A Theoretical Model to Predict the Vibration Response of Rolling Bearings in a Rotor Bearing System to Distributed Defects Under Radial Load

1999 ◽  
Vol 122 (3) ◽  
pp. 609-615 ◽  
Author(s):  
N. Tandon ◽  
A. Choudhury
Keyword(s):  
Theoretical Model ◽  
Vibration Response ◽  
Radial Load ◽  
Outer Race ◽  
Rolling Element ◽  
Spectral Components ◽  
Rotor Bearing ◽  
Defect Frequency ◽  
Inner Race ◽  
Bearing System

A theoretical model to predict the vibration response of rolling element bearing in a rotor bearing system to distributed defects under radial load has been developed. The rotor bearing system has been considered as a three degrees of freedom model. The distributed defects considered are, the waviness of outer and inner races, and off size rolling element. The model predicts discrete spectrum with specific frequency components for each order of waviness. For outer race waviness, the spectrum has components at outer race defect frequency and its harmonics. In the case of inner race waviness, the waviness orders equal to number of rolling elements and its multiples give rise to spectral components at inner race defect frequency and its multiples. Other orders of waviness generate sidebands at multiples of shaft frequency about these peaks. The model predicts the amplitudes of the spectral components due to outer race waviness to be much higher as compared to those due to inner race waviness. In the case of an off-size rolling element, the model predicts discrete spectra having significant components at multiples of cage frequency. [S0742-4787(00)00603-2]

Vibration Response of Rolling Element Bearings in a Rotor Bearing System to a Local Defect Under Radial Load

2005 ◽  
Vol 128 (2) ◽  
pp. 252-261 ◽  
Author(s):  
A. Choudhury ◽  
N. Tandon
Keyword(s):  
Theoretical Model ◽  
Vibration Response ◽  
Local Defect ◽  
Radial Load ◽  
Rolling Element ◽  
Spectral Components ◽  
Rotor Bearing ◽  
Defect Frequency ◽  
Inner Race ◽  
Bearing System

In the present investigation, a theoretical model has been developed to obtain the vibration response due to a localized defect in various bearing elements in a rotor-bearing system under radial load conditions. The rotor-bearing system has been modeled as a three degrees-of-freedom system. The model predicts significant components at the harmonics of characteristic defect frequency for a defect on the particular bearing element. In the case of a defect on the inner race or a rolling element, the model predicts sidebands about the peaks at defect frequencies, at multiples of shaft and cage frequencies, respectively. The model has also predicted some additional components at harmonics of shaft and cage frequencies due to a local defect on the inner race and a rolling element, respectively. The expressions for all these spectral components have also been derived. Typical numerical results for an NJ 204 bearing have been obtained and plotted. The amplitude of the component at defect frequency, for an outer race defect, is found to be much higher as compared to those due to inner race defect or a rolling element defect of the same size and under similar conditions of load and speed. The results of vibration measurements on roller bearings with simulated local defects have also been presented to experimentally validate the theoretical model proposed. It can be observed from the results that the spectral components predicted by the theoretical model find significant presence in the experimental spectra. Comparison of the normalized analytical values of the spectral components with their experimental values shows fair agreement for most of the cases considered. Probable area of the generated excitation pulses has been calculated and the effects of pulse area variation on the experimental results have been studied.

A Theoretical Model to Predict Vibration Response of Rolling Bearings to Distributed Defects Under Radial Load

1998 ◽  
Vol 120 (1) ◽  
pp. 214-220 ◽  
Author(s):  
A. Choudhury ◽  
N. Tandon
Keyword(s):  
Theoretical Model ◽  
Discrete Spectrum ◽  
Analytical Model ◽  
Relative Frequency ◽  
Vibration Response ◽  
Radial Load ◽  
Rolling Bearings ◽  
Rolling Element ◽  
Amplitude Level ◽  
Inner Race

An analytical model has been presented to predict the vibration response of rolling bearings due to distributed defects under radial load. For bearings without defect and with race defect, the model predicts a discrete spectrum with components at outer and inner race characteristic defect frequencies for the response of the respective races. The amplitude level for race defect significantly increases at the respective frequencies in comparison to the response of a bearing without defect. For a bearing with off-size rolling element, the response is at the relative frequency of cage with respect to the frequency of motion of the corresponding race.

Analysis of faults in rotor-bearing system using three-level full factorial design and response surface methodology

2021 ◽  
pp. 095745652110307
Author(s):  
Hara P Mishra ◽  
Arun Jalan
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Fault Analysis ◽  
Vibration Response ◽  
Effect Analysis ◽  
Outer Race ◽  
Surface Plot ◽  
Rotor Bearing ◽  
Full Factorial ◽  
Bearing System

This article presents the experimental and statistical methodology for localized fault analysis in the rotor-bearing system. These defects on outer race, on inner race, and on a combination of ball and outer race are considered. In this study speed, load and defects were considered as the essential process variables to understand their significance and effects on vibration response for the rotor-bearing system. Three factors at three levels were considered for experimentation, and the experiment was designed for L27 based on design of experiments (DOE) methodology. From the experiments, the vibration response results are recorded in terms of root mean square value for the analysis. Response surface methodology (RSM) is used for identifying the interaction effect of varying process parameters upon the response of vibrations by response surface plot. The rotor-bearing test setup is used for experimentation and is analyzed by using DOE. This study establishes the prediction of fault in the rotor-bearing system in combined parametric effect analysis and its influence with DOE and RSM.

scholarly journals A theoretical model for predicting the vibration response of outer race defective ball bearing

