Electronic Journal Technical Acoustics ISSN 1819-2408

D. Stepanenko, V. Zhukov, A. Rogovcova

Design and modeling of bar ultrasonic horns by means of harmonic balance method

language: Russian

received 21.05.2019, published 12.07.2019

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ABSTRACT

The article considers application of harmonic balance method for solving problems of design and modeling of bar ultrasonic horns. For application of harmonic balance method function describing distribution of vibration parameters along the horn length and function describing shape of horn longitudinal section are continued in even way onto the interval [-L; +L], where L is horn length, and represented as Fourier polynomials. Equation of horn longitudinal vibration is represented as non-uniform integral-differential equation which is reduced to non-uniform system of linear algebraic equations by means of harmonic balance method. Solution of this system with minimal norm is determined by means of pseudoinverse Moore-Penrose matrix and gives coefficients of Fourier polynomial for the function describing distribution of vibration parameters along the horn length. Application of the proposed method is illustrated with numerical examples of design and modeling of conical horn and composite horn for ultrasonic welding of electrical connections of microelectronic devices. Obtained results are in good agreement with parameters calculated for conical horn using formulae known from the literature and parameters calculated for composite horn using transfer matrix method (relative error of calculated vibratory displacement amplitude is 0,2 % for conical horn for the number of harmonics N = 4 and 0,8 % for composite horn for the number of harmonics N = 7).
Key words: bar ultrasonic horn, ultrasound oscillations, harmonic balance method, Fourier polynomials.

11 pages, 5 figures

Сitation: D. Stepanenko, V. Zhukov, A. Rogovcova. Design and modeling of bar ultrasonic horns by means of harmonic balance method. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2019, 3.

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		Dmitry Stepanenko - PhD, Assoc. Prof. Graduated from the Belarusian national technical university (Minsk, Republic of Belarus), Department of instrumental engineering, Instrument-making faculty in 2004. Scientific interests: applications of low-frequency ultrasound in engineering and medicine, methods of design of low-frequency ultrasonic vibratory systems. E-mail: stepd(at)tut.by
		Vitalij Zhukov student, Belarusian national technical university (Minsk, Republic of Belarus).
		Angelina Rogovcova - student, Belarusian national technical university (Minsk, Republic of Belarus).