The value of the contact stress between a band saw blade and the driving wheel is
modeled using the theory of an elastic Cosserat surface. Specifically, we use nonlinear
Cosserat theory to model the bending of an elastic plate into a rotating right circular
cylindrical tube with associated end moments. The resulting equations are then
linearized, the end moments are relieved and the reference length of the plate is
adjusted to cause contact of the blade with the wheel. The results indicate that the
nonuniformity in the deformed shape of the saw blade significantly influences
the predictions of the value and distribution of the contact stress between
the blade and the wheel even though the blade is thin. This is in addition
to the influence of a crowned wheel, and the deformed shape due to the
tensioning process, which are typically used to help control tracking of the
blade on the wheel. Also, we showed that the value of this contact stress
predicted by a simple Lamé type solution remains about 50% of that predicted
by the Cosserat solution and that the effect of the rotational speed of the
wheel is negligible for typical operating conditions of thin wood-cutting
saws.
Keywords
band saw blade, Cosserat surface, contact stress, elastic
