Analytical solutions for radial pressure distribution including the effects of the quadratic-gradient term

1993 ◽  
Vol 29 (4) ◽  
pp. 1171-1177 ◽  
Author(s):  
Chayan Chakrabarty ◽  
S. M. Farouq Ali ◽  
W. S. Tortike
Keyword(s):  
Pressure Distribution ◽  
Analytical Solutions ◽  
Radial Pressure ◽  
Gradient Term ◽  
Quadratic Gradient

The Elastic Distortion of Rollers Under Combined Radial and Thrust Loads

1983 ◽  
Vol 105 (2) ◽  
pp. 189-197 ◽  
Author(s):  
H. So ◽  
R. Gohar
Keyword(s):  
Pressure Distribution ◽  
Solid Body ◽  
Axial Load ◽  
Axial Loading ◽  
Radial Pressure ◽  
Approximate Analysis ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Elastic Distortion ◽  
Radial Loading

This paper describes an approximate analysis for finding the elastostatic radial and end face distortion, radial pressure distribution, and solid body rotation of a flat ended axially profiled bearing roller under combined radial and axial loading through the ribs. It is found that a small but significant end face bulge occurs at each roller end when there is radial loading only. Upon the addition of an axial load, this bulge becomes a small depression. The altered geometry there may become significant during bearing operation, as it affects roller skew, wear, and lubrication between the ribs and roller and faces.

Elastohydrostatic Lubrication of Circular Plate Thrust Bearings

1967 ◽  
Vol 89 (3) ◽  
pp. 237-242 ◽  
Author(s):  
D. Dowson ◽  
C. M. Taylor
Keyword(s):  
Pressure Distribution ◽  
Circular Plate ◽  
Thrust Bearing ◽  
Elastohydrodynamic Lubrication ◽  
Radial Pressure ◽  
Simplified Approach ◽  
Thrust Bearings ◽  
Low Modulus ◽  
Elastic Distortion ◽  
Equivalent Modulus

The subject of elastohydrodynamic lubrication has developed considerably in recent years and in the present paper the influence of elastic distortion upon the performance of a hydrostatic thrust bearing is considered. A circular plate hydrostatic thrust bearing is considered and one of the pads is assumed to be lined by a thin layer of elastic material. A simplified approach to the calculation of elastic displacements is used and an approximate analytical solution of the governing elastohydrostatic equations is presented. Theoretical solutions showing the influence of elastic distortion upon pressure distribution are presented. Experimental measurements of radial pressure distribution are recorded for bearings lined with low modulus nitrile and polyurethane rubber. Difficulties encountered in the measurement of the rubber properties prevented a strict comparison between experimental and theoretical results but the selection of an equivalent modulus enabled qualitative agreement to be demonstrated. Elastohydrostatic behavior is shown to have a beneficial effect upon bearing performance.

An Engineering Approach to Non-Hertzian Contact Elasticity—Part II

2000 ◽  
Vol 123 (3) ◽  
pp. 589-594 ◽  
Author(s):  
Luc Houpert
Keyword(s):  
Pressure Distribution ◽  
Analytical Solutions ◽  
Curve Fitting ◽  
Numerical Solutions ◽  
Companion Paper ◽  
Hertzian Contact ◽  
Line Contact ◽  
Correction Factors ◽  
Analytical Development ◽  
Single Radius

Roller/race misalignment and deformation are used for calculating analytically the pressure distribution along the roller/race contact and the final roller/race load and moment. Use is made of the surface crowns and race undercuts for calculating contact dimensions with their possible truncations at large misalignment or loads. The pressure distribution is not symmetrical when misalignment occurs. This analytical development was possible by using a slicing technique in which the local roller/race geometrical interference was calculated in each slice of the contact. A mix of point and line contact Hertzian solutions developed in a companion paper “Part I” is used for obtaining the final load per slice. The final analytical solutions (load, moment and pressure) are successfully compared to two numerical solutions described briefly. The analytical model has been slightly fine-tuned using correction factors obtained by curve-fitting for matching the results to the numerical ones. In the curve-fitting, the single radius profile and multi-radius profile are distinguished.

scholarly journals Elliptic equations having a singular quadratic gradient term and a changing sign datum

2012 ◽  
Vol 11 (5) ◽  
pp. 1875-1895 ◽  
Author(s):  
Daniela Giachetti ◽  
Francesco Petitta ◽  
Sergio Segura de León
Keyword(s):  
Elliptic Equations ◽  
Gradient Term ◽  
Quadratic Gradient

scholarly journals A new class of analytical solutions describing anisotropic neutron stars in general relativity

2021 ◽  
pp. 2150091
Author(s):  
Jay Solanki ◽  
Bhashin Thakore
Keyword(s):  
General Relativity ◽  
Neutron Stars ◽  
Analytical Solutions ◽  
Radial Pressure ◽  
Compact Stars ◽  
Theory Of Relativity ◽  
Field Equations ◽  
Inherent Anisotropy ◽  
Anisotropic Matter ◽  
New Class

A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for realistic anisotropic neutron stars was obtained using the general theory of relativity. Assuming a physically acceptable nonsingular form of one metric potential and radial pressure containing the curvature parameter [Formula: see text], the constant [Formula: see text] and the radius [Formula: see text], analytical solutions to Einstein’s field equations for anisotropic matter distribution were obtained. Taking the value of [Formula: see text] as −0.44, it was found that the proposed model obeys all necessary physical conditions, and it is potentially stable and realistic. The model also exhibits a linear equation of state, which can be applied to describe compact stars.

Contact Area Variation in Elastic Indentation Problems

2009 ◽  
Author(s):  
Roman Riznychuk
Keyword(s):  
Contact Problem ◽  
Pressure Distribution ◽  
Half Space ◽  
Analytical Solutions ◽  
Contact Area ◽  
Elastic Half Space ◽  
Exact Expression ◽  
Rigid Punch ◽  
Contact Pressure Distribution ◽  
Area Variation

Contact problem of the frictionless indentation of elastic half-space by smooth rigid punch of curved profile is investigated. An exact expression of the contact pressure distribution for a curved profile punch in terms of integral involving the pressure distribution for sequence of flat punches is derived. The method is illustrated and validated by comparison with some well-known analytical solutions.

Hydrodynamics of Wire-Drum Contact

1987 ◽  
Vol 109 (4) ◽  
pp. 679-683
Author(s):  
A. Magnin ◽  
J. M. Piau ◽  
J. Frene ◽  
D. Bois ◽  
M. Godet
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Wire Tension ◽  
Active Pressure ◽  
Tension Level ◽  
Foil Bearing ◽  
Pressure Zone ◽  
Minimum Film Thickness

The hydrodynamics of a wire-drum contact is analyzed using theoretical techniques developed in foil bearing studies. Analytical solutions and numerical solutions are obtained. Results show that: when for a given minimum film thickness the wire tension increases, the pressure arc extent decreases and reaches a minimum for certain wire tension level; the pressure distribution is independent of wire tension for large values of tension; and the active pressure zone depends strongly on film thickness.

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