A New Approach on Vibrating Horns Design

Abstract

An optimization method of the vibrating horns is presented considering the smallest action principle and the attached cutting tool mass. The model is based on Webster’s wave propagation equation and as an objective function the minimization of the volume in structural equilibrium conditions was considered. The considered input parameters were working frequency, maximum cross-sectional area, magnification coefficient, and the attached mass. At the end of the study, a new shape function of the horn’s cross section is obtained. The particularity of the new obtained shape is given by the nodal point position that is the same with the position of the maximum cross-sectional area. The obtained horn was analyzed from the modal point of view using theoretical and experimental methods. As theoretical methods, both the state-space method and the finite element method were used. An experimental setup for frequency response function determination was developed using a random input signal. The verification of the magnitude value was done considering a harmonic steady-state signal. The recorded values were compared with the predicted values. The numerical simulations and tests support the validity of the assumptions used in the horns optimization design.