ISSN 1068-798X, Russian Engineering Research, 2017, Vol. 37, No. 7, pp. 596–602. © Allerton Press, Inc., 2017.
Original Russian Text © P.P. Usov, 2017, published in Vestnik Mashinostroeniya, 2017, No. 4, pp. 50–56.
Influence of Viscoelastic Coatings on the Contact
of Lubricated Bodies
P. P. U s o v
Moscow Institute of Electronic Technology, Zelenograd, Moscow, Russia
Abstract—The contact of elastic bodies with viscoelastic coatings is considered, in the presence of lubrication.
The one-dimensional Kelvin model is employed for the viscoelastic coatings. The pressure distribution in the
lubricant layer and the layer thickness are investigated on transition from low to large loads.
Keywords: contact, lubricant, viscoelastic coatings, Kelvin model
Currently, the calculation of lubricated frictional
units is based on the elastohydrodynamic theory of
lubrication, which considers the f low of a thin lubri-
cant layer between the surfaces of elastic bodies. How-
ever, the mechanical properties of the surface layers of
contacting bodies differ from those of the basic mate-
rial and depend on the relative velocity of the interact-
ing bodies. In addition, frictional units based on com-
posites with rheological properties have been
employed recently. In that context, we need to study
the influence of imperfect elasticity of the contacting
bodies on the characteristics of the intervening lubri-
Little research has been published on this topic.
The influence of viscoelastic coatings on the contact
of elastic cylindrical bodies with lubrication was inves-
tigated in a plane formulation in [1–3]. The Maxwell
model was used for the viscoelastic coatings. It was
found that the viscous properties of the coating signifi-
cantly affect the contact interaction. The results differ
significantly from those for the contact of uniform
elastic bodies at small relative velocity. With increase
in velocity, the inf luence of the viscous properties
declines to the point of insignificance.
The motion of a thin layer of viscous lubricant
between the rigid surface of a sphere and the surface of
a viscoelastic layer adhering to a rigid base was consid-
ered in . The Kelvin model was adopted for the vis-
coelastic layer. The influence of the mechanical prop-
erties of the viscoelastic layer on the pressure distribu-
tion in the lubricant layer, its thickness, and the
frictional coefficient was studied. The results for the vis-
coelastic layer differed from the results of the elastohy-
drodynamic theory of lubrication for elastic bodies.
Lubricated contact of a rigid cylinder with regular
relief and a viscoelastic layer moving at constant speed
relative to the cylinder was considered in . The
dependence of the lubricant thickness, the pressure
distribution in the contact zone, and the frictional
force on the viscoelastic properties of the surface layer
and on the relief was analyzed.
In the present work, we study the change in lubri-
cant thickness and pressure distribution in the lubri-
cant layer on switching from the contact of rigid bodies
to elastohydrodynamic contact in which deformation
of the bodies is fundamental to the formation of the
lubricant layer. The one-dimensional Kelvin model is
used for the viscoelastic layer.
We investigate the influence of the viscoelastic
properties of the contacting bodies on the pressure dis-
tribution in the lubricant layer and its thickness.
Consider the motion of a thin lubricant layer
between elastic cylinders coated with thin viscoelastic
layers (Fig. 1). We assume a velocity at contact. The
contact zone is regarded as small relative to the radii of
cylinders 1 and 2.
The coordinate origin (point O) lies on the load of
action of the load; the x axis is in the direction of
motion of the contacting surfaces. Then the thickness
of the lubricant layer is
= h(c), where c is the boundary coordinate of
the lubricant layer; R = R
) is the reduced
are the cylinder radii; w
(i = 1, 2)
are the radial surface displacements due to elastic
deformation of cylinders 1 and 2; w
(i = 1, 2) are the
radial surface displacements due to deformation of the
viscoelastic coatings of cylinders 1 and 2.
=+ + +
−− + +
,1 ,2 ,1 ,2
EE V V
hh w x w x
wcwc wxw x