Mechanical Impedance Transformers in Relation to Ultrasonic Machining

Abstract

Ultrasonic machining of hard materials, such as cemented carbides, steel, sapphire, etc., requires the use of an acoustical transmission line. This line generally consists of a specially shaped solid body designed so as to convey the ultrasonic vibrations of the transducer to the tool which operates on the work piece. This paper deals with a general type of mechanical impedance transformer suitable for the above‐stated purposes. The theory has been cast in such form that the design of such lines may be made from universal equations and graphs. Because such equations appear in terms of ratios, one set of curves applies to all materials and to any desired frequency range. Several cases will be treated in detail so as to make the method employed clear. In addition examples will be given of actual transformers with an account of their performance in practical cases. As is the case generally with transformers, the systems described in this paper have applications in many cases where transformation of the ultra...