2018 ◽  
Vol 7 (2) ◽  
pp. 289
Author(s):  
Samir Shaikh ◽  
Sham Kulkarni
Keyword(s):  
Theoretical Model ◽  
Ball Bearing ◽  
Mathematical Formulation ◽  
Vibration Response ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Outer Race ◽  
Rolling Element ◽  
Rolling Elements ◽  
Extended Type

The theoretical model with 2 degree-of-freedom system is developed for predicting the vibration response and analyze frequency properties in an extended type defective ball bearing. In the mathematical formulation, the contact between the races and rolling element considered as non-linear springs. The contact forces produced during the collaboration of rolling elements are obtained by utilizing Hertzian contact deformation hypothesis. The second order nonlinear differential equation of motion is solved using a state space variable method with the help of MATLAB software and the vibration acceleration response of the defective ball bearing presented in the frequency spectrum. The effects of variation in speed and size of the defect on characteristic frequency of extended fault on the outer raceway of the ball bearing have been investigated. The theoretical results of the healthy (non defective) and defective bearing are compared with each other.

Vibration model of rolling element bearings in a rotor-bearing system for fault diagnosis

2013 ◽  
Vol 332 (8) ◽  
pp. 2081-2097 ◽  
Author(s):  
Feiyun Cong ◽  
Jin Chen ◽  
Guangming Dong ◽  
Michael Pecht
Keyword(s):  
Fault Diagnosis ◽  
Rolling Element Bearings ◽  
Vibration Model ◽  
Rolling Element ◽  
Rotor Bearing ◽  
Bearing System

Vibration Signature Analysis of a Rotor Bearing System Using Response Surface Method

2009 ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
High Speed ◽  
Vibration Response ◽  
Radial Clearance ◽  
System Response ◽  
Surface Waviness ◽  
Surface Method ◽  
Rotor Bearing ◽  
Bearing System

The vibration response of a rotor bearing system is extremely important in industries and is challenged by their highly non-linear and complex properties. This paper focuses on performance prediction using response surface method (RSM), which is essential to the design of high performance rotor bearing system. Response surface method is utilized to analysis the effects of design and operating parameters on the vibration response of a rotor-bearing system. A test rig of high speed rotor supported on rolling bearings is used. Vibration response of the healthy ball bearing and ball bearings with various faults are obtained and analyzed. Distributed defects are considered as surface waviness of the bearing components. Effects of internal radial clearance and surface waviness of the bearing components and their interaction are analyzed using design of experiment (DOE) and RSM.

Advanced Rolling-Element Bearing Diagnostics Based on Cyclic Spectral Analysis

2007 ◽  
Vol 347 ◽  
pp. 265-270
Author(s):  
Jerome Antoni ◽  
Roger Boustany
Keyword(s):  
Background Noise ◽  
Rolling Element Bearing ◽  
Outer Race ◽  
Spectral Signatures ◽  
Bearing Diagnostics ◽  
Rolling Element ◽  
Cyclical Behaviour ◽  
Element Bearing ◽  
Incipient Fault ◽  
Inner Race

Rolling-element bearing vibrations are random cyclostationary, that is they exhibit a cyclical behaviour of their statistical properties while the machine is operating. This property is so symptomatic when an incipient fault develops that it can be efficiently exploited for diagnostics. This paper gives a synthetic but comprehensive discussion about this issue. First, the cyclostationarity of bearing signals is proved from a simple phenomenological model. Once this property is established, the question is then addressed of which spectral quantity can adequately characterise such vibration signals. In this respect, the cyclic coherence - and its multi-dimensional extension in the case of multi-sensors measurements -- is shown to be twice optimal: first to evidence the presence of a fault in high levels of background noise, and second to return a relative measure of its severity. These advantages make it an appealing candidate to be used in adverse industrial environments. The use and interpretation of the proposed tool are then illustrated on actual industrial measurements, and a special attention is paid to describe the typical "cyclic spectral signatures" of inner race, outer race, and rolling-element faults.

Dynamic Parameters Estimation and Fault Identification From Random Response of Rolling Element Bearing in a Rotor Bearing System

2019 ◽  
Author(s):  
Pankaj Kumar ◽  
S. Narayanan ◽  
Sayan Gupta
Keyword(s):  
Random Vibration ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parameters Estimation ◽  
Rolling Element Bearing ◽  
Vibration Signals ◽  
Rolling Element ◽  
Rotor Bearing ◽  
Element Bearing ◽  
Bearing System

Abstract This paper presents a procedure for determination of dynamic properties of rolling element bearing by using the vibration signals picked up at the bearing caps. The rotor-bearing assembly is idealized as Duffing oscillator and random vibration signals modelled as exponentially correlated (Ornstein-Uhlenbeck) colored noise. Expressing the excitation as a first order filtered white noise enables the direct formulation of the 3D-Fokker Planck (FP) equation for system response through the Markov vector approach. Closed form solution of the stationary FP equation is derived. Subsequently the response statistics of experimentally obtained random vibration signal are processed through the closed form solution of the FP equation as the inverse process of parameters estimation from the measured response. Further, the dynamic behavior of rigid rotor-bearing system is investigated under combined excitation of white noise and harmonic forces arising due to rotor unbalance force. The effect of system nonlinearities, stiffness, damping and unbalanced excitation force on the dynamic response are investigated using the bifurcation plot. For assessment of structural degradation of bearings, a novel entropy based approach is developed. Experimental studies on roller bearing are carried out to demonstrate the effectiveness of the proposed approach.

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