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Correlation between vibration and power consumption of angular contact ball bearings under structural size combinations based on nonlinear dynamic model

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Abstract

To explore the correlation between vibration and power consumption of angular contact ball bearings, the evaluation of power consumption was merged into the original nonlinear dynamic model of ball bearings and this model was validated by the experimental method. On this basis, a comprehensive analysis of vibration and power consumption of ball bearings was conducted, then, the variations in the power consumption and vibration at different numbers of balls and groove curvature radii were studied again, their optimal combinations were determined to attain the acceptable power consumption, dynamic stability and vibration in the bearing system. The corresponding results illustrate that reducing the maximum number of balls by one or two can obtain the good dynamic performance of friction consumption, dynamic stability and vibration of ball bearings, besides, the combination of inner and outer groove curvature radii should both strengthen contact loads and effectively guide the motion of the ball to get the favorable comprehensive performances. Compared to existing methods, this innovative approach can effectively guide the structure matching design of bearing components to mitigate the vibration and power consumption of ball bearings, as a result, the experimental cost and period can be significantly reduced in engineering applications.

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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

v :

Differential sliding speed

p :

Pressure in contact area

v :

Relative skidding 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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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, Wuhan University of Technology, Wuhan, 430070, China

    Song Deng, Chuang Zhao & Can Yang

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

    Song Deng & 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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Correspondence to Can Yang or Dongsheng Qian.

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Deng, S., Zhao, C., Yang, C. et al. Correlation between vibration and power consumption of angular contact ball bearings under structural size combinations based on nonlinear dynamic model. Nonlinear Dyn 111, 16021–16047 (2023). https://doi.org/10.1007/s11071-023-08707-0

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  • DOI: https://doi.org/10.1007/s11071-023-08707-0

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