Analytical design method of a device for ultrasonic elliptical vibration cutting

Ultrasonic elliptical vibration cutting (UEVC) is effective in ultraprecision diamond cutting of hard-brittle materials and ferrous metals. However, its design is quite empirical and tedious. This paper proposes an analytical design method for developing the UEVC device which works at the Flexural-Flexural complex-mode to generate the elliptical vibration. For such UEVC device, the resonant frequencies of the two flexural vibrations are required to be the same. In addition, the nodal points of the two flexural vibrations should be coincident so that the device can be clamped without affecting the vibrations. Based on the proposed analytical design method, an UEVC device was first designed. Modal analysis of the designed UEVC device was performed by using the finite element method, which shows that the resonant frequencies coincide well with the targeted ones. Then a prototype UEVC device was fabricated, and its vibration characteristics were measured by an impedance analyzer and a laser displacement sensor. Experimental results indicate that the designed UEVC device can generate elliptical vibration with the resonant frequencies closed to the target ones. In addition, the vibration trajectory can be precisely tuned by adjusting the phase difference and the amplitude of the applied voltage. Simulation and experimental results validated the effectiveness of the analytical design method.