Inertia effects in circular squeeze films containing a central air bubble

Rheodynamic lubrication of a squeeze film bearing under sinusoidal squeeze motion

Abstract: Lubricants with variable viscosity are assuming importance for their applications in polymer industry, thermal reactors and in biomechanics. With the bearing operations in machines being subjected to high speeds, loads, increasing mechanical shearing forces and continually increasing pressures, there has been an increasing interest to use non-Newtonian fluids characterized by an yield value. The most elementary constitutive equation in common use that describes a material which yields is that of Bingham fluid. In the present work, the problem of a circular squeeze film bearing lubricated with Bingham fluid under the sinusoidal squeeze motion has been analyzed. The shape and extent of the core for the case of sinusoidal squeeze motion has been determined numerically for various values of the Bingham number. Numerical solutions have been obtained for the bearing performances such as pressure distribution and load capacity for different values of Bingham number, Reynolds number and for various amplitudes of squeeze motion. The effects of fluid inertia, non-Newtonian characteristics, and the amplitudes of squeeze motion on the bearing performances have been discussed.

Inertia Effects in Rheodynamic Lubrication of an Externally Pressurized Converging Thrust Bearing using Bingham Fluids

Abstract: Thrust bearing are innately developed to withstand axial load. When the bearing is subjected to high speed operations, heavy load, high stiffness etc., suggesting a change in the design of the bearing plays a vital role in its performance. Friction is developed between the circular plates while the bearing operates. To reduce this friction, the bearing is lubricated with lubricants such as mineral oil, greases etc., Generally, lubricants are classified into two types that is Newtonian and non-Newtonian. However, non-Newtonian fluids characterized by an yield value such as Bingham, Casson and Herschel Bulkley, are attracting the tribologists, at present. And also, the study of fluid inertia on thrust bearing is required to optimize the performance of the bearings. In this investigation, we have ventured to analyze the performance of the bearing by considering the combined effects of fluid inertia forces and non-Newtonian characteristic with Bingham fluid as lubricant in an externally pressurized converging circular thrust bearing. Such studies will be useful in the design of the bearing for the optimum performance using the appropriate lubricant in various machineries operating in an extreme condition in the industries. Averaging the inertia terms over film thickness and defining a modified pressure gradient, the rheodynamic lubrication equation containing inertia terms has been analyzed. Using the appropriate boundary conditions and considering externally pressurized flow in narrow clearance between two converging discs is symmetric w.r.t r and z axis, the velocity distributions, the modified pressure gradient and thereby the film pressure and the load capacity of the bearing have been obtained numerically for different values of Bingham number, Reynolds number and angle of convergence. In addition to that, the effects of the inertia forces, non-Newtonian characteristics and angle of convergence on the bearing performances have been discussed.

Lumped Parameter Analysis of an Enclosed Incompressible Squeeze Film and a Central Gas Bubble

Abstract: A lumped-parameter dynamic model for an enclosed incompressible squeeze film with a central gas bubble has been derived. A new approach was applied to derive closed-form expressions for the lumped-parameter mass and damping coefficients caused by liquid motion. It was assumed that plate motions were small and the fluid behaved as a continuum. The values of the lumped-parameter mass and damping were found to depend on the aspect ratio and nondimensional squeeze-film thickness. The nondimensional thickness was given by the ratio of the actual squeeze-film thickness to the viscous penetration depth of the liquid. A nondimensional squeeze-film thickness of a value of 5 was found to divide between categories of thick and thin incompressible squeeze films. Amplification of the liquid mass and damping over and above squeeze films open to the atmosphere at the edges was found. The amplification was attributed to converging flow caused by enclosed boundaries. Comparisons between the lumped-parameter model predictions and finite-element computations showed a surprising degree of accuracy for the lumped-parameter model despite large liquid velocities in the squeeze film.

Inertia Effects in an Externally Pressurized Thrust Bearing Using Herschel - Bulkley Lubricants

Abstract: The combined effects of fluid inertia and viscous forces of a Herschel-Bulkley lubricant in an externally pressurized thrust bearing with circular geometry have been analyzed theoretically. Although the researchers of the past, laid out a foundation for the hydrodynamic lubrication, modern researchers intend to use non-Newtonian fluids characterized by a yield-value, such as Bingham, Casson and Herschel-Bulkley fluids as lubricants. More over, Tribologists emphasize a fact that in order to analyze the performance of the bearings adequately, it is necessary to consider the combined effects of fluid inertia and viscous forces of non-Newtonian lubricants. Therefore, in this research article, the combined effects of fluid inertia and viscous forces have been investigated theoretically in an externally pressurized thrust bearing with circular ge- ometry using Herschel-Bulkley fluid as lubricant. The shape and extent of the core, along the radius, have been determined numerically for various values of the Herschel-Bulkley number and the power-law index. Using the appropriate boundary conditions, the velocity distributions in the flow and the core regions have been obtained. By considering the equilibrium of an element of the core in the fluid, the modified pressure gradient has been evaluated and thereby the film pressure and the load capacity of the bearing have been obtained numerically for different values of Reynolds number, Herschel-Bulkley number and power-law index. The effects of the inertia forces and the non-Newtonian characteristics of the lubricant, on the bearing performances have also been discussed.

Fluid inertia effects in squeeze films

Abstract: Fluid inertia effects in squeeze films are analyzed. Experimental results are also presented. The agreement between theory and experiment is very good.

A study of squeezing flow

Abstract: The problem of the squeezing of a film of liquid between two parallel surfaces is considered. Approximate expressions are deduced for the instantaneous distribution of velocity within the fluid and the reaction on the surfaces. These are obtained by an approximate iterative solution of the continuity and momentum equations. The radial pressure distribution in a squeezed film is found to be due partly to the action of viscosity and partly to inertia effects. The latter cause the relationship between the reaction on the surfaces and their relative velocity to be non-linear. This effect is significant for conditions where the Reynolds number based upon the distance between the surfaces and their relative velocity is greater than unity. The results obtained should be of interest in connection with the study of the performance of transiently loaded bearings in reciprocating engines, and a possible application in the field of chemical engineering might arise in connection with the phenomenon of adhesion.

The Unsteady Laminar Flow between Two Parallel Discs with Arbitrarily Varying Gap Width

Abstract: A theoretical analysis is presented for the unsteady laminar flow of an incompressible fluid in a narrow gap between two parallel discs of which gap-width h (t) varies arbitrarily with time. An infinite set of the non-dimensional time-dependent parameters [numerical formula], …… is introduced providing that the function h (t) is continuously differentiable, and the exact solutions of the Navier-Stokes equations and the thermal energy equation are obtained as the "multifold"series of these non-dimensional parameters. As an application, a detailed numerical study has been made of the fundamental case when the walls perform reciprocating harmonic oscillations with finite amplitudes {h (t)=h0 (1+asinωt)}. The flow characteristics are governed by the two non-dimensional parameters a and Rω=(h02ω)/υ. As compared with the sinusoidal velocity of the gap-width change, (dh)/(dt)=aωh0cosωt, the varying hydrodynamical force acting on the wall surface becomes more distorted in wave form as a increases, and becomes more advanced in phase as Rω increases. Heat is generated in the fluid between the walls through viscous friction : when the fluid is cooled by only one wall surface the fluid temperature becomes very much higher than when the cooling is done by both the two walls.