Dynamics of Air-Lubricated Slider Bearings for Noncontact Magnetic Recording

1971 ◽  
Vol 93 (2) ◽  
pp. 272-278 ◽  
Author(s):  
T. Tang
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Direct Access ◽  
Slider Bearing ◽  
Storage Devices ◽  
Disk Storage ◽  
Slider Bearings

One of the key technologies which led to the success of modern magnetic disk storage devices is the development of self acting gas lubricated slider bearings for positioning a magnetic head precisely over a high speed rotating recording disk. This paper covers a dynamic simulation of such an air bearing system used in direct access disk storage devices. In the simulation model, the Reynolds equation, which describes the dynamics of the lubricating air film, is solved by finite difference techniques in two dimensions and time for compressible, isothermal flow. The equations of motion of the slider bearing are solved simultaneously with the Reynolds equation for three degrees of freedom. Applications of the simulation are demonstrated, and experimental measurements to verify the theory are presented and discussed.

Railway Truck Response to Random Rail Irregularities

1975 ◽  
Vol 97 (3) ◽  
pp. 957-964 ◽  
Author(s):  
Neil K. Cooperrider
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Tangential Force ◽  
Contact Forces ◽  
Guidance Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Rail Irregularities ◽  
Frequency Domain Techniques

This paper discusses the random response of a seven degree of freedom, passenger truck model to lateral rail irregularities. Power spectral densities and root mean square levels of component displacements and contact forces are reported. The truck model used in the study allows lateral and yaw degrees of freedom for each wheelset, and lateral, yaw and roll freedoms for the truck frame. Linear creep relations are utilized for the rail-wheel contact forces. The lateral rail irregularities enter the analysis through the creep expressions. The results described in the paper were obtained using frequency domain techniques to solve the equations of motion. The reported results demonstrate that the guidance force needed when traveling over irregular rail at high speed utilizes a significant portion of the total available tangential force between wheel and rail.

The Rotor Dynamic Coefficients of Eccentric Mechanical Face Seals

1996 ◽  
Vol 118 (1) ◽  
pp. 215-224 ◽  
Author(s):  
J. Wileman ◽  
I. Green
Keyword(s):  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Shear Stresses ◽  
Dynamic Coefficients ◽  
Angular Deflection ◽  
Face Seals ◽  
Radial Forces ◽  
Rotor Dynamic ◽  
Additional Coupling

The Reynolds equation is extended to include the effects of radial deflection in a seal with two flexibly mounted rotors. The resulting pressures are used to obtain the forces and moments introduced in the axial and angular modes by the inclusion of eccentricity in the analysis. The rotor dynamic coefficients relating the forces and moments in these modes to the axial and angular deflection are shown to be the same as those presented in the literature for the concentric case. Additional coefficients are obtained to express the dependence of these forces and moments upon the radial deflections and velocities. The axial force is shown to be decoupled from both the angular and radial modes, but the angular and radial modes are coupled to one another by the dependence of the tilting moments upon the radial deflections. The shear stresses acting upon the element faces are derived and used to obtain the radial forces acting upon the rotors. These forces are used to obtain rotor dynamic coefficients for the two radial degrees of freedom of each rotor. The additional rotor dynamic coefficients can be used to obtain the additional equations of motion necessary to include the radial degrees of freedom in the dynamic analysis. These coefficients introduce additional coupling between the angular and radial degrees of freedom, but the axial degrees of freedom remain decoupled.

Hydrodynamic Lubrication of Finite Slider Bearings: Effect of One Dimensional Film Shape, and Their Computer Aided Optimum Designs

1983 ◽  
Vol 105 (1) ◽  
pp. 48-63 ◽  
Author(s):  
C. Bagci ◽  
A. P. Singh
Keyword(s):  
Numerical Solution ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Design Data ◽  
Slider Bearings ◽  
Load Carrying ◽  
Computer Aided

The effect of the film shape on the load carrying capacity of a hydrodynamically lubricated bearing has not been considered an important factor in the past. Flat-faced tapered bearing and the Raileigh’s step bearing of constant film thickness have been the primary forms of film shapes for slider bearing studies and design data developments. This article, by the computer aided numerical solution of the Reynolds equation for two dimensional incompressible lubricant flow, investigates hydrodynamically lubricated slider bearings having different film shapes and studies the effect of the film shape on the performance characteristics of finite bearings; and it shows that optimized bearing with film shapes having descending slope toward the trailing edge of the bearing has considerably higher load carrying capacity than the optimized flat-faced tapered bearing of the same properties. For example the truncated cycloidal film shape yields 26.3 percent higher load carrying capacity for Lz/Lx = 1 size ratio, and 44 percent higher for Lz/Lx = 1/2. The article then presents charts for the optimum designs of finite slider bearings having tapered, exponential, catenoidal, polynomial, and truncated-cycloidal film shapes, and illustrates their use in numerical bearing design examples. These charts also furnish information on flow rate, side leakage, temperature rise, coefficient of friction, and friction power loss in optimum bearings. Appended to the article are analytical solutions for infinitely wide bearings with optimum bearing characteristics. The computer aided numerical solution of the Reynolds equation in most general form is presented by which finite or infinitely wide hydrodynamically or hydrostatically lubricated bearings, externally pressurized or not, can be studied. A digital computer program is made available.

