Factored-lmplicit Finite Difference Solution of a Non-Newtonian Fluid Lubrication Equation for Three-Dimensional Bearings

1996 ◽  
Vol 118 (4) ◽  
pp. 824-831 ◽  
Author(s):  
J. W. White
Keyword(s):  
Shear Stress ◽  
Finite Difference ◽  
Strain Rate ◽  
Data Storage ◽  
Newtonian Fluid ◽  
Time Interval ◽  
Finite Width ◽  
Disk Interface ◽  
Static And Dynamic Analysis ◽  
Lubrication Equation

A time dependent lubrication equation is developed for a non-Newtonian fluid whose shear stress is expressed in terms of instantaneous strain rate. By expanding the shear stress through a two function Taylor series, the stress/strain-rate relationship is linearized within the time interval (tn ≤ t ≤ tn+1) but accurate to O(Δt2). This produces a linear lubrication equation which is second-order time-accurate. The resulting finite difference form of the lubrication equation is then factored and split into two equations, each of which represents a sequence of one-dimensional systems of tri-diagonal scalar equations. A finite difference code based on this algorithm was written called VISQUSFLO which provides static and dynamic analysis of the head/disk interface of data storage systems. Numerical examples of a shear-thinning fluid are presented for clearances in the range of 25-50 nm for finite width slider bearings.

Application and Prospect of the Non-Newtonian Fluid in Industrial Field

2013 ◽  
Vol 770 ◽  
pp. 396-401 ◽  
Author(s):  
Yan Peng ◽  
Bing Hai Lv ◽  
Ju Long Yuan ◽  
Hong Bo Ji ◽  
Lei Sun ◽  
...  
Keyword(s):  
Shear Stress ◽  
Strain Rate ◽  
Shear Strain ◽  
Linear Relationship ◽  
Rheological Properties ◽  
Newtonian Fluid ◽  
Shear Strain Rate ◽  
Mechanical Processing ◽  
Different Types ◽  
Individual Protection

Non-Newtonian fluid is a kind of fluid that its shear stress is not always keeps a linear relationship with the shear strain rate. An overview of its applications was made here. Based on the special rheological properties, non-Newtonian fluids are divided into different types and used as additives, mediums and protective materials in many fields. The paper focuses on its applications in fluid rheological properties improving, damping devices, individual protection equipments and mechanical processing. The main achievements in application of the non-Newtonian fluid were introduced and a further prospect was also summarized.

Elastohydrodynamic Analysis of Head to Flexible Disk Interface Phenomena

1981 ◽  
Vol 48 (4) ◽  
pp. 763-768 ◽  
Author(s):  
J. P. Licari ◽  
F. K. King
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Numerical Models ◽  
Disk Interface ◽  
Disk Rotation ◽  
Lubrication Equation ◽  
Interface Phenomena ◽  
Element Approach ◽  
Flexible Disk ◽  
Finite Difference Techniques

The finite-element and finite-difference techniques are used to develop an analytical model which describes the interaction between a magnetic recording head and a flexible disk. The finite-element approach is used to describe disk deformation. Both disk bending stiffness and stiffness effects due to disk rotation are included. The finite-difference scheme is used to solve the Reynold’s or lubrication equation which describes the flow interaction between head and disk. The procedure used to couple the two numerical models into a complete head-to-disk interface simulator is outlined. Accuracy of the simulator is verified experimentally, and results of studies showing the sensitivities of various parameters are given.

Based on Rheological to Calculate Anchor Parameter for Foundation Pit

2012 ◽  
Vol 538-541 ◽  
pp. 665-668
Author(s):  
Xin Wen Suo ◽  
Chen Min Gu
Keyword(s):  
Shear Stress ◽  
Numerical Calculation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Strain Rate ◽  
Difference Method ◽  
Rheological Model ◽  
Shear Strain Rate ◽  
Axial Distribution ◽  
Foundation Pit

Pointed to character of rheological mechanics and limited equilibrium method, a new viso-elasto-plastic rheological model is builded with minimum locked load formula abtained.The finite difference method with C++ and inline FISH program ,is applied to analyze engineering instance. Based on calculated results and testing on spot, plentiful key parameters on whole bonged and prestressed bolt is studied.Lastly,the conclusions are open out ,including minimum locked loading,stress and maximal axial distribution of prestressed steal, hump distribution of shear stress on grount,shear strain rate of surface and displacement of reinforced foundation pit and so on.The numerical calculation is coincident with testing factors.

Stability of discontinuous steady states in shearing motions of a non-Newtonian fluid

1990 ◽  
Vol 115 (1-2) ◽  
pp. 39-59 ◽  
Author(s):  
John A. Nohel ◽  
Robert L. Pego ◽  
Athanasios E. Tzavaras
Keyword(s):  
Shear Stress ◽  
Strain Rate ◽  
Newtonian Fluid ◽  
Space Dimension ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Steady States ◽  
Constitutive Law ◽  
Shear Strain Rate ◽  
Initial Boundary Value

SynopsisWe study the nonlinear stability of discontinuous steady states of a model initial-boundary value problem in one space dimension for incompressible, isothermal shear flow of a non-Newtonian fluid driven by a constant pressure gradient. The non-Newtonian contribution to the shear stress is assumed to satisfy a simple differential constitutive law. The key feature is a non-monotone relation between the total steady shear stress and shear strain-rate that results in steady states having, in general, discontinuities in the strain rate. We show that every solution tends to a steady state as t → ∞, and we identify steady states that are stable.

