Squeeze film behavior in a hemispherical porous bearing using the Brinkman model

On the basis of the Brinkman model, the main objective of this paper is to theoretically predict the effects of viscous shear stresses on the pure squeeze film behavior in a hemispherical porous bearing under a constant load. The modified Reynolds equation is derived by using the Brinkman equations to account for the viscous shear effects. According to the results, the influence of viscous shear stresses on the squeeze film characteristics is significant and not negligible. It is also found that the Brinkman model predicts a quite different squeeze film action than those derived by the Darcy model and the slip-flow model. Compared with that derived by the Darcy model for thin-walled porous bearings, the viscous shear effects of the Brinkman model reduce the load capacity and the response time of the squeeze film, but the viscous shear effects increase the load capacity and lengthen the response time of the squeeze film action for rotor-bearing contact to occur as compared to that of the slip-flow model. Moreover, by considering the viscous shear effects and the bearing thickness ratio, the Brinkman model provides an appropriate prediction of the squeeze film characteristics for a wide range of the porous bearing thickness.