Theoretical Analysis of Thin Curved Rod Displacements

Abstract

The paper presents a comparative theoretical analysis of the movements of the curved rods of various curvature forms, which can be applied as tools for ultrasonic treatment of holes in fragile materials. It has been shown that the traditional processing of holes by an ultrasonic method is based on the use of straight rods, in which the amplitudes of displacements on the working – free end corresponds to the value of displacements at the point of its attachment to the ultrasonic oscillation concentrator. Supplementing the configuration of a straight rod with a curvilinear shape in the form of a circular arc or a spiral twisted by one turn will allow obtaining additional displacements caused by the elastic properties of a section with a curved shape. The paper considers several calculated schemes of a curvilinear rod bounded by angles j equal to p/2, p and 2p, fferent direction of the external force action. The obtained results have shown that an increase in the circular arc angle leads to a corresponding increase in the elastic displacement index of the rod free end. In this case, the total displacements of the rod free end will be made from displacements caused by vibrations of the acoustic system and the displacements of a curved thin rod from an external force. Calculations have established that the magnitude of the elastic displacements of curved rods is influenced by the shape and magnitude of the angle, the direction of the external force, the radius of curvature, the rigidity of the cross section. The considered schemes of thin rods with curvilinear sections can find practical application in ultrasonic oscillatory systems for processing small-diameter holes in fragile materials. This increases the intensity of tool oscillations and improves the process performance.