The Effect of Two-Dimensional Surface Roughness on the Load-Carrying Capacity of a Thin Compressible Gas Film

1993 ◽  
Vol 115 (2) ◽  
pp. 246-252 ◽  
Author(s):  
J. W. White
Keyword(s):  
Surface Roughness ◽  
Data Storage ◽  
Perturbation Expansion ◽  
Expansion Method ◽  
Order Effect ◽  
Finite Width ◽  
Two Dimensional ◽  
Lubrication Equation ◽  
Unit Depth ◽  
Dimensional Surface

The influence of two-dimensional surface roughness on a very low clearance gas bearing slider is analyzed for conditions typical of current and near term hard disk data storage products. A model lubrication equation including finite width effects, compressibility and molecular slip is first developed and expressed in terms of the product variable, Z = PH. The analytical solution is then obtained by a combined variation of parameters and perturbation expansion method. Results obtained show that the product variable, which is proportional to longitudinal mass flow per unit depth, is not influenced by the details of surface roughness but is instead influenced by the statistics of the roughness distribution. The gas film pressure, however, is found to be a function of both the roughness details and statistics. The bearing load support is increased by the surface roughness, with the roughness first influencing the load through a second order effect.

scholarly journals Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting

2020 ◽  
Vol 7 (1) ◽  
pp. 48-55 ◽  
Author(s):  
Bolat Duissenbekov ◽  
Abduhalyk Tokmuratov ◽  
Nurlan Zhangabay ◽  
Zhenis Orazbayev ◽  
Baisbay Yerimbetov ◽  
...  
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Difference Equations ◽  
Constant Load ◽  
Time Interval ◽  
Test Case ◽  
Algebraic Equations ◽  
Nonlinear Properties ◽  
Finite Difference Equations ◽  
Concrete Shells

AbstractThe study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations. All stiffness properties of the shell are taken as variables, i.e., stiffness surface and through-thickness stiffness. Differential equations under consideration were evaluated in the form of algebraic equations with the finite element method. For a reinforced shell, a system of 98 equations on a 8×8 grid was established, which was next solved with the approximation method from the nonlinear plasticity theory. A test case involved computing a 1×1 shallow shell taking into account the nonlinear properties of concrete. With nonlinear equations for the concrete creep taken as constitutive, equations for the quasi-static shell motion under constant load were derived. The resultant equations were written in a differential form and the problem of solving these differential equations was then reduced to the solving of the Cauchy problem. The numerical solution to this problem allows describing the stress-strain state of the shell at each point of the shell grid within a specified time interval.

Overcoats and Lubrication for Thin Film Disks

MRS Bulletin ◽  
1990 ◽  
Vol 15 (3) ◽  
pp. 45-52 ◽  
Author(s):  
A.M. Homola ◽  
C.M. Mate ◽  
G.B. Street
Keyword(s):  
Thin Film ◽  
Data Storage ◽  
Magnetic Particles ◽  
Areal Density ◽  
Magnetic Film ◽  
Alloy Thin Film ◽  
Magnetic Media ◽  
Disk Interface ◽  
Storage Devices ◽  
Particulate Media

Metallic alloy thin film media and ever decreasing head-to-media spacing make severe demands on storage devices. Decreasing head-to-media separation is critical for high storage densities but it also leads to increased slider-disk interactions, which can cause slider and disk wear or even head crashes. Wear can also occur when drives start and stop when the slider contacts the disk at relatively high speeds. The reliability and durability of thin film disks, which provide much higher areal density than conventional oxide disks with particulate media, are achieved by the use of very thin overcoat materials and surface lubricants. This article summarizes the approaches taken in the industry to enhance the tribological performance of magnetic media, with special emphasis on the basic understanding of the processes occurring at the slider-disk interface.The continuous rise in the demand for storage capacity at a competitive price is the prime motivator of the changes we have seen in the data storage industry. It is clearly stimulating the present move away from particulate media, which has long dominated all fields of data storage, i.e., tape, rigid, and flexible disks, to the thin film storage media. Particulate storage devices use magnetic media formulated by dispersing magnetic particles, usually iron oxides, in an organic binder. In thin film storage devices, the storage medium is a continuous magnetic film, usually a cobalt alloy, made either by sputtering or by electroless plating.

Static Determinacy in the Theory of Finite Width Foil Bearings

1974 ◽  
Vol 41 (1) ◽  
pp. 51-54 ◽  
Author(s):  
W. E. Langlois
Keyword(s):  
Force Balance ◽  
Finite Width ◽  
Foil Bearings ◽  
Lubrication Equation ◽  
Foil Bearing ◽  
Edge Conditions ◽  
Single Force ◽  
Static Determinacy ◽  
Force Balance Equation ◽  
Determinate Problem

The assumption of “perfect flexibility” is shown to be self-consistent in an important class of finite-width foil bearing problems. When the membrane equations are written in the “stretched coordinates” of foil bearing theory, the usual edge conditions on the tape result in a statically determinate problem. The tape dynamics couples to the Reynolds lubrication equation through a single force-balance equation which does not entail the elastic strain.

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