Squeeze Film Behaviour Research Articles

Magnetohydrodynamics and viscosity variation in couple stress squeeze film lubrication between rough flat and curved circular plates

A simplified mathematical model has been developed for understanding combined effects of surface roughness, viscosity variation and couple stresses on the squeeze film behaviour of a flat and a curved circular plate in the presence of transverse magnetic field. The Stokes (1966) couple stress fluid model is included to account for the couple stresses arising due to the presence of microstructure additives in the lubricant. In the context of Christensen’s (1969) stochastic theory for the lubrication of rough surfaces, two types of one-dimensional roughness patterns (radial and azimuthal) are considered. The governing modified stochastic Reynolds type equations are derived for these roughness patterns. Expressions for the mean squeeze film characteristics are obtained. Numerical computations of the results show that the azimuthal roughness pattern on the curved circular and flat plate results in more pressure buildup whereas performance of the squeeze film suffers due to the radial roughness pattern. Further the Lorentz force characterized by the Hartmann number, couple stress parameter and viscosity variation parameter improve the performance of the squeeze film lubrication as compared to the classical case (Non-magnetic, Newtonian case and non-viscous case).

Effects of both cavitation and non-Newtonian behavior on the performance of oscillatory anisotropic poroelastic squeeze film

PurposeThe purpose of this study is to present a theoretical investigation of the effects of cavitation and couple stress on the squeeze film behavior between an anisotropic poroelastic rigid disc and a sinusoidally oscillating rigid disc.Design/methodology/approachBased on the microcontinuum theory of Vijay Kumar Stokes and the Elrod–Adam algorithm, the non-Newtonian Reynolds equation coupled with modified Darcy's law for lubricant flow through the porous disc is derived. This numerical study includes the continuity of tangential velocity at the porous–fluid interface and the effects of percolation of the polar additives into the anisotropic porous disc.FindingsThe effects of couple stress, oscillating amplitude, percolation additives, permeability and anisotropic permeability on the squeeze film characteristics are discussed. It is found that both the percolation effect of the lubricant additives and the anisotropic structure of the porous surface reduce the flow in the porous disc, resulting in a decrease in pressure. It is also observed that cavitation effects are more pronounced for Newtonian fluids than couple stress fluids.Originality/valueThe results of this study can be used to design a variety of engineering applications such as bearings, wet clutches and non-contact mechanical seals.

Squeeze Film Lubrication on a Rigid Sphere and a Flat Porous Plate with Piezo-Viscosity and Couple Stress Fluid

The paper aims to conduct a theoretical analysis about squeeze film behaviour with piezo-viscosity on a fluid lubricated with polar additives on a rigid sphere and a flat porous plate. By taking into account of microcontinum theory of stokes, Barus formula and Darcy’s equations, Reynolds equation in modified form is derived by bearing in mind the variation of viscosity along film thickness. An approximate analytical solution for fluid film pressure, dimensionless load and squeezing time is derived. The results are presented numerically and graphically. To make obvious the accuracy, the results are compared with accessible literature and a remarkable similarity is been reported

Non-Newtonian couple-stress squeeze film behaviour between oscillating anisotropic porous circular discs with sealed boundary

The thrust of this paper is to investigate theoretically the non-Newtonian couple stress squeeze film behaviour between oscillating circular discs based on V. K. Stokes micro-continuum theory. The lubricant squeezed out between parallel porous and rigid facings is supposed to be a concentrated suspension which consists of small particles dispersed in a Newtonian base fluid (solvent). The effective viscosity of the suspension is determined by using the Krieger-Dougherty viscosity model for a given volume fraction of particles in the base fluid. For low frequency and amplitude of sinusoidal squeezing where cavitation as well as turbulence are unlikely, the governing equations including the modified Reynolds equation coupled with the modified Darcy's equation are derived and solved numerically using the finite difference method and a sub-relaxed iterative procedure. The slip velocity at the porous-fluid interface is directly evaluated by means of the modified Darcy's law considering laminar and isothermal squeezing flow. For a given volume fraction, the couple stress effects on the squeeze film characteristics are analyzed through the dimensionless couple stress parameterℓ˜considering sealed and unsealed boundary of the porous disc. The obtained relevant results reveal that the use of couple stress suspending fluids as lubricants and the effect of sealing the boundary of the porous matrix improves substantially the squeeze film behaviour by increasing the squeeze film force. On the other hand, side leakage flow calculated in the sealed case remains constant in comparison to that of open end (unsealed) porous disc for all values of couple stress parameter and volume fraction of particle.

