Influence of the Fillet Radius on the Performance of an Ultrasonic Stepped Velocity Transformer

Authors

DOI:

https://doi.org/10.20535/2521-1943.2025.9.4(107).343198

Keywords:

ultrasound, velocity transformer, fillet radius, resonance frequency, amplification coefficient, finite element method.

Abstract

This study presents the results of a numerical investigation into the influence of geometric parameters, particularly the fillet radius, on the dynamic characteristics of an ultrasonic stepped velocity transformer. Such transformers are employed in high-frequency electromechanical systems to match the acoustic impedances between the transducer and the load, as well as to increase the amplitude of mechanical vibrations. Modeling was carried out using the finite element method (FEM), which enables consideration of the spatial distribution of stresses and strains within the transformer volume. The effects of the step diameter and acoustic length on the resonance frequency and amplification coefficient were analyzed. It has been established that an increase in the step diameter leads to a decrease in the resonance frequency, whereas an increase in the fillet radius results in its rise. Quantitative relationships between the fillet radius, transformation coefficient, and resonance frequency were obtained, allowing for approximate determination of optimal design parameters. It was shown that enlarging the fillet radius reduces stress concentration in the transition zone between steps, thereby enhancing the fatigue strength of the structure. An empirical relationship was proposed for preliminary estimation of the fillet radius to ensure agreement between the actual and the calculated resonance frequencies. The results obtained can be applied in the design and optimization of ultrasonic amplification systems and transducers used in ultrasonic welding, material processing, and surface modification technologies.

References

  1. A. Gallego-Juárez, K. F. Graff, and M. Lucas, Power Ultrasonics: Applications of High-Intensity Ultrasound, 2nd ed. Oxford, U.K.: Woodhead Publishing, 2023. ISBN: 978-0-323-85144-2.
  2. O. F. Luhovskyi, A. V. Movchanyuk, I. M. Bernyk, A. V. Shulha, and I. A. Hryshko, “Apparatne zabezpechennia ultrazvu-kovykh kavitatsiinykh tekhnolohii”, [Hardware support of ultrasonic cavitation technologies], Kyiv: Igor Sikorsky Kyiv Poly-technic Institute, 2021, [Online]. Available: https://ela.kpi.ua/items/880c19df-9b97-45cd-bd4b-b0a6384862ab.
  3. Y. Bai and Y. Chen, “Research on ultrasonic plastic flexible welding equipment for automobile steering wheel,” 2020 3rd Inter-national Conference on Electron Device and Mechanical Engineering (ICEDME), Suzhou, China, 2020, pp. 264–269, doi: https://doi.org/10.1109/ICEDME50972.2020.00067.
  4. C. Gao and Y. Xing, “Ultrasonic Metal Welding Technology of Cascaded Battery Connection,” 2019 3rd International Confer-ence on Electronic Information Technology and Computer Engineering (EITCE), Xiamen, China, 2019, pp. 28–31, doi: https://doi.org/10.1109/EITCE47263.2019.9094804.
  5. M. Acharya, V. Badheka, (2024). Application of Ultrasonic Welding for Dissimilar Metals: A Review. In: Dikshit, M.K., Khan-na, N., Soni, A., Markopoulos, A.P. (eds) Advances in Manufacturing Engineering. ICFAMMT 2024. Lecture Notes in Me-chanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-97-4324-7_20.
  6. G. Xu, F. Liu, L. Gao, et al., Study on the Effects of Ultrasonic Impact Treatment on Microstructure and Properties of 316L Laser Welded Joints, J. of Materi Eng. and Perform, Vol. 34, pp. 23877–23890, 2025, doi: https://doi.org/10.1007/s11665-025-11129-1.
  7. F. Chen, Y. Yang, & N. Li, Effect of ultrasonic impact time on microstructure and properties of 7A52 aluminum alloy tandem MIG welded joint. Int. J. Adv. Manuf. Technol., Vol. 116, pp. 2687–2696, 2021, doi: https://doi.org/10.1007/s00170-021-07599-x.
  8. O. Lugovskyi, A. Movchanyuk, and V. Fesich, “To the question about the calculation of the ultrasonic step-up transformer of vibrating speed with the developed radiance surface”, Mech. Adv. Technol., no. 1(85), pp. 49–56, Apr. 2019, doi: https://doi.org/10.20535/2521-1943.2019.85.164346.
  9. A. Y azdian, M. R. Karafi, An analytical approach to design horns and boosters of ultrasonic welding machines, SN Appl. Sci., Vol. 4, 166, 2022, doi: https://doi.org/10.1007/s42452-022-05044-6.
  10. D. Krishnakumar, S. Periyannan, (2024). “Design and Magnification Factor Analysis of Multi-linear Stepped Ultrasonic Horn for Machining Application Using FEM Approach”, In: Ghose, B., Manoharan, V., Mulaveesala, R. (eds) Advances in Non-Destructive Evaluation (NDE). NDE 2021. Lecture Notes in Mechanical Engineering. Springer, Singapore. doi: https://doi.org/10.1007/978-981-97-1036-2_14.
  11. Jagadish, A. Ray, “Design and performance analysis of ultrasonic horn with a longitudinally changing rectangular cross section for USM using finite element analysis”, J Braz. Soc. Mech. Sci. Eng., Vol. 40, 359, 2018, doi: https://doi.org/10.1007/s40430-018-1281-7.
  12. K. Anand, S. Elangovan, “Studies on dynamic characteristic of stepped horn utilized in ultrasonic insertion process using finite element analysis and experimental methods”, Materials Today: Proceedings, Vol. 46, Part 17, pp. 8165–8171, 2021, doi: https://doi.org/10.1016/j.matpr.2021.03.110.
  13. A. S. Nanu, N. I. Marinescu, and D. Ghiculescu, “Study on ultrasonic stepped horn geometry design and FEM simulation,” Nonconventional Technologies Review, vol. XV, no. 4, pp. 25–30, 2011. [Online]. Available: https://revtn.ro/_legacy/pdf4-2011/05%20-%20Nanu%20-%20Study%20On%20Ultrasonic%20Stepped%20Horn%20Geometry%20Design%20And%20FEM%20Simulation%20.pdf
  14. A. Gallego-Juárez, K. F. Graff, and M. Lucas, Power Ultrasonics: Applications of High-Intensity Ultrasound, 2nd ed. Oxford, U.K.: Woodhead Publishing, 2023. ISBN: 978-0-323-85144-2. Available: https://www.researchgate.net/publication/291859299_Power_Ultrasonics_Applications_of_High-Intensity_Ultrasound.

Downloads

Published

2025-12-29

How to Cite

[1]
A. Movchanuk, O. Luhovskyi, A. Shulha, and A. Novosad, “Influence of the Fillet Radius on the Performance of an Ultrasonic Stepped Velocity Transformer”, Mech. Adv. Technol., vol. 9, no. 4(107), pp. 425–431, Dec. 2025.

Issue

Vol. 9 No. 4(107) (2025)

Section

Mechanics

License

Copyright (c) 2025 Андрій Мовчанюк, Олександр Луговський, Аліна Шульга, Андрій Нововсад

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The ownership of copyright remains with the Authors.
 
Authors may use their own material in other publications provided that the Journal is acknowledged as the original place of publication and National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” as the Publisher.

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under CC BY 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work