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1

Hydrodynamic squeeze-film characteristic in porous annular disks using the Brinkman model

Lin J. R., Liao W. H.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 3

413-424

EN

Based on the Brinkman model (BM) with the assumption that the pressure gradient across the porous region is an unknown function, the effects of viscous shear stresses upon the squeezing-film motion in porous annular disks are considered. Using the Brinkman equations and applying the continuity conditions at the interface for the velocities, shear stresses and pressures, two coupled modified Reynolds equations governing the squeeze-film pressure are obtained. The film pressure equation is solved and applied to evaluate the load-carrying capacity and the height-time relationship. According to the results obtained, the BM predicts quite a different squeezing action to those derived by the slip-flow model (SFM) and the Darcy model (DM). Comparing with the SFM, the viscous shear effects of the BM increase the load-carrying capacity and the response time. But, these trends are reversed as compared to the DM. On the whole, the effects of viscous shear stresses are more pronounced for moderate-value permeability parameters and a higher-value radius ratio. A design example for porous annular disks is also illustrated for engineering applications.

2

Magneto-hydrodynamic lubrication of finite slider bearings

Lin J. R.

International Journal of Applied Mechanics and Engineering

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2002

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Vol. 7, no 4

1229-1246

EN

In this paper, the effect of a transverse magnetic field on the performance characteristics of finite slider bearings with an electrically conducting fluid is presented. To take account of the Lorentz force on the lubricant film, a generalized two-dimensional Reynolds-type equation is derived by using the MHD motion equations with Maxwell equations. This MHD Reynolds equation is applicable to the analysis of finite slider bearings with different film shapes. To illustrate the MHD bearing characteristics, the slider profile with an inclined plane is considered. The film pressure is numerically solved from the MHD Reynolds-type equation and applied to evaluate the bearing characteristics. According to the results obtained, the application of the magnetic field signifies an influence on the load capacity, power loss and friction parameter of slider bearings, depending upon the values of the Hartmann number, aspect ratio and inlet-outlet film thickness ratio.

3

Effects of surface roughness and rotational inertia on the optimal stiffness of hydrostatic thrust bearings

Lin J. R., Chiang Ch., F.

International Journal of Applied Mechanics and Engineering

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2002

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Vol. 7, no 4

1247-1261

EN

Based upon Christensen's stochastic model, this paper studies the optimal stiffness of hydrostatic thrust bearings including the effects of surface roughness and rotational inertia. The mean film pressure for a capillary-compensated circular step bearing is solved from the stochastic Reynolds-type equation together with the stochastic recess flow continuity equation. By applying the maximum principle, a closed-form equation determining the critical recess pressure is obtained for the bearing operating at any given film thickness. From the results obtained, the apparent influence of surface roughness upon the maximum bearing stiffness is more pronounced with higher values of radius ratio, rotation number, and roughness parameter. For engineering practice, a guiding example for the optimal operation is also given.

4

The effects of couple stresses in the squeeze film behavior between isotropic rough rectangular plates

Lin J. R.

International Journal of Applied Mechanics and Engineering

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2001

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Vol. 6, no 4

1007-1024

EN

On the basis of the Stokes microcontinuum theory and the Christensen stochastic model, a theoretical study of squeeze film performance for isotropic rough rectangular plates with couple stress fluids as lubricants is presented. A stochastic non-Newtonian Reynolds-type equation is derived and solved analytically for the mean film presure distribution. Squeeze film characteristics are then evaluated. According to the results, bearing surfaces with isotropic roughness pattern result in poor bearing characteristics as compared to the smooth-surface case. However. the isotropic rough plates with a non-Newtonian couple stress fluid provide a significant increase in the mean load-carrying capacity, and compensate the response time by more than the reduction caused by surface roughness.