Research on Conical Hole Ladder Horn Based on Transmission Matrix Method in Ultrasonic Milling

In order to solve the problem of efficient and accurate tool change in vibration system, horn with a conical hole and a center via hole which connects tool is proposed. In connection with the shape of the horn, an equivalent model of the horn is built up. Based on the transmission matrix method, the frequency equation and magnification factor of the horn is deduced. And the finite element method was employed to verify the derived formulas. Compared the simulation results with the theoretical results, the derived formulas can be applied to design the complex horn.