A Complete Solution for Thermal-Elastohydrodynamic Lubrication of Line Contacts Using Circular Non-Newtonian Fluid Model

1992 ◽  
Vol 114 (3) ◽  
pp. 540-551 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock
Keyword(s):  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Energy Equation ◽  
Control Volume ◽  
Fluid Model ◽  
Complete Solution ◽  
Circular Model ◽  
Line Contacts ◽  
Stress Boundary Conditions ◽  
Stress Boundary

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.

Couette Dominance Used for Non-Newtonian Elastohydrodynamic Lubrication

1994 ◽  
Vol 116 (1) ◽  
pp. 47-55 ◽  
Author(s):  
C. M. Myllerup ◽  
A. A. Elsharkawy ◽  
B. J. Hamrock
Keyword(s):  
Newtonian Fluid ◽  
Fluid Model ◽  
Elastohydrodynamic Lubrication ◽  
Shear Strain Rate ◽  
High Shear Stress ◽  
Line Contacts ◽  
Stress Boundary Conditions ◽  
Stress Boundary ◽  
Good Agreement ◽  
Low Shear

The perturbational approach that assumes Couette dominance in non-Newtonian elastohydrodynamic lubrication analysis is discussed. The assumption is found valid for non-Newtonian fluid models exhibiting Newtonian properties at low shear strain rate. A general non-Newtonian fluid model which meets that requirement is incorporated into elastohydrodynamic lubrication analysis of line contacts by using the perturbational approach. In the case of a circular fluid model the results obtained from the perturbational approach are in good agreement with those obtained from the direct approach. However, a better convergence and the possibility of avoiding using stress boundary conditions at high shear stress can be achieved by using the perturbational approach. Results are presented for various values of the shape exponent in the general model, and it transpires that this also is an important parameter of the fluid model.

Dynamic thermo-elastic response of a discrete multi-layered cylindrical shell subjected to transient thermal loading

2008 ◽  
Vol 222 (4) ◽  
pp. 549-561 ◽  
Author(s):  
J Y Zheng ◽  
X D Wu ◽  
Y J Chen ◽  
G D Deng ◽  
Q M Li ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Elastic Response ◽  
Elastic Part ◽  
Dynamic Part ◽  
Layered Cylindrical Shell ◽  
Stress Boundary Conditions ◽  
Transient Thermal ◽  
Stress Boundary

Explosion containment vessels (ECVs) are used to fully contain the effects of explosion events. A discrete multi-layered cylindrical shell (DMC) consisting of a thin inner cylindrical shell and helically cross-winding flat steel ribbons has been proposed, which has obvious advantages of fabrication convenience and low costs. The applications of ECVs are closely associated with blast and thermal loads, and thus, it is important to understand the response of a DMC under transient thermal load in order to develop a design code and operation procedures for the use of DMC as ECV. In this paper, a mathematical model for the elastic response of a DMC subjected to thermal loading due to rapid heating is proposed. Based on the axisymmetric plane strain assumption, the displacement solution of the dynamic equilibrium equations of both inner shell and outer ribbon layer are decomposed into two parts, i.e. a thermo-elastic part satisfying inhomogeneous stress boundary conditions and a dynamic part for homogeneous stress boundary conditions. The thermo-elastic part is solved by a linear method and the dynamic part is determined by means of finite Hankel transform and Laplace transform. The thermo-elastic solution of a DMC is compared with the solution of a monobloc cylindrical shell, and numerical results are presented and discussed in terms of winding angle and material parameters.

scholarly journals Metastability effects in strained and stressed SrTiO3 films

2016 ◽  
Vol 06 (03) ◽  
pp. 1650016
Author(s):  
Alexander I. Lebedev
Keyword(s):  
Boundary Conditions ◽  
Density Functional ◽  
Ground States ◽  
Lattice Parameter ◽  
Metastable Phases ◽  
Polar Phase ◽  
Rotation Pattern ◽  
Phase Sequence ◽  
Stress Boundary Conditions ◽  
Stress Boundary

The sequence of ground states for SrTiO3 film subjected to epitaxial strain as well as to mechanical stress along the [001] and [110] axes is calculated from first principles within the density functional theory. Under the fixed-strain boundary conditions, an increase in the lattice parameter of a substrate results in the [Formula: see text](II) sequence of ground states. Under the fixed-stress boundary conditions, the phase sequence is different and depends on how the stress is applied. It is revealed that the simultaneous presence of competing ferroelectric and antiferrodistortive instabilities in SrTiO3 gives rise to the appearance of metastable phases, whose number increases dramatically under the fixed-stress conditions. In the metastable phases, the octahedral rotation patterns are shown to differ substantially from those in the ground state. It is suggested that in systems with competing instabilities, each polar phase has its optimal octahedral rotation pattern which stabilizes this phase and creates a potential barrier preventing this phase to be transformed into other structures.

On Stress Boundary Conditions in Shell Theory

1980 ◽  
Vol 47 (1) ◽  
pp. 202-204 ◽  
Author(s):  
J. Lyell Sanders
Keyword(s):  
Boundary Conditions ◽  
Boundary Data ◽  
Shell Theory ◽  
Thin Shells ◽  
First Approximation ◽  
Stress Functions ◽  
Stress Boundary Conditions ◽  
Stress Boundary

Boundary conditions on the stress-functions of shell theory in terms of given boundary data are derived. The results are shown to be fully equivalent to the Kirchhoff boundary conditions and have the same form for all first-approximation theories of thin shells.

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