Comparative Analysis of Movements of Curved Ultrasonic Instruments

The paper presents a theoretical analysis of vibrations of a curvilinear  rod in the form of a loop of low rigidity formed from a quarter of a circle with a constant radius, limited by an angle π/2 < γ < π and two rectilinear rods. It is indicated that in the practice of ultrasonic technology, some types of structures are known in which elastic elements are used as resonators, waveguides, oscillation transformers and instruments for influencing the processed materials. Their use makes it possible to obtain an additional impulse of force in the working area by using the potential energy caused by the action of the elastic properties of such elements. However, insufficient attention has been paid to the theoretical justification of the use of elastic elements in ultrasonic systems. In this regard, the present work is devoted to the theoretical  substantiation of the use of an elastic tool made of a thin rod having the shape of a loop. The diagram and calculation of displacements of the free end of a curved rod under the action of forces directed along the longitudinal axis are given in the paper. It is shown that elastic displacements are caused by a curved shape in the form of an arc of a circle of a curved rod. For comparison, calculation schemes of two types of curved rod with an attached rod are given. In the first case, the free ends of the rectilinear rods, directed vertically downwards, make elastic movements along two coordinates. In the second case, the ends of rectilinear rods directed at a certain angle to the vertical axis and converging at the bottom point due to the symmetry of their location, make vertical movements only along one coordinate. The considered shape of the curved rod can be successfully used as a tool for performing technological tasks in the ultrasonic method of processing holes in brittle materials, spot welding, etc. Such a scheme, in contrast to the traditional ultrasonic treatment scheme based on the use of rectilinear rods, makes it possible to increase the magnitude of the vibration amplitude of the instrument due to elastic displacements of the curved section of the rod of low rigidity. The proposed form will increase the intensity of tool vibrations and increase process productivity and processing accuracy. The resulting calculation formula shows that the amount of elastic displacements of curved rods is affected by the cross-sectional stiffness and the radius of curvature of the curved part, as well as the angle of inclination of the rectilinear rod. The theoretical calculation is supplemented by a comparative experimental study of the Chladni forms for both schemes obtained on the sheet surface using abrasive particles.

1. Berker A. X., Vagner I. P., Vebster H. V., Dodzh D. X., Zhimanskii L. V., Zeigler S. M., Koinis Dzh., Kuni S. I., Laions D. M., Miller F. F., Neidzhel F. S., Pauers R. V., Troyanovskii T. S., Kholzinger D. V. (1984) Design of Universal Joints and Drive Shafts. Leningrad, Mashinostroenie Publ. 464 (in Russian).

2. Malokhovsky Ya. E., Lapin L. A., Vedeneev N. K. (1962) Cardan Gears. Moscow, Mashgiz Publ. 156 (in Russian).

3. Ivanov S. N., Kozadaev A. I., Pivovarov B. I., Sokruto I. V. (1992) Truck Drive Lines. Problems and Solutions. Avtomobilnaya Promyshlennost [Automotive Industry], (11), 35–37 (in Russian).

4. Ivanov S. N., Saveliev V. A., Kocheshkov N. P. (1988) Transmission Drivelines. Perspectives of the Problem. Avtomobilnaya Promyshlennost [Automotive Industry], (12), 40–43 (in Russian).

5. Ivanov S. N. (1998) New Generation Transmission Shafts. Avtomobilnaya Promyshlennost [Automotive Industry], (11), 25–28 (in Russian).

6. Trikozyuk V. A. (1980) Vehicle Reliability. Moscow, Transport Publ. 88 (in Russian).

7. Lavrinovich M. F., Shusternyak M. M. (1981) Analysis of Parts Durability of MAZ Cars Family and Technical Methods for Improving it. Moscow, Research Institute of Technology of the Automotive Industry. 56 (in Russian).

8. Zaslavsky O. Ya. (1981) Systematic Approach as Method for Studying Durability of Driveline. Avtomobilnaya Promyshlennost [Automotive Industry], (11), 21–24 (in Russian).

9. Rotenberg R. V. (1981) Systematic Approach to the Problem of Reliability and Issues of its Provision. Moscow, Znanie Publ. 341 (in Russian).