Natural Convection Flow of Nanofluids in Squeeze Film with an Exponential Curvature

A theoretical study of the laminar squeeze flow of copper water and alumina water nanofluids between a flat circular stationary disk and a curved circular moving disk is carried out using energy integral method. The squeeze film behaviour is examined analytically and the effects of inertia and curvature on the squeeze film pressure, load carrying capacity of the fluid and temperature are analysed. Further, the problem is solved numerically for a sinusoidal motion of the upper curved disk taking an exponential form of the gap width. It is found that the copper water nanofluid is better than alumina water nanofluid for better heat transfer rates. While high inertia forces strongly influence the squeeze film behaviour, low inertia forces are favourable for temperature distribution. Further, concave nature of the upper disk gives better squeeze film characteristics than convex disk. However, convex disk is better than concave disk as far as the temperature distribution is concerned.

Squeezing flow between rigid tilted surfaces: A general solution and case study for MEMS

AbstractSqueeze film flow occurs when two surfaces move in a normal direction relative to each other and is a phenomenon of importance to many engineering systems, from macro to microscale. Squeeze film damping is widely used in large‐scale rotating machinery but even more so presently in microsystems. In the latter case, for modelling purposes, the two surfaces producing the squeeze film flow are typically assumed perfectly parallel, which is often not the case in practice. This paper presents a general formula for squeezing flow between two rigid surfaces for both parallel and tilted configurations in the 1‐dimensional case (2‐dimensional flow). The solution is derived from the Reynolds equation. The results in the parallel case compare favorably to previous literature data. A case study is presented for plates with dimensions characteristic of microelectromechanical systems. The important contribution of this paper is to isolate and study this “tilt effect” which can contribute to discrepancies and confusion in interpreting squeeze film behaviour, particularly at the microscale.

Squeeze film behavior in porous transversely circular stepped plates with a couple stress fluid

Purpose The purpose of this work is to carry our a study of the effect of surface roughness on squeeze film behavior between two transversely circular stepped plates with couple stress lubricant when the upper circular stepped plate has porous facing which approaches the lower plate with uniform velocity. Design/methodology/approach The modified Stochastic Reynolds equation is derived for Christensen Stochastic theory for the rough surfaces. Closed form solution of the Stochastic Reynolds equation is obtained in terms of Fourier-Bessel series. Findings It is found that the effect of couple stress fluid and surface roughness is more pronounced compared to classical case. Originality/value The problem is original that it consider a couple stress fluid in this type of applications.

On the ferrofluid lubricated squeeze film characteristics between a rotating sphere and a radially rough plate

Ferrofluid lubricated squeeze film bearing design system formed by a rotating upper spherical surface and a radially rough lower flat plate considering variable magnetic field, which is oblique to the lower plate, have been analyzed. The variable magnetic field is important because of its advantage of generating maximum field at the required active contact zone. The problem is motivated because squeeze film behaviour is widely observed in many industrial applications like in machine tools, gears, rolling elements, hydraulic systems, engines, clutch plates, force pendulum apparatus, etc. Moreover, the squeeze film behaviour is also observed in skeletal joints of human body. On the basis of ferrohydrodynamic theory and Christensen’s stochastic theory for hydrodynamic lubrication of rough surfaces, the modified Reynolds equation is derived and expressions for squeeze film characteristics are obtained which are calculated numerically and interpreted. While deriving Reynolds equation effects of various parameters like rotation, width of the nominal minimum film thickness and squeeze velocity are also considered.

Couple stress fluids in porous circular squeeze films

The squeeze film flow characteristics of a couple stress fluid between porous circular disks is investigated. The modified Reynold’s equation is derived using Stokes microcontinuum theory and is solved analytically. The expressions for the squeeze film pressure and the squeeze film force are obtained in terms of Fourier-Bessel series. Numerical results are presented for the sinusoidal motion of the upper porous disk. Further, the equation for the gap width between the disks is obtained by considering a constant force squeezing state and is solved numerically. The effects of couple stresses and the porous facing on the squeeze film behaviour are analysed through the squeeze film pressure, force and the film thickness as a function of response time.

Effect of Surface Roughness on the Squeeze Film Lubrication of Finite Poroelastic Partial Journal Bearings with Couple Stress Fluids: A Special Reference to Hip Joint Lubrication

A simplified mathematical model has been developed for understanding the combined effects of surface roughness and couple stresses on the squeeze film behavior of poroelastic bearings in general and that of hip joints in particular. The cartilage is modeled as biphasic poroelastic matrix and synovial fluid is modeled as couple stress fluid. The modified form of averaged Reynolds equation which incorporates the randomized roughness structure as well as elastic nature of articular cartilage with couple stress fluid as lubricant is derived. For the study of rough surfaces, Christensen's stochastic theory is used to study the effect of two types of one-dimensional random roughness, namely, longitudinal roughness pattern and the transverse roughness pattern. The averaged film pressure distribution equations are solved numerically by using the conjugate gradient method. It is observed that the surface roughness effect is dominant and pattern dependent and the influence of couple stresses is to improve the joint performance.

