Page 84 - Tribology in Machine Design

Elements of contact mechanics 71

1.5 times the average value P/nab. However, for cylinders with parallel axes,
the results are not usable in this form, and the contact area is a rectangle of
known length, not an ellipse. The principal stresses shown in the table occur
at the centre of the contact area, where they are maximum and compressive.
At the edge of the contact ellipse, the surface stresses in a radial direction
(along lines through the centre of contact) become tensile. Their magnitude
is considerably less than that of the maximum compressive stresses, e.g.
only 0.133p 0 with two spheres and v=0.30 by an equation of case 1, Table
3.2, but the tensile stresses may have more significance in the initiation and
propagation of fatigue cracks. The circumferential stress is everywhere
equal to the radial stress, but of opposite sign, so there is a condition of pure
shear. With the two spheres i =0.133p 0- Forces applied tangentially to the
surface, such as by friction, have a significant effect upon the nature and
location of the stresses. For example, two of the three compressive principal
stresses immediately behind the tangential force are changed into tensile
stresses. Also, the location of the maximum shear stress moves towards the
surface and may be on it when the coefficient of friction exceeds 0.10.
More information on failure criteria in contacts under combined normal
and tangential loading can be found in ESDU-84017.

3.5. Failures of There are several kinds of surface failures and they differ in action and
contacting surfaces appearance. Indentation (yielding caused by excessive pressure), may
constitute failure in some machine components. Non-rotating but loaded
ball-bearings can be damaged in this way, particularly if vibration and
therefore inertia forces are added to dead weight and static load. This may
occur during shipment of machinery and vehicles on freight cars, or in
devices that must stand in a ready status for infrequent and short-life
operations. The phenomena is called false brinelling, named after the
indentations made in the standard Brinell hardness test.
The term, surface failure, is used here to describe a progressive loss of
quality by the surface resulting from shearing and tearing away of particles.
This may be a flat spot, as when a locked wheel slides on a rail. More
generally the deterioration in surface quality is distributed over an entire
active surface because of a combination of sliding and rolling actions, as on
gear teeth. It may occur in the presence of oil or grease, where a lubricating
film is not sufficiently developed, for complete separation of the contacting
surfaces. On dry surfaces, it may consist of a flaking of oxides. If pressures
are moderate, surface failures may not be noticeable until loose particles
develop. The surface may even become polished, with machining and
grinding marks disappearing. The generation of large amounts of particles,
may result from misalignments and unanticipated deflections, on only a
portion of the surface provided to take the entire load. This has been
observed on the teeth of gears mounted on insufficiently rigid shafts,
particularly when the gear is overhung. Rapid deterioration of surface
quality may occur from insufficient lubrication, as on cam shafts, or from
negligence in lubrication and protection from dirt.
A type of surface failure, particularly characteristic of concentrated