Systematic design of an ultrasonic horn profile for high displacement amplification

A new analytical-numerical technique is proposed to design a high displacement amplification ultrasonic horn. The profile of the horn is a NURBS curve whose parameters can be optimized to attain a high displacement amplification factor. Compared to the traditional finite element-based design approach of ultrasonic horns, which is case dependent, our approach formulates and solves the optimal horn profile problem in nondimensional space. Therefore, both the working frequency and the length of the system can be readily adjusted. Depending on the number of control points and their associated weights, the NURBS profile can be simplified to a Bezier, a rational Bezier or a B-spline curve. The optimum profile for each type of curve is then sought and the corresponding amplification factor, natural frequency and maximum strain are verified using finite element analysis. Considering a horn with a cross-sectional ratio of 16, amplification factors of 11.55, 12.12, 13.55 and 15.97 are obtained for the optimum profiles of Bezier, rational Bezier, B-spline and NURBS curves, respectively.