Ferrofluid lubrication of circular squeeze film bearings controlled by variable magnetic field with rotations of the discs, porosity and slip velocity

Abstract

Based on the Shliomis ferrofluid flow model (SFFM) and continuity equation for the film as well as porous region, modified Reynolds equation for lubrication of circular squeeze film bearings is derived by considering the effects of oblique radially variable magnetic field (VMF), slip velocity at the film–porous interface and rotations of both the discs. The squeeze film bearings are made up of circular porous upper disc of different shapes (exponential, secant, mirror image of secant and parallel) and circular impermeable flat lower disc. The validity of Darcy's Law is assumed in the porous region. The SFFM is important because it includes the effects of rotations of the carrier liquid as well as magnetic particles. The VMF is used because of its advantage of generating maximum field at the required active contact area of the bearing design system. Also, the effect of porosity is included because of its advantageous property of self-lubrication. Using Reynolds equation, general form of pressure equation is derived and expression for dimensionless load-carrying capacity is obtained. Using this expression, results for different bearing design systems (due to different shapes of the upper disc) are computed and compared for variation of different parameters.

Lubrication impact of ferrofluid on cylinder‐plate system: A comparative study using two flow models

“…Thus, FF effects result in a very large increase in pressure for both the models in the small vicinity of the minimum film height. This happens because as X moves away from the upper surface of the cylinder become more and more convex with respect to lower plate, and it is known that such situation does not support increase in pressure and integrated due to increase in side leakage 6,14 . These behaviour of P also agrees with the observations of References 12,13.…”

“…Again, from Figures 3 and 4, it is observed that out of the total pressure generation in the interval , maximum generation (greater than 0.75) takes place approximately in the interval that is, in the 20% of the region symmetric about the z ‐axis as shown in Figure 5. This happens because beyond this interval the upper surface of the cylinder becomes more and more convex with respect to lower plate, and it is known that convex shape does not support increase in pressure and integrated dimensionless load‐carrying capacity due to increase in side leakage 6,14 …”

Rheological Properties and Drag Reduction Performance of Puffer Epidermal Mucus

“…As mentioned above, different drag reduction effects were possessed by puffer epidermal mucus with different rheological properties. The relationship between apparent viscosity and drag reduction performance can be described using the following equation. − …”

Generalized ferrofluid based lubrication equation and its application to porous journal bearing

“…The results for the dimensionless load‐carrying capacity $$\bar{W}$$ given by Equation () are computed, where integral is evaluated using Simpson's one‐third rule by dividing the interval [0, 2π] into 10 subintervals of width $$\pi /5$$. The representative values of the different parameters taken in computations are as follows [1, 15, 16, 21–25]. These values remain fixed unless and until the calculations of $$\bar{W}$$ are made with respect to the variation of the particular parameter.…”

“…Assuming steady flow, neglecting inertia and the second derivative of the internal angular momentum S , Equations () and () of the Appendix , respectively, becomes [15, 16] $$\begin{equation} - {\bm{\nabla }}p + \eta {\nabla ^2}{\bf v} + \mu ({\bf M}\centerdot {\bm{\nabla }}){\bf H} + \frac{1}{2}\mu {\bm{\nabla }} \times ({\bf M} \times {\bf H}) = {\bf 0}, \end{equation}$$ $$\begin{equation} {\bf M} = {M_1}\frac{{\bf H}}{H} + {\tau _B}({\bm{\Omega }} \times {\bf M}) - \frac{{\mu {\tau _s}{\tau _B}}}{I}[{\bf M} \times ({\bf M} \times {\bf H})], \end{equation}$$where $$\begin{equation} {M_1} = nm\left( {\coth \;{\xi _1} - \frac{1}{{{\xi _1}}}} \right),\;\;{\xi _1} = \;\frac{{\mu mH}}{{{k_B}T}}. \end{equation}$$…”