Page 88 - Tribology in Machine Design

Elements of contact mechanics 75

rise in the contact area above the bulk temperature of the solid as a result of
friction energy dissipation. However, the temperature level, not rise, in the
contact area is frequently of major concern in predicting problems
associated with excessive local temperatures. The surface temperature rise
can influence local surface geometry through thermal expansion, causing
high spots on the surface which concentrate the load and lead to severe local
wear.
The temperature level, however, can lead to physical and chemical
changes in the surface layers as well as the surface of the solid. These
changes can lead to transitions in lubrication mechanisms and wear
phenomena resulting in significant changes in the wear rate. Therefore, an
overall system-heat transfer analysis may be required to predict the local
bulk temperature and therefore the local surface temperature. Procedures
are available for modelling the system-heat transfer problems by network
theory and numerical analysis using commercially available finite element
modelling systems. ESDU items 78026 to 78029 are especially recom-
mended in this respect.
There is considerable literature on the subject of surface temperatures,
covering both general aspects and specific special situations, but compared
to theoretical analysis, little experimental work has been reported.

3.7.1. Analysis of line contacts
Blok proposed a theory for line contacts which will be summarized here.
The maximum conjunction temperature, T c, resulting from frictional
heating between counterformal surfaces in a line contact is

where T b, the bulk temperature, is representative of the fairly uniform level
of the part at some distance from the conjunction zone. T f represents the
maximum flash temperature in the conjunction zone resulting from
frictional heating. T f may be calculated from the following formula:

where/is the instantaneous coefficient of friction, w is the instantaneous
width of the band shaped conjunction, m, W is the instantaneous load on
the conjunction, JV, L is the instantaneous length of the conjunction
perpendicular to motion, m, K 1? V 2 are the instantaneous velocities of
surfaces 1 and 2 tangential to the conjunction zone and perpendicular to the
conjunction band length, m/s, />i, b 2 are the thermal contact coefficients of
bodies 1 and 2 and

where /c ;, p- t, c { and a Ti are the thermal conductivity, density, specific heat per
unit mass and thermal diffusivity of solid i, respectively.