The design theory of cup-shaped tool transformer plays a significant role in promoting the application of ultrasonic grinding in the processing of brittle materials and composite materials. The transformer consists of three parts: conical horn, thick disk and tube. The thick disc functions of displacement, rotary angle, bending moment and shear force are obtained by Mindlin theory. The displacement and stress functions of the conical horn and the tube are established. The frequency equation of the transformer is established through the continuous and boundary conditions. Transformers are designed according to the frequency equation. The design theory is verified by FEM (finite element method) modal analysis, impedance analysis test and ultrasonic vibration test. The FEM results show that the resonant frequencies of transformers are consistent with the design frequencies. The tests results show that the measured frequencies of the resonance systems are consistent with the design frequencies. The validity of the design method is verified, which providing a theoretical basis for the design of ultrasonic grinding system.

ultrasonic grinding; cup-shaped tool; transformer; Mindlin theory; resonance characteristic