This paper proposes a novel four degrees of freedom model of angular contact ball bearings (ACBBs) under high-speed effect, in order to characterize the dynamic behavior of rolling bearings with coupling waviness and local defects on the outer race in detail. Firstly, based on bearing quasi-static model, considering centrifugal force, gyroscope moment, the bearing contact stiffness is calculated. Then, the representation model of outer race waviness and the time-varying displacement excitation expression of the bearing with local defects are put forward respectively. On the basis, a dynamic model of ACBBs with coupling factors is built. Finally, the vibration characteristics of the bearing with faults are investigated, the model is verified by the existing experimental results and the influence of different parameters on the bearing dynamics is analyzed. The results show that the bearing fault characteristic frequency is unchanged when the high-speed effect is considered, but the vibration amplitude is smaller than that without the high-speed effect. With the increase of speed, the bearing fault characteristic frequency and vibration amplitude increase. When considering the coupling of outer race waviness and local defects, with the increase of the two factors, the bearing fault characteristic frequency remains unchanged but the vibration amplitude increase.
QinYWuXLuoJ. Data-model combined driven digital twin of life-cycle rolling bearing. IEEE Trans Ind Inform2021; 18: 1530–1540.
2.
GaoSChattertonSPennacchiP,et al.Behaviour of an angular contact ball bearing with three-dimensional cubic-like defect: a comprehensive non-linear dynamic model for predicting vibration response. Mech Mach Theory2021; 163: 104376.
3.
ArslanHAktürkN. An investigation of rolling element vibrations caused by local defects. J Tribol2008; 130: 041101.
4.
SalunkheVGDesavaleRGKumbharSG. Vibration analysis of deep groove ball bearing using finite element analysis and dimension analysis. J Tribol2022; 144: 081202.
5.
AshtekarASadeghiFStackeL. Surface defects effects on bearing dynamics. Proc Inst Mech Eng J-J Eng2010; 224: 25–35.
6.
PatelSPUpadhyaySH. Influence of roller defect and coupled roller–inner–outer race defects on the performance of cylindrical roller bearing. Proc Inst MechE, Part K: J Multi-Body Dynamics2019; 233: 731–746.
7.
EppsIK. An investigation into vibrations excited by discrete faults in rolling element bearings. Ph.D Thesis, University of Canterbury, 1991.
8.
NiuLCaoHHeZ,et al.Dynamic modeling and vibration response simulation for high speed rolling ball bearings with localized surface defects in raceways. J Manuf Sci Eng2014; 136: 041015.
9.
LiXYuKMaH, et al.Analysis of varying contact angles and load distributions in defective angular contact ball bearing. Eng Fail Anal2018; 91: 449–464.
10.
WuXQinYLuoJ, et al.Fault dynamic model of high-speed rolling bearing by a compound displacement excitation function considering the effect of defect roughness. Mech Mach Theory2022; 177: 105061.
11.
QinYLiCWuX, et al.Multiple-degree-of-freedom dynamic model of rolling bearing with a localized surface defect. Mech Mach Theory2020; 154: 104047.
12.
LiYLiZHeD,et al.Effect of clearance on the dynamic characteristics of high-speed rolling bearings with multiple defects. Mech Syst Signal Process2023; 200: 110512.
13.
CaoZWuGHeC, et al.A new instantaneous contact based dynamic model of rolling element bearings with local defects. Mech Syst Signal Process2023; 200: 110600.
14.
AiniRRahnejatHGoharR. A five degrees of freedom analysis of vibrations in precision spindles. Int J Mach Tools Manuf1990; 30: 1–18.
15.
AiniRRahnejatHGoharR. An experimental investigation into bearing-induced spindle vibration. Proc I MechE, Part C: J Mech Eng Sci1995; 209: 107–114.
16.
SopanenJMikkolaA. Dynamic model of a deep-groove ball bearing including localized and distributed defects. Part 1: theory. Proc Inst MechE, Part K: J Multi-Body Dynamics2003; 217: 201–211.
17.
AkturkN. The effect of waviness on vibrations associated witli ball bearings. J Tribol1999; 121: 667–677.
