A Theory of Lubrication by Microirregularities

1966 ◽  
Vol 88 (1) ◽  
pp. 177-185 ◽  
Author(s):  
D. B. Hamilton ◽  
J. A. Walowit ◽  
C. M. Allen
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Load Capacity ◽  
Face Seal ◽  
Lubrication Mechanism ◽  
Surface Asperity ◽  
Parallel Surfaces ◽  
Theoretical Results

This paper describes a theory of liquid lubrication applicable to parallel surfaces, such as the surfaces of a rotary-shaft face seal. The lubrication mechanism presented is based on surface microirregularities and associated film cavities. Closed-form analytical solutions are obtained giving load capacity as a function of speed, viscosity, and surface-asperity dimensions. The theoretical results agree qualitatively with load capacity determined experimentally for three asperity distributions.

A Theory of an Externally Pressurized Circular Thrust Gas Bearing With Consideration of the Effects of Lubricant Inertia

1963 ◽  
Vol 85 (2) ◽  
pp. 304-309 ◽  
Author(s):  
Haruo Mori
Keyword(s):  
Velocity Distribution ◽  
Pressure Distribution ◽  
Elliptic Function ◽  
Load Capacity ◽  
Hydrodynamic Theory ◽  
Pressure Curve ◽  
Parabolic Shape ◽  
Parallel Surfaces ◽  
Gas Bearing ◽  
Theoretical Results

A hydrodynamic theory, with consideration of the effects of compressibility and inertia of the lubricant, is applied to externally pressurized gas bearings which consist of circular and parallel surfaces. The ordinary velocity distribution in a bearing clearance with a parabolic shape is changed to a velocity distribution with a shape of elliptic function due to the effect of lubricant inertia. The pressure distribution in this case differs from the ordinary pressure curve calculated without consideration of inertia, but the load capacity seems to be almost the same in both cases. The theoretical results agree in general with the experimental results reported in a previous publication [3].

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

Closed-form solutions of an elliptical crack subjected to coupled phonon–phason loadings in two-dimensional hexagonal quasicrystal media

2018 ◽  
Vol 24 (6) ◽  
pp. 1821-1848 ◽  
Author(s):  
Yuan Li ◽  
CuiYing Fan ◽  
Qing-Hua Qin ◽  
MingHao Zhao
Keyword(s):  
Closed Form ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Elliptical Crack ◽  
Two Dimensional ◽  
Crack Face ◽  
Penny Shaped Crack ◽  
Crack Problems

An elliptical crack subjected to coupled phonon–phason loadings in a three-dimensional body of two-dimensional hexagonal quasicrystals is analytically investigated. Owing to the existence of the crack, the phonon and phason displacements are discontinuous along the crack face. The phonon and phason displacement discontinuities serve as the unknown variables in the generalized potential function method which are used to derive the boundary integral equations. These boundary integral equations governing Mode I, II, and III crack problems in two-dimensional hexagonal quasicrystals are expressed in integral differential form and hypersingular integral form, respectively. Closed-form exact solutions to the elliptical crack problems are first derived for two-dimensional hexagonal quasicrystals. The corresponding fracture parameters, including displacement discontinuities along the crack face and stress intensity factors, are presented considering all three crack cases of Modes I, II, and III. Analytical solutions for a penny-shaped crack, as a special case of the elliptical problem, are given. The obtained analytical solutions are graphically presented and numerically verified by the extended displacement discontinuities boundary element method.

scholarly journals A Method for the Statistical Evaluation of Crosstalk Effect Between Three Parallel Conductors

1999 ◽  
Vol 22 (2) ◽  
pp. 111-119
Author(s):  
P. T. Trakadas ◽  
C. N. Capsalis
Keyword(s):  
Closed Form ◽  
Uniform Distribution ◽  
Transmission Lines ◽  
Statistical Evaluation ◽  
Unit Length ◽  
Surrounding Medium ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Mutual Inductance ◽  
Theoretical Results

There are several cases at which, in order to evaluate the crosstalk effect among transmission lines carrying useful signals, there is a need for probabilistic approach. This paper considers the problem of crosstalk estimation between transmission lines consisting of three conductors in a homogeneous surrounding medium, where the distance between the conductors is a random variable described by uniform distribution. The transmission lines are considered as electrically short. A closed-form equation is developed for the statistical distribution of the per-unit-length mutual inductance(lm)and an analytical one is described for the evaluation of the per-unit-length capacitance(cm). Theoretical results are compared with simulated ones for validation purposes.

