**Paper:
Finite-element analysis of layered rolling contacts.**

**Authors:
****Nikas,
G. K.**, Sayles, R. S.

** Published
in: **Proceedings of the Institution of Mechanical Engineers
(IMechE), Part J: Journal of Engineering Tribology, 2008, 222(7),
865-886

**Abstract**

A fundamental, two-dimensional finite element analysis of coated surfaces in rolling contact is presented with detailed listing of all modelling steps. A large number of basic results from a parametric study has been derived, focusing on the stress analysis and the effect of coatings on the life expectancy of coated surfaces, without actually getting into the ambiguities of fatigue life evaluation. Parameters included in the study are the metallic coating thickness (from zero to 50 µm) and elastic modulus (from 180 to 240 GPa), the Coulomb friction coefficient (zero, 0.05 and 0.10) and the endurance limit of the coated substrate. A generalisation involves the application of traction to simulate driving or driven wheels. The effect of that traction on the stress results is thoroughly examined. The set of results, summarized in a figure with nine diagrams, assists the quick selection of the optimum parameter values for maximising coating performance and minimising the risk of contact fatigue within the design limits used in the study. The model is realistic in that it does not use idealised load distributions in the rolling contact but actual geometrical solids in contact under normal operating conditions, letting the finite element analysis software resolve the loads and stresses, which are subsequently validated.

**Some figures
from this work**

Figure 1 shows the finite element mesh for the
rolling contact of a coated cylinder on a coated substrate in plane strain
(two-dimensional analysis). The mesh is intelligently constructed to be
dense in the areas of interest and coarse in areas where accuracy is of
less importance, such that computational speed is not compromised. This
model contains approximately 21,000 to 33,000 solid, 9-node elements. The
minimum element size in the coatings is equal to about 1 µm. A prescribed,
downward vertical displacement is applied to a rigid line on the top of
the roller to compress the roller on to the substrate. The vertical
displacement is followed by the application of a uniformly distributed,
horizontal force *F* on the axis of the roller.

**Fig. 1.** Finite
element mesh for the 2-d rolling contact of a coated cylinder on a coated
substrate.

Figure 2 shows
the effect of the substrate coating thickness and the elastic
modulus of both coatings on the maximum absolute normal z-stress (see
contour lines with labels in MPa) for *F* = 150 N, assuming that
the Coulomb friction coefficient between the contacting coatings is
equal to 0.05. The vertical displacement of the roller is equal to 1 µm.

**Fig. 2.** Effect
of the substrate coating thickness and coatings elastic modulus on the
maximum absolute normal z-stress (see contour lines with labels in MPa)
for *F* = 150 N, assuming a Coulomb friction coefficient between
the contacting coatings equal to
0.05.

The paper contains a total of 60 performance diagrams. The results are summarized in a figure with nine diagrams, which facilitates the selection of the optimum parameter values for maximising coating performance and minimising the risk of contact fatigue within the design limits used in the study.