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Dynamic behaviors of angular contact ball bearings based on nonlinear dynamic model with flexible ring and cage motion whirl

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Abstract

As the fundamental supporting structure in rotating machinery, the dynamic behaviors of angular contact ball bearings directly affect the operational performances of high-speed machine tools and aero-engine. In this work, a novel dynamic model considers flexible ring and cage motion whirl so that the deformations of flexible rings can change the contacts between balls and raceways to influence the dynamic behaviors of ball bearings, which is a novel solution for the dynamic performance analysis of angular contact ball bearings under different loads, assemblies and bearing structures. Then, the experimental validation conducted by a high-precision instrument demonstrated the reliability of this original model. On this basis, the effects of the clearances between housing and outer ring, the thickness of flexible ring and radial loads on the sliding of the ball, interaction forces between bearing components, vibration of inner ring, and cage whirl motion were investigated. The results show that the thick flexible ring and the minimal clearance can improve the dynamic stability of cage and mitigate the bearing vibration.

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Data availability

All data generated during this study are included in this article, and the datasets are available from the corresponding author on reasonable request.

Abbreviations

δ :

Displacements of bearing

φ :

Components azimuth angle

α:

Contact angle

Q :

Contact force

F :

Force acting on bearing

M :

Components moment

I :

Moment of inertia

Ψ :

Azimuth angle of the ball

Φ :

Position angle

d m :

Bearing pitch diameter

µ :

Friction coefficient

K :

Coefficients

E ho :

Equivalent elasticity modulus

K g :

Matrix of coefficients

e H :

Coefficient of restitution

\(\alpha^{o}\) :

Initial contact angle

l :

Effective contact length

K r :

Influence coefficient

T :

Time

g o :

Assembly clearance

Λ :

Coefficient of groove curvature

Ω :

Angle velocity

M :

Mass

V :

Poisson's ratio

D :

Diameter

Z :

Number of the ball

Ρ :

Effective density

Η :

Viscosity of lubricant

β :

Semi-angle of contact

F :

Frequency

Г c :

Thickness of outer ring

E :

Equivalent modulus

Θ :

The centroid offset angle of the cage

E :

Relative eccentricity of the cage center

P :

Contact pressure

C :

Clearance

R :

Radius

ξ:

Damping

K´:

Stiffness coefficient

x/y/z :

Directions along three axes of the global coordinate system

x′/y′/z′:

Directions along three axes of the local coordinate system

x′′/y′′/z′′:

Directions along three axes of the moving coordinate system

x c /y c /z c :

Directions along three axes of the cage coordinate system

V :

Skidding speed

d m ´(φ):

Variable bearing pitch diameter

r :

Radius

\(\Re^{\prime}\)(φ):

Radius of groove curvature center locus

u(φ):

Contact interference

∆z c / ∆y c :

Displacements of cage mass center

σ :

Acceleration

\(\vartheta\) :

Deflection angle

A :

The distance between inner and outer race groove curvature radii centers

B :

Guide face width of the cage

i:

Inner ring

o:

Outer ring

n :

Represent i or o

b:

Ball

c:

Cage

h:

Housing

j :

jth ball

τ:

Friction effect

t:

Traction effect

e:

Retardation effect of lubricant

m:

Orbital revolution direction

g:

Cage guide surface

p:

Cage pockets

r:

Radial

a:

Axial

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Acknowledgements

The authors would like to thank the Important Science and Technology Innovation Program of Hubei province (No. 2021BAA019), Innovative Research Team Development Program of Ministry of Education of China (No. IRT_17R83), 111 Project (B17034) and National Key Research and Development Program of China (2019YFB2004304) for the support given to this research.

Funding

This work was funded by the Important Science and Technology Innovation Program of Hubei province (No. 2021BAA019), Innovative Research Team Development Program of Ministry of Education of China (No. IRT_17R83), 111 Project (B17034) and National Key Research and Development Program of China (2019YFB2004304).

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Authors and Affiliations

  1. Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan, 430070, China

    Song Deng, Chuang Zhao & Dongsheng Qian

  2. Hubei Engineering Research Center for Green Precision Material Forming, Wuhan University of Technology, Wuhan, 430070, China

    Lin Hua & Dongsheng Qian

  3. Luoyang Bearing Research Institute Co., Ltd, Luoyang, 471039, China

    Song Deng & Shaofeng Jiang

Authors
  1. Song Deng
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  2. Chuang Zhao
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  3. Lin Hua
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  4. Dongsheng Qian
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  5. Shaofeng Jiang
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Correspondence to Lin Hua or Dongsheng Qian.

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Deng, S., Zhao, C., Hua, L. et al. Dynamic behaviors of angular contact ball bearings based on nonlinear dynamic model with flexible ring and cage motion whirl. Nonlinear Dyn 111, 10879–10909 (2023). https://doi.org/10.1007/s11071-023-08412-y

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  • DOI: https://doi.org/10.1007/s11071-023-08412-y

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