Nonlinear dynamic investigations on rolling element bearings: A review

Rolling element bearings are one of the most precarious components and play an important role in the effective operation of rotating machinery. Bearings are one of the foremost sources of nonlinearity in rotating machineries which significantly affect the behavior of the system. The main sources of nonlinearity are radial internal clearance, unbalanced force, bearing preload, stiffness, damping, number of rolling element, and so on. Surface defects such as localized and distributed defects are also accountable for the nonlinear behavior of the system. A large number of studies and methodologies have been proposed in the last two decades to understand the nonlinear dynamic behavior of rolling element bearings considering various bearing parameters and surface defects. In this work, the authors have presented a review of different theoretical models and experimental works proposed for the analysis of the nonlinear behavior of rotating systems. This review article first quotes various techniques which have been explored for the nonlinearity analysis in rolling contact elements such as rotor-bearing system and gears. Some of the important gaps are highlighted in this work which can be considered for future studies.

[1]  Juan Antonio Ortega-Redondo,et al.  Multiple-Fault Detection Methodology Based on Vibration and Current Analysis Applied to Bearings in Induction Motors and Gearboxes on the Kinematic Chain , 2016 .

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

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

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

[5]  S. Narayanan,et al.  Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method , 1999 .

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

[7]  Shiyu Wang,et al.  Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance , 2012 .

[8]  R. S. Sayles,et al.  Surface topography and rolling element vibration , 1981 .

[9]  R. L. Ruhl,et al.  A Finite Element Model for Distributed Parameter Turborotor Systems , 1972 .

[10]  A. Diez-Ibarbia,et al.  Enhanced model of gear transmission dynamics for condition monitoring applications: Effects of torque, friction and bearing clearance , 2017 .

[11]  S. P. Harsha,et al.  Analysis of Nonlinear Phenomena in High Speed Ball Bearings due to Radial Clearance and Unbalanced Rotor Effects , 2010 .

[12]  C. Walters.  The dynamics of ball bearings , 1971 .

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

[14]  Har Prashad.  Diagnosis of failure of rolling-element bearings of alternators—a study , 1996 .

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

[16]  N. Tandon,et al.  Nonlinear Vibration Analysis of an Elastic Rotor Supported on Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races , 2014 .

[17]  Pavan Kumar Kankar,et al.  Mathematical Model for Rotor Bearing System by Considering the Effect of Shaft Dynamics and Localized Bearing Defects , 2016 .

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

[19]  N. Upadhyay,et al.  Modelling of a rotor-ball bearings system using Timoshenko beam and effects of rotating shaft on their dynamics , 2016 .

[20]  Pavan Kumar Kankar,et al.  Novel ensemble techniques for classification of rolling element bearing faults , 2017 .

[21]  Jian Chen,et al.  THE APPLICATION OF CORRELATION DIMENSION IN GEARBOX CONDITION MONITORING , 1999 .

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

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

[24]  Teruo Igarashi,et al.  Studies on the Vibration and Sound of Defective Rolling Bearings : Second Report : Sound of Ball Bearings with One Defect , 1983 .

[25]  Y.-T. Su,et al.  On initial fault detection of a tapered roller bearing: Frequency domain analysis , 1992 .

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

[27]  Y.-T. Su,et al.  The Effects of Surface Irregularities on Roller Bearing Vibrations , 1993 .

[28]  S. P. Harsha,et al.  The effect of bearing cage run-out on the nonlinear dynamics of a rotating shaft , 2008 .

[29]  Michel Fillon,et al.  Thermohydrodynamic analysis of a worn plain journal bearing , 2004 .

[30]  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 .

[31]  Sanjay H Upadhyay,et al.  A review on signal processing techniques utilized in the fault diagnosis of rolling element bearings , 2016 .

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

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

[34]  Toshio Yamamoto,et al.  On the Vibrations of a Shaft supported by Bearings having Radial Clearances , 1955 .

[35]  Ruqiang Yan,et al.  Permutation entropy: A nonlinear statistical measure for status characterization of rotary machines , 2012 .

