Combined Effect of Slip Velocity and Roughness on the Jenkins Model Based Ferrofluid Lubrication of a Curved Rough Annular Squeeze Film

Abstract

This paper theoretically analyzes the combined effect of slip velocity and surface roughness on the performance of Jenkins model based ferrofluid squeeze film in curved annular plates. The effect of slip velocity has been studied resorting to the slip model of Beavers and Joseph. The stochastically averaging method of Christensen and Tonders has been deployed for studying the effect of surface roughness. The pressure distribution is derived by solving the associated stochastically averaged Reynolds type equation with suitable boundary conditions, leading to the computation of load carrying capacity. The graphical representations reveal that the transverse surface roughness adversely affects the bearing performance. However, Jenkins model based ferrofluid lubrication offers some scopes in minimizing this adverse effect when the slip parameter is kept at minimum. Of course, an appropriate choice of curvature parameters adds to this positive effect in the case of negatively skewed roughness. Moreover, it is established that this type of bearing system supports certain amount of load; even when there is no flow which does not happen in the case of conventional lubricant based bearing system.

Combined effect of circumferential roughness and squeeze velocity on ferrofluid squeeze film with rotating sphere and rough plate

“…When normalΩu→0 and normalΩl→0 (i.e., there is no rotation of the upper sphere or lower plate), the present study reduces the findings of Patel and Deheri. 22 In their study, they evaluated combined effects of surface roughness and slip velocity on the Jenkins model based ferrofluid lubrication of a curved rough annular squeeze film. When applying the Jenkins model to magnetic fluid flow, it was found that combined effects of negatively skewed roughness and variance delay in justifying the adverse influence of slip velocity and standard deviation.4.…”

“…Equations of the basic flow for the motion of ferrofluids in the film region, based on ferrohydrodynamic theory governed by Jenkins model with continuity equation in cylindrical polar coordinates (r,θ,z) are given by 16,22,28 andwhere η is the fluid viscosity, p is the film pressure p , is the fluid density, μ¯ is the magnetic susceptibility, μ¯0 is the initial susceptibility of fluid, μ0 is the permeability of free space, q is the fluid velocity vector, boldH is the applied magnetic field vector, boldM is the magnetization vector, M is the magnitude of magnetization vector, boldM∗ is the co-rotational derivative of M, Ms is the saturation mag...…”

“…Equations of the basic flow for the motion of ferrofluids in the film region, based on ferrohydrodynamic theory governed by Jenkins model with continuity equation in cylindrical polar coordinates ðr, θ, zÞ are given by 16,22,28…”

“…Also, it was observed that combined effects of magnetism and negatively skewed roughness is relatively more for exponential shape as compared to hyperbolic and secant. Patel and Deheri 22 examined ferrofluid lubrication on curved rough annular squeeze film considering the effects of slip velocity and surface roughness and concluded that the Jenkins model is superior to the NR model in terms of reducing the adverse effect of roughness. They also found that in the absence of flow this type of bearing system can support a certain amount of load.…”

A Newtonian thermal elastohydrodynamic lubrication model for ferrofluid‐lubricated involute spur gear pair

“…Xiujiang Shi conducted numerical analysis of EHL under different carrier fluid ferrofluids lubrication of sliding bearing systems. Patel et al used the Jenkins model to address the influences of field strength, slip velocity, and surface roughness on squeeze films. Tipei, Shah, and Chi et al discovered that higher field strength could mean higher carrying capacity for magnetic liquids.…”