D.H. Lammlein PhD Dissertation - Vanderbilt University

The heat input on the tool surface is typically treated by defining a constant
heat flux (e.g. W/m 2 ) over the interface surface or one which varies with some spatial
parameter, typically radius. While frictional heating does occur essentially at the
interface, the assignment of the viscous dissipation heating contribution to the interface is
an approximation based on the assumption that the layer of dissipation surrounding the
tool is reasonably thin. Again, this assumption can generally be made without loss of
model accuracy for thermal-fluid models. The heat generation in both the pin and
shoulder is typically treated as axis-symmetric since tool rotation and circumferential
material flow around the tool largely render this to be the case. The following
formulation for shoulder surface heat flux input, Q ss , distribution over the tool shoulder is
commonly used [8,9,26].
q
ss
⎛ 3 ⎞⎛
Q ⋅r
⎞
= ⎜ ⎟ with R
⎝ 2π
⎠ ⎜ R − R ⎟ p ≤ r ≤ R s (1.14)
⎝ ⎠
ss
( r )
3 3
s
p
Shoulder heat input per unit area increases with radial distance from the probe surface as
the tangential velocity increases. The probe side surface heat flux input, Q ps , is
distributed as an even heat flux over its height:
(1.15)
Simar et al. [9] neglect the probe tip surface heat flux input distributing the full probe
heat contribution over its side surface. A probe tip surface distribution could be
formulated in the manner of equation (1.14) (with R p =0, R s = R p , and Q probe_tip in place of
Q ss ) if desired. Q ss , Q ps , and Q probe_tip can be found analytically via equations (1.6), (1.7),
and again (1.6) respectively. Heat generation in the pin can be modeled as a uniform,
volume heat source (i.e. W/m 3 ) without loss of model accuracy.
The majority of heat of heat is dissipated ultimately through the backing
plate (through the clamps, un-modeled plate portions of the plate, and directly through
the backing plate) as opposed to the tool shank and surface convection of the plate in air
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