An approximating mathematical model of interaction between a freely rotating disk and soil

Authors

  • Aleksandr Akimov Federal State Budgetary Educational Institution of Higher Education “Chuvash State Agricultural Academy” K. Marx str., 29, Cheboksary, Chuvash Republic, Russia, 428003, Russian Federation https://orcid.org/0000-0003-4629-8394
  • Yuriy Konstantinov Federal State Budgetary Educational Institution of Higher Education “Chuvash State Agricultural Academy” K. Marx str., 29, Cheboksary, Chuvash Republic, Russia, 428003, Russian Federation https://orcid.org/0000-0002-2076-0432
  • Vladimir Medvedev Federal State Budgetary Educational Institution of Higher Education “Chuvash State Agricultural Academy” K. Marx str., 29, Cheboksary, Chuvash Republic, Russia, 428003, Russian Federation https://orcid.org/0000-0001-8007-5325
  • Petr Mishin Federal State Budgetary Educational Institution of Higher Education “Chuvash State Agricultural Academy” K. Marx str., 29, Cheboksary, Chuvash Republic, Russia, 428003, Russian Federation https://orcid.org/0000-0002-2728-3579
  • Mikhail Volkhonov Federal State Budget Educational Institution of Higher Education "Kostroma State Agricultural Academy" Training Town, 34, Karavaevo Village, Kostroma Region, Russia, 156530, Russian Federation https://orcid.org/0000-0003-0332-8848
  • Petr Lekomtsev Federal State Budgetary Educational Institution of Higher Education “Izhevsk State Agricultural Academy” Studencheskaya str., 11, Izhevsk, Udmurt Republic, Russia, 426069, Russian Federation https://orcid.org/0000-0002-9554-7636
  • Nikolai Obolensky State Budget Educational Institution of Higher Education “Nizhny Novgorod State Engineering and Economics University” Oktyabrskaya str., 22, Knyaginino, Nizhny Novgorod region, Russia, 606340, Russian Federation https://orcid.org/0000-0001-6292-7539
  • Gubeydulla Yunusov Federal State Budgetary Educational Institution of Higher Education “Mari State University” Lenin sq., 1, Yoshkar-Ola, Republic of Mari El, Russia, 424000, Russian Federation https://orcid.org/0000-0001-8498-8930

DOI:

https://doi.org/10.15587/1729-4061.2018.148500

Keywords:

freely rotating disk, interaction with soil, power characteristics, analytical approximation, explicit expressions

Abstract

A generalized mathematical model of disk interaction with soil was built under general assumptions regarding the mode of the disk knife motion in soil, namely, in a mode of slippage, skidding or rolling without slippage and skidding. Previously constructed models follow from it as particular cases at certain values of parameters. However, because of computational complexity of this model for the case of a freely rotating disk knife consisting in the need for a preliminary numerical solution of a transcendental equation to determine the mode of disk motion, the generalized mathematical model has not found wide application. Therefore, an analytical two-dimensional approximation of a generalized model of disk interaction with soil which is a new model of approximation type was constructed on the basis of a computer experiment using the least squares method.

An explicit expression was obtained for the kinematic parameter of a freely rotating disk knife which determines its mode of motion. It was established that this parameter is a rational function of relative depth of the disk penetration and the dimensionless dynamic coefficient characterizing soil properties. Also, explicit expressions were obtained for the projections of the resultant soil reaction forces acting on the blade of the disk knife and its side faces depending on the data of dimensionless parameters. It has been established that the horizontal component of the reaction which determines tractive resistance of the disk is also a rational function of the relative penetration depth and the dimensionless dynamic coefficient. It was established that the magnitude of the kinematic parameter significantly affects the magnitude and direction of the resultant soil reactions to the disk. The expressions obtained make it possible to significantly simplify experiments to determine the resultant soil reaction forces to a freely rotating disk knife and reduce their required number. These expressions make it possible to carry out strength calculations of soil-cultivating working tools with disks and determine their optimal parameters according to the strength criteria and the minimum specific energy consumption with accuracy sufficient for engineering practice. Adequacy of the obtained expressions was confirmed by comparison with experimental data of the disk knife dynamometry

Author Biographies

Aleksandr Akimov, Federal State Budgetary Educational Institution of Higher Education “Chuvash State Agricultural Academy” K. Marx str., 29, Cheboksary, Chuvash Republic, Russia, 428003

Doctor of Technical Sciences, Professor

Department of transport technological machines and complexes

Yuriy Konstantinov, Federal State Budgetary Educational Institution of Higher Education “Chuvash State Agricultural Academy” K. Marx str., 29, Cheboksary, Chuvash Republic, Russia, 428003

PhD, Associate Professor

Department of mathematics, physics and information technologies

Vladimir Medvedev, Federal State Budgetary Educational Institution of Higher Education “Chuvash State Agricultural Academy” K. Marx str., 29, Cheboksary, Chuvash Republic, Russia, 428003

Doctor of Technical Sciences, Professor

Department of transport technological machines and complexes

Petr Mishin, Federal State Budgetary Educational Institution of Higher Education “Chuvash State Agricultural Academy” K. Marx str., 29, Cheboksary, Chuvash Republic, Russia, 428003

Doctor of Technical Sciences, Professor

Department of transport technological machines and complexes

Mikhail Volkhonov, Federal State Budget Educational Institution of Higher Education "Kostroma State Agricultural Academy" Training Town, 34, Karavaevo Village, Kostroma Region, Russia, 156530

Doctor of Technical Sciences, Professor

Department of Technical systems in the agro-industrial complex

Petr Lekomtsev, Federal State Budgetary Educational Institution of Higher Education “Izhevsk State Agricultural Academy” Studencheskaya str., 11, Izhevsk, Udmurt Republic, Russia, 426069

