Lubricated Sliding of a Rigid Cylinder on a Viscoelastic Half Space

Abstract

We study the lubricated sliding of a rigid cylinder on a viscoelastic half space with a single characteristic retardation time. Besides the generalized inverse Hersey number , which is the sole parameter governing elastic lubrication, the viscoelastic lubrication solution depends on two additional dimensionless parameters: and f . is the characteristic retardation time divided by the time for the rigid cylinder to move one contact width and f determines the strength of viscoelasticity. We have developed a numerical scheme to solve this viscoelastic lubrication problem. Our numerical results show that the total friction force can be decomposed into viscoelastic and hydrodynamic components. The viscoelastic component of the friction is well approximated by the dry limit in which the liquid layer is all squeezed out and the resistance to sliding is due entirely to viscoelastic dissipation. The hydrodynamic limit is well approximated by a modification of the elastic limit in which friction is due entirely to hydrodynamics. We also study the dependence of the hydrodynamic pressure, film thickness and the friction coefficient on these parameters.

Solid viscoelasticity in contact mechanics and elastohydrodynamic lubrication

“…The form of Eq. (4.5) for the viscoelastic deformation equation has also been used by Hooke and Huang [67] and by Wu et al [152] in the study of VEHL line contact problems. For further details of the derivation of Eq.…”

“…is the dimensionless load/speed parameter, which for an elastic solid can also be seen as the ratio of the elastic force deforming the body and the viscous forces in the lubricant lm in the inlet region, see Snoeijer et al [124]. Note that Wu et al [152] use parameter = 1/ and refer to it as the inverse generalized Hersey number. The second equation is the gap height equation which, approximating the undeformed body by a parabola, is given by:…”

“…For contacts between common viscoelastic materials the Hertzian pressures are often quite limited, and in that case the piezoviscous parameter will not be dominant. As in [67,152] for the line contact, and in the numerical parameter study in the present work, see Sec.4.4.1, an isoviscous lubricant is assumed and the emphasis is on the analysis of the viscoelastic e ect of the solid on the pressure and lm thickness in the lubricated contact, and to investigate the e ect of the dimensionless parameters , Hertz , and . However, when comparing with experimental results the piezoviscous parameter is considered.…”