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Numerical analyses of rectangular micro-textures in hydrodynamic lubrication regime for sliding contacts

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Abstract

Hydrodynamic lubrication of rectangular micro-textures on sliding contact surfaces is investigated using numerical calculation methods. The theoretical models for the slider surface are developed and the film pressure is used to evaluate the hydrodynamic lubrication based on the Reynolds equation. Meanwhile, the geometry and distribution of the rectangular dimples are optimized for maximizing the average film pressure. Results show that the film pressure is dependent on the geometry and distribution of the rectangular micro-dimples. The optimal geometry of the single rectangular dimple is obtained, and the spacing has an important influence on the film pressure. The distribution types of rectangular dimples affect the hydrodynamic lubrication significantly and the interlaced array of the rectangular micro-dimples is beneficial to enhancing the hydrodynamic lubrication. Meanwhile, the rectangular dimples with 72° interlaced angle exhibits the best effectivity.

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Abbreviations

h 0 :

Film thickness

v :

Relative sliding velocity

a :

X-width of single rectangular dimple

b :

Y-width of single rectangular dimple

d :

Depth of rectangular dimples

φ :

Array angle

l a :

X-width of an imaginary rectangular cell (horizontal direction)

l b :

Y-width of an imaginary rectangular cell (vertical direction)

s x :

X-spacing (horizontal direction)

s y :

Y-spacing (vertical direction)

l x :

Distributed width of textures in x direction (horizontal direction)

l y :

Distributed width of textures in y direction (vertical direction)

ε :

Area ratio of single rectangular dimple

h :

Local film thickness

p :

Local film pressure

η :

Dynamic viscosity

g :

Switch function

θ :

Fraction film content

ρ :

Lubricant density

ρ c :

Lubricant density in cavitation zone

p c :

Cavitation pressure

β :

Lubricant bulk modulus

x :

Cartesian coordinate paralleled to the sliding direction

y :

Cartesian coordinate perpendicular to the sliding direction

p ave :

Average film pressure

w a :

Dimensionless reference value of dimple width

h a :

Dimensionless reference value of dimple depth

P :

Dimensionless local film pressure

H :

Dimensionless local film thickness

D :

Dimensionless dimple depth

H 0 :

Dimensionless film thickness

A :

Dimensionless x-width of single rectangular dimple

B :

Dimensionless y-width of single rectangular dimple

D :

Dimensionless depth of rectangular dimples

L a :

Dimensionless x-width of an imaginary rectangular cell (horizontal direction)

L b :

Dimensionless y-width of an imaginary rectangular cell (vertical direction)

S x :

Dimensionless x-spacing (horizontal direction)

S y :

Dimensionless y-spacing (vertical direction)

L x :

Dimensionless distributed width of textures in x direction (horizontal direction)

L y :

Dimensionless distributed width of textures in y direction (vertical direction)

P c :

Dimensionless cavitation pressure

\( \bar{\beta } \) :

Dimensionless lubricant bulk modulus

X :

Dimensionless cartesian coordinate paralleled to the sliding direction

Y :

Dimensionless cartesian coordinate perpendicular to the sliding direction

s :

Number of iterations

w :

Relaxation factor

E r :

Error limit

P ave :

Dimensionless average film pressure

ξ :

Error in polynomial function

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Acknowledgements

This work is supported by the Natural Science Foundation of Jiangsu Province (BK20170676), China; National Natural Science Foundation of China (52075097, 51775105); the Technology Foundation for the Selected Returned Overseas Chinese Scholars in Nanjing (1102000219), China; and the Zhishan Young Scholar Foundation of Southeast University, China (2242020R40111), China. The authors would also like to thank the Advanced Manufacturing Processes Laboratory in Northwestern University (USA).

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Authors and Affiliations

  1. School of Mechanical Engineering, Southeast University, Nanjing, 211189, Jiangsu, People’s Republic of China

    Youqiang Xing, Xiang Li, Ruoyu Hu, Xueying Long, Ze Wu & Lei Liu

  2. Biomanufacturing Engineering Laboratory, Advanced Manufacturing Division, Tsinghua Shenzhen International Graduate School, Shenzhen, 518055, Guangdong, People’s Republic of China

    Xiang Li

  3. Department of Industrial Engineering and Management, Shanghai Jiaotong University, Shanghai, 200240, People’s Republic of China

    Xueying Long

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  1. Youqiang Xing
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Xing, Y., Li, X., Hu, R. et al. Numerical analyses of rectangular micro-textures in hydrodynamic lubrication regime for sliding contacts. Meccanica 56, 365–382 (2021). https://doi.org/10.1007/s11012-020-01296-x

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