Overview of dynamic modelling and analysis of rolling element bearings with localized and distributed faults

Rolling element bearings (REBs) play a most critical role in various industrial machinery. A clearly and in-depth understanding of vibration characteristics of REBs is very helpful for condition monitoring and diagnosis applications for the machinery. This work presented a comprehensive review of dynamic modelling and analysis methods for predicting the vibration characteristics of REBs with and without localized and distributed faults. Main capabilities and limitations of those methods for both the localized and distributed faults have been described. Explanations for the generations of the bearing vibrations were also reviewed. A summary of the literature was given followed by the recommendations of current and future research works. Moreover, recent challenges, directions and implications in research works on the dynamic modelling and analysis methods of the localized and distributed faults in REBs have also been conducted.

[1]  Hui Ma,et al.  Time-varying mesh stiffness calculation of cracked spur gears , 2014 .

[2]  J. K. Dutt,et al.  Multi-Event Excitation Force Model for Inner Race Defect in a Rolling Element Bearing , 2016 .

[3]  Li Cui,et al.  Nonlinear vibration and stability analysis of a flexible rotor supported on angular contact ball bearings , 2014 .

[4]  S. N. Panigrahi,et al.  Precise measurement of defect width in tapered roller bearing using vibration signal , 2014 .

[5]  H. Zantopulos The Effect of Misalignment on the Fatigue Life of Tapered Roller Bearings , 1972 .

[6]  Bomidi John Abhishek Raj,et al.  Three-Dimensional Finite Element Elastic–Plastic Model for Subsurface Initiated Spalling in Rolling Contacts , 2014 .

[7]  Seong-Wook Hong,et al.  Characteristics of tapered roller bearing with geometric error , 2015 .

[8]  David Mba,et al.  Development of Acoustic Emission Technology for Condition Monitoring andDiagnosis of Rotating Machines; Bearings, Pumps, Gearboxes, Engines and RotatingStructures. , 2006 .

[9]  Francesco Massi,et al.  Coupling system dynamics and contact behaviour: Modelling bearings subjected to environmental induced vibrations and ‘false brinelling’ degradation , 2010 .

[10]  Jing Liu,et al.  Effects of spall edge profiles on the edge plastic deformation for a roller bearing , 2019 .

[11]  Xiao-Qing Zhang,et al.  Dynamic Analysis of a High-Speed Rotor-Ball Bearing System Under Elastohydrodynamic Lubrication , 2014 .

[12]  Wouter Ost,et al.  Failure analysis of the deep groove ball bearings of an electric motor , 2005 .

[13]  W. Scheithe Better bearing vibration analysis , 1992 .

[14]  Kyosuke Ono,et al.  Theoretical analysis of shaft vibration supported by a ball bearing with small sinusoidal waviness , 1996 .

[15]  Teik C. Lim,et al.  Impulse vibration transmissibility characteristics in the presence of localized surface defects in deep groove ball bearing systems , 2014 .

[16]  T. E. Tallian Prediction of Rolling Contact Fatigue Life in Contaminated Lubricant: Part I—Mathematical Model , 1976 .

[17]  Farshid Sadeghi,et al.  A finite element model for rolling contact fatigue of refurbished bearings , 2015 .

[18]  Rajendra Singh,et al.  Vibration Transmission through Rolling Element Bearings, Part V: Effect of Distributed Contact Load on Roller Bearing Stiffness Matrix , 1994 .

[19]  F. Sadeghi,et al.  Residual stresses due to debris effects in EHL contacts , 1997 .

[20]  Jari Halme,et al.  Rolling contact fatigue and wear fundamentals for rolling bearing diagnostics - state of the art , 2010 .

[21]  S. Harsha,et al.  Nonlinear Dynamic Response of a Rotor Bearing System Due to Surface Waviness , 2004 .

[22]  Daniel Nelias,et al.  Nonlinear dynamic analysis of cylindrical roller bearing with flexible rings , 2009 .

[23]  J. M. de Mul,et al.  Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction—Part II: Application to Roller Bearings and Experimental Verification , 1989 .

[24]  F. Sadeghi,et al.  Effects of surface defects on rolling contact fatigue of heavily loaded lubricated contacts , 2010 .

[25]  H. Karagülle,et al.  Simulation and analysis of vibration signals generated by rolling element bearing with defects , 2003 .

[26]  H. Karagülle,et al.  Vibration analysis of rolling element bearings with various defects under the action of an unbalanced force , 2006 .

[27]  A. Muszynska,et al.  Rotor-To-Stationary Element Rub-Related Vibration Phenomena in Rotating Machinery -- Literature Suryey , 1989 .

[28]  S. Harsha,et al.  Nonlinear dynamic analysis of high speed bearings due to combined localized defects , 2014 .

[29]  M. While Rolling Element Bearing Vibration Transfer Characteristics: Effect of Stiffness , 1979 .