[36]  Pavan Kumar Kankar,et al.  Effect of Unbalanced Rotor on the Dynamics of Cylindrical Roller Bearings , 2015 .

[37]  Hongyan Zhang,et al.  Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system , 2008 .

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

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

[40]  Teruo Igarashi,et al.  Studies on Vibration and Sound of Defective Rolling Bearings : Third Report, Vibration of Ball Bearing with Multiple Defects , 1985 .

[41]  Farid Golnaraghi,et al.  Effect of localized faults on chaotic vibration of rolling element bearings , 2008 .

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

[43]  J. Guyader,et al.  Routes To Chaos In Ball Bearings , 1993 .

[44]  Satish C. Sharma,et al.  Fault Diagnosis of High Speed Rolling Element Bearings Due to Localized Defects Using Response Surface Method , 2011 .

[45]  J. M. Franco,et al.  Vibration of a Rigid Shaft Supported by Radial Ball Bearings With Several Defects , 1992 .

[46]  Singiresu S Rao,et al.  A fuzzy approach for the analysis of unbalanced nonlinear rotor systems , 2005 .

[47]  Ioannis Antoniadis,et al.  Effect of rotational speed fluctuations on the dynamic behaviour of rolling element bearings with radial clearances , 2006 .

[48]  Jean-Jacques Sinou,et al.  Non-linear dynamics and contacts of an unbalanced flexible rotor supported on ball bearings , 2009 .

[49]  P. K. Gupta.  Dynamics of Rolling-Element Bearings—Part II: Cylindrical Roller Bearing Results , 1979 .

[50]  Joseph Mathew,et al.  USING THE CORRELATION DIMENSION FOR VIBRATION FAULT DIAGNOSIS OF ROLLING ELEMENT BEARINGS—I. BASIC CONCEPTS , 1996 .

[51]  Min Tang,et al.  Nonlinear dynamic mechanism of rolling element bearings with an internal clearance in a rotor-bearing system , 2016 .

[52]  F. F. Ehrich,et al.  Observations of Subcritical Superharmonic and Chaotic Response in Rotordynamics , 1992 .

[53]  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 .

[54]  George T. Flowers,et al.  Disk/shaft vibration induced by bearing clearance effects : Analysis and experiment , 1996 .

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

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

[57]  S. Harsha.  Non-linear dynamic response of a balanced rotor supported on rolling element bearings , 2005 .

[58]  Yourong Li,et al.  Detecting nonlinearity from a continuous dynamic system based on the delay vector variance method and its application to gear fault identification , 2010 .

[59]  章義 田村,et al.  玉軸受の振動 : 第1報, 半径方向の玉通過振動について , 1960 .

[60]  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 .

[61]  Ian Howard,et al.  A Review of Rolling Element Bearing Vibration 'Detection, Diagnosis and Prognosis', , 1994 .

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

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

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

[65]  John A. Williams,et al.  Wear and wear particles—some fundamentals , 2005 .

[66]  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 .

[67]  C. S. Sunnersjö.  Varying compliance vibrations of rolling bearings , 1978 .

[68]  P. K. Gupta,et al.  Dynamics of Rolling-Element Bearings—Part I: Cylindrical Roller Bearing Analysis , 1979 .

[69]  Jun Ma,et al.  Detection of localised defects in rolling element bearings via composite hypothesis test , 1995 .

[70]  Teruo Igarashi,et al.  Studies on the Vibration and Sound of Defective Rolling Bearings : First Report : Vibration of Ball Bearings with One Defect , 1982 .

[71]  Aditya Sharma,et al.  Feature extraction and fault severity classification in ball bearings , 2016 .

[72]  Joseph Mathew,et al.  USING THE CORRELATION DIMENSION FOR VIBRATION FAULT DIAGNOSIS OF ROLLING ELEMENT BEARINGS—II. SELECTION OF EXPERIMENTAL PARAMETERS , 1996 .

[73]  Saburo Aiba.  On the Vibration of a Rotating Shaft System Having Two Rotors , 1974 .

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

[75]  Minel J. Braun,et al.  Vibration Monitoring and Damage Quantification of Faulty Ball Bearings , 2004 .

[76]  Girish Kumar Singh,et al.  Induction machine drive condition monitoring and diagnostic research—a survey , 2003 .

[77]  Alberto Rolo-Naranjo,et al.  A method for the correlation dimension estimation for on-line condition monitoring of large rotating machinery , 2005 .

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

[79]  H. D. Nelson,et al.  The Dynamics of Rotor-Bearing Systems Using Finite Elements , 1976 .

[80]  Cai-Wan Chang-Jian,et al.  Strong nonlinearity analysis for gear-bearing system under nonlinear suspension—bifurcation and chaos , 2010 .

[81]  Pavan Kumar Kankar,et al.  Failure Analysis of a Grease-Lubricated Cylindrical Roller Bearing , 2014 .

[82]  T. C. Gupta,et al.  Instability and Chaos of a Flexible Rotor Ball Bearing System: An Investigation on the Influence of Rotating Imbalance and Bearing Clearance , 2010 .

[83]  Nizami Aktürk,et al.  The Effect of Waviness on Vibrations Associated Witli Ball Bearings , 1999 .

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

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

[86]  S. P. Harsha,et al.  Nonlinear dynamic analysis of an unbalanced rotor supported by roller bearing , 2005 .

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

[88]  Jayanta Datta,et al.  of Factors Influencing the Structural Vibration in Ball Bearings , 2000 .

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

[90]  P. Gupta.  Frictional Instabilities in Ball Bearings , 1988 .

[91]  E. M. Yhland,et al.  Paper 29: Waviness Measurement-An Instrument for Quality Control in Rolling Bearing Industry , 1967 .

[92]  S. P. Harsha,et al.  Nonlinear dynamic analysis of a rotor bearing system due to distributed defects using factorial design of experiments , 2007 .

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

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

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

[96]  A. Nayfeh,et al.  Linear and Nonlinear Structural Mechanics , 2002 .

[97]  I︠u︡. A. Mitropolʹskiĭ.  Problems of the asymptotic theory of nonstationary vibrations , 1965 .

[98]  S. P. Harsha,et al.  Nonlinear dynamic dnalysis of high speed rolling element bearings due to cage run-out , 2005 .

[99]  Pavan Kumar Kankar,et al.  Effect of Varying the Number of Rollers on Dynamics of a Cylindrical Roller Bearing , 2014 .

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

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

[102]  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 .

[103]  Jean Frene,et al.  Experimental Study of Tilting-Pad Journal Bearings—Comparison With Theoretical Thermoelastohydrodynamic Results , 1992 .

[104]  R. Gohar,et al.  The effects of number of balls and preload on vibrations associated with ball bearings , 1997 .

[105]  S. P. Harsha,et al.  Nonlinear dynamic response of a balanced rotor supported by rolling element bearings due to radial internal clearance effect , 2006 .

[106]  J. K. Dutt,et al.  Model updating of rotors supported on ball bearings and its application in response prediction and balancing , 2013 .

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

[108]  S. P. Harsha,et al.  Rolling Bearing Vibrations—The Effects of Surface Waviness and Radial Internal Clearance , 2006 .

[109]  Xiaoyao Shen,et al.  Numerical Analysis of a Rub-impact Rotor-bearing System with Mass Unbalance: , 2007 .

[110]  S. Saito,et al.  Calculation of Nonlinear Unbalance Response of Horizontal Jeffcott Rotors Supported by Ball Bearings With Radial Clearances , 1985 .

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

[112]  Fawzi M.A. El-Saeidy,et al.  Dynamics of a Rigid Rotor Linear/Nonlinear Bearings System Subject to Rotating Unbalance and Base Excitations , 2010 .

[113]  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 .

[114]  Abdallah A. Elsharkawy,et al.  Effects of axial preloading of angular contact ball bearings on the dynamics of a grinding machine spindle system , 2003 .

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

[116]  J. I. Inayat-Hussain.  Chaos via torus breakdown in the vibration response of a rigid rotor supported by active magnetic bearings , 2007 .

[117]  Eihab M. Abdel-Rahman,et al.  Vibrations of balanced fault-free ball bearings , 2010 .