Numerical modeling and experimental verification of compressible squeeze film pressure

The validity of using the Reynolds equation for compressible squeeze film pressure was tested with computational fluid dynamics (CFD). A squeeze film air bearing was instrumented with pressure sensors and non-contacting displacement probes to provide transient measurements of film thickness and pressure. The film thickness measurements also provided input parameters to the numerical prediction. However, numerical results showed a larger load capacity than those suggested from the experimental results. Furthermore, the nonlinear time averaged positive pressure described by the Reynolds equation was not evident in the experimental study.     

Squeeze film characteristics of conical bearings with combined effects of piezo-viscous dependency and non-Newtonian couple stresses

In this paper, the analysis of squeeze film characteristics of conical bearings with combined effects of piezo-viscous dependency and couple stress fluid is presented. On the basis of the Stokes microcontinuum theory of couple stress fluid model and Barus experimental research, a modified Reynolds equation is derived, the standard perturbation technique is used to solve the highly non-linear Reynolds equation and approximate analytical solution is obtained for the squeeze film pressure, load carrying capacity and squeeze film time. According to the results obtained, the effect of viscosity pressure dependency on the squeeze film lubrication of conical bearings with couple stress fluids is to improve the load carrying capacity significantly and lengthen the squeeze film time as compared to iso-viscous Newtonian case.     

The squeeze film between rotating porous annular disks

The problem of a squeeze film between two rotating disks, one with a porous facing, is analyzed. The analytical model takes account of the porosity of one disk and the inertia due to centrifugal force on the fluid both in the film and in the porous region. The governing equations are derived according to lubrication theory. It is found that the fluid in the film region satisfies the modified Reynolds equation and the flow in the porous region satisfies Poisson's equation. The problem is solved analytically using Fourier expansions. Solutions for load capacity and pressure distribution are presented in series form. The film-thickness and time relation is given in integral form. Results are plotted for selected parameter values. The conditions under which inertia effects can be important are determined and as a result the criteria for neglecting the inertia effects are given.     

Effect of Piezoviscous Dependency and Couple Stress on Squeeze Film Lubrication Between Parallel Stepped Plates

Theoretical analysis of the effect of piezoviscous dependency and couple stress on squeeze film lubrication between parallel stepped plates is presented in this article. According to the Stokes microcontinuum theory of couple stress fluids, the modified Reynolds equation is derived by considering viscosity variation along the film thickness. The standard perturbation technique is used to solve the nonlinear Reynolds equation and an approximate analytical solution for the film pressure is obtained. It is found that the effect of couple stresses and pressure-dependent viscosity variation increases the load-carrying capacity and lengthens the squeeze film time.     

Hydraulic Squeeze Bearing

Prior researchers find that: Where one of two horizontal parallel plates immersed in a fluid is forced to oscillate up and down, a load may be carried, providing the fluid is compressible. Application of Reynolds equation to such a squeeze film bearing supports the condition of compressibility.

However, analysis of the squeeze film bearing, including inertia terms in the Navier-Stokes equations, removes the restriction on compressibility.

Theoretical design of a hydraulic squeeze bearing driven sinusoidally shows that load capacity is improved over a similar gas squeeze bearing under usual design conditions, provided cavitation is prevented. Two cases are considered of a fixed and a free bearing. Torque, work input, and the effects of centrifugal force are analysed.     

Self-levitating sliding air contact

A linear sliding contact with self-lifting capability due to squeeze film action was theoretically investigated. It was found that this type of contact can operate under a wide range of frequency and load conditions. Calculations for frequency of up to 4000 Hz and the mass of up to 800 g indicate that a air film with thickness of a few microns can be created.It is the unsymmetrical pressure distribution in a time period or positive mean film force that makes squeeze air film contact able of self-levitation. The mean film force is equal to the weight supported. A physical rationale for the load-carrying capacity of a squeeze air film is that because of the viscous resistance around contact boundary, the air is repeatedly compressed and expanded in the central part of the contact, which results in a positive mean film force.     

Effect of surface roughness on the couple-stress squeeze film between a sphere and a flat plate

In this paper, a theoretical study of the effect of surface roughness on the hydrodynamic lubrication of couple-stress squeeze film between a sphere and a flat plate is presented on the basis of Christensen's stochastic theory for hydrodynamic lubrication of rough surfaces. The modified Reynolds equation accounting for the couple stresses and the surface roughness is mathematically derived. The modified Reynolds equation is solved for the fluid film pressure and the bearing characteristics, such as the load carrying capacity and the time–height relationship, are obtained. It is found that the surface roughness considerably influences the squeeze film characteristics. The load carrying capacity and squeeze film time are found to increase for an azimuthal roughness pattern as compared to the corresponding smooth case, whereas the reverse trend is observed for a radial roughness pattern.     

Damping and added mass coefficients for a squeeze film damper using the full 3-D Navier-Stokes equation

Direct and cross-coupled damping coefficients are developed for the 2π-film, π-film (Gumbel cavitation condition) and homogeneous two-phase mixture films in a squeeze film damper. The numerical simulation uses the CFD-ACE+ commercial software, which employs a finite volume method for the discretization of the Navier-Stokes equations (NSE). In order to determine the dynamic coefficients, the NSE is combined with a finite perturbation method applied to the ‘equivalent journal’ of the damper. It was found that for the 2π-film and the Gumbel conditions, the damping coefficients exhibit linear characteristics, while the homogeneous cavitation model yields nonlinear coefficients. Using the CFD-ACE+, the inertia/added mass coefficients are derived for the limiting cases of the short and long dampers, respectively. The first set of forces is calculated by setting the fluid density to its actual value. The second set of forces is calculated when the density of the fluid is set close to zero (1E-10 kg/m³), thus practically eliminating the effects of the inertia terms. Subtracting the two sets of forces from each other, allows the determination of the inertia component contribution and the corresponding inertia coefficients. By varying the density, dynamic viscosity and whirling speed, it was found that the inertia coefficients follow a single curve represented by a function dependent on the modified Reynolds number, Re*. The inertia coefficients presented in this study are compared with the ones reported by other researchers that used the modified Reynolds equation. Some differences were found between the NSE based results and the Reynolds equation based outcomes. This is attributed to the three-dimensional effects introduced by the totality of the terms comprised in the full NSE.     

Pressure distribution in a fluid film between two axially oscillating parallel circular plates in the presence of a transverse magnetic field

A study of a viscous incompressible electrically conducting fluid between two parallel circular plates, one of which is oscillating axially, in the presence of a transverse magnetic field shows that the pressure in the fluid film increases with both the Hartmann number and the Reynolds number. The increase in pressure due to inertia is not significant for a large Hartmann number. The effects of inertia and of the magnetic field on the pressure distribution when the plate is in its downwards motion are qualitatively similar to those effects in a hydromagnetic squeeze film bearing.     

Performance analysis of four-pad hydrostatic squeeze film dampers loaded between pads under laminar and turbulent flow conditions

This paper presents a theoretical study of the effects of Poiseuille Reynolds number and eccentricity ratio on the performance of four-pad hydrostatic squeeze film dampers. The finite difference method has been used to solve Reynolds equation based on Constantinescu’s turbulent lubrication theory. The numerical results obtained are analysed and compared between three and four-lobe hybrid journal bearings. The computed results indicate that the performance of a hydrostatic squeeze film damper loaded between pads is significantly influenced by the flow regimes. The results presented in this work can be useful to the bearing designers.     

Elastohydrodynamic Lubrication of Rough Surfaces under Oscillatory Line Contact with Non-Newtonian Lubricant

This paper presents the results of a transient analysis of elastohydrodynamic lubrication (EHL) of two parallel cylinders in line contact with a non-Newtonian lubricant under oscillatory motion. Effects of the transverse harmonic surface roughness are also investigated in the numerical simulation. The time-dependent Reynolds equation uses a power law model for viscosity. The simultaneous system of modified Reynolds equation and elasticity equation with initial conditions was solved using the multigrid, multilevel method with full approximation technique. The film thickness and the pressure profiles were determined for smooth and rough surfaces in the oscillatory EHL conjunctions, and the film thickness predictions were verified experimentally.

For an increase in the applied load on the cylinders or a decrease in the lubricant viscosity, there is a reduction in the minimum film thickness, as expected. The predicted film thickness for smooth surfaces is slightly higher than the film thickness obtained experimentally, owing primarily to cavitation that occurred in the experiments. The lubricant film under oscillatory motion becomes very thin near the ends of the contact when the velocity goes to zero as the motion direction changes, but a squeeze film effect keeps the fluid film thickness from decreasing to zero. This is especially true for surfaces of low elastic modulus. Harmonic surface roughness and the viscosity and power law index of the non-Newtonian lubricant all have significant effects on the film thickness and pressure profile between the cylinders under oscillatory motion.     

Effect of roughness on hydromagnetic squeeze films between porous rectangular plates

The theoretical investigations made in this paper are to study the combined effects of unidirectional surface roughness and magnetic effect on the performance characteristics of a porous squeeze film lubrication between two rectangular plates. The stochastic Reynolds equation accounting for the magnetic effect and randomized surface roughness structure is mathematically derived. The expressions for dimensionless pressure, load carrying capacity and squeeze film time are obtained. Results are computed numerically and it is observed that a roughness effect enhances pressure, load carrying capacity and squeeze film time.     

Numerical solution of couplestress finite Reynolds equation for squeeze film lubrication of partial porous journal bearings

Abstract

In this paper, the general Reynolds equation of finite porous journal bearing lubricated with couplestress fluid is solved numerically for the assessment of dynamic characteristics of the bearings. The Reynolds type equation governing the steady performance is obtained and solved numerically by finite difference technique. From the numerical results, it is observed that the effect of couple stresses is to increase the load carrying capacity and to lengthen the squeeze film time as compared to the corresponding solid case. The effect of permeability is to reduce the load capacity and to decrease the squeeze film time as compared to the solid case.     

A new theory of lubrication for rough surfaces

A new theory of lubrication for rough surfaces is presented and a generalized form of the Reynolds equation is derived. A form of the Reynolds equation applicable to mixed lubrication conditions is obtained.In the case of a squeeze film it is shown that the load capacity increases as surface roughness increases.     

Thermo-elasto-hydrodynamic lubrication analysis of piston skirt considering oil film inertia effect

Influence of oil film inertia forces on thermo-elasto-hydrodynamic lubrication performances of a piston skirt is analyzed, based on a proposed Reynolds lubrication equation for the consideration of oil film inertia force effects. Further, a scheme to solve the inertia effects is given. The numerical results show that oil film inertia forces can result in increments in film pressure and temperature, hydrodynamic friction force and load capacity, deformation, and transverse displacements of the piston skirt. Moreover, the influences are obvious for a big reduced Reynolds number. Therefore, oil film inertia force effects on thermo-elasto-hydrodynamic lubrication performances of a piston skirt in a high speed internal combustion engine should be considered.     

Effects of fluid inertia forces on the squeeze film characteristics of conical plates—ferromagnetic fluid model

On the basis of the Shliomis ferromagnetic fluid model, this paper is mainly concerned with the influences of convective fluid inertia forces in magnetic fluid‐based conical squeeze film plates in the presence of external magnetic fields. By applying the averaged momentum principle, a lubrication equation governing the film pressure is derived. Some previous contributions can be obtained from special cases of the present studies. Comparing with the non‐inertia non‐magnetic case, better squeeze film performances are predicted for the magnetic fluid‐based conical plates operating with a larger value of the inertial parameter of fluid inertia forces, the volume concentration of ferrite particles and the strength of applied magnetic fields. Some numerical results with specific cone angles are also provided in tables for engineering applications. Copyright © 2012 John Wiley & Sons, Ltd.     

The Dynamic Properties of Annular Gas Squeeze Film Dampers

The step jump method is used to characterize the stiffness and damping of flat-faced gas lubricated squeeze film dampers. Analytic solution of a linearized form of the isothermal and compressible Reynolds equation yields closed form expressions for the step and frequency responses of the gas film. Results from the step jump method obtained both analytically and numerically are shown to be good approximations of the gas film stiffness and damping. A Prony series is proven to be an effective constitutive model capable of representing the stiffness and damping of the gas film in both the time and frequency domains in analytic form. Using the analytic constitutive model, closed form solutions for the motion of squeeze film dampers are now possible.     

Fluid inertia force effects in hydromagnetic sphere-plate squeeze films

This paper investigates the influences of fluid inertia forces in hydromagnetic sphere-plate squeeze films. Applying the averaged inertia principle, a megnetohydrodynamic pressure gradient equation has been derived. From the results obtained, the combined effects of fluid inertia forces and electrical conducting fluids in the presence of external magnetic fields provide better squeeze film characteristics, and lengthen the operating life of the sphere-plate system as compared to the non-inertia non-conducting-fluid case.     

Inertia force effects in the non-Newtonian couple stress squeeze film between a sphere and a flat plate

On the basis of the Stokes micro-continuum theory together with the method of mean averaged inertia, the influences of fluid inertia forces on the non-Newtonian squeeze film characteristics between a sphere and a flat plate have been presented. Comparing with the case of a non-inertia non-Newtonian lubricant, the consideration of fluid inertia forces provides a longer squeeze film time especially for the squeeze film operating with a lower film height, and a larger non-Newtonian parameter and density parameter. It prolongs the life of squeeze films.     

Squeeze film characteristics between a sphere and a rough porous flat plate with micropolar fluids

The effects of surface roughness on the squeeze film characteristics between a sphere and flat plate covered with a thin porous layer are investigated in this paper. The sphere and the plate are separated with a non‐Newtonian lubricant of a micropolar fluid. The well‐established Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to incorporate the effects of surface roughness into the Reynolds equation. The film pressure distribution is solved and other squeeze film characteristics, such as the load‐carrying capacity,and time–height relationship, are obtained. The results indicate that lubrication by a micropolar fluid will increase the load‐carrying capacity and lengthen the squeeze film time, regardless to the surface rough and porosity of the flat plate. It is also found that excessive permeability of the porous layer causes a significant drop in the squeeze film characteristics and minimises the effect of surface roughness. For the case of limited or no permeability, the azimuthal roughness is found to increase the load‐carrying capacity and squeeze time, whereas the reverse results are obtained for the case of radial roughness.