This study presents a comprehensive analytical and numerical investigation of load distribution in deep groove ball bearings with variable radial clearance under combined axial, radial, and moment loading conditions. Unlike previous models that assume constant clearance, the proposed approach incorporates an elliptical outer race geometry to simulate realistic clearance variation. An analytical model based on Hertzian contact theory and the Newton–Raphson iterative method is developed to estimate ball deformation, load sharing, and contact angle variation. The influence of ball angular position and outer race orientation on internal load behavior is systematically analyzed. A 3D finite element model is also constructed to validate the analytical findings. Results demonstrate that the proposed design reduces the peak load on the most heavily loaded ball by approximately 3.5% compared to conventional constant-clearance bearings. The finite element analysis confirms a peak stress of 1337 MPa and a maximum inner race deformation of 0.0426 mm. These findings highlight the potential of variable clearance designs in enhancing load distribution, and reducing stress concentrations in high-load and precision applications.
LiXYuKMaH, et al. Analysis of varying contact angles and load distributions in defective angular contact ball bearing. Eng Fail Anal2018; 91: 449–464.
2.
FangBWanSZhangJ, et al. Research on the influence of clearance variation on the stiffness fluctuation of ball bearing under different operating conditions. J Mech Des2021; 143(2): 023403.
3.
FangBZhangJ.Analytical determination of the optimal clearance for the fatigue life of ball bearing under different load conditions. J Tribol2022; 144(2): 021203.
4.
SjovallH. The load distribution within ball and roller bearings under given external radial and axial load. Teknisk Tidskrift Mek1933; 9: 97–102.
5.
JonesAB.A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. Wear1960; 3: 484.
6.
HarrisTACreceliusWJ. Rolling bearing analysis. 4th ed.John Wiley & Sons, 2001.
7.
TomovićR.Calculation of the boundary values of rolling bearing deflection in relation to the number of active rolling elements. Mech Mach Theory2012; 47: 74–88.
8.
TomovićR.Calculation of the necessary level of external radial load for inner ring support on q rolling elements in a radial bearing with internal radial clearance. Int J Mech Sci2012; 60(1): 23–33.
9.
HoupertL.Load-displacement relationships for ball and spherical roller bearings. J Tribol2015; 137(2): 021102.
10.
RicciMC.Internal loading distribution in statically loaded ball bearings subjected to an eccentric thrust load. Math Probl Eng2009; 2009(1): 471804.
11.
KorolevAVKorolevAAKreheľR.Character of distribution of the load between the balls in the ball bearings under the action combined of external load. Mech Mach Theory2014; 81: 54–61.
12.
ZhangYSunGLimTC, et al. A fast and reliable numerical method for analyzing loaded rolling element bearing displacements and stiffness. J Vibroengineering2015; 17(2): 620–642.
13.
YangLDengSLiHX.Numerical analysis of loaded stress and central displacement of deep groove ball bearing. J Central South Univ2016; 23(10): 2542–2549.
14.
LiuJTangCWuH, et al. An analytical calculation method of the load distribution and stiffness of an angular contact ball bearing. Mech Mach Theory2019; 142: 103597.
15.
LiKTangW.Load-displacement relationship model and measurement of deep groove ball bearing and 4-point contact ball bearing. J Mech Sci Technol2021; 35(7): 3045–3058.
16.
XiHLinTRWangF, et al. Contact probabilities of an angular ball bearing under a combined axial and radial load. Mech Mach Theory2021; 157: 104196.
17.
DharapGTalbotD.A quasi-static load distribution model for deep groove ball bearings. J Mech Des2026; 148(1): 013501.
18.
DharapGTalbotD. A model and an experimental methodology to validate deep groove ball bearing load distribution. In: International design engineering technical conferences and computers and information in engineering conference, 25 August 2025, Vol. 88445, p.V010T10A018. American Society of Mechanical Engineers. DOI:10.1115/DETC2024-146371.
19.
ShanWChenYWangX, et al. Nonlinear dynamic characteristics of deep groove ball bearings with an improved contact model. Machines2023; 11(3): 340.
20.
TuWLiuCWangH, et al. Influences of external moment on the contact characteristics of angular contact ball bearings under combined loads. Int J Non Linear Mech2024; 161: 104698.
21.
LiuMXuKWeiX, et al. Study on internal load distribution of deep groove ball bearings considering raceway surface waviness. J Tribol2025; 147(1): 014302.
22.
XuHWangPMaH, et al. Analysis of axial and overturning ultimate load-bearing capacities of deep groove ball bearings under combined loads and arbitrary rotation speed. Mech Mach Theory2022; 169: 104665.
23.
WangMYanKZhangX, et al. A comprehensive study on dynamic performance of ball bearing considering bearing deformations and ball-inner raceway separation. Mech Syst Signal Process2023; 185: 109826.
24.
AokiS.Study on the radial ball bearing. Report of the Government Mechanical Laboratory. Report no. 44, 1961.
25.
OhtaHSakaguchiTUchiumiM.Load–displacement relationship of a ball bearing with axial, radial, and angular displacements for both the inner and outer rings. J Tribol2017; 139(1): 011103.
26.
XiaoliRJiaZGeR.Calculation of radial load distribution on ball and roller bearings with positive, negative and zero clearance. Int J Mech Sci2017; 131–132: 1–7.
27.
OswaldFBZaretskyEVPoplawskiJV.Effect of internal clearance on load distribution and life of radially loaded ball and roller bearings. Tribol Trans2012; 55(2): 245–265.
28.
SinhaRSahooV.Effect of relative movement between bearing races on load distribution on ball bearings. SN Appl Sci2020; 2(12): 2100.
29.
GaoSWangLZhangY.Modeling and dynamic characteristic analysis of high speed angular contact ball bearing with variable clearance. Tribol Int2023; 182: 108330.
30.
JainPHBhosleSP.Mathematical modeling, simulation and analysis of non-linear vibrations of a ball bearing due to radial clearance and number of balls. Mater Today Proc2023; 72: 927–936.
31.
TijareVNagarajSSastryJ, et al. Load capacity estimation of elliptical contact rolling bearings. Mater Today Proc2020; 24: 1686–1695.
32.
SinhaRSahooVPaswanM.Radial load distribution by balls in a ball bearing with variable clearance. Mech Based Des Struct Mach2023; 51(6): 3538–3563.
33.
SinhaRSahooVPaswanM, et al. An analytical method of axial load distribution of deep groove variable clearance radial ball bearings. Mech Based Des Struct Mach2024; 52(3): 1669–1685.
34.
SahooVSinhaRPaswanM.A ball bearing assembly with variable radial clearance for enhanced load distribution. Australian Patent AU 2021106954, 2022.
35.
VermaASahooV.Analytical and numerical analysis of load distribution in a thin walled flexible race ball bearing. J Strain Anal Eng Des2025; 60: 526–539.
36.
TabatabaeiRAasiAJafariSM, et al. Experimental investigation of the diagnosis of angular contact ball bearings using acoustic emission method and empirical mode decomposition. Adv Tribol2020; 2020(1): 1–14.
