Simulation of rod vibrations process with an independent pendular suspension and vertical stabilization system

Continuous improvement of field sprayer design aimed at performance increase by increasing the working width, requires a special approach to ensure reliability of the supporting rod structure and quality of technological process. The question of rod vibrations, which arise when the driving systems copy field rough surface and abrupt changes in speed of the unit, remains topical. At the design stage of supporting structures of the rods, special attention is paid to the substantiation of its geometrical parameters in the longitudinal and transverse sections; studies of changes in the characteristics of vertical and horizontal vibrations, taking into account the method of the rod hanging and the system used for its stabilization. This allows to ensure the reliability of the rod design and the required quality of the technological process. The article proposes construction of the rod independent pendulum suspension on the sprayer frame and its stabilization system based on the use of damping elements. The analytical studies sequence system was developed for rod vibrations analysis, depending on initial conditions, parameters and characteristics of the used damping elements, under which they are effectively damped. It is shown that at certain numerical values of the geometrical parameters of the rod, the suspension and vibrations damping methods, not only the numerical values of the functions are changed, but also the functions themselves that describe the process of the rod's vertical movement, including cases of resonance. The obtained theoretical results can be used for design and testing of machines with rod working units and allow, at design stages, to simulate the process of movement of various rod structures from external excitatory forces, and to determine patterns of changes in the characteristics of damped vibrations using different damping elements and their installation parameters.

rod, vibrations, amplitude, force, energy, parameters, conditions, rod working units, rod sprayers, mechanical engineering

1. Shpaar D. (ed.). Plant protection in sustainable land use systems. Book. 4. Minsk, 2004. 346 p. (in Russian).

2. Kruk I. S. Evenness of chemicals application and the mechanisms of its provision in the constructions of modern boom applicators. Aktual’nye problemy povysheniya kvalifikatsii i perepodgotovki kadrov agropromyshlennogo kompleksa: doklady Mezhdunarodnoi nauchno-prakticheskoi konferentsii, Minsk, 24–26 noyabrya 2010 g. [Current issues of further training and retraining of personnel of agro-industrial complex: reports of the International scientific and practical conference, Minsk, November 24–26, 2010]. Minsk, 2010, pt. 2, pp. 67–72 (in Russian).

3. Kruk I. S., Gaidukovskii A. I. Increasing the effectiveness of chemical protection of vegetable crops by improving the hitch and stabilization system of the rod of a sprayer. Ovoshchevodstvo: sbornik nauchnykh trudov [Vegetable growing: a collection of scientific papers]. Minsk, 2008, vol. 15, pp. 215–222 (in Russian).

4. Kruk I. S., Gaidukovskii A. I. Use of an independent linkage and a boom stabilization system in the construction of agricultural sprayers. Ekologiya i sel’skokhozyaistvennaya tekhnika: materialy 6-i Mezhdunarodnoi nauchno-prakticheskoi konferentsii, Sankt-Peterburg, 13–14 maya 2009 g. [Ecology and agricultural machinery: materials of the 6th International scientific and practical conference, St. Petersburg, May 13–14, 2009]. St. Petersburg, vol. 2, pp. 191–197 (in Russian).

5. Ozols Ya. G. Analysis of the factors affecting the quality of boom sprayers operation. Issledovanie dinamiki shtangovykh opryskivatelei. Trudy Latviiskoi sel’skokhozyaistvennoi akademii. Vyp. 239 [Study of the dynamics of boom sprayers. Proceedings of the Latvian Agricultural Academy. Iss. 239]. Jelgava, 1987, pp. 18–33 (in Russian).

6. Vartukapteinis K. E. Substantiation of the parameters and design elements of boom sprayers. Doctoral thesis in engineering. Jelgava, 1984. 253 p. (in Russian).

7. Vіkovich І. A. Structures and dynamics of boom sprayers. Lviv, National University “Lviv Polytechnic”, 2003. 458 p. (in Ukrainian).

8. Vіkovich І. A. Calculation of the pendulum-spring system of vibration protection of large-sized hinged elements of wheeled cars. Vіsnik Derzhavnogo unіversitetu «L’vіvs’ka polіtekhnіka»: zbіrnik naukovikh prats’ [Bulletin of the State University “Lviv Polytechnic”: a collection of scientific works]. Lviv, 1999, no. 371, pp. 86–92 (in Ukrainian).

9. Vіkovich І. A. Vibrations of a simple pendulum sprayer boom with kinematic excitation. Dinamicheskaya prochnost’ mashin i priborov. Vestnik L’vovskogo politekhnicheskogo instituta. № 220 [Dynamic strength of machines and devices. Bulletin of the Lviv Polytechnic Institute. No. 220]. Lviv, 1988, pp. 12–15 (in Russian).

10. Ozols Ya. G., Bumazhkin V. A., Vartukapeitis K. E., Puntsulis P. A. Evaluation of hitches of boom sprayers used in the Latvian SSR. Dinamika i nadezhnost’ sel’skokhozyaistvennykh mashin. Trudy Latviiskoi sel’skokhozyaistvennoi akademii. Vyp. 202 [Dynamics and reliability of agricultural machinery. Proceedings of the Latvian Agricultural Academy. Iss. 202]. Jelgava, 1982, pp. 2–7 (in Russian).