AN INTEGRABLE MODEL WITH SOLITON SOLUTIONS WHICH HAVE APPLICATIONS TO TWO-DIMENSIONAL GRAVITY

2005 ◽  
Vol 20 (07) ◽  
pp. 1503-1514 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Integrable Model ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Two Dimensions ◽  
Spin Connection ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Chern Simons

The equations of motion for a theory described by a Chern–Simons type of action in two dimensions are obtained and investigated. The equation for the classical, continuous Heisenberg model is used as a form of gauge constraint to obtain a result which provides a completely integrable dynamics and which partially fixes the gauge degrees of freedom. Under a particular form of the spin connection, an integrable equation which can be analytically extended to a form of the nonlinear Schrödinger equation is obtained. Some explicit solutions are presented, and in particular a soliton solution is shown to lead to an integrable two-dimensional model of gravity.

On the study of Rayleigh step slider bearings lubricated with non-Newtonian Rabinowitsch fluid

2017 ◽  
Vol 69 (5) ◽  
pp. 666-672
Author(s):  
N.B. Naduvinamani ◽  
Siddharam Patil ◽  
S.S. Siddapur
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Maximum Load ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Content Type ◽  
Slider Bearings ◽  
Load Carrying ◽  
Modified Reynolds Equation ◽  
Frictional Coefficients

Purpose Nowadays, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of non-Newtonian fluids has gained importance. This paper presents an analysis of the static characteristics of Rayleigh step slider bearing lubricated with non-Newtonian Rabinowitsch fluid, which has not been studied so far. The purpose of this paper is to derive the modified Reynolds equation for Rabinowitsch fluids for two regions and to obtain the optimum bearing parameters for the Rayleigh step slider bearings. Design/methodology/approach The governing equations relevant to the problem under consideration are derived. The modified Reynolds equation is derived, and it is found to be highly non-linear and hence small perturbation method is adopted to find solution. Findings From this study it is found that there is an increase in the load-carrying capacity, pressure and frictional coefficients for dilatant fluids as compared to the corresponding Newtonian case. Further, for dilatant lubricants the maximum load-carrying capacity is attained for the slightly larger values of entry region length of Rayleigh step bearing as compared to Newtonian and pseudoplastic lubricants. Originality/value Rabinowitsch fluid is used for the study of lubrication characteristics of Rayleigh step bearings. The author believes that the paper presents these results for the first time.

A New Approach to Modeling Surface Defects in Bearing Dynamics Simulations

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Ankur Ashtekar ◽  
Farshid Sadeghi ◽  
Lars-Erik Stacke
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Surface Defects ◽  
Equations Of Motion ◽  
Infinite Domain ◽  
Step Size ◽  
Deep Groove ◽  
Dynamics Simulations ◽  
Bearing Dynamics

A dynamic model for deep groove and angular contact ball bearings was developed to investigate the influence of race defects on the motions of bearing components (i.e., inner and outer races, cage, and balls). In order to determine the effects of dents on the bearing dynamics, a model was developed to determine the force-deflection relationship between an ellipsoid and a dented semi-infinite domain. The force-deflection relationship for dented surfaces was then incorporated in the bearing dynamic model by replacing the well-known Hertzian force-deflection relationship whenever a ball/dent interaction occurs. In this investigation, all bearing components have six degrees-of-freedom. Newton’s laws are used to determine the motions of all bearing elements, and an explicit fourth-order Runge–Kutta algorithm with a variable or constant step size was used to integrate the equations of motion. A model was used to study the effect of dent size, dent location, and inner race speed on bearing components. The results indicate that surface defects and irregularities like dent have a severe effect on bearing motion and forces. Furthermore, these effects are even more severe for high-speed applications. The results also demonstrate that a single dent can affect the forces and motion throughout the entire bearing and on all bearing components. However, the location of the dent dictates the magnitude of its influence on each bearing component.