[30]  Sanjay H Upadhyay,et al.  Theoretical model to predict the effect of localized defect on dynamic behavior of cylindrical roller bearing at inner race and outer race , 2014 .

[31]  Farshid Sadeghi,et al.  Cage Instabilities in Cylindrical Roller Bearings , 2004 .

[32]  Carl Q. Howard,et al.  Varying stiffness and load distributions in defective ball bearings: Analytical formulation and application to defect size estimation , 2015 .

[33]  Hamid Moeenfard,et al.  Nonlinear dynamic modeling of surface defects in rolling element bearing systems , 2009 .

[34]  Yimin Shao,et al.  A numerical investigation of the plastic deformation at the spall edge for a roller bearing , 2017 .

[35]  B. C. Nakra,et al.  TECHNICAL ARTICLE practical articles in shock and vibration technology: Vibration and Acoustic Monitoring Techniques for the Detection of Defects in Rolling Element Bearings -- a Review , 1992 .

[36]  P. K. Kankar,et al.  Stability analysis of a rotor bearing system due to surface waviness and number of balls , 2004 .

[37]  Sadok Sassi,et al.  A Numerical Model to Predict Damaged Bearing Vibrations , 2007 .

[38]  F. Sadeghi,et al.  An Approach for Modeling Material Grain Structure in Investigations of Hertzian Subsurface Stresses and Rolling Contact Fatigue , 2010 .

[39]  Aki Mikkola,et al.  Modeling and Dynamic Analysis of Spherical Roller Bearing with Localized Defects: Analytical Formulation to Calculate Defect Depth and Stiffness , 2016 .

[40]  N S Swansson,et al.  Applications of Vibration Analysis to the Condition Monitoring of Rolling Element Bearings , 1984 .

[41]  Utkarsh Kumar A. Patel,et al.  An analytical model (7 D.O.F.) for the prediction of the vibration response of cylindrical roller element bearings due to a combined localized defect , 2015 .

[42]  Hongrui Cao,et al.  Mechanical model development of rolling bearing-rotor systems: A review , 2018 .

[43]  Renata Klein,et al.  A new model for spall-rolling-element interaction , 2017 .

[44]  F. Sadeghi,et al.  A Voronoi FE Fatigue Damage Model for Life Scatter in Rolling Contacts , 2010 .

[45]  N Aktärk,et al.  The effect of ball size variation on vibrations associated with ball-bearings , 1998 .

[46]  Aki Mikkola,et al.  Dynamic model of a deep-groove ball bearing including localized and distributed defects. Part 2: Implementation and results , 2003 .

[47]  Steven Y. Liang,et al.  Damage mechanics approach for bearing lifetime prognostics , 2002 .

[48]  Ye Zhenhuan,et al.  Effects of axial misalignment of rings on the dynamic characteristics of cylindrical roller bearings , 2016 .

[49]  J. Y. Liu,et al.  Analysis of Tapered Roller Bearings Considering High Speed and Combined Loading , 1976 .

[50]  Yu Zhang,et al.  Vibration response mechanism of faulty outer race rolling element bearings for quantitative analysis , 2016 .

[51]  F. Sadeghi,et al.  Spall initiation and propagation due to debris denting , 1996 .

[52]  N. Morozov,et al.  Thermal Effect in Dynamic Yielding and Fracture of Metals and Alloys , 2009 .

[53]  R. A. Collacott,et al.  Vibration monitoring and diagnosis: Techniques for cost-effective plant maintenance , 1979 .

[54]  Qi An,et al.  Influences of off-sized rollers on mechanical performance of spherical roller bearings , 2015 .

[55]  Jen Fin Lin,et al.  An Analysis of Misaligned Single-Row Angular-Contact Ball Bearing , 2004 .

[56]  D.P. Skinner,et al.  The cepstrum: A guide to processing , 1977, Proceedings of the IEEE.

[57]  Donald R. Houser,et al.  Vibration Signal Analysis Techniques , 1973 .

[58]  J. D. Cogdell,et al.  Debris Denting Effects on Elastohydrodynamic Lubricated Contacts , 1997 .

[59]  Young Sup Kang Debris effects and denting process on lubricated contacts , 2004 .

[60]  F. Ville,et al.  Early Fatigue Failure Due to Dents in EHL Contacts , 1999 .

[61]  Qi An,et al.  Dynamic analysis of an unbalanced rotor-water pump-bearing system considering varying compliance effect and localized defects on bearing races , 2015 .

[62]  Rajesh Kumar,et al.  Discrete Wavelet Transform Based Measurement of Inner Race Defect Width in Taper Roller Bearing , 2013 .

[63]  Joseph Mathew,et al.  A COMPARISON OF AUTOREGRESSIVE MODELING TECHNIQUES FOR FAULT DIAGNOSIS OF ROLLING ELEMENT BEARINGS , 1996 .

[64]  P. D. McFadden,et al.  The vibration produced by multiple point defects in a rolling element bearing , 1985 .

[65]  G. Jang,et al.  Stability Analysis of a Rotating System Due to the Effect of Ball Bearing Waviness , 2003 .

