Friction of polymers

When either or both of the surfaces are polymers, Equation 3.1
no longer applies. Polymers deform viscoelastically: the deformation
depends not only on the normal load N but also on the geometry and time
of loading. With fixed geometry and duration of loading, the area of true
contact is proportional to tex2html_wrap_inline6517 where tex2html_wrap_inline6519 . For a
truly elastic solid (for example rubber), tex2html_wrap_inline6521 [Lincoln,

From Figure 3.2 for tex2html_wrap_inline6523
(typical for a hard sphere on a Plexiglas surface),
a 16-fold increase in
load from 1 to 16 pounds produces an 8-fold increase in frictional
force, hence the
coefficient of friction is halved. This is a general feature of polymers;
the effective coefficient of friction reduces at higher loads.


  • Figure 3.2: Friction of a hard sphere
    sliding over a clean flat surface of Plexiglas. As the
    contact force is increased the ratio of frictional force to
    contact force is reduced, this is a general feature of
    polymeric materials. [Bowden and Tabor, 1974]

Howell and Mazur [1953] performed some of the first experiments to study
the effect that the elastic behaviour of the asperity-to-asperity contact
has on the nature of sliding for polymeric materials.
The stress-strain curves of three
hypothetical materials are shown in Figure 3.3.
The dashed lines represent the stress range in the contacting asperities.
The asperities of material (a)
deform plastically, so Amontons' law applies. The asperity-to-asperity

contact in material (b) is
elastic; so the true asperity-on-asperity contact area
will be of the form tex2html_wrap_inline6525 where C
involves the modulus and dimensions of the asperities, hence
tex2html_wrap_inline6527 (where S is the shear breaking strength).
Increasing the normal stress would cause plastic
deformations as for material (a).


  • Figure 3.3: Stress-strain curves for various hypothetical asperity models
    (Howell, 1953). The dashed lines represent the stress range in
    the contacting asperities. The models are:
    (a) plastic deformation of asperities, so Amontons' law applies,
    (b) elastic deformation of asperities, so tex2html_wrap_inline6529 ,
    (c) elastic and plastic deformation of asperities, so tex2html_wrap_inline6531 .

For material (c) the deformation of the asperity contact starts with
a linear elastic region followed by a gradual
yield; the true asperity-on-asperity contact area is thus
likely to lie between the bounds of
(a) (plastic tex2html_wrap_inline6533 ) and (b) (elastic tex2html_wrap_inline6535 ). Therefore a possible equation for the friction could be the
empirical one, tex2html_wrap_inline6537 , where tex2html_wrap_inline6539 . Most
synthetic polymers used in ropes correspond most closely to material (c)
where the actual mechanism of asperity deformation is indeterminate.

The relationship tex2html_wrap_inline6541 fits Howell and Mazur's test
results very well; some of their results are shown in
Table 3.2 and Figure 3.4.


Material K tex2html_wrap_inline6543
cellulose acetate 0.60 0.96
viscose rayon 0.49 0.91
drawn nylon 0.92 0.80
undrawn nylon 0.85 0.90
Table 3.2: Coefficients and indices of friction for various polymers.
[Howell, 1953]



  • Figure 3.4: Frictional behaviour of nylon-on-nylon contact [Howell, 1953].
    Best fits were obtained for drawn nylon with tex2html_wrap_inline6545 , and
    for undrawn nylon with tex2html_wrap_inline6547 , where F is the static frictional
    force and N is the normal load. It can be seen that the F-N curve
    falls below a straight line; the ratio of F to N decreases with load.

Howell's equation for friction can be re-written as
tex2html_wrap_inline6549 , where tex2html_wrap_inline6551 is the ``equivalent
coefficient of friction''. For use in the finite element analysis
it was decided that expressing this relationship in terms of
stresses would make modelling possible. Therefore, it is proposed
here that Howell's equation can be re-expressed as; tex2html_wrap_inline6553 ,
where tex2html_wrap_inline6555 is the frictional stress, tex2html_wrap_inline6557 is
the contact pressure, and A and tex2html_wrap_inline6559 are frictional constants.

Due to the viscoelastic properties of polymers, when a polymer is in
contact with another surface for a period of time, the asperities start to
creep under the normal load. This increases the actual area of contact,
thereby increasing the frictional limit. This creep explains why
contact involving polymers
typically has a greater difference between static and dynamic
coefficients of friction, than for metal-to-metal contact. Summation of friction components.

An alternative view of friction is put forward by Kragelsky et al. [1982].
They support the hypothesis that the coefficient of friction is
the sum of two terms; molecular and mechanical, i.e.;


Molecular interaction processes take place in the surface `film' and
affect the surface layers to a depth of a few hundredths of a
micron. Mechanical interaction takes place in layers with a thickness of
a few tenths of a micron. As these processes occur at different levels
they are largely uncorrelated and hence can be separated.

This equation suggests a very complex relationship between the normal
load and the coefficient of friction; both components of tex2html_wrap_inline6567
include a pressure
term, as well as extra terms for the hysteresis loss during sliding, the
surface roughness, and the strength of the molecular bond, amongst

The additional complexity of Kragelsky's model does not seem justified;
Howell's equation
has been shown to adequately represent experimental data.
Therefore a modified Howell's equation, tex2html_wrap_inline6569 , is used. Effect of spin finish on friction.

Spin finish is a surface coating, added to the fibres during
manufacture, for the purpose of gluing together the fibres during
the processing of the yarn [Piller, 1973]. This prevents
them being snagged by the guides and thus being broken or drawn
out of the yarn. The finish also evens out, and so improves, the
running properties and friction coefficients, as well as removing
any electrostatic charge; these keep the draw-off conditions as
even as possible.

Yarn sizes are also used; these coat the yarn with a protective film to
reduce the abrasion damage during processing and service.

By selecting the right finish, the abrasion resistance of the yarn
can be increased [Beers and Ramirez, 1990; Crawford and McTernan,
1988; Schick, 1975, 1977].
The yarns used in the tests referred to in
this chapter are from spools used to make Parafil
ropes and so carry the finishes present in actual ropes.