Behaviour of Couple Stress Fluids in Porous Annular Squeeze Films

The laminar squeeze flow of an incompressible couple stress fluid between porous annular disks is studied using hydrodynamic lubrication theory. The modified Reynolds’ equation is derived using Stokes microcontinuum theory and is solved analytically. Analytical expressions for the squeeze film pressure and the load carrying capacity are obtained in terms of Fourier-Bessel series. Numerical results are obtained for the sinusoidal motion of the upper disk. The effect of couple stresses and that of porous facing on the squeeze film behaviour are analysed through the squeeze film pressure and the load carrying capacity. Further, the equation for the gap width between the disks is obtained from the inverse problem.

Limits of linearity in squeeze film behavior of a single degree of freedom microsystem

This paper presents a theoretical investigation of squeeze film flow in systems employing microplates parallel to a substrate and undergoing large amplitude normal vibration. Most previous models of squeeze film damping assume small oscillation amplitude with linear system behavior, but it is often unclear how small the vibrations must be to actually elicit this response. In addition, fluid inertia effects are usually overlooked. This study provides a compact nonlinear solution for the incompressible hydrodynamic forces with specific terms describing fluid inertia and viscous damping. Numerical analysis (the explicit Runge-Kutta method) is applied to solve the nonlinear governing equation. The effects of frequency, oscillation amplitude, aspect ratio (of gap to length), and Reynolds number on the dynamic response of the system are investigated. The overall system response depends strongly on the actuation frequency and system properties. It is found that a simple criterion of validity for the linear system assumption is not possible. Near resonance, the vibration input amplitude (relative to the initial gap) must be very small indeed for linearity (∼0.001), while in other cases the relative amplitude can be greater than one.

Surface roughness effect on a magnetic fluid-based squeeze film between a curved porous circular plate and a flat circular plate

Efforts have been made to investigate the magnetic fluid-based squeeze film behaviour between the curved rough porous circular plate and the flat rough porous circular plate. The curved film thickness is determined by an exponential function. A magnetic fluid is used as a lubricant in the presence of an external magnetic field oblique to the lower plate. The Reynolds Equation governing the film pressure is stochastically averaged with respect to the random roughness parameter and this equation is solved to obtain pressure distribution which results in the calculation of the load carrying capacity. The results establish that the performance of bearing system improves significantly as compared with that of a bearing system dealing with a conventional lubricant. Although the bearing suffers due to surface roughness, there exist ample scopes for obtaining a better performance in the case of negatively skewed roughness by suitably choosing the curvature parameter because the load carrying capacity increases sharply due to magnetization. In addition, this improved performance gets further enhanced due to negative variance, particularly when lower or moderate values of porosity parameter are involved. Besides, this investigation makes it clear that the bearing can support a load even when there is no flow.

Squeeze Film Lubrication between Rough Poroelastic Rectangular Plates with Micropolar Fluid: A Special Reference to the Study of Synovial Joint Lubrication

The effects of surface roughness and poroelasticity on the micropolar squeeze film behavior between rectangular plates in general and that of synovial joints in particular are presented in this paper. The modified Reynolds equation, which incorporates the randomized surface roughness structure as well as elastic nature of articular cartilage with micropolar fluid as lubricant, is derived. The load-carrying capacity and time of approach as functions of film thickness during normal articulation of joints are obtained by using Christensen stochastic theory for rough surfaces with the assumption that the roughness asperity heights are to be small compared to the film thickness. It is observed that the effect of surface roughness has considerable effects on lubrication mechanism of synovial joints.

Combined Non-Newtonian and Viscous Shear Effects on Porous Squeeze Film Behavior

On the basis of the Stokes microcontinuum theory, a numerical study of the combined effects of non-Newtonian couple stress and viscous shear forces on porous squeeze film behavior for parallel circular plates is presented in this article. A modified Reynolds equation governing the film pressure is derived using the Stokes constitutive equations to account for lubricant couple stress effects due to the presence of additives or suspended particles. The Darcy-Brinkman equations describing the fluid flow within the porous plate are used to account for viscous shearing forces. Numerical solutions for the squeeze film characteristics including film pressure, radial velocity, squeeze velocity, and response time are calculated for various values of the couple stress and viscous shear parameters. The simulation results indicate that the combined effects of couple stresses and viscous shearing forces are considerable.

Magnetic Fluid-Based Squeeze Film Behaviour in Curved Porous-Rotating Rough Annular Plates and Elastic Deformation Effect

Efforts have been directed to study and analyze the squeeze film performance between rotating transversely rough curved porous annular plates in the presence of a magnetic fluid lubricant considering the effect of elastic deformation. A stochastic random variable with nonzero mean, variance, and skewness characterizes the random roughness of the bearing surfaces. With the aid of suitable boundary conditions, the associated stochastically averaged Reynolds' equation is solved to obtain the pressure distribution in turn, which results in the calculation of the load-carrying capacity. The graphical representations establish that the transverse roughness, in general, adversely affects the performance characteristics. However, the magnetization registers a relatively improved performance. It is found that the deformation causes reduced load-carrying capacity which gets further decreased by the porosity. This investigation tends to indicate that the adverse effect of porosity, standard deviation and deformation can be compensated to certain extent by the positive effect of the magnetic fluid lubricant in the case of negatively skewed roughness by choosing the rotational inertia and the aspect ratio, especially for suitable ratio of curvature parameters.

EFFECT OF TRANSVERSE SURFACE ROUGHNESS ON THE PERFORMANCE OF HYDROMAGNETIC SQUEEZE FILM BETWEEN CONDUCTING TRUNCATED CONICAL PLATES

An attempt has been made to study and analyze the behavior of a hydromagnetic squeeze film between conducting porous transversely rough truncated conical plates. The associated Reynolds' equation is solved with appropriate boundary conditions to investigate the behavior of performance characteristics. The results indicate that the performance of the bearing system gels enhanced vis-a-vis a bearing system working with a conventional lubricant. This article reveals that the negative effect induced by porosity and standard deviation can be overcome completely by the positive effect of the magnetization parameter and conductivities by choosing suitable aspect ratio and the semi-vertical angle in the case of negatively skewed roughness.

Theoretical Investigation of Couple Stress Squeeze Films in a Curved Circular Geometry

A theoretical investigation of the laminar squeeze flow of a couple-stress fluid between a flat circular static disk and an axisymmetric curved circular moving disk has been carried out using modified lubrication theory and microcontinuum theory. The combined effects of fluid inertia forces, curvature of the disk and non-Newtonian couple stresses on the squeeze film behavior are investigated analytically. Each of these effects and their combinations show a significant enhancement in the squeeze film behavior, and these are studied through their effects on the squeeze film pressure and the load carrying capacity of the fluid film as a function of time. Two different forms of the gapwidth between the disks have been considered, and the results have been shown to be in good agreement with the existing literature.

Magnetic fluid‐based squeeze film behavior between transversely rough curved annular plates: a comparative study

PurposeThis paper aims to improve upon the performance of magnetic fluid‐based squeeze film between transversely rough curved annular plates by embarking on a comparative study of the geometrical structure of the curved annular plates.Design/methodology/approachThe objectives are met by mathematically modeling a magnetic fluid‐based squeeze film between transversely rough curved annular plates. The standard method is to solve the associated Reynolds' equation with appropriate boundary conditions by describing the random roughness through a stochastic random variable with non‐zero mean, variance and skewness. Results for bearing performance characteristics such as pressure distribution and load‐carrying capacity are numerically computed. In order to analyze the quantitative effect of the roughness, different geometrical structures of surfaces have been considered and the results are compared.FindingsCertainly, the performance of the bearing with the magnetic fluid lubricant is comparatively better than the conventional lubricant. The findings indicate that although the effect of roughness is adverse in general, the adverse effect introduced by roughness and aspect ratio can be compensated for, to a considerable extent, by the positive effect of magnetization parameter in the case of negatively skewed roughness by choosing the curvature parameters properly.Practical implicationsFrom the industry point of view, this investigation will be definitely useful for improving the performance of the squeeze film based on magnetic fluid between transversely rough curved annular plates by minimizing the effect of roughness. Furthermore, it offers an additional degree of freedom from a design point of view in the form of the geometrical structure of the surfaces.Originality/valueThe paper presents significant information as it compares shapes and offers suggestions for the best improved performance from a bearing's longevity point of view. This study presents an approach for the enhanced performance of the magnetic fluid‐based squeeze film between transversely rough curved annular plates.

Effect of surface roughness on magnetohydrodynamic squeeze film characteristics between finite rectangular plates

The effect of surface roughness on the magnetohydrodynamic squeeze film behavior between two rectangular plates is analyzed. A generalized form of surface roughness pattern is considered. A stochastic random variable with non-zero mean, variance and skewness is used to model mathematically the surface roughness of the squeeze film bearings. The modified averaged stochastic Reynolds equation governing the squeeze film pressure is derived. The expressions for the squeeze film pressure, load carrying capacity and squeeze film time are obtained. Numerical computations of the results show that the negatively skewed surface roughness pattern increases the load carrying capacity and squeeze film time. On the contrary the performance of squeeze film suffers due to positively skewed surface roughness pattern. Further the magnetic effect characterized by the Hartmann number improves the performance of the squeeze film lubrication as compared to the classical non-conducting lubricant case.