[66]  F. Sadeghi,et al.  A 3D Finite Element Study of Fatigue Life Dispersion in Rolling Line Contacts , 2011 .

[67]  F. Ville,et al.  Influence of the nature and size of solid particles on the indentation features in EHL contacts , 1998 .

[68]  Qinkai Han,et al.  Nonlinear dynamic modeling of rotor system supported by angular contact ball bearings , 2017 .

[69]  Yimin Shao,et al.  Dynamic simulation for a tapered roller bearing considering a localized surface fault on the rib of the inner race , 2017 .

[70]  Satish C. Sharma,et al.  Vibration based performance prediction of ball bearings caused by localized defects , 2012 .

[71]  Peter J. Kootsookos,et al.  MODELING OF LOW SHAFT SPEED BEARING FAULTS FOR CONDITION MONITORING , 1998 .

[72]  Seong-Wook Hong,et al.  Study on the stiffness and fatigue life of tapered roller bearings with roller diameter error , 2017 .

[73]  Lixin Xu,et al.  Modeling of a deep-groove ball bearing with waviness defects in planar multibody system , 2015 .

[74]  Fabrice Bolaers,et al.  Low speed bearings fault detection and size estimation using instantaneous angular speed , 2016 .

[75]  X. Qin,et al.  A study on the effect of subsurface crack propagation on rolling contact fatigue in a bearing ring , 2015 .

[76]  Zoran Ren,et al.  Surface initiated crack growth simulation in moving lubricated contact , 2002 .

[77]  Hiroyuki Ohta,et al.  VIBRATION CHARACTERISTICS OF TAPERED ROLLER BEARINGS , 1996 .

[78]  T. Fujiwara,et al.  Paper II(i) Measurement of propagation initiation and propagation time of rolling contact fatigue cracks by observation of acoustic emission and vibration , 1987 .

[79]  Mohsen Nakhaeinejad Fault detection and model-based diagnostics in nonlinear dynamic systems , 2010 .

[80]  F. Sadeghi,et al.  Dent Initiated Spall Formation in EHL Rolling/Sliding Contact , 1998 .

[81]  Rajesh Kumar,et al.  Outer race defect width measurement in taper roller bearing using discrete wavelet transform of vibration signal , 2013 .

[82]  Srečko Glodež,et al.  Numerical Analysis of 3D Subsurface Crack Propagation in Large Slewing Bearing , 2013, CP 2013.

[83]  M. W. Washo,et al.  A quick method for determining root causes and corrective actions of failed ball bearings , 1996 .

[84]  F P Wardle,et al.  Vibration Forces Produced by Waviness of the Rolling Surfaces of Thrust Loaded Ball Bearings Part 2: Experimental Validation , 1988 .

[85]  J. Antoni Fast computation of the kurtogram for the detection of transient faults , 2007 .

[86]  Jacob Bortman,et al.  Toward a 3D dynamic model of a faulty duplex ball bearing , 2015 .

[87]  E. Yhland,et al.  A Linear Theory of Vibrations Caused by Ball Bearings With Form Errors Operating at Moderate Speed , 1992 .

[88]  Carl Q. Howard,et al.  Analyses of contact forces and vibration response for a defective rolling element bearing using an explicit dynamics finite element model , 2014 .

[89]  Homer Rahnejat,et al.  Bearing induced vibration in precision high speed routing spindles , 2000 .

[90]  Fagang Zhao,et al.  Vibration response of ball bearings with different defect sizes in the outer raceway: Simulation with a 3-D finite element model , 2015 .

[91]  Chong-Won Lee,et al.  Modelling and Vibration Analysis of Misaligned Rotor-Ball Bearing Systems , 1999 .

[92]  Xu Qingyu,et al.  Dynamic model of ball bearings with internal clearance and waviness , 2006 .

[93]  Yimin Shao,et al.  An investigation of a detection method for a subsurface crack in the outer race of a cylindrical roller bearing , 2017 .

[94]  Srečko Glodež,et al.  Numerical modelling of crack path in the lubricated rolling-sliding contact problems , 2008 .

[95]  Michael D. Bryant,et al.  Dynamic Modeling of Rolling Element Bearings With Surface Contact Defects Using Bond Graphs , 2011 .

[96]  G. Jang,et al.  Nonlinear excitation model of ball bearing waviness in a rigid rotor supported by two or more ball bearings considering five degrees of freedom , 2001 .

[97]  Raouf A. Ibrahim,et al.  Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part II: Dynamics and Modeling , 1994 .

[99]  P. K. Gupta,et al.  On the Geometrical Imperfections in Cylindrical Roller Bearings , 1988 .

[100]  Linkai Niu,et al.  A systematic study of ball passing frequencies based on dynamic modeling of rolling ball bearings with localized surface defects , 2015 .

[101]  F. Sadeghi,et al.  A Statistical Damage Mechanics Model for Subsurface Initiated Spalling in Rolling Contacts , 2008 .