11. Markovskii M. G. Rationale of kinetic and potential energy when driving boom sprayers in the vertical-transverse plane. Konstruirovanie, ispol’zovanie i nadezhnost’ mashin sel’skokhozyaistvennogo naznacheniya [Design, use and reliability of agricultural machinery], 2017, no. 1 (16), pp. 179–183 (in Russian).

12. Markovskii M. G. Method of damping vibration energy of the boom of a sprayer. Konstruirovanie, ispol’zovanie i nadezhnost’ mashin sel’skokhozyaistvennogo naznacheniya [Design, use and reliability of agricultural machines], 2017, no. 1 (16), pp. 184–191 (in Russian).

13. Orekhova G. V. The rationale for the dissipative energy and the generalized forces in the movement of the sprayer boom in the vertical transverse plane. Konstruirovanie, ispol’zovanie i nadezhnost’ mashin sel’skokhozyaistvennogo naznacheniya [Design, use and reliability of agricultural machines], 2017, no. 1 (16), pp. 191–197 (in Russian).

14. Kuznetsov V. V. Substantiation of the method of damping the oscillation energy of the boom of a field sprayer. Sbornik nauchnykh trudov Instituta energetiki i prirodopol’zovaniya [Collection of scientific papers of the Institute of Energy and Environmental Management]. Bryansk, 2017, pp. 93–100 (in Russian).

15. Kuznetsov V. V. Development of shock absorber barbell experimental field sprayer. Konstruirovanie, ispol’zovanie i nadezhnost’ mashin sel’skokhozyaistvennogo naznacheniya [Design, use and reliability of agricultural machines], 2016, no. 1 (15), pp. 105–109 (in Russian).

16. Dzenis A. A., Silnieks A. O. Spray boom suspension with spatial vibration isolation. Issledovanie dinamiki shtangovykh opryskivatelei. Trudy Latviiskoi sel’skokhozyaistvennoi akademii. Vyp. 239 [Study of the dynamics of boom sprayers. Proceedings of the Latvian Agricultural Academy. Iss. 239]. Jelgava, 1987, pp. 50–57 (in Russian).

17. Kruk I. S., Biza Yu. S., Markevich A. E. Theoretical researches on fluctuations of the boom rigidly fixed on the skeleton of a sprayer. Inzhenernyi vestnik [Engineering Herald], 2007, no. 1 (23), pp. 82–84 (in Russian).

18. Biza Yu. S., Gaidukovskii A. I., Kolosko D. N., Kruk I. S., Chigarev Yu. V. Research of process of fluctuations of a bar of a sprayer in a vertical plane in view of a bend of its design. Inzhenernyi vestnik [Engineering Herald], 2007, no. 2 (24), pp. 73–77 (in Russian).

19. Biza Yu. S., Gaidukovskii A. I., Kruk I. S., Stepuk L. Ya., Novikov A. A., Sadovskii V. V. Peculiarities of calculation of elements of system of stabilization of a boom at simultaneous moving of sprayer wheels on an obstacle. Inzhenernyi vestnik [Engineering Herald], 2008, no. 2 (26), pp. 70–72 (in Russian).

20. Biza Yu. S., Kruk I. S., Gaidukovskii A. I., Novikov A. A., Yakubovskii S. V., Grinkevich P. E. Substantiation of the use of shock absorbers to ensure the smooth progress of the boom of an agricultural sprayer. Inzhenernyi vestnik [Engineering Herald], 2010, no. 1 (29), pp. 41–43 (in Russian).

21. Panovko Ya. G. Fundamentals of applied theory of vibrations and shock. 3nd ed. Leningrad, Mashinostroenie Publ., Leningradskoe otdelenie, 1976. 320 p. (in Russian).

22. Timoshenko S., Young D. H., Weaver W. Vibration problems in engineering. 4nd ed. New York, Wiley, 1974. 521 p. (Russ. ed.: Timoshenko S. P., Yang D. Kh., Uiver U. Kolebaniya v inzhenernom dele. Moscow, Mashinostroenie Publ., 1985. 472 p.).

23. Yablonskii A. A., Noreiko S. S. Oscillation theory course. 2nd ed. Moscow, Vysshaya shkola Publ., 1966. 255 p. (in Russian).

24. Vіkovich І. A. Influence of rotational oscillations on evenness of spraying. Vіsnik Derzhavnogo unіversitetu «L’vіvs’ka polіtekhnіka»: zbіrnik naukovikh prats’ [Bulletin of the State University “Lviv Polytechnic”: a collection of scientific works]. Lviv, 1999, no. 376, pp. 11–14 (in Ukrainian).

25. Rybak T. I. Methods for assessing the carrying capacity and durability of machines for chemical protection in crop production. Kiev, Naukova dumka Publ., 1985. 231 p. (in Russian).