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Dynamic and wear characteristics of self-lubricating bearing cage: effects of cage pocket shape

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Abstract

The frequent impulse collisions and wear between the ball and cage pocket not only affect the bearing stability but also significantly impact the deterioration of the bearing service life. A comprehensive dynamic model for analyzing the stability, skidding degree, ball–cage collision, wear distribution, and wear rate of four types of cage pocket is proposed. A series of tests of cage whirling conducted on self-lubricating bearing test bench using high-speed photographic technology have proven the accuracy of the model. It is found that the cage with a combination of circle and rectangle pockets has the highest stability. The circle pocket has a larger collision area and higher wear rate than rectangle and diamond pockets. The combined rectangle–diamond pocket has a better wear resistance.

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Data availability

All data generated or analyzed during this study are included in this published article.

Abbreviations

\(\left({x}_{r},{y}_{r},{z}_{r}\right)\) :

Bearing global coordinate system

\(\left({x}_{c},{y}_{c},{z}_{c}\right)\) :

Cage coordinate system

\(\left({x}_{b},{y}_{b},{z}_{b}\right)\) :

Rolling element coordinate system

\(\left({x}_{p},{y}_{p},{z}_{p}\right)\) :

Cage pocket reference system

\(\left({x}_{h},{y}_{h}\right)\) :

Hertzian contact area reference system

j :

Subscripts for jth rolling element or cage segment

i :

Subscripts for inner ring

o :

Subscripts for outer ring

\({a}_{p},{b}_{p}\) :

Long and short axis of the contact ellipse

\(A(m,n)\) :

Area of the (mth, nth) discretized Hertzian contact patch

\(C, {K}_{0}^{^{\prime}}, {K}_{0}\) :

Lubricant parameter under certain operating conditions

\({c}_{p}\) :

The viscous damping coefficient

\({D}_{m}\) :

Bearing pitch diameter

D b :

Ball diameter

\({D}_{p}\) :

Cage pocket diameter

\(E,\upsilon \) :

Young’s modulus and Poisson’s ratio

\({E}_{bp}\) :

Effective elasticity modulus for ball–pocket pair

\({F}_{a},{F}_{r}\) :

External force on the bearing

\({F}_{p}\) :

Normal contact force

\({F}_{g}\), \({f}_{g}\) :

Contact normal and tangential force of the cage-guide ring rubbing

\({F}_{c}\) :

Cage force

\({f}_{h}\) :

Friction force of ball–cage pocket

\({h}_{p}\) :

Oil film thickness

\({h}_{c}\) :

Radial height position of the collision point

\(H\) :

The Brinell hardness

\({K}_{c}\) :

Contact stiffness

\({K}_{w}\) :

The Archard wear coefficients

\({L}_{r},{L}_{z}\) :

Displacements of the center position of the rolling elements

\({m}_{c}\) :

Ball and cage mass

\({m}_{node}\),\({n}_{node}\) :

Discretized node number of Hertzian contact area

\({N}_{b}\) :

Number of rolling elements

\(Q\) :

Contact force

\({q}_{p}\) :

The discretize contact pressure

\({r}_{p}\) :

Curvature radius

\(R\) :

Distance between ball center and node of contact patch

S :

Area of contact patch

t :

Operating time

\(\Delta {V}_{h}\) :

Ball–pocket relatively friction speed

\({V}_{c}\) :

Relative revolution tangential speed of the cage and ball

\({w}_{rate}\) :

Wear rate

\(\alpha \) :

Contact angle

\(\gamma \) :

Angle of the cage-guide ring contact force

\({\delta }_{p}\) :

The ball–pocket collision deformation

\({\mu }_{0}\) :

Oil viscosity at a reference temperature

\(\mu \) :

Oil viscosity

\(\theta \) :

Pocket angular position

\({\theta }_{b}\) :

Ball angular position

\(\lambda \) :

Constant to determine whether the cage collides with ball

\({\omega }_{x},{\omega }_{y}, {\omega }_{z}\) :

Ball self-rotation speed

\({\omega }_{m}\) :

Ball orbital rotating speed

\({\omega }_{th}\) :

Cage rotation speed as the rolling element under pure rolling

\({\omega }_{c}\) :

Cage rotating speed

\(\psi \) :

Angle of contact point in the pocket coordinate system

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Funding

This research was supported in part by a scholarship from the China Scholarship Council (CSC) under Grant CSC N° 201806880007, National Science Foundation of China under Grant No. 11872222, and the State Key Laboratory of Tribology under Grant No. SKLT2021D11.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Politecnico Di Milano, Via G. La Masa 1, 20156, Milan, Italy

    Shuai Gao, Steven Chatterton & Paolo Pennacchi

  2. State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Shuai Gao, Qinkai Han & Feibin Zhang

  3. Beijing Institute of Control Engineering, Beijing, 100000, China

    Ningning Zhou

  4. School of Aeronautics, Northwestern Polytechnical University, Xi’an, 710072, China

    Zhaohui Yang

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  1. Shuai Gao
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Correspondence to Qinkai Han.

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Gao, S., Han, Q., Zhou, N. et al. Dynamic and wear characteristics of self-lubricating bearing cage: effects of cage pocket shape. Nonlinear Dyn 110, 177–200 (2022). https://doi.org/10.1007/s11071-022-07611-3

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