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Study on power losses of angular contact ball bearings with and without thermal expansions of bearing components

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Abstract

In this work, thermal expansions and thermal displacements of bearing components are firstly integrated into the dynamic model of ball bearings; on this basis, the contact loads, contact angles, sliding and spinning velocities of bearings are calculated to evaluate the heat generation for the heat sources of multi-node thermal network model. Then, thermal expansions and thermal displacements of bearing components are estimated through the multi-node thermal network model to adjust the dynamic model real time. Subsequently, the effects of dynamic behaviors of bearings with thermal expansions on the power loss are revealed under various rotational speeds and loads. Research results provide a theoretical basis for engineering application of angular contact ball bearings.

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Abbreviations

ϑ :

Thermal expansion

χ :

Thermal expansion coefficient

ΔT :

Uniform temperature change

n :

The number of the balls

d :

Diameter of bearing components

Ω :

Poisson’s ratio

ω :

Angular speed

dℓ :

Bearing pitch diameter

ρ :

Material density

E :

Young’s modulus

a :

Contact angle

δ :

Displacement

p max :

Maximum contact pressure

θ :

Angular displacement of inner ring

ψ :

Angular position of balls

ƒ :

Coefficient of groove curvature

F :

Interaction force

Q :

Contact load

µ :

Asperity friction coefficient

a :

Major of the contact elliptical region

b :

Minor of the contact elliptical region

p :

Hertzian contact pressure

Δυ :

Velocity differential

Δu :

Relative skidding velocity

ƞ :

Lubricating oil viscosity

\(\Re\) :

Radius of locus of raceway groove curvature centers

H :

Oil film thickness

P :

Power loss

ε :

Elastic hysteresis loss coefficient

ba:

Balls

ru:

Rotary unit

i:

Inner ring

o:

Outer ring

sat:

Shaft

h:

Bearing house

k:

Inner diameter

l:

Outer diameter

nl:

Normal contact direction

cen:

Centrifugal direction

0:

Initial value

j:

The serial number of balls

v:

Viscous effect of lubricant

m:

Orbital revolution direction

L:

Tangential friction effect

s:

Spin motion of balls

ɩ:

Elastic material hysteresis

eff:

Oil–air mixture

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′′:

Directions along three axes of the moving coordinate system

t:

Differential slipping between balls and raceways

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Acknowledgements

The authors would like to thank the Important Science and Technology Innovation Program of Hubei Province (No. 2021BAA019) and National Key Research and Development Program of China (2019YFB2004304) for the support given to this research.

Author information

Authors and Affiliations

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

    Yi Jiang

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

    Song Deng

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

    Dongsheng Qian

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

    Song Deng & Shaofeng Jiang

Authors
  1. Yi Jiang
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  2. Song Deng
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  3. Dongsheng Qian
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  4. Shaofeng Jiang
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Corresponding authors

Correspondence to Song Deng or Dongsheng Qian.

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Technical Editor: Jarir Mahfoud.

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Appendix

Appendix

See Fig. 

Fig. 20
figure 20

Variation of ωx′(absolute), ωy′ and ωz′ in the convergent state with thermal expansion (TE) and without thermal expansion (WTE): a Fx = 100 N, b Fx = 1000 N

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20.

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Jiang, Y., Deng, S., Qian, D. et al. Study on power losses of angular contact ball bearings with and without thermal expansions of bearing components. J Braz. Soc. Mech. Sci. Eng. 45, 174 (2023). https://doi.org/10.1007/s40430-023-04086-0

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  • DOI: https://doi.org/10.1007/s40430-023-04086-0

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