Abstract
In this paper, theoretical analysis of combined effects of micropolarity and surface roughness on the performance characteristics of hydrodynamic lubrication of slider bearings with various film shapes such as plane slider bearing, exponential slider bearing, secant-shaped slider bearing and hyperbolic slider bearing is presented. A stochastic random variable with non-zero mean, variance and skewness is assumed to mathematically model the surface roughness of the slider bearing. The Eringen’s (J Math Mech 16:1–18, 1) micropolar fluid is used to characterize the rheological behavior of the lubricant with polymer additives. The averaged modified Reynolds equation is derived and the closed form of expressions for the bearing characteristics such as load carrying capacity, frictional force, center of pressure are obtained. Numerical results are compared for various film shapes under consideration, the negatively skewed surface roughness increases the load carrying capacity, frictional force and temperature.
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Abbreviations
- \( C_{\text{f}} \) :
-
Coefficient of friction
- C :
-
Maximum deviation from the mean film thickness
- \( F^{*} \) :
-
Frictional force per unit width on the surface \( y = 0 \)
- \( F \) :
-
Dimensionless frictional force corresponding to \( \left( { = \frac{{F^{*} s_{h} }}{{\mu UL_{1} }}} \right) \)
- \( H \) :
-
Film thickness [given is Eq. (1)]
- \( h(x) \) :
-
Mean film thickness
- \( h_{1} \) :
-
Inlet film thickness
- \( H_{0} \) :
-
Outlet film thickness
- \( \bar{h} \) :
-
Dimensionless film thickness \( \left(= h /{s_h}\right)\)
- \( \bar{h}_{\text{m}} \) :
-
Is the non-dimensional film thickness when P is maximum
- \( h_{\text{s}} \) :
-
Stochastic film thickness measured from the mean levels of the bearing
- \( l \) :
-
Characteristic length of micropolar fluid \( \left(= ({\gamma/{4\mu })}^{1/2}\right) \)
- \( L \) :
-
Length ratio \( \left(= s_h/l\right) \)
- \( N \) :
-
Coupling number \( \left(= {(\chi/2\mu + \chi)}^1/2\right) \)
- \( p \) :
-
Lubricant film pressure
- \( \bar{p} \) :
-
Expected value of the lubricant film pressure \( \left( { = E(p)} \right) \)
- \( P \) :
-
Dimensionless film pressure \( \left( { = \frac{{\bar{p}s_{h}^{2} }}{{\mu UL_{1} }}} \right) \)
- \( W \) :
-
Non-dimensional load carrying capacity per unit width \( \left( { = \frac{{ws_{h}^{2} }}{{\mu UL_{1}^{2} }}} \right) \)
- \( x,y \) :
-
Cartesian coordinates
- X :
-
Dimensionless form of x \( = x/L_1 \)
- \( \alpha^{*} \) :
-
Mean of the stochastic film thickness
- \( \sigma^{*} \) :
-
Standard deviation of the film thickness
- \( \varepsilon^{*} \) :
-
Measure of symmetry of the stochastic random variable
- \( \alpha \) :
-
Non-dimensional form of \( \alpha^{*} \) \( (= \alpha^*/s_h) \)
- \( \varepsilon \) :
-
Non-dimensional form of \( \varepsilon^{*} \) \( (= \varepsilon^*/s_h^3) \)
- \( \sigma \) :
-
Non-dimensional form of \( \sigma^{*} \) \( (= \sigma^*/s_h^2) \)
- \( \gamma ,\,\chi \) :
-
Viscosity coefficients for micropolar fluids
- \( \mu \) :
-
Classical viscosity coefficient
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Siddangouda, A., Biradar, T.V. & Naduvinamani, N.B. Combined effects of micropolarity and surface roughness on the hydrodynamic lubrication of slider bearings. J Braz. Soc. Mech. Sci. Eng. 36, 45–58 (2014). https://doi.org/10.1007/s40430-013-0053-7
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DOI: https://doi.org/10.1007/s40430-013-0053-7