Experimental and numerical study on an ultrasonic horn with shape designed with an optimization algorithm

• Theoretical, computational and experimental studies on an optimized ultrasonic horn.
• Transfer-matrix, coupled-oscillators and 3D FEM methods were used for simulations.
• The influence of added couplings at input and output is also treated.

The paper presents the design and characterization of an axisymmetrical ultrasonic horn held by its circumference, with specified working frequency, amplification factor and nodal point position. To this purpose theoretical, experimental and computational methods are used in an efficient manner. The longitudinal waveform that ensures the imposed conditions is obtained in 2 stages: first it is determined theoretically according to conditions, then the working setup that gives the required waveform at resonance is designed. The waveform and corresponding horn shape are designed by using an optimization method based on Webster’s horn equation, Hooke’s law and variational calculus theory. The influence of added couplings at input and output in order to emulate transducer and tool is also treated. The separate optimization of these couplings allows setting different working frequencies for the ultrasonic horn system. Two 1-D methods, transfer-matrix and coupled-oscillators method and a 3-D finite element method are used in computer simulations. The proposed model of ultrasonic horn has the advantage of a more convenient placement of the nodal point, which is very important in industrial applications.