Hydrodynamic Pressure of Thrust Step Bearings

2009 ◽  
Author(s):  
Shuangbiao Liu ◽  
W. Wayne Chen ◽  
Diann Y. Hua
Keyword(s):  
Analytical Solution ◽  
Coordinate System ◽  
Laplace Equation ◽  
Analytical Solutions ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Hydrodynamic Pressure ◽  
Finite Width ◽  
Cylindrical Coordinate ◽  
Lubrication Models

Step bearings are frequently used in industry for better load capacity. Analytical solutions to the Rayleigh step bearing and a rectangular slider with a finite width are available in literature, but none for a fan-shaped thrust step bearing. This study starts with a known solution to the Laplace equation in a cylindrical coordinate system, which is in the form of infinite summation. An analytical solution to pressure is derived in this paper for hydrodynamic lubrication problems encountered in the fan-shaped step bearing. The presented solutions can be useful for designers to maximize bearing performance as well as for researchers to benchmark numerical lubrication models.

Generalized Couette Flow of a Third-Grade Fluid with Slip: The Exact Solutions

2010 ◽  
Vol 65 (12) ◽  
pp. 1071-1076 ◽  
Author(s):  
Rahmat Ellahi ◽  
Tasawar Hayat ◽  
Fazal Mahmood Mahomed
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Closed Form ◽  
Analytical Solutions ◽  
Present Note ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Flow Problems ◽  
Grade Fluid

The present note investigates the influence of slip on the generalized Couette flows of a third-grade fluid. Two flow problems are considered. The resulting equations and the boundary conditions are nonlinear. Analytical solutions of the governing nonlinear problems are found in closed form.

scholarly journals Static characteristics of hydrostatic thrust bearing considering the inertia effect on the region of supply hole

2018 ◽  
Vol 233 (1) ◽  
pp. 188-193
Author(s):  
Zhuxin Tian ◽  
Haiyin Cao ◽  
Yu Huang
Keyword(s):  
Flow Rate ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Experimental Results ◽  
Inertia Effect ◽  
Static Characteristics ◽  
Hole Radius ◽  
Inertia Parameter ◽  
Theoretical Results ◽  
Inertia Theory

In the previous studies on the hydrostatic thrust bearing, the differences between the theoretical results and experimental results are obvious when the inertia parameter S and the ratio of supply hole radius to bearing radius r0/ R become large enough. To explain the differences, in this study, the inertia effect on the region of supply hole is considered in discussing the static characteristics of hydrostatic thrust bearing, and then new expressions of pressure, load capacity, and flow rate are given. For the continuous parallel bearing, the results of this study agree well with experiments, thus there is no need for the extra modified inertia theory. For the step bearing with a large inertia parameter (e.g., S = 2), the results of this study agree with experiments on the recess region, and are closer to the experimental results than those of old method on the region of bearing land. So when the inertia parameter S and the ratio of supply hole radius to bearing radius r0/ R are large enough, the inertia effect on the region of supply hole cannot be ignored in discussing the static characteristics of hydrostatic thrust bearing.

Seismic reflectivity of hydraulic fractures approximated by thin fluid layers

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. T79-T87 ◽  
Author(s):  
A. Oelke ◽  
D. Alexandrov ◽  
I. Abakumov ◽  
S. Glubokovskikh ◽  
R. Shigapov ◽  
...  
Keyword(s):  
Analytical Solutions ◽  
Fluid Layer ◽  
Synthetic Data ◽  
P Wave ◽  
Hydraulic Fractures ◽  
Reflection Coefficients ◽  
S Wave ◽  
Reservoir Properties ◽  
Thin Fluid ◽  
Theoretical Results

We have analyzed the angle-dependent reflectivity of microseismic wavefields at a hydraulic fracture, which we modeled as an ideal thin fluid layer embedded in an elastic, isotropic solid rock. We derived full analytical solutions for the reflections of an incident P-wave, the P-P and P-S reflection coefficients, as well as for an incident S-wave, and the S-S and S-P reflection coefficients. The rather complex analytical solutions were then approximated and we found that these zero-thickness limit approximations are in good agreement with the linear slip model, representing a fracture at slip contact. We compared the analytical solutions for the P-P reflections with synthetic data that were derived using finite-difference modeling and found that the modeling confirmed our theoretical results. For typical parameters of microseismic monitoring by hydraulic fracturing, e.g., a layer thickness of [Formula: see text] and frequencies of [Formula: see text], the reflection coefficients depend on the Poisson’s ratio. Furthermore, the reflection coefficients of an incident S-wave are remarkably high. Theoretical results suggested that it is feasible to image hydraulic fractures using microseismic events as a source and to solve the inverse problem, that is, to interpret reflection coefficients extracted from microseismic data in terms of reservoir properties.

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