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Squeeze film characteristics of circular contacts at impact and rebound motion with micropolar lubricants

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Abstract

In this paper, pure squeeze elastohydrodynamic lubrication (EHL) motion of circular contacts with micropolar lubricant is explored at the impact and rebound processes from a lubricated surface. On the basis of micro-continuum theory, the transient modified Reynolds equation is derived. Then it is solved simultaneously with the elasticity deformation, rheology, and ball motion equations in order to obtain the transient pressure profiles, film shapes, normal squeeze velocities, and accelerations. The simulation results reveal that the effect of the micropolar lubricant is equivalent to enhancing the lubricant viscosity, which would also enlarge the damper effect. Therefore, as the characteristic length (L) and coupling number (N) of the micropolar lubricants increase, the pressure spike and the dimple form earlier, the maximum pressure and the film thickness increase, the diameter of the dimple decreases, the rebounding velocity and the maximum acceleration decrease, and the maximum relative impact force decreases. Furthermore, the secondary peak of central pressure occurred at the rebound end is greater than the first peak of central pressure occurred at maximum impact force. As the effects of micropolar lubricants increase, the first and second peaks form earlier, the total impact time decreases, and the first and the second peaks increase.

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Abbreviations

\(a_{c}\) :

Normal acceleration of the ball’s center (\(m/s^{2}\))

\(A_{c}\) :

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

b :

Reference Hertzian radius at load w 0 (m)

C w :

Relative impact force, w/w 0

D ij :

Influence coefficients for deformation calculation

\(E'\) :

Equivalent elastic modulus (Pa)

g:

Acceleration of gravity (\(m/s^{2} )\)

\(\bar{g}\) :

Dimensionless acceleration of gravity, \(g\mu_{0}^{2} R/E^{{{\prime }2}} b^{2}\)

G :

Dimensionless material parameter, α \(E'\)

h :

Film thickness

h 0 :

Rigid separation

h 00 :

Thickness of lubricant layer

h c :

Central film thickness

h min :

Minimum film thickness

H :

Dimensionless film thickness, hR/b 2

K :

Constant in Reynolds equation, \(8\pi /W_{0}\)

m :

Mass of ball (kg)

\(l\) :

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

\(L\) :

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

N :

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

p :

Pressure (Pa)

p c :

Central pressure (Pa)

p h :

Reference Hertzian pressure at load w 0 (Pa)

P :

Dimensionless pressure, p/p h

r :

Radial coordinate (m)

R :

Ball radius (m)

t :

Time (sec)

T :

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

\(\Delta\) T :

Dimensionless time step

v 0 :

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

v 00 :

Initial normal velocity of the ball’s center

V 0 :

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

w :

Impact force (N)

w 0 :

Reference load, w 0  = mg (N)

W :

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

X :

Dimensionless radial coordinate, r/b

z :

Axial coordinate

z’ :

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 m−3)

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Acknowledgments

The authors would like to express their appreciation to the Ministry of Science and Technology (MOST 103-2221-E-218-036), (MOST 103-2221-E-214-018) and the National Science Council (NSC 102-2221-E-218 -042) in Taiwan, R. O. C. for financial support.

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Authors and Affiliations

  1. Department of Applied Science, National Taitung University, Taitung, 95092, Taiwan, ROC

    Li-Ming Chu

  2. Interdisciplinary Program of Green and Information Technology, National Taitung University, Taitung, 95092, Taiwan, ROC

    Li-Ming Chu

  3. Department of Mechanical Engineering, Nanya Institute of Technology, Taoyuan, 32091, Taiwan, ROC

    Jaw-Ren Lin

  4. Department of Mechanical Engineering, Kun Shan University, Tainan, 71070, Taiwan, ROC

    Yuh-Ping Chang

  5. Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung, 84001, Taiwan, ROC

    Hsiang-Chen Hsu

  6. Department of Industrial Management, I-Shou University, Kaohsiung, 84001, Taiwan, ROC

    Hsiang-Chen Hsu

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  1. Li-Ming Chu
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  2. Jaw-Ren Lin
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  3. Yuh-Ping Chang
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Correspondence to Hsiang-Chen Hsu.

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Chu, LM., Lin, JR., Chang, YP. et al. Squeeze film characteristics of circular contacts at impact and rebound motion with micropolar lubricants. Microsyst Technol 23, 465–472 (2017). https://doi.org/10.1007/s00542-016-3132-8

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  • DOI: https://doi.org/10.1007/s00542-016-3132-8

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