Based on a set of formulae for calculating elliptical contact parameters and elastic deformation developed by Houpert and mechanical analysis, a numerical model is established for calculating the roller load distribution and shaft axis orbit of spherical roller bearings with considering off-sized rollers in this paper. A numerical calculation example is carried out to investigate the effects of single off-sized roller and multiple off-sized rollers on spherical roller bearing roller load distribution and axis orbit. Results show that the roller maximum load will increase as its off-sized diameter becomes larger than the nominal diameter, and the roller maximum load will decrease as its off-sized diameter is smaller than the nominal diameter. The maximum loads of the rollers in the two rows neighboring on the off-sized roller/rollers can also be affected. Meanwhile, roller diameter error will largely affect the axis orbit and inner ring radial displacement of spherical roller bearings.
Krzemiński-FredaHWardaB. Correction of the roller generators in spherical roller bearings. Wear1996; 192: 29–39.
5.
HoupertL. An engineering approach to Hertzian contact elasticity—part I. J Tribol2001; 123: 582–588.
6.
BerceaINéliasDCavallaroG. A unified and simplified treatment of the non-linear equilibrium problem of double-row rolling bearings. Part 1: rolling bearing model. Proc IMechE, Part J: J Engineering Tribology2003; 217: 206–212.
7.
SakaguchiTAkamatsuY. Effect of roller profile on characteristics of spherical roller bearing (part 1): examination using a quasi-static analysis program. Jpn J Tribol2006; 51: 267–281.
8.
SakaguchiTAkamatsuY. Effect of roller profile on characteristics of spherical roller bearing (part 2): experimental validation of the quasi-static analysis in terms of bearing torque. Jpn J Tribol2006; 51: 284–291.
9.
CaoM. A refined double-row spherical roller bearing model and its application in performance assessment of moving race shaft misalignments. J Vib Control2007; 13: 1145–1168.
10.
CaoMXiaoJ. A comprehensive dynamic model of double-row spherical roller bearing-model development and case studies on surface defects, preloads, and radial clearance. Mech Syst Sig Process2008; 22: 467–489.
11.
FiedlerSKiekbuschTSauerB. Investigation of inner contact and friction conditions of a spherical roller bearing using multi-body simulation. Period Polytech Mech Eng2011; 55: 79–84.
12.
GhalamchiBSopanenJMikkolaA. Simple and versatile dynamic model of spherical roller bearing. Int J Rotating Mach2013; 2013: 1–13.
13.
Ghalamchi B, Sopanen JT and Mikkola AM. Dynamic model of spherical roller bearing. In: ASME 2013 international design engineering technical conferences and computers and information in engineering conference. Portland, USA, 4 August–7 August 2013, pp.1–10. New York: ASME.
14.
TallianTEGustafssonOG. Progress in rolling bearing vibration research and control. ASLE Trans1965; 8: 195–207.
15.
WardleFP. Vibration forces produced by waviness of the rolling surface of thrust loaded ball bearings. Part 1: theory. Proc IMechE, Part C: J Mechanical Engineering Science1988; 202: 305–312.
16.
WardleFP. Vibration forces produced by waviness of the rolling surface of thrust loaded ball bearings. Part 2: experimental validation. Proc IMechE, Part C: J Mechanical Engineering Science1988; 202: 313–319.
17.
YhlandE. A linear theory of vibrations caused by ball bearings with form errors operating at moderate speed. J Tribol1992; 114: 348–359.
18.
LynaghNRahnejatHEbrahimiM. Bearing induced vibration in precision high speed routing spindles. Int J Mach Tools Manuf2000; 40: 561–577.
19.
VafaeiSRahnejatH. Indicated repeatable runout with wavelet decomposition (IRR-WD) for effective determination of bearing-induced vibration. J Sound Vib2003; 260: 67–82.
20.
NoguchiSTanakaK. Theoretical analysis of a ball bearing used in HDD spindle motors for reduction of NRRO. IEEE Trans Magn1999; 35: 845–850.
21.
NoguchiSOnoK. Reduction of NRRO in ball bearings for HDD spindle motors. Precis Eng2004; 28: 409–418.
22.
NoguchiSHirumaKKawaH. The influence of location of balls and ball diameter difference in rolling bearings on the nonrepetitive ronout (NRRO) of retainer revolution. Precis Eng2005; 29: 11–18.
23.
HarshaSP. The effect of ball size variation on nonlinear vibrations associated with ball bearings. Proc IMechE, Part K: J Multi-body Dynamics2004; 218: 191–210.
24.
UpadhyaySHJainSCHarshaSP. Non-linear vibration signature analysis of high speed rotating shaft due to ball size variations and varying number of balls. Proc IMechE, Part K: J Multi-body Dynamics2009; 223: 83–105.
25.
ChenGCMaoFHWangBK. Effects of off-sized cylindrical rollers on the static load distribution in a cylinder roller bearing. Proc IMechE, Part J: J Engineering Tribology2012; 226: 687–696.
26.
ChenGCWangBKMaoFH. Effects of raceway roundness and roller diameter errors on clearance and runout of a cylindrical roller bearing. Proc IMechE, Part J: J Engineering Tribology2013; 227: 275–285.
27.
PatelUAUpadhyaySH. Theoretical model to predict the effect of localized defect on dynamic behavior of cylindrical roller bearing at inner race and outer race. Proc IMechE, Part K: J Multi-body Dynamics2014; 228: 152–171.
28.
PetersenDHowardCSawalhiN. Analysis of bearing stiffness variations, contact forces and vibrations in radially loaded double row rolling element bearings with raceway defects. Mech Syst Sig Process2015; 50–51: 139–160.
29.
HertzH. On the contact of elastic solids. J Reine Angew1881; 92: 156–171.
30.
RahnejatHGoharR. The vibrations of radial ball bearings. Proc IMechE, Part C: J Mechanical Engineering Science1985; 199: 181–193.
31.
KushwahaMRahnejatH. Transient concentrated finite line roller-to-race contact under combined entraining, tilting and squeeze film motions. J Phys D: Appl Phys2004; 37: 2018–2034.
32.
LuoJWLuoTY. Analysis, calculation and application of rolling element bearings, 1st ed. Beijing: China Machine Press, 2009, pp. 59–59. (in Chinese).
33.
HarrisTAKotzalasMN. Rolling bearing analysis: essential concepts of bearing technology, 5th ed. New York: Taylor and Francis Group, 2006, pp. 135–136.
34.
LiuJY. The effect of misalignment on the life of high speed cylindrical roller bearings. J Lubr Technol1971; 93: 60–68.
