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Effects of surface roughness on transient squeeze EHL motion of circular contacts with micropolar fluids

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Abstract

A numerical method was developed to study the effects of the micropolar (MP) lubricants at pure squeeze action in an isothermal elastohydrodynamic lubrication point contact with surface roughness under constant load condition, but without asperities contact. The modified transient stochastic Reynolds equation was derived in polar coordinates by means of the Christensen’s stochastic theory and the Eringen’s MP fluid theory. The Gauss–Seidel method and the finite difference method were both used to solve simultaneously the modified transient stochastic Reynolds, the load balance, the lubricant rheology and the elasticity deformation equations. The simulation results revealed that the effect of the MP lubricant was equivalent to enhancing the lubricant viscosity. Therefore, the central pressure and film thickness for MP lubricants were larger than those of Newtonian fluids under the same load in the elastic deformation stage. The maximum central pressure of the radial type roughness (RN) was greater than that of the circular type RN. The film thickness of the radial type RN was smaller than that of the circular type RN.

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Abbreviations

b :

Reference Hertzian radius at load w (m)

c :

Half total range of the random film thickness variable

C :

Dimensionless half total range of the random film thickness variable, cR/b2

D ij :

Influence coefficients for deformation calculation

\( E^{\prime} \) :

Equivalent elastic modulus (Pa)

G :

Dimensionless material parameter, α\( E^{\prime} \)

h :

Film thickness (m)

h 0 :

Rigid separation (m)

H :

Dimensionless film thickness, hR/b2

K :

Constant in Reynolds equation, \( 8\pi /W \)

\( l \) :

Characteristic length of the micropolar fluids, \( l = (\gamma /4\mu )^{1/2} \)

\( L \) :

Dimensionless characteristic length of the micropolar fluids, \( lR/b^{2} \)

N :

Coupling parameter, \( N = [\chi /(2\mu + \chi )]^{1/2} \)

p :

Pressure (Pa)

p h :

Reference Hertzian pressure at load w (Pa)

P :

Dimensionless pressure, p/ph

r :

Radial coordinate (m)

R :

Ball radius (m)

t :

Time (sec)

T :

Dimensionless time, \( tE^{\prime}/\mu_{0} \)

\( u \), \( v \) :

Velocity of the lubricant in r and z directions, respectively (m/s)

\( v_{c} \) :

Normal velocity of the ball’s center (m/s)

V c :

Dimensionless normal velocity of the ball’s center, \( v_{c} \mu_{0} R/E^{\prime}b^{2} \)

w :

Load (N)

W :

Dimensionless load, \( w/E^{\prime}R^{2} \)

X :

Dimensionless radial coordinate, r/b

z :

Axial coordinate

\( z^{\prime} \) :

Pressure–viscosity index

\( \mu \) :

Viscosity of lubricant (Pa s)

\( \mu_{0} \) :

Viscosity at ambient pressure (Pa s)

\( \bar{\mu } \) :

Dimensionless viscosity, \( \mu /\mu_{0} \)

\( \rho \) :

Density of lubricant (kg/m3)

\( \rho_{0} \) :

Density of lubricant at ambient pressure (kg/m3)

\( \bar{\rho } \) :

Dimensionless density of lubricant, \( \rho /\rho_{0} \)

\( \delta \) :

Random part due to the surface asperities

\( \sigma \) :

Standard deviation

\( \Delta \) :

Elastic deformation (m)

\( \bar{\Delta } \) :

Dimensionless elastic deformation, R\( \Delta \)/b2

ψ:

ψ = N/l

ξ:

Random variable characterizing the definite roughness arrangement

\( \gamma ,\chi \) :

Two additional viscosity coefficients for MP fluids

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Acknowledgements

The authors would like to express their appreciation to the Ministry of Science and Technology (MOST-107-2221-E-143-006) in Taiwan, R.O.C. for financial support.

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Authors and Affiliations

  1. Interdisciplinary Program of Green and Information Technology, Department of Applied Science, National Taitung University, Taitung City, 95092, Taiwan, R.O.C.

    Li-Ming Chu

  2. Department of Mechanical Engineering, Kun Shan University, Tainan City, 71070, Taiwan, R.O.C.

    Yuh-Ping Chang

  3. Department of Industrial Management, I-Shou University, Kaohsiung City, 84001, Taiwan, R.O.C.

    Hsiang-Chen Hsu

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  1. Li-Ming Chu
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  2. Yuh-Ping Chang
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Correspondence to Hsiang-Chen Hsu.

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Chu, LM., Chang, YP. & Hsu, HC. Effects of surface roughness on transient squeeze EHL motion of circular contacts with micropolar fluids. Microsyst Technol 26, 2903–2911 (2020). https://doi.org/10.1007/s00542-020-04861-2

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  • DOI: https://doi.org/10.1007/s00542-020-04861-2

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