Page 30 - Tribology in Machine Design
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Basic principles of tribology 17
coefficient of friction, which is given by
where K k is the fracture toughness, E is the elastic modulus and H is the
hardness.
The ploughing due to the presence of hard wear particles in the contact
zone has received quite a lot of attention because of its practical
importance. It was found that the frictional force produced by ploughing is
very sensitive to the ratio of the radius of curvature of the particle to the
depth of penetration. The formula for estimating the coefficient of friction in
this case has the following form:
2.5 Friction due to Mechanical energy is dissipated through the deformations of contacting
deformation bodies produced during sliding. The usual technique in analysing the
deformation of the single surface asperity is the slip-line field theory for a
rigid, perfectly plastic material. A slip-line deformation model of friction,
shown in Fig. 2.4, is based on a two-dimensional stress analysis of Prandtl.
Three distinct regions of plastically deformed material may develop and, in
Fig. 2.4, they are denoted ABE, BED and BDC. The flow shear stress of the
material defines the maximum shear stress which can be developed in these
regions. The coefficient of friction is given by the expression
Figure 2.4
where A = A(£; H) is the portion of plastically supported load, E is the elastic
modulus and H is the hardness.
The proportion of load supported by the plastically deformed regions
and related, in a complicated way, to the ratio of the hardness to the elastic
modulus is an important parameter in this model. For completely plastic
asperity contact and an asperity slope of 45°, the coefficient of friction is 1.0.
It decreases to 0.55 for an asperity slope approaching zero.
Another approach to this problem is to assume that the frictional work
performed is equal to the work of the plastic deformation during steady-
state sliding. This energy-based plastic deformation model of friction gives
the following expression for the coefficient of friction:
