Since the invention of ultrasonic vibration assisted turning, this process has been widely considered and investigated. The reason for this consideration is the unique features of this process which include reducing machining forces, reducing wear and friction, increasing the tool life, creating periodic cutting conditions, increasing the machinability of difficult-to-cut material, increasing the surface quality, creating a hierarchical structure (micro-nano textures) on the surface and so on. Different methods have hitherto been used to apply ultrasonic vibration to the tip of the tool during the turning process. In this research, a unique horn has been designed and constructed to convert linear vibrations of piezoelectrics to three-dimensional vibrations (longitudinal vibrations along the z-axis, bending vibrations around the x-axis, and bending vibrations around the y-axis). The advantage of this ultrasonic machining tool compared with other similar tools is that in most other tools it is only possible to apply one-dimensional (linear) and two-dimensional (elliptical) vibrations, while this tool can create three-dimensional vibrations. Additionally, since the nature of the designed horn can lead to the creation of three-dimensional vibrations, there is no need for piezoelectric half-rings (which are stimulated by a 180-phase difference) to create bending vibrations around the x and y axes. Reduction of costs as well as the simplicity of applying three-dimensional vibrations in this new method can play an important role in industrializing the process of three-dimensional ultrasonic vibration assisted turning.

In this example, how to model all the components of an ultrasonic transducer and its modal and harmonic analysis are taught in full detail.