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Effect of dynamic behaviors of bearing components on friction consumptions of ball bearings at various structural sizes of cage

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Abstract

In this work, a novel dynamic model with estimating its friction consumptions is developed to study the effect of dynamic behaviors of bearing components on friction consumptions at various structural sizes of cage, which is a novel solution for effectively guiding the structure matching design of bearing components to mitigate the power consumption of ball bearings. Based on this model, the influencing factors for different friction consumptions are analyzed at various structural sizes of cage. The effects of structural sizes of cage on the friction consumptions are revealed. The results indicate that a favorable combination of pocket diameter and large diameter of cage can attain the low friction consumption of ball bearings, also, a compromise between the good dynamic stability of cage and the low friction consumption of ball bearings can be conducted to determine the thickness of cage.

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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

a :

Major axis of the elliptical area

b :

Minor axis of the elliptical area

δ :

Displacements of bearing components

θ :

Deflection angle of the bearing ring

l :

Effective contact length

λ :

Poisson's ratio

P :

Power

Q :

Contact force

α:

Contact angle

F :

Force acting on bearing components

M :

Moment

I :

Moment of inertia

ω :

Angle velocity

m :

Mass

ρ :

Density of lubricant

β :

Attitude angle of ball

η :

Viscosity of lubricant

D :

Diameter

d :

Bearing pitch diameter

κ :

MDR to the maximum whirl diameter

T :

Temperature

γ :

Groove curvature coefficient

h :

Oil film thickness

K’ c :

Oil film stiffness

p :

Pressure in contact area

v :

Sliding speed

u :

Rolling velocity

h o :

Center oil film thickness

R :

Equivalent radius of curvature

ϑ :

Elastic deformation

E’ :

Equivalent modulus of elasticity

w :

External load

p H :

Maximum Hertz contact pressure

E rp :

Relative errors of pressure

E rw :

Relative errors of load

k :

Ellipticity

ϕ :

Position angle

K’ :

Coefficient of contact stiffness

ξ :

Viscous damping coefficient

C :

Clearance

µ :

Friction coefficient

r :

Radius

ħ :

Eccentricity of the cage center

ħ ’ :

Relative eccentricity of the cage center

B :

Guide face width of the cage

ρ e :

Effective density of the oil

E :

Elasticity modulus

e H :

Coefficient of restitution

P T :

Total power

ζ :

Proportionality coefficient of the oil–gas mixture

A :

Acreage

ε :

Radius of vortex trajectory

L :

Acceleration level

σ :

Acceleration

Z :

Number of the ball

f :

Frequency

Г:

Thickness of cage

Ω:

sample size

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

i :

Inner ring

o :

Outer ring

n :

Represent i or o

b :

Ball

c :

Cage

j :

jTh ball

τ :

Friction effect

t :

Traction effect

e :

Retardation effect of lubricant

m :

Orbital revolution direction

ς :

Centrifugal direction

q :

Gyroscopic effect

v :

Viscous effect of lubricant

s :

Spin motion of balls

0:

Initial value

p :

Cage pockets

g :

Cage guidance

χ :

Unbalanced mass effect

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Acknowledgements

The authors would like to thank the Important Science and Technology Innovation Program of Hubei province (2021BAA019), Innovative Research Team Development Program of Ministry of Education of China (IRT_17R83), 111 Project (B17034) and Hubei Provincial Science and Technology Innovation Talents and Service Project (2022EJD012) for the support given to this research.

Funding

This work was funded by the Important Science and Technology Innovation Program of Hubei province (2021BAA019), Innovative Research Team Development Program of Ministry of Education of China (IRT_17R83), 111 Project (B17034) and Hubei Provincial Science and Technology Innovation Talents and Service Project (2022EJD012).

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Authors and Affiliations

  1. Hubei Key Laboratory of Advanced Technology for Automotive Components and Hubei Engineering Research Center for Green Precision Material Forming, Wuhan University of Technology, Wuhan, 430070, China

    Song Deng, Chuang Zhao, Min Wu & Dongsheng Qian

  2. Research Center of Cultural and Tourism Industries of Wuhan Business University, Wuhan, 430056, China

    Yi Jiang

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  1. Song Deng
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  4. Min Wu
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Correspondence to Min Wu or Dongsheng Qian.

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Deng, S., Jiang, Y., Zhao, C. et al. Effect of dynamic behaviors of bearing components on friction consumptions of ball bearings at various structural sizes of cage. Nonlinear Dyn 112, 5247–5267 (2024). https://doi.org/10.1007/s11071-024-09295-3

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  • DOI: https://doi.org/10.1007/s11071-024-09295-3

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