Vibration analysis and development of an ultrasonic elliptical vibration tool based on a portal frame structure

An ultrasonic elliptical vibration tool utilizing the coupled resonant vibration modes is the key component in the elliptical vibration cutting/texturing process, which has been successfully applied to ultra-precision machining and surface texturing. In this paper, an analytical approach is proposed to analyze the resonant frequency and mode shapes of the ultrasonic elliptical vibration tool. A new design of ultrasonic elliptical vibration tool based on a portal frame structure is presented and analyzed using the proposed model. The model assumes Euler-Bernoulli beams and utilizes the transfer matrix technique to reduce the order of the system to only six variables. The model can be utilized to provide a systematic approach for an optimal design and be extended to dynamic analysis of the tool for study of machine-tool dynamics. Finite element simulation results as well as experimental data based on the prototype design are presented to verify the model. An application of the proposed tool is also demonstrated in machining micro/nano-structured surfaces for structural coloration.