Contact stress on a rotating elastic band saw blade using the theory of a cosserat surface

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 Lame 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.