speed and having a single defect on the inner race and outer race have been acquired for different operating speeds of the test rig in the presence of extraneous vibration (noise) generated by running a nearby compressor. The signal obtained after the application of Kalman and H∞ filter demonstrates a significant enhancement in signal to noise ratio resulting in a clear identification of defect frequencies in the vibration spectrum. Therefore, Kalman or H∞ based state estimation approach may be used with confidence to extract bearing signals from noisy vibration signals.

Force Analysis Due to Local Defect in Rolling Bearings for Fault Diagnosis

Local defects in races of rolling bearings generate periodic forces whose strength is largely governed by the defect size. An insight into force generation mechanism and its relationship with defect size is essential to identify the bearing health. This work presents an engineering mechanics based approach to model the forces at different events as a rolling element negotiates a fault on the race. The forcing function is modeled at entry, as a function of load, speed and curvature of defect and due to impact as a function of defect size, defect location, speed and load on the bearing. The impulse of impact force and the duration between entry and impact forces, termed as Time to Impact (TTI), are indicators of the defect size. The proposed model may provide a potential basis for implementing direct monitoring with embedded force sensor module.