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Investigation on the friction heat generation rate of ball bearings at ultra-high rotation speed

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Abstract

Position and velocity vectors between ball-rings, ball-cage, and cage-ring in space were considered to refine the friction heat generation rate model of ball bearings. The relationship between the position vectors of each part of a bearing in space was analyzed to determine the bearing’s status of contact bearing. Hertz contact theory and Coulomb friction law were employed to calculate the normal and friction forces at the contact points, respectively. The relationship between the velocity vectors of each part in space was analyzed, and the relative sliding velocity between two parts in contact was obtained. Friction heat generation rate of bearings was calculated as the product of friction force and relative velocity. Parameters such as bearing speed, axial load, radial load, and the groove curvature radius coefficient of bearing inner and outer rings were all investigated in the case of ball bearing heat generation. Theoretical calculation and experimental results indicate that the bearing friction heat generation rate is associated with the bearing rotation speed and bearing thrust load at ultra-high rotation speed, whereas the radial load has insignificant effect. Meanwhile, a suitable inner-outer groove curvature radius coefficient can significantly reduce the bearing friction heat generation rate.

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Abbreviations

O-XYZ :

The inertial coordinate system

o-x a y a z a :

The azimuth coordinate system of ball

o r -x r y r z r :

The fixed body coordinate system of ring

o c -x c y c z c :

The coordinate system of cage

o p -x p y p z p :

The coordinate system cage pocket

o-x g y g z g :

The contact coordinate system

α :

Semi-major axis of the contact area(mm)

B c :

The width of the cage (mm)

C g :

The guide clearance of the cage (mm)

C D :

The drag coefficients

D b :

Ball diameter (mm)

D m :

Bearing pitch diameter (mm)

E′ :

The equivalent elastic modulus

f i :

Inner raceway groove curvature radius ratios

f e :

Outer raceway groove curvature radius ratios

F :

Friction force (N)

g :

Acceleration of gravity (mm/s2)

H :

Friction Heat generation rate (W)

h :

The thickness of oil film between ball and cage wall (mm)

K :

Stiffness coefficients

R x :

Equivalent r curvature radius of x (mm)

R y :

Equivalent r curvature radius of y (mm)

R i :

Circular radius of inner ring channel curvature center (mm)

R e :

Circular radius of outer ring channel curvature center (mm)

R :

Equivalent r curvature radius (mm)

r :

Position vector (mm)

T :

Transformation matrix between coordinate systems

K l :

Hertz contact stiffness coefficient of a finite length

K c :

Contact stiffness coefficient of ball and the cage pocket

ω :

Angular speed (rad/s)

ω m :

Orbital angular velocity (rad/s)

U :

Dimensionless velocity parameters

u bc :

Relative sliding speed of the ball and the pocket wall (mm/s)

u o :

The drag speed of the lubricant (mm/s)

α:

Contact angle (rad)

β :

Spiral angle (rad)

δ :

Contact deformation (mm)

ε :

Complete elliptic integral of the first kind

Γ:

Complete elliptic integral of the second kind

μ :

Friction coefficient

v :

Relative sliding speed (mm/s)

V :

Relative velocity (mm/s)

ρ ef :

Lubricant density (g/cm3)

ϑ:

Intersection angle (rad)

η o :

Dynamic viscosity of lubricant (Pa.s)

ξ :

Relative offset of the center of the cage (mm)

I :

The inertial rectangular coordinate system of bearing

r :

The fixed body coordinate system of the inner ring raceway

a :

The azimuth coordinate system of the ball

p :

The coordinate system cage pocket

g :

The contact coordinate system

i :

Inner ring

e :

Outer ring

b :

Ball

r :

Ring

c :

Cage

j :

The jth ball

x,y,z :

The ball coordinate components

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Funding

This work has been partly supported by the Key R&D project of Shandong Province (2019GGX104081, 2019GGX104033), National Natural Science Foundation of China (No. 51805299), Shandong Province’s Key Support Regions Introducing Urgently Needed Talent Projects, and Young Innovative Talents Introduction and Training Program Project of Shandong Provincial Department of Education, China Postdoctoral Science Foundation (2022M712393).

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Authors and Affiliations

  1. School of Mechanical Engineering, Shandong University of Technology, Zibo, 255049, China

    Jie Yu, Shuailun Zhu, Wei Yuan, Xiaoyang Chen, Lei He & Qianjian Guo

  2. Shanghai Key Laboratory of Mechanical Automation and Robotics, Shanghai University, Shanghai, 200072, China

    Jie Yu

  3. Tianrun Industrial Technology Co., Ltd., Weihai, 264200, China

    Shuailun Zhu & Wei Yuan

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  1. Jie Yu
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Contributions

Investigation, data curation, formal analysis, visualization, software, writing—original draft, and writing—review and editing, Jie Yu; formal analysis, and software, graphics processing, Shuailun Zhu; conceptualization, methodology, resources, supervision, and writing—review and editing, Wei Yuan; supervision, and review—editing, Qianjian Guo. All the authors have read and agreed to the published version of the manuscript.

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Correspondence to Wei Yuan.

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Yu, J., Zhu, S., Yuan, W. et al. Investigation on the friction heat generation rate of ball bearings at ultra-high rotation speed. Int J Adv Manuf Technol 128, 57–79 (2023). https://doi.org/10.1007/s00170-023-11649-x

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