[102]  Lang Hu,et al.  Modeling high-speed angular contact ball bearing under the combined radial, axial and moment loads , 2014 .

[103]  Jinglin Wen,et al.  Finite element analysis of a subsurface penny-shaped crack with crack-face contact and friction under a moving compressive load , 2012 .

[104]  I. Epps An investigation into vibrations excited by discrete faults in rolling element bearings , 1991 .

[105]  Robert B. Randall,et al.  Vibration response of spalled rolling element bearings: Observations, simulations and signal processing techniques to track the spall size , 2011 .

[106]  P. D. McFadden,et al.  Vibration monitoring of rolling element bearings by the high-frequency resonance technique — a review , 1984 .

[107]  A. Palmgren Ball and roller bearing engineering , 1945 .

[108]  Tejas H. Patel,et al.  Vibration response of misaligned rotors , 2009 .

[109]  Xiaojun Zhou,et al.  Dynamic analysis of double-row self-aligning ball bearings due to applied loads, internal clearance, surface waviness and number of balls , 2014 .

[110]  A. Lubrecht,et al.  Transient Analysis of Surface Features in an EHL Line Contact in the Case of Sliding , 1994 .

[111]  N. Tandon,et al.  An analytical model for the prediction of the vibration response of rolling element bearings due to a localized defect , 1997 .

[112]  Hugh Hunt,et al.  A dynamic model to predict the occurrence of skidding in wind-turbine bearings , 2011 .

[113]  D. Nélias,et al.  Contact Fatigue Analysis of a Dented Surface in a Dry Elastic–Plastic Circular Point Contact , 2008 .

[114]  T. E. Tallian Prediction of Rolling Contact Fatigue Life in Contaminated Lubricant: Part II—Experimental , 1976 .

[115]  Robert B. Randall,et al.  Vibration-based Condition Monitoring: Industrial, Aerospace and Automotive Applications , 2011 .

[116]  R. K. Purohit,et al.  Dynamic analysis of ball bearings with effect of preload and number of balls , 2006 .

[117]  Homer Rahnejat,et al.  The Vibrations of Radial Ball Bearings , 1985 .

[118]  Robert B. Randall,et al.  Simulating gear and bearing interactions in the presence of faults Part II. Simulation of the vibrations produced by extended bearing faults , 2008 .

[119]  Farshid Sadeghi,et al.  A New Approach to Modeling Surface Defects in Bearing Dynamics Simulations , 2008 .

[120]  Xuening Zhang,et al.  A comprehensive dynamic model to investigate the stability problems of the rotor–bearing system due to multiple excitations , 2016 .

[121]  Delun Wang,et al.  A new method for determining load distributions among rollers of bearing with manufacturing errors , 2013 .

[122]  Song Deng,et al.  Subsurface crack propagation under rolling contact fatigue in bearing ring , 2013 .

[123]  Zhengjia He,et al.  Dynamic Modeling and Vibration Response Simulation for High Speed Rolling Ball Bearings With Localized Surface Defects in Raceways , 2014 .

[124]  Chanan Singh,et al.  Report of Large Motor Reliability Survey of Industrial and Commercial Installations, Part II , 1985, IEEE Transactions on Industry Applications.

[125]  S. Harsha Nonlinear dynamic analysis of a high-speed rotor supported by rolling element bearings , 2006 .

[126]  Xi Zhang,et al.  Mechanical analysis of spherical roller bearings due to misalignments between inner and outer rings , 2017 .

[127]  Nalinaksh S. Vyas,et al.  ESTIMATION OF NON-LINEAR STIFFNESS PARAMETERS OF ROLLING ELEMENT BEARINGS FROM RANDOM RESPONSE OF ROTOR-BEARING SYSTEMS , 1995 .

[128]  Zhang Zhi-qiang,et al.  Investigation of rolling contact fatigue damage process of the coating by acoustics emission and vibration signals , 2012 .

[129]  Fulei Chu,et al.  Stability analysis of a rotor-bearing system with time-varying bearing stiffness due to finite number of balls and unbalanced force , 2013 .

[130]  Yimin Shao,et al.  An analytical model to predict vibrations of a cylindrical roller bearing with a localized surface defect , 2017 .

[131]  Lin Liang,et al.  Quantitative diagnosis of a spall-like fault of a rolling element bearing by empirical mode decomposition and the approximate entropy method , 2013 .

[132]  Robert B. Randall,et al.  Simulating gear and bearing interactions in the presence of faults. Part I. The combined gear bearing dynamic model and the simulation of localised bearing faults , 2008 .

[133]  Robert B. Randall,et al.  Rolling element bearing diagnostics—A tutorial , 2011 .

[134]  Daniel Nelias,et al.  Analysis of Double-Row Tapered Roller Bearings, Part I - Model , 2003 .

[135]  J. Morlet,et al.  Wave propagation and sampling theory—Part II: Sampling theory and complex waves , 1982 .