Doctor of Technical Sciences, Professor

Department of Energy and electrotechnologies

Nikolai Obolensky, State Budget Educational Institution of Higher Education “Nizhny Novgorod State Engineering and Economics University” Oktyabrskaya str., 22, Knyaginino, Nizhny Novgorod region, Russia, 606340

Doctor of Technical Sciences, Professor

Department of Labor protection and safety of vital activity

Gubeydulla Yunusov, Federal State Budgetary Educational Institution of Higher Education “Mari State University” Lenin sq., 1, Yoshkar-Ola, Republic of Mari El, Russia, 424000

Doctor of Technical Sciences, Professor

Department of Mechanization of Production and Processing of Agricultural Products

References

  1. Hann, M. J., Giessibl, J. (1998). Force Measurements on Driven Discs. Journal of Agricultural Engineering Research, 69 (2), 149–157. doi: https://doi.org/10.1006/jaer.1997.0241
  2. Singh, S. P., Singh, B., Vatsa, D. K. (1995). Design and development of powered one-way plough. Agricultural mechanization in Asia, Africa and Latin America, 26 (3), 9–12.
  3. Nalavade, P. P., Salokhe, V. M., Niyamapa, T., Soni, P. (2010). Performance of Free Rolling and Powered Tillage Discs. Soil and Tillage Research, 109 (2), 87–93. doi: https://doi.org/10.1016/j.still.2010.05.004
  4. Kumar, S., Singh, T. P. (2015). Assessment of power requirement of a powered disc through soil bin study. International Journal of Basic and Applied Agricultural Research, 13 (1), 105–111.
  5. Nerli, N. (1929–1930). Sul Problema dinamico dell’aratro a disco. Annali delle Università Toscane, 14 (48), 51–78.
  6. Nerli, N. (1940). Sul vantaggio dinamico del coltro rotante. Sobr. soch. Vol. IV. Moscow: Sel'hozgiz, 231.
  7. Nartov, P. S. (1972). Diskovye pochvoobrabatyvayushchie orudiya. Voronezh: izd-vo VGU, 184.
  8. Sineokov, G. N. (1949). Diskovye rabochie organy pochvoobrabatyvayushchih mashin. Moscow: Mashgiz, 86.
  9. Luchinskiy, N. D. (1977). Nekotorye voprosy zemledel'cheskoy mekhaniki. Teoreticheskie osnovy mekhanizacii vazhneyshih processov sel'skohozyaystvennogo proizvodstva: Trudy VIM, 75, 3–77.
  10. Medvedev, V. I., Vedeneev, A. I., Akimov, A. P. (1974). Metodika rascheta dvizhushchey sily na ploskom diske-dvizhitele. Traktory i sel'hozmashiny, 8, 18–20.
  11. Medvedev, V. I., Konstantinov, Yu. V., Akimov, A. P. (2001). Obobshchennaya matematicheskaya model' vzaimodeystviya diskovogo nozha s pochvoy. Traktory i sel'skohozyaystvennye mashiny, 2, 34–37.
  12. Konstantinov, Yu. V. (2000). Vybor optimal'nyh parametrov i rezhimov funkcionirovaniya rotacionnyh rabochih organov. Cheboksary, 176.
  13. Akimov, A. P., Konstantinov, Yu. V. (2005). Skol'zhenie-buksovanie diskovogo nozha v pochve i ego silovye harakteristiki. Traktory i sel'hozmashiny, 4, 30–34.
  14. Nieuwenburg, P. I. J. J., Speelman, L., Wensink, H. E. (1992). An evaluation of some disk coulter designs. Journal of Agricultural Engineering Research, 51, 67–80. doi: https://doi.org/10.1016/0021-8634(92)80026-o
  15. Turovskiy, B. V., Efremova, V. N. (2013). Zavisimost' energoemkosti diskovogo rabochego organa ot rezhimov raboty. Tekhnika i oborudovanie dlya sela, 10, 16–18.
  16. Kobyakov, I. D., Evchenko, A. V. (2016). Issledovanie dvizheniya shestiugol'nogo i kruglogo diskov rabochih organov pochvoobrabatyvayushchih orudiy. Traktory i sel'hozmashiny, 1, 49–51.
  17. Kobyakov, I. D., Evchenko, A. V. (2017). Research of the moments of rotation drcular knives. Aekonomika: ekonomika i sel'skoe hozyaystvo. Available at: https://cyberleninka.ru/article/n/issledovaniya-momentov-vrascheniya-diskovyh-nozhey
  18. Kurilov, E. V., Furmanov, D. V. (2014). Razrabotka dorozhnogo asfal'tobetona diskovym svobodnovrashchayushchimsya instrumentom. Mekhanizaciya stroitel'stva, 8, 4–7.
  19. Furmanov, D. V., Kurilov, E. V. (2013). Teoreticheskoe obosnovanie processa rezaniya asfal'tobetona diskovym nozhom. Ekologiya i nauchno-tekhnicheskiy progress. Urbanistika, 2, 498–505.
  20. Kurilov, E. V. (2013). Vliyanie iznosa rezhushchey kromki diskovogo nozha na energoemkost' kosogo rezaniya grunta. Mekhanizaciya stroitel'stva, 832 (10), 28–31.
  21. Kurilov, E. V., Shcherbakov, A. S. (2010). K voprosu effektivnosti kosogo rezaniya grunta diskovym nozhom. Vestnik Belorussko-Rossiyskogo universiteta, 26 (1), 24–32.
  22