Contents: 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001

2019, 3

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

Download article (PDF, 594 kb)

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.

REFERENCES

1. Ultrasonics: data, equations and their practical uses / Ed. by D. Ensminger and F.B. Stulen. – Boca Raton [etc.]: CRC Press, 2009. – 496 p.
2. Степаненко, Д.А. Теоретическое обоснование возможности усиления ультразвуковых колебаний с помощью составных кольцевых упругих элементов / Д.А. Степаненко [и др.] // Электронный журнал «Техническая акустика». – 2017, 2. – 13 с.
3. Киселев, М.Г. Ультразвук в медицине / М.Г. Киселев, В.Т. Минченя, Д.А. Степаненко. – Мн.: БНТУ, 2009. – 428 с.
4. Биргер, И.А. Сопротивление материалов / И.А. Биргер, Р.Р. Мавлютов. – М.: Наука, 1986. – 560 с.
5. Li, L. Use of Fourier series in the analysis of discontinuous periodic structures / L. Li // Journal of the Optical Society of America. – 1996. – Vol. 13, No. 9. – P. 1870-1876.
6. Ланкастер, П. Теория матриц / П. Ланкастер. – М.: Наука, 1982. – 272 с.
7. Акуленко, Л.Д. Исследование влияния дефектов на спектры собственных частот и формы колебаний стержней / Л.Д. Акуленко, С.В. Нестеров // Вестник Нижегородского университета им. Н.И. Лобачевского. – 2011. – № 4 (2). – С. 32-33.
8. Fedotov, I. Application of eigenfunction orthogonalities to vibration problems / I. Fedotov [et al.] // Proc. of the World Congress on Engineering. – London, 2009. – Vol. II. – P. 1169-1173.
9. Степаненко, Д.А. Исследование продольных колебаний гибких ультразвуковых волноводов с помощью метода передаточных матриц / Д.А. Степаненко, В.Т. Минченя, Н.Т. Минченя // Механика машин, механизмов и материалов. – 2011. – № 2 (15). – С. 71-75.
10. Ланин, В.Л. Повышение качества микросварных соединений в интегральных схемах с использованием ультразвуковых систем повышенной частоты / В.Л. Ланин, И.Б. Петухов, Д. Мордвинцев // Технологии в электронной промышленности. – 2010. – № 1. – С. 48-50.


 

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).