10. Kravchenko V. I., Kostyukovich G. A., Struk V. A. (2006) Cardan Gears: Designs, Materials, Application. Minsk, Tekhnologiya Publ. 409 (in Russian).

11. Lobozov V. P., Nikitin S. I., Shepelyakovsky K. Z., Kuznetsov A. A., Kravchenko V. I., Kostyukovich G. A., Semenyako M. M., Gagasov A. M., Dostanko G. A. (2021) Articulated Transmission of the Wheel Drive of a Motor Vehicle. Patent Russian Federation No 2188134 (in Russian).

12. Drozdov V. A., Kostyukovich G. A., Kravchenko V. I. (2002) Cardan Shaft of Ground Vehicles. Patent Russian Federation No 2212345 (in Russian).

13. Drozdov V. A., Kostyukovich G. A., Kravchenko V. I. (1999) Cardan Shaft of Ground Vehicles. Patent Republic of Belarus No 4418 (in Russian).

14. ISO 12667:1993 Commercial Vehicles and Buses – Cross-Tooth Propeller Shaft Flanges, Type T. Available at: https://www.iso.org/standard/19694.html.

15. ISO 8667:1986 Commercial Vehicles and Buses – Cross-Tooth Gearbox Flanges, Type T. Available at: https://www.iso.org/standard/16054.html.

16. Veremeychik A. I., Sazonov M. I., Khvisevich V. M. (2008) Plasma Technologies as One of the Main Technologies for Improving the Performance Properties of Metal Products. Mekhanika. Nauchnye Issledovaniya i Uchebno-Metodicheskie Razrabotki: Mezhdunar. Sb. Nauch. Tr. Vyp. 2 [Mechanics. Scientific Research and Educational and Methodological Developments: International Collection of Scientific Papers. Iss. 2]. Gomel, Belarusian State University of Transport, 6–12 (in Russian).

17. Chekan N. M., Akula I. P., Gorelchik A. N. (2018) Nitriding and Deposition of Extra Hard Composite Coatings on the Surface of Tool Steels in a Single Technological Cycle. 60 Mezhdunarodnaya Nauchnaya Konferentsiya “Aktual'nye Problemy Prochnosti”: Materialy Konferentsii, Vitebsk, 14–18 Maya 2018 goda [60th International Scientific Conference “Actual Strength Issues”: Proceedings of the Conference, Vitebsk, May 14–18, 2018]. Vitebsk, 176–180 (in Russian).

18. Ovchinnikov E. V., Chekan N. M., Khvisevich V. M., Veremeichyk A. I., Mikhaylov V. V., Kazak N. N. (2021) Structure of Electrospark Nanocomposite Coatings on a Metal Matrix. Vestnik Brestskogo Gosudarstvennogo Tekhnicheskogo Universiteta = Vestnik of Brest State Tech-nical University, (1), 49–53. https://doi.org/10.36773/1818-1212-2021-124-1-49-53 (in Russian).

19. Ovchinnikov E. V., Khvisevich V. M., Chekan N. M., Veremeichyk A. I., Eysmont E. I., Kostukovich G. A. (2021) Lubricants Based on Polar and Non-Polar Liquids Modified with Hybrid Carbon Nanomaterials. Vestnik Brestskogo Gosudarstvennogo Tekhnicheskogo Universiteta = Vestnik of Brest State Technical University, (2), 58–62. https://doi.org/10.36773/1818-1212-2021-125-2-58-62 (in Russian).

20. Veremeichyk A. I., Onysko S. R., Khvisevich V. M., Sosnovsky A. A. (2021) Simulation of Hole Punching with a Cylindrical Punch. Novye Tekhnologii i Materialy, Avtomatizatsiya Proizvodstva: Sb. St. Mezhd. Nauch.-Tekhn. Konf., Brest, Posv. 55-letiyu Brest. Gos. Tekhn. Un-ta [New Technologies and Materials, Production Automation: Collection of Papers of International Scientific and Technical Conference, Brest, Conference Dedicated to 55th Anniversary of Brest State Technical University]. Brest, Brest State Technical University, 107–111 (in Russian).