[136]  F P Wardle,et al.  Vibration Forces Produced by Waviness of the Rolling Surfaces of Thrust Loaded Ball Bearings Part 1: Theory , 1988 .

[137]  Carl Q. Howard,et al.  A nonlinear dynamic vibration model of defective bearings – The importance of modelling the finite size of rolling elements , 2015 .

[138]  Long Tran,et al.  Ball Bearing Dynamic Analysis Using Computer Methods—Part I: Analysis , 1996 .

[139]  Carl Q. Howard,et al.  A defect size estimation method based on operational speed and path of rolling elements in defective bearings , 2016 .

[140]  Neil R. Paulson,et al.  A New Approach for Fatigue Damage Modeling of Subsurface-Initiated Spalling in Large Rolling Contacts , 2017 .

[141]  Staffan Andréason,et al.  Load distribution in a taper roller bearing arrangement considering misalignment , 1973 .

[142]  N. Tandon,et al.  A theoretical model to predict the vibration response of rolling bearings in a rotor bearing system to distributed defects under radial load , 2000 .

[143]  Hui Ma,et al.  Fault features analysis of cracked gear considering the effects of the extended tooth contact , 2015 .

[144]  N. Tandon,et al.  A Theoretical Model to Predict Vibration Response of Rolling Bearings to Distributed Defects Under Radial Load , 1998 .

[145]  M. Feldman Hilbert transform in vibration analysis , 2011 .

[146]  F. Ville,et al.  Detrimental Effects of Debris Dents on Rolling Contact Fatigue , 2000 .

[147]  S. P. Harsha,et al.  Non-linear vibration signature analysis of a high-speed rotating shaft due to ball size variations and varying number of balls , 2009 .

[148]  X Yuan,et al.  Multi-body vibration modelling of ball bearing–rotor system considering single and compound multi-defects , 2014 .

[149]  Pavle Boškoski,et al.  Distributed bearing fault diagnosis based on vibration analysis , 2016 .

[150]  P. D. McFadden,et al.  Model for the vibration produced by a single point defect in a rolling element bearing , 1984 .

[151]  Y. Kadin,et al.  Modeling of surface cracks in rolling contact , 2012 .

[152]  G Simon Prediction of Vibration Behaviour of Large Turbo-Machinery on Elastic Foundations Due to Unbalance and Coupling Misalignment , 1992 .

[153]  Yimin Shao,et al.  A New Model for the Relationship Between Vibration Characteristics Caused by the Time-Varying Contact Stiffness of a Deep Groove Ball Bearing and Defect Sizes , 2015 .

[154]  C. Nataraj,et al.  Nonlinear modeling and analysis of a rolling element bearing with a clearance , 2011 .

[155]  Sriramachandra Aithal,et al.  Effect of manufacturing errors on load distribution in large diameter slewing bearings of fast breeder reactor rotatable plugs , 2016 .

[156]  Qi An,et al.  Influences of roller diameter error on contact stress for cylindrical roller bearing , 2015 .

[157]  Jing Liu,et al.  An improved analytical model for a lubricated roller bearing including a localized defect with different edge shapes , 2018 .

[158]  Hongrui Cao,et al.  Dynamic modeling and vibration response simulations of angular contact ball bearings with ball defects considering the three-dimensional motion of balls , 2017 .

[159]  T. Yoshioka,et al.  Detection of rolling contact sub-surface fatigue cracks using acoustic emission technique , 1993 .

[160]  L. D. Meyer,et al.  An Analytic Model for Ball Bearing Vibrations to Predict Vibration Response to Distributed Defects , 1980 .

[161]  S. Harsha,et al.  Non-linear dynamic behaviors of rolling element bearings due to surface waviness , 2004 .

[162]  Zhengjia He,et al.  Method for Vibration Response Simulation and Sensor Placement Optimization of a Machine Tool Spindle System with a Bearing Defect , 2012, Sensors.

[163]  S. Pincus Approximate entropy (ApEn) as a complexity measure. , 1995, Chaos.

[164]  Idriss El-Thalji,et al.  Dynamic modelling of wear evolution in rolling bearings , 2015 .

[165]  Jing Liu,et al.  A comparative study of surface waviness models for predicting vibrations of a ball bearing , 2017 .

[166]  J. K. Dutt,et al.  Impact Force Based Model for Bearing Local Fault Identification , 2015 .

[167]  Yimin Shao,et al.  A new method to model a localized surface defect in a cylindrical roller-bearing dynamic simulation , 2014 .

[168]  L. M. Rogers The application of vibration signature analysis and acoustic emission source location to on-line condition monitoring of anti-friction bearings , 1979 .

[169]  Wennian Yu,et al.  The dynamic coupling behaviour of a cylindrical geared rotor system subjected to gear eccentricities , 2017 .

[170]  Raouf A. Ibrahim,et al.  Vibro-Impact Dynamics , 2009 .

