Meccanica

, Volume 20, Issue 1, pp 79–84 | Cite as

A perturbation method in elastohydrodynamic lubrication of cylindrical surfaces

  • A. Baroncelli
  • R. Bassani
Article
  • 34 Downloads

Summary

The typical relations of elastohydrodynamics are linearized through geometrical considerations and a single integro-differential equation, where the pressure is the unknown quantity, is found. A perturbation method is used for the solution, and, in the assumption of an incompressible and isoviscous fluid, an explicit expression of the pressure gradient and, consequently, of the total load and the film thickness is obtained when displacements are not high.

Keywords

Mechanical Engineer Civil Engineer Film Thickness Pressure Gradient Alla 

Nomenclature

A

h/h′

Amin

h min /h′

EA,EB

moduli of elasticity ofA andB

E′

\(\frac{1}{2}\left\{ {\left( {\frac{{1 - v_A^2 }}{{E_A }} + \frac{{1 - v_B^2 }}{{E_B }}} \right)} \right\}^{ - 1} \)

H

h′/R

h

film thickness

hmin

minimum film thickness

h′

h(0)

h*

h(x 0 )

M

\(W/(E'R\sqrt {2U} )\)

P

\(ph'/(12 \mu u\sqrt {2Rh'} )\)

p

pressure

R

R A R B /(R A +R B )

RA,RB

radii of cylindersA andB

S

\(A_{\min } T = h_{\min } /(R\sqrt {2U} )\)

T

\(H/\sqrt {2U} \)

t

Δv/(h′+x2/2R)

u

half sum of surface velocities

U

μu/E′R

Δv

v−v(0)

W

\(\smallint _{ - \infty }^{\chi _o } PdX\)

w

load per unit of length

X

\(x/\sqrt {2Rh'} \)

X0

\(x_0 /\sqrt {2Rh'} \)

x

film coordinate

x0

film outlet coordinate

β

h*/h′

vA,vB

Poisson ratios ofA andB

μ

absolute viscosity

Sommario

Le relazioni caratteristiche della elastoidrodinamica vengono linearizzate con considerazioni geometriche e si giunge cosi ad un 'unica equazione integro-differenziale ove l'incognita è la pressione; il metodo usato per la sua soluzione è perturbativo e si perviene, nell'ipotesi di fluido incompressibile ed isoviscoso, ad una espressione esplicita del gradiente della pressione e, conseguentemente, alla portanza totale ed alla altezza del meato, qualora le deformazioni siano sufficientemente piccole.

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References

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Copyright information

© Pitagora Editrice Bologna 1985

Authors and Affiliations

  • A. Baroncelli
    • 1
  • R. Bassani
    • 1
  1. 1.Dipartimento di Costruzioni Meccaniche e NucleariUniversità degli Studi di PisaPisaItaly

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