Design of an ultrasonic elliptical vibration device with two stationary points for ultra-precision cutting

Ultrasonic elliptical vibration cutting (UEVC) is a promising hybrid machining technique for ultra-precision cutting. In this paper, an available and propagable design of the UEVC device is proposed through detailed mechanism analysis. The one-dimensional longitudinal vibration theory and Timoshenko beam theory are utilized and the frequency equations of the designed structure are proposed and solved by analytical solution. Thus, the preliminary size parameters of the proposed structure are obtained according to theoretical analysis, and then appropriate structural adjustment and dimensional parameters optimization are performed based on the modal analysis. The resonance frequencies of the longitudinal and bending vibrations can be adjusted to be the same, and two installation holes are determined near the wave node of the second longitudinal vibration mode and the fourth bending mode. Then the resonant frequency and tool trajectory of the manufactured prototype are verified by laser vibrometer, which are consistent with the design. Cutting experiments on pure iron with the proposed device shows that the mirror surface is achieved with nearly no tool wear. Therefore, the proposed design of the device which works in these two resonant modes can be applied for ultra-precision elliptical vibration cutting.