[171]  Seong-Wook Hong,et al.  The effect of angular misalignment on the stiffness characteristics of tapered roller bearings , 2017 .

[172]  Kyosuke Ono,et al.  Reduction of NRRO in ball bearings for HDD spindle motors , 2004 .

[173]  C. S. Sunnersjö Rolling bearing vibrations—The effects of geometrical imperfections and wear , 1985 .

[174]  J. Mathew,et al.  The condition monitoring of rolling element bearings using vibration analysis , 1984 .

[175]  Subsurface propagation of partial ring cracks under rolling contact: Part II. Fracture mechanics analysis , 2006 .

[176]  Guanci Chen,et al.  Effects of off-sized cylindrical rollers on the static load distribution in a cylinder roller bearing , 2012 .

[177]  Daming Lin,et al.  A review on machinery diagnostics and prognostics implementing condition-based maintenance , 2006 .

[178]  J. A. Wensing,et al.  THE INFLUENCE OF LUBRICATION ON THE DYNAMIC BEHAVIOUR OF BALL BEARINGS , 1999 .

[179]  Pyung Hwang,et al.  Dynamic Model to Predict Effect of Race Waviness on Vibrations Associated with Deep-Groove Ball Bearing , 2014 .

[180]  Johannes Brändlein,et al.  Ball and roller bearings: Theory, design, and application , 1985 .

[181]  F. Sadeghi,et al.  Explicit finite element modeling of subsurface initiated spalling in rolling contacts , 2010 .

[182]  Zheng Dezhi,et al.  Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System with Radial Clearances and Waviness Considered , 2008 .

[183]  A. Nabhan,et al.  Vibration analysis of deep groove ball bearing with outer race defect using ABAQUS , 2016 .

[184]  Diego Galar,et al.  Methodology for the physics-based modelling of multiple rolling element bearing configurations , 2017 .

[185]  Pavan Kumar Kankar,et al.  Nonlinear Vibration Signature Analysis of a High Speed Rotor Bearing System Due to Race Imperfection , 2012 .

[186]  Ming J. Zuo,et al.  The effects of the shape of localized defect in ball bearings on the vibration waveform , 2013 .

[187]  Idriss El-Thalji,et al.  Fault analysis of the wear fault development in rolling bearings , 2015 .

[188]  B. Eftekharnejad,et al.  The application of spectral kurtosis on Acoustic Emission and vibrations from a defective bearing , 2011 .

[189]  Robert X. Gao,et al.  Mechanical Systems and Signal Processing Approximate Entropy as a Diagnostic Tool for Machine Health Monitoring , 2006 .

[190]  Diego Galar,et al.  Multi-body modelling of rolling element bearings and performance evaluation with localised damage , 2016 .

[191]  Daniel Nelias,et al.  A unified and simplified treatment of the non-linear equilibrium problem of double-row rolling bearings. Part 2: Application to taper rolling bearings supporting a flexible shaft , 2003 .

[192]  Anil Kumar,et al.  Enhancing Weak Defect Features Using Undecimated and Adaptive Wavelet Transform for Estimation of Roller Defect Size in a Bearing , 2017 .

[193]  M. Cao,et al.  A comprehensive dynamic model of double-row spherical roller bearing—Model development and case studies on surface defects, preloads, and radial clearance , 2008 .

[194]  Nizami Aktürk,et al.  An Investigation of Rolling Element Vibrations Caused by Local Defects , 2008 .

[195]  J. Y. Liu The Effect of Misalignment on the Life of High Speed Cylindrical Roller Bearings , 1971 .

[196]  Jing Lin,et al.  Feature Extraction Based on Morlet Wavelet and its Application for Mechanical Fault Diagnosis , 2000 .

[197]  Mark Hadfield,et al.  Subsurface propagation of partial ring cracks under rolling contact. Part I. Experimental studies , 2006 .

[198]  T. A. Harris,et al.  Essential Concepts of Bearing Technology , 2006 .

[199]  Gun-Hee Jang,et al.  Vibration analysis of a rotating system due to the effect of ball bearing waviness , 2004 .

[200]  Lei Hou,et al.  Application of the HB–AFT method to the primary resonance analysis of a dual-rotor system , 2017 .

[201]  Pradeep K. Gupta,et al.  Transient Ball Motion and Skid in Ball Bearings , 1975 .

[202]  Yimin Shao,et al.  Dynamic modeling for rigid rotor bearing systems with a localized defect considering additional deformations at the sharp edges , 2017 .

[203]  R. Ibrahim Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part I: Mechanics of Contact and Friction , 1994 .

[204]  J. K. Dutt,et al.  2nd International Conference on Innovations in Automation and Mechatronics Engineering, ICIAME 2014 Fault size estimation in the outer race of ball bearing using discrete wavelet transform of the vibration signal , 2014 .

[205]  Yimin Shao,et al.  Dynamic modelling of a rotor-bearing-housing system including a localized fault , 2018 .

[206]  Yimin Shao,et al.  An investigation for the friction torque of a needle roller bearing with the roundness error , 2018 .

