In the paper, a combined model of traction and ball bearings dynamics is established, considering the interaction among the cage, races, and balls. A curve-fitted traction model, which can be used to analyze the effect of the geometry of the bearing and parameters of the lubricant, is applied. The traction that is affected by certain parameters is analyzed; then, the effect of the traction on ball bearings is investigated. The displacements of balls and contact angles are different under different surface roughness. The changes in displacements of balls and contact angles are obtained with different roughness, load, and velocities. The amplitudes of axial displacement of balls are bigger with the roughness being higher. The amplitudes of ball-inner contact angles increase with greater roughness, and the amplitudes of ball-outer race contact angles decrease with greater roughness. The simulated vibration results of ball bearings under different levels agree with the actual by the model.
HarrisTA. Ball motion in thrust-loaded, angular contact bearings with Coulomb friction. J Tribol1971; 93: 32–38.
2.
JonesAB. Ball motion and sliding friction in ball bearings. J Basic Eng1959; 81: 1–12.
3.
JonesAB. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. J Fluids Eng Trans ASME1960; 82: 309–320.
4.
WaltersCT. The dynamics of ball bearings. J Tribol1971; 93: 1–10.
5.
GuptaPK. Advanced dynamics of rolling elements. New York: Springer Science & Business Media, 1984, Epub ahead of print1984: 23–99.
6.
MeeksCRNgKO. The dynamics of ball separators in ball bearings—part I: analysis. ASLE Trans1985; 28: 277–287.
7.
MeeksCR. The dynamics of ball separators in ball bearings—part II: results of optimization study. ASLE Trans1985; 28: 288–295.
8.
HoupertL. CAGEDYN: a contribution to roller bearing dynamic calculations part I: basic tribology concepts. Tribol Trans2009; 53: 1–9.
9.
HoupertL. CAGEDYN: a contribution to roller bearing dynamic calculations part II: description of the numerical tool and its outputs. Tribol Trans2009; 53: 10–21.
10.
HoupertL. CAGEDYN: a contribution to roller bearing dynamic calculations. Part III: experimental validation. Tribol Trans2010; 53: 848–859.
11.
StackeLEFritzsonDNordlingP. BEAST—A rolling bearing simulation tool. Proc Inst Mech Eng Part K J Multi-body Dyn1999; 213: 63–71.
12.
AiniRRahnejatHGoharR. A five degrees of freedom analysis of vibrations in precision spindles. Int J Mach Tools Manuf1990; 30: 1–18.
13.
RahmanAKAiniRGoharR. On the effects of bearing settings on the dynamic performance of a three-bearing machine tool spindle assembly. Proc Inst Mech Eng Part K J Multi-body Dyn2002; 216: 133–141.
14.
HuangDLiuYLiuH, et al.Resonances of elastic rotor induced by roller bearing with consideration of cage vibration. Proc Inst Mech Eng Part K J Multi-body Dyn2018; 232: 446–456.
15.
AshtekarASadeghiF. A new approach for including cage flexibility in dynamic bearing models by using combined explicit finite and discrete element methods. J Tribol2012; 134: 041502.
16.
WagnerCKrinnerAThümmelT, et al.Full dynamic ball bearing model with elastic outer ring for high speed applications. Lubricants2017; 5: 17.
17.
GaoYLiZWangJ, et al.Influences of bearing housing deflection on vibration performance of cylinder roller bearing–rotor system. Proc Inst Mech Eng Part K J Multi-body Dyn2013; 227: 106–114.
18.
TurnbullRRahmaniRRahnejatH. The effect of outer ring elastodynamics on vibration and power loss of radial ball bearings. Proc Inst Mech Eng Part K J Multi-body Dyn2020; 234: 707–722.
19.
JohnsonKLTevaarwerkJL. Shear behaviour of elastohydrodynamic oil films. Proc R Soc London A Math Phys Sci1977; 356: 215–236.
20.
BairSWinerWO. A rheological model for elastohydrodynamic contacts based on primary laboratory data. J. of Lubrication Tech. Jul1979; 101: 258–264.
21.
EvansCRJohnsonKL. The rheological properties of elastohydrodynamic lubricants. Proc Inst Mech Eng Part C J Mech Eng Sci1986; 200: 303–312.
22.
RahnejatHGoharR. The vibrations of radial ball bearings. Proc Inst Mech Eng Part C J Mech Eng Sci1985; 199: 181–193.
23.
MohammadpourMJohns-RahnejatPMRahnejatH. Roller bearing dynamics under transient thermal-mixed non-Newtonian elastohydrodynamic regime of lubrication. Proc Inst Mech Eng Part K J Multi-body Dyn2015; 229: 407–423.
24.
AlfaresMSaleemOMajeedM. Analytical study of thermal variation impact on dynamics of a spindle bearing system. Proc Inst Mech Eng Part K J Multi-body Dyn2019; 233: 871–898.
25.
MasjediMKhonsariMM. An engineering approach for rapid evaluation of traction coefficient and wear in mixed EHL. Tribol Int2015; 92: 184–190.
26.
HertzH. Über die berührung fester elastischer körper. J für die reine und Angew Math1882; 92: 156–171.
27.
HarrisTAKotzalasMN. Advanced concepts of bearing technology: rolling bearing analysis. London: CRC press, 2006.
28.
BovetCZamponiL. An approach for predicting the internal behaviour of ball bearings under high moment load. Mech Mach Theory2016; 101: 1–22.
29.
WangWHuLZhangS, et al.Modeling angular contact ball bearing without raceway control hypothesis. Mech Mach Theory2014; 82: 154–172.
30.
LiaoNTLinJF. A new method for the analysis of deformation and load in a ball bearing with variable contact angle. J Mech Des2001; 123: 304–312.