18.
BabuCTandonNPandeyR. 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. J Vib Acoust2012; 134: 011006–1–12.
19.
AdamczakSZmarzłyP. Influence of raceway waviness on the level of vibration in rolling-element bearings. B Pol Acad of Sci-Tech2017; 65: 541–551.
20.
SavaliaRGhoshMKPandeyRK. Vibration analysis of lubricated angular contact ball bearing of rigid rotor considering waviness of ball and races. Tribol Online2008; 3: 322–327.
21.
BaiCXuQ. Dynamic model of ball bearings with internal clearance and waviness. J Sound Vib2006; 294: 23–48.
22.
WangLLiCDezhiZ,et al.Nonlinear dynamics behaviors of a rotor roller bearing system with radial clearances and waviness considered. Chin J Aeronaut2008; 21: 86–96.
23.
LiuJShaoY. Vibration modelling of nonuniform surface waviness in a lubricated roller bearing. Journal Vib Control2017; 23: 1115–1132.
24.
NiuL. A simulation study on the effects of race surface waviness on cage dynamics in high-speed ball bearings. J Tribol2019; 141: 051101.
25.
ShahDSPatelV. Theoretical and experimental vibration studies of lubricated deep groove ball bearings having surface waviness on its races. Measurement2018; 129: 405–423.
26.
TuWWangHZhangG,et al.The influence of race waviness on skidding characteristics of rolling bearings. Int J Nonlin Mech2023; 156: 104520.
27.
LiuJLiXDingS,et al.A time-varying friction moment calculation method of an angular contact ball bearing with the waviness error. Mech Mach Theory2020; 148: 103799.
28.
NanGZhangYZhuY,et al.Nonlinear dynamics of rotor system supported by bearing with waviness. Sci Progress2020; 103: 0036850420944092.
29.
MeyerLAhlgrenFWeichbrodtB. An analytic model for ball bearing vibrations to predict vibration response to distributed defects. J Mech Des1980; 102: 205–210.
30.
LynaghNRahnejatHEbrahimiM,et al.Bearing induced vibration in precision high speed routing spindles. Int J Mach Tools Manuf2000; 40: 561–577.
31.
WardleF. Vibration forces produced by waviness of the rolling surfaces of thrust loaded ball bearings Part 1: theory. Proc Inst Mech E, Part C: J Mech Eng Sci1988; 202: 305–312.
32.
LiuJPangRXuY, et al.Vibration analysis of a single row angular contact ball bearing with the coupling errors including the surface roundness and waviness. Sci China Tech Sci2020; 63: 943–952.
33.
ZhangXYanCLiuY, et al.Dynamic modeling and analysis of rolling bearing with compound fault on raceway and rolling element. Shock Vib2020; 2020: 1–16.
34.
GaoSWangLZhangY. Modeling and dynamic characteristic analysis of high speed angular contact ball bearing with variable clearance. Tribol Int2023; 182: 108330.
35.
HarrisTA. Rolling bearing analysis. 4th ed. New York: Wiley, 2001.
36.
HarshaSPSandeepKPrakashR. Non-linear dynamic behaviors of rolling element bearings due to surface waviness. J Sound Vib2004; 272: 557–580.
37.
ChengHZhangYLuW,et al.Mechanical characteristics and nonlinear dynamic response analysis of rotor-bearing-coupling system. Appl Mathl Model2021; 93: 708–727.
38.
MohammadpourMJohns-RahnejatPRahnejatH. Roller bearing dynamics under transient thermal-mixed non-Newtonian elastohydrodynamic regime of lubrication. Proc Inst Mech E, Part K: J Multi-Body Dynamics2015; 229: 407–423.
39.
AlfaresMSaleemOMajeedM. Analytical study of thermal variation impact on dynamics of a spindle bearing system. Proc Inst Mech E, Part K: J Multi-Body Dynamics2019; 233: 871–898.
40.
LiJLeiCGongB, et al.Modeling and analysis of the composite stiffness for angular contact ball bearings. Shock Vib2020; 2020: 1–22.