[207]  T. A. Harris The Effect of Misalignment on the Fatigue Life of Cylindrical Roller Bearings Having Crowned Rolling Members , 1969 .

[208]  Homer Rahnejat,et al.  Vibration Modeling of Rotating Spindles Supported by Lubricated Bearings , 2002 .

[209]  Robert B. Randall,et al.  The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines , 2006 .

[210]  V. N. Patel,et al.  A Dynamic Model for Vibration Studies of Deep Groove Ball Bearings Considering Single and Multiple Defects in Races , 2010 .

[211]  Fengtao Wang,et al.  Dynamic modelling for vibration analysis of a cylindrical roller bearing due to localized defects on raceways , 2015 .

[212]  T. E. Tallian,et al.  Failure atlas for Hertz contact machine elements , 1992 .

[213]  Tae-Jo Park Effect of Roller Profile and Misalignment in EHL of Finite Line Contacts , 2010 .

[214]  S. Harsha Nonlinear dynamic analysis of rolling element bearings due to cage run-out and number of balls , 2006 .

[215]  M. Elforjani,et al.  Assessment of natural crack initiation and its propagation in slow speed bearings , 2009 .

[216]  Yimin Shao,et al.  Vibration modelling of nonuniform surface waviness in a lubricated roller bearing , 2017 .

[217]  N. Tandon,et al.  A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings , 1999 .

[218]  Yang Yu,et al.  A fault diagnosis approach for roller bearings based on EMD method and AR model , 2006 .

[219]  F. Sadeghi,et al.  Surface defects effects on bearing dynamics , 2010 .

[220]  Jose Mathew,et al.  A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing , 2010 .

[221]  O. Prakash,et al.  EFFECT OF RADIAL INTERNAL CLEARANCE OF A BALL BEARING ON THE DYNAMICS OF A BALANCED HORIZONTAL ROTOR , 2000 .

[222]  Yang Yu,et al.  A roller bearing fault diagnosis method based on EMD energy entropy and ANN , 2006 .

[223]  Umberto Meneghetti,et al.  Application of the envelope and wavelet transform analyses for the diagnosis of incipient faults in ball bearings , 2001 .

[224]  A. D. Sahasrabudhe,et al.  A dynamic model of ball bearing for simulating localized defects on outer race using cubic hermite spline , 2014, Journal of Mechanical Science and Technology.

[225]  Raouf A. Ibrahim,et al.  Vibro-Impact Dynamics: Modeling, Mapping and Applications , 2009 .

[226]  S. Suresh Fatigue of materials , 1991 .

[227]  Raouf A. Ibrahim Handbook of Structural Life Assessment , 2017 .

[228]  Jeroen Anton Wensing,et al.  On the dynamics of ball bearings , 1998 .

[229]  Idriss El-Thalji,et al.  A summary of fault modelling and predictive health monitoring of rolling element bearings , 2015 .

[230]  J. Antoni The spectral kurtosis: a useful tool for characterising non-stationary signals , 2006 .

[231]  Miha Boltežar,et al.  Improved model of a ball bearing for the simulation of vibration signals due to faults during run-up , 2011 .

[232]  Wennian Yu,et al.  Effects of tooth plastic inclination deformation due to spatial cracks on the dynamic features of a gear system , 2017 .

[233]  A. Olver The Mechanism of Rolling Contact Fatigue: An Update , 2005 .

[234]  Yuebin Guo,et al.  A fundamental study on the impact of surface integrity by hard turning on rolling contact fatigue , 2006 .

[235]  Hideyuki Tamura,et al.  On the Radial Vibration of Ball Bearings : Computer Simulation , 1985 .

[236]  Colin H. Hansen,et al.  An extensive review of vibration modelling of rolling element bearings with localised and extended defects , 2015 .

[237]  E.L. Owen,et al.  Assessment of the Reliability of Motors in Utility Applications - Updated , 1986, IEEE Transactions on Energy Conversion.

[238]  Shoji Noguchi,et al.  The Influence of location of balls and ball diameter difference in rolling bearings on the nonrepetitive runout (NRRO) of retainer revolution , 2005 .

[239]  Jing Liu,et al.  Vibration analysis of ball bearings with a localized defect applying piecewise response function , 2012 .

[240]  Thomas G. Habetler,et al.  A survey of condition monitoring and protection methods for medium voltage induction motors , 2009, 2009 IEEE Energy Conversion Congress and Exposition.

[241]  Hui Ma,et al.  Review on dynamics of cracked gear systems , 2015 .

[242]  T. E. Tallian,et al.  Progress in Rolling Bearing Vibration Research and Control , 1965 .

[243]  Trevor S. Slack,et al.  A Review of Rolling Contact Fatigue , 2009 .

[244]  Yongyong He,et al.  Approximate Entropy Analysis of the Acoustic Emission From Defects in Rolling Element Bearings , 2012 .

