Solving the Stress Problem in a Sharp Wedge-Whaped Cutting Tool Using the Quick Decomposition Method and the Problem of Matching Boundary Conditions

Abstract

The fast decompositions method in analytical form was used to solve the elastic problem with mixed boundary conditions for stresses in a sharp wedge-shaped cutting tool of finite dimensions in the form of a truncated sector. A load is applied to the faces of the wedge and its nose, which rapidly decreases with distance from the nose. At a larger radius, the wedge is rigidly fixed. The resulting solution is valid for any angle of the wedge spread. If we take a small enough inner radius and the angle of the spread, then the shape of the proposed cutter will be close enough to real. The influence of the angle of the spread and the inner radius of the wedge on the magnitude and location of the highest stress σ̃ was investigated. The critical dimensions of the wedge were found, but for any of its sizes the stresses are finite everywhere.