Ferrofluid (FF) lubricated bearing design system formed by upper spherical surface and a flat porous plate considering variable magnetic field, which is oblique to the lower plate, have been analysed. The porous plate is considered because of having its advantageous property of self-lubrication. The analytical model with squeeze behaviour of the phenomenon is developed, considering the validity of the Darcy's law in the porous region, using equation of continuity, and equations from ferrohydrodynamics theory. The expressions for squeeze film characteristics are obtained and calculated numerically. The results indicate the better performance of the system, when FF is used as lubricant.

Based on ferrofluid flow model given by R.E. Rosensweig, a general equation for different slider squeeze film-bearing design systems, formed by solid upper surface and lower porous plate, is theoretically derived considering the effects of porosity, permeability, squeeze velocity, tangential velocity and oblique variable magnetic field. While deriving the general equation, continuity equation and Darcy’s law are also considered. Expressions for pressure and load-carrying capacity for different squeeze film-bearing design systems are obtained. The results for dimensionless load-carrying capacity are computed and compared with previous results in some cases. The results indicate the better performance of different bearing systems when ferrofluid is used as lubricant. Further, some important conclusions are also made. Two permeability models – globular sphere and capillary fissures are discussed. The variable magnetic field is considered because uniform magnetic field does not enhance bearing performances.

Based on the Jenkins model for ferrofluid flow regarding the performance of squeeze-film lubrication between rotating upper spherical surface and circumferentially rough lower plate is presented. Here, for hydrodynamic lubrication, we have adopted the ferrohydrodynamic theory. Further, using Christensen’s stochastic model, surface roughness is examined. In the paper, in the presence of a radially variable magnetic field, rotations of both the upper and lower surfaces as well as roughness of the surface, the Reynolds type equation for the squeeze-film bearing is established. By using the Reynolds type equation, expressions for the non-dimensional film pressure and load-carrying capacity are obtained for circumferential roughness pattern. Neuringer–Rosensweig (NR) model results are computed using the Jenkins model. The results show that non-dimensional film pressure increases remarkably when the non-dimensional radial parameter ( R) increases. Also, as the nominal minimum film thickness increases, load-carrying capacity decreases in the Jenkins model. However, as a result of Tables 5 and 6, the non-dimensional load-carrying capacity of the Jenkins model is improved compared to that of the NR model.

Modified Reynolds-Darcy equation for ferrofluid lubricated squeeze-film bearing, made by flat circular porous upper and flat circular impermeable lower discs, is derived. The ferrofluid is controlled by oblique variable magnetic field (VMF) and VMF is important because of its advantage of generating maximum field at the required active contact zone. The porous matrix is considered because of its advantageous property of self-lubrication. Moreover, the validity of the Darcy's law is assumed in the porous matrix. Expression for dimensionless film pressure p in terms of Bessel function by considering the effect of existence of pressure difference at the film-porous interface is obtained. The expression for dimensionless load-carrying capacity W is also obtained. The effects of dimensionless radial parameter, inverse of the dimensionless film thickness parameter (h 0 / h) , magnetization parameter and squeeze velocity are studied on p, whereas the effects of the inverse of the dimensionless film thickness parameter and magnetization parameter and squeeze velocity are studied on W. Moreover, the effect of dimensionless pressure difference P at the film-porous interface is studied on W n (which is the term because of existence of the pressure difference at the film-porous interface). The results show that p increases for smaller values of radial parameter, larger values of magnetization parameter and when (h 0 / h) ≤ 12, whereas W increases for larger values of magnetization parameter and when (h 0 / h) ≤ 12. The squeeze velocity have no effects on the variation of p and W. Moreover, the results for W n show that it increases with the increase of P.