Lubrication theory for micropolar fluids and its application to a journal bearing

Prakash, J.; Sinha, Prawal

doi:10.1016/0020-7225(75)90031-2

Cited by 157 publications

(104 citation statements)

References 7 publications

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“…We will show the sensitiveness for two operational parameters: the load W and the friction coefficient c f . We aim to compare the results obtained with our model with those of [16,34] which are related to infinitely long devices in 2D.…”

Section: Comparison With Previous Studiesmentioning

confidence: 97%

“…As with the slider bearing, we aim to compare the results (loads and friction coefficients) obtained by our model with those of [16] (namely W 1 , c 1 f ) and [34] (namely W 2 , c 2 f ). Although the geometry of the slider and journal bearings are different and in spite of the occurrence of the cavitation phenomenon, numerical results are very similar in both cases.…”

Section: The Journal Bearingmentioning

confidence: 99%

“…Various models can be used to take such a phenomenon into account. To compare with [16], We will use the half Sommerfeld boundary-condition model in which the pressure is assumed to be zero for θ ≥ π . For the computation of W and F we take only the positive part of the pressure.…”

Section: The Journal Bearingmentioning

confidence: 99%

“…Using this set of boundary conditions, micropolar models have been widely used in tribology [11,[14][15][16][17][18]. In these papers, detailed equations are given as well as the procedure to obtain a generalized 1D or 2D Reynolds equation from the 2D or 3D (Navier) Stokes micropolar equations (1-3) It was pointed out in [19], see also [20], that another boundary condition can be used for microrotation.…”

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confidence: 99%

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Wall slip induced by a micropolar fluid

2007

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Lubrication theory is devoted to the study of thin-film flows, More often, the fluid can be considered as a Newtonian one and no-slip boundary conditions can be retained for the velocity at the fluid solid interface. With these assumptions it is possible to deduce from the (Navier) Stokes system a simplified equation describing the flow: the Reynolds equation. It allows to compute the pressure distribution inside the film and to obtain overall performances of a lubricated device such as load and friction coefficient. For very thin films, however, surface effects at the fluid solid interface become very important and no-slip conditions cannot be retained. Solid surfaces exert some influence on the liquid molecules and the effective shear viscosity along the boundary differs from the classical bulk shear viscosity. Moreover, the microstructure of the fluid cannot be ignored, especially the effects of solid-particle additives in the lubricant. Micropolar theory for fluids is often adopted to account of such microstructure and microrotation. In the present study, a thin micropolar fluid model with new boundary conditions at the fluid-solid interface is considered. This condition links velocity and microrotation at the interface by introducing a so-called "boundary viscosity". By way of asymptotic analysis, a generalized micropolar Reynolds equation is obtained. Numerical results show the influence of the new boundary conditions for the load and friction coefficients. Comparisons are made with other works that retain the no-slip boundary conditions.

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Section: Comparison With Previous Studiesmentioning

confidence: 97%

Section: The Journal Bearingmentioning

confidence: 99%

Section: The Journal Bearingmentioning

confidence: 99%

mentioning

confidence: 99%

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Wall slip induced by a micropolar fluid

2007

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“…In 1975, Shukla and Isa [3] presented the generalized Reynolds equation for micropolar fluids with the application to one-dimensional slider bearings. Meanwhile, Prakash and Sinha [4] analyzed the infinitely long journal bearing, with the lubrication of micropolar fluids. In 1978, Zaheeruddin and Isa [5] noted the steady-state characteristics for one-dimensional journal bearings and took both the infinitely short and long bearings, under micropolar lubrication, into consideration.…”

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confidence: 99%

Bifurcation and chaos for porous squeeze film damper mounted rotor–bearing system lubricated with micropolar fluid

Chang‐Jian

Kuo

2009

Nonlinear Dyn

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This study presents a dynamic analysis of a flexible rotor supported by two porous squeeze micropolar fluid-film journal bearings with nonlinear suspension. The dynamics of the rotor center and bearing center are studied. The analysis of the rotorbearing system is investigated under the assumptions of non-Newtonian fluid and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various nondimensional speed ratios. The dynamic equations are solved using the Runge-Kutta method. The methods of analysis employed in this study are inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincaré maps, and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the dynamic system varies with the nondimensional speed ratios, the nondimensional parameter, and permeability. The modeling results obtained by using the method proposed in this paper can be employed to predict the

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A finite element formulation for laminar flow of a fluid with microstructure

Hogan

Henriksen

1991

Numerical Methods in Fluids

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SUMMARYA finite element formulation for the steady laminar flow of an incompressible fluid with microstructure has been developed. The particular fluids considered are commonly known as micropolar fluids, in which case suspended particulate microstructures are modelled by an 'extended' continuum formulation. The particle microspin is a new kinematic variable which is independent of the classical vorticity vector and thereby allows relative rotation between particles and the surrounding fluid. This formulation also gives rise to couple stresses in addition to classical force or traction stresses. The finite element formulation utilizes a variational approach and imposes conservation of mass through a penalty function. A general boundary condition for microspin has been incorporated whereby microspin at a solid boundary is constrained to be proportional to the fluid vorticity. The proportionality constant in this case can vary from zero to unity. Sample solutions are presented for fully developed flow through a straight tube and compared with an analytical solution. Results are also generated for flow through a constricted tube and compared with a Newtonian fluid solution.

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Lubrication theory for micropolar fluids and its application to a journal bearing

Cited by 157 publications

References 7 publications

Wall slip induced by a micropolar fluid

Wall slip induced by a micropolar fluid

Bifurcation and chaos for porous squeeze film damper mounted rotor–bearing system lubricated with micropolar fluid

A finite element formulation for laminar flow of a fluid with microstructure

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