[245]  Aki Mikkola,et al.  Dynamic model of a deep-groove ball bearing including localized and distributed defects. Part 1: Theory , 2003 .

[246]  M. J. Hine Absolute ball bearing wear measurements from SSME turbopump dynamic signals , 1989 .

[247]  Rajendra Singh,et al.  VIBRATION TRANSMISSION THROUGH ROLLING ELEMENT BEARINGS, PART II: SYSTEM STUDIES , 1990 .

[248]  Saeid Vafaei,et al.  Indicated repeatable runout with wavelet decomposition (IRR-WD) for effective determination of bearing-induced vibration , 2003 .

[249]  J. A. Wensing,et al.  The dynamic behaviour of a system that includes a rolling bearing , 2001 .

[250]  F. Sadeghi,et al.  Experimental and Analytical Investigation of High Speed Turbocharger Ball Bearings , 2011 .

[251]  C. K. Babu,et al.  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 , 2012 .

[252]  O. Prakash,et al.  DYNAMIC RESPONSE OF AN UNBALANCED ROTOR SUPPORTED ON BALL BEARINGS , 2000 .

[253]  A. Lubrecht,et al.  Numerical Simulation of a Transverse Ridge in a Circular EHL Contact Under Rolling/Sliding , 1994 .

[254]  F. Sadeghi,et al.  Numerical modeling of sub-surface initiated spalling in rolling contacts , 2013 .

[255]  S. Yuan,et al.  Jet cooling for rolling bearings: Flow visualization and temperature distribution , 2016 .

[256]  Seong-Wook Hong,et al.  The effect of angular misalignment on the running torques of tapered roller bearings , 2016 .

[257]  David,et al.  A New Model for Estimating Vibrations Generated in the Defective Rolling Element Bearings of the vibration response due to defects on rolling element bearings requires , 2011 .

[258]  Y.-T. Su,et al.  On the Detectability of Roller Bearing Damage by Frequency Analysis , 1993 .

[259]  Marc A. Meyers,et al.  Dynamic fracture (spalling) of metals , 1983 .

[260]  N. Tandon,et al.  Application of acoustic emission technique for the detection of defects in rolling element bearings , 2000 .

[261]  S. Creju,et al.  A dynamic analysis of tapered roller bearing under fully flooded conditions part 1: theoretical formulation , 1995 .

[262]  Desheng Li,et al.  Simulation and Experimental Validation of Tapered Roller Bearing Vibration Induced by Geometrical Imperfection on Cup Raceway , 2014 .

[263]  Seong-Wook Hong,et al.  Fatigue life of tapered roller bearing subject to angular misalignment , 2016 .

[264]  Utkarsh Kumar A. Patel,et al.  Nonlinear Dynamic Response of Cylindrical Roller Bearing–Rotor System with 9 Degree of Freedom Model Having a Combined Localized Defect at Inner–Outer Races of Bearing , 2017 .

[265]  Rajendra Singh,et al.  Effect of bearing preloads on the modal characteristics of a shaft-bearing assembly: Experiments on double row angular contact ball bearings , 2012 .

[266]  Yimin Shao,et al.  A theoretical study on vibrations of a ball bearing caused by a dent on the races , 2018 .

[267]  G. H. Jang,et al.  Analysis of a Ball Bearing With Waviness Considering the Centrifugal Force and Gyroscopic Moment of the Ball , 2003 .

[268]  Michael Yu Wang,et al.  Research on the rotational accuracy measurement of an aerostatic spindle in a rolling bearing performance analysis instrument , 2014 .

[269]  S. P. Harsha,et al.  The effect of ball size variation on nonlinear vibrations associated with ball bearings , 2004 .

[270]  Jin Zhou,et al.  Active magnetic bearings used as exciters for rolling element bearing outer race defect diagnosis. , 2016, ISA transactions.

[271]  S Kabus,et al.  A new quasi-static multi-degree of freedom tapered roller bearing model to accurately consider non-Hertzian contact pressures in time-domain simulations , 2014 .

[272]  F. Sadeghi,et al.  Effects of plasticity on subsurface initiated spalling in rolling contact fatigue , 2012 .

[273]  Jing Liu,et al.  A new dynamic model for vibration analysis of a ball bearing due to a localized surface defect considering edge topographies , 2015 .

[274]  Yimin Shao,et al.  A numerical investigation of effects of defect edge discontinuities on contact forces and vibrations for a defective roller bearing , 2016 .

[275]  Farshid Sadeghi,et al.  A Numerical Model for Life Scatter in Rolling Element Bearings , 2008 .

[276]  Jing-Shan Zhao,et al.  A study on waviness induced vibration of ball bearings based on signal coherence theory , 2014 .

[277]  Guanci Chen,et al.  Effects of raceway roundness and roller diameter errors on clearance and runout of a cylindrical roller bearing , 2013 .

[278]  Takashi Yamamoto,et al.  Relationship between Growth of Rolling Contact Fatigue Cracks and Load Distribution , 2000 .