Determination of frequency of transverse oscillations of an elasticly fixed disc of a circular saw

Abstract

The object of the study is a circular saw blade. An annular plate of constant thickness with a free outer contour and a fixed inner contour was taken as the calculation scheme of the saw blade. The real conditions for fixing the internal circuit correspond to the elastic fixing of the saw blade with clamping flanges on the shaft of the machine. For the accepted calculation scheme of the circular saw, the dynamic model was a fourth-order nonlinear differential equation of the transverse oscillations of the annular plate with the corresponding boundary conditions. The rotation of the circular saw was taken into account in the dynamic model due to the radial force in the middle surface of the ring plate. This force arises as a result of the action of centrifugal forces during the rotation of the saw blade. The solution to the fourth-order nonlinear differential equation was constructed using the Bubnov-Galyorkin numerical method.