Cutting theory of unsupported brushes using peripheral blades

Recently, a theory for cutting supported brushes was published for a blade with an inclined edge. When the angle of inclination is large, the inclined edge may be called a peripheral edge or shear edge, to distinguish the edge from conventional radial edges. However, it is difficult to find a theory for cutting unsupported brushes (most flexible brushes are unsupported brushes). In this study, an inertia force that resists cutting is derived kinetically as a function of time and other conditions. Based on this resisting inertia force, the stresses of the brush are analyzed; the brush is in contact with the edge of the nose with radius r_e. The outer part of the brush is subject to a high tensile stress owing to the inertia force and bending curvature. The inner part of the brush is subject to a high shear stress due to the inertia force and high contact stress. And also the brush properties determine the conditions that cause fracture of the brush.