Dynamic modeling for rigid rotor bearing systems with a localized defect considering additional deformations at the sharp edges

Abstract Rotor bearing systems (RBSs) play a very valuable role for wind turbine gearboxes, aero−engines, high speed spindles, and other rotational machinery. An in−depth understanding of vibrations of the RBSs is very useful for condition monitoring and diagnosis applications of these machines. A new twelve−degree−of−freedom dynamic model for rigid RBSs with a localized defect (LOD) is proposed. This model can formulate the housing support stiffness, interfacial frictional moments including load dependent and load independent components, time−varying displacement excitation caused by a LOD, additional deformations at the sharp edges of the LOD, and lubricating oil film. The time−varying displacement model is determined by a half−sine function. A new method for calculating the additional deformations at the sharp edges of the LOD is analytical derived based on an elastic quarter−space method presented in the literature. The proposed dynamic model is utilized to analyze the influences of the housing support stiffness and LOD sizes on the vibration characteristics of the rigid RBS, which cannot be predicted by the previous dynamic models in the literature. The results show that the presented method can give a new dynamic modeling method for vibration formulation for a rigid RBS with and without the LOD on the races.

[1]  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 .

[2]  Homer Rahnejat,et al.  An Experimental Investigation into Bearing-Induced Spindle Vibration , 1995 .

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

[4]  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 .

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

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

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

[8]  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 .

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

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

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

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

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

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

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

[16]  David P. Fleming Vibration Transmission through Bearings with Application to Gearboxes , 2007 .

[17]  Debra F. Laefer,et al.  A Ritz’s method based solution for the contact problem of a deformable rectangular plate on an elastic quarter-space , 2010 .

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

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

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

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

[22]  J. J. Blech,et al.  In Situ Determination of Rolling Bearing Stiffness and Damping by Modal Analysis , 1987 .

[23]  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 .

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

[25]  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 .

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

[27]  Hui Ma,et al.  Nonlinear dynamic analysis of a rotor-bearing-seal system under two loading conditions , 2013 .

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

[29]  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 .

[30]  Yamin Li,et al.  A New Dynamic Model of Ball-Bearing Rotor Systems Based on Rigid Body Element , 2016 .

[31]  T. E. Tallian,et al.  Ball bearing lubrication: The elastohydrodynamics of elliptical contacts , 1982 .

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

[33]  Qi An,et al.  Influences of bearing housing deflection on vibration performance of cylinder roller bearing–rotor system , 2013 .

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

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

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

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

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

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

[40]  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 .

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