Generalized Reynolds Equation for Micropolar Lubricants and its Application to Optimum One-Dimensional Slider Bearings: Effects of Solid-Particle Additives in Solution

1975 ◽  
Vol 17 (5) ◽  
pp. 280-284 ◽  
Author(s):  
J. B. Shukla ◽  
M. Isa
Keyword(s):  
Calculus Of Variations ◽  
Solid Particle ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slider Bearing ◽  
One Dimensional ◽  
Slider Bearings ◽  
Generalized Reynolds Equation

The effects of solid-particle additives in the lubricant are considered by characterizing this suspension as a micropolar fluid. The generalized Reynolds equation for this case has been derived and the optimum one-dimensional slider bearing is studied by using the techniques of the calculus of variations.

High-Speed Vehicle Models Based on a New Concept of Vehicle/Structure Interaction Component: Part II—Algorithmic Treatment and Results for Multispan Guideways

1993 ◽  
Vol 115 (1) ◽  
pp. 148-155 ◽  
Author(s):  
L. Vu-Quoc ◽  
M. Olsson
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Structural Equations ◽  
Component Part ◽  
Vehicle Speed ◽  
Vehicle Structure ◽  
Algorithmic Treatment ◽  
Nonlinear Equations Of Motion ◽  
High Speed Vehicle

The predictor structural equations for the vehicle models developed in Part I are derived here for use with a new class of predictor/corrector algorithms to solve the mildly nonlinear equations of motion of the vehicle/structure models. Having all accelerations of the vehicle component eliminated, and with the aid of further simplifying approximations, the predictor structural equations are linear with respect to the structural degrees of freedom. In the algorithms, the predictor structural equations are different from the corrector structural equations; the proposed algorithmic treatment has been proved (elsewhere) to yield accurate energy balance. Results obtained for both continuous and discontinuous guideways are discussed, and optimal guideway configurations suggested. Effects of high-speed vehicle braking on a flexible guideway are analyzed using the vehicle models and the proposed algorithmic treatment. The influence of the guideway flexibility on the vehicle speed, an important feature of the present formulation, is clearly demonstrated.

Pressure Boundary Layer in a Transient or Steady Gas Film and Mass Interaction

1970 ◽  
Vol 37 (4) ◽  
pp. 945-953 ◽  
Author(s):  
F. C. Hsing ◽  
H. S. Cheng
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
High Speed ◽  
Numerical Scheme ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Pressure Profile ◽  
Tilting Pad ◽  
Static Solutions ◽  
Gas Bearing

This paper presents a numerical scheme capable of yielding accurate pressure profile for the transient and steady hydrodynamic gas film generated by high-speed relative motion of two nonparallel surfaces. The numerical difficulties associated with high compressibility numbers for the gas film Reynolds equation were overcome by employing a set of systematically generated irregular grid spacings based on a coordinate transformation. By coupling the fluid-film solution with the equations of motion of a tilting pad, the dynamics of the mass film interaction were treated. Results are presented for both steady-state and dynamical solutions. Static solutions for a 120-deg partial-arc gas bearing have been used for comparison.

Tribological Study of a Slider Bearing in the Supersonic Regime

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Florence Dupuy ◽  
Benyebka Bou-Saïd ◽  
Mathieu Garcia ◽  
Grégory Grau ◽  
Jérôme Rocchi ◽  
...  
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slider Bearing ◽  
Navier Stokes Equations ◽  
Supersonic Regime ◽  
Two Dimensional Flow ◽  
Modified Reynolds Equation ◽  
The One

Aerodynamic slider bearings are currently used in various types of turbomachinery. Many such systems perform at increasingly faster speeds and may operate in the supersonic regime. Although there is extensive research on compressible lubrication extrapolated to high-speeds, very little of it addresses the potential supersonic nature of the flow. It is well known in compressible flow that many of the tendencies of subsonic flow actually reverse themselves as the singularity at Mach one is traversed. Thus, examination of this high-speed regime may yield some unanticipated results. The behavior of a thin film of air in the supersonic regime is studied in the two-dimensional flow case with rigid sliding surfaces. The one-dimensional bearing studied has a dual profile consisting of an inlet region converging wedge of constant slope and an exit region of constant gap. Two approaches are compared: the solution of a modified Reynolds equation, and the solution to a version of Navier–Stokes equations adapted to thin films. The results show that the modified Reynolds equation approach, which is useful to describe the behavior of lubricating fluids at high subsonic speeds may be inadequate in the supersonic regime. The present studies show the absence of shock and expansion wave phenomena for cases in which the film thickness ratio does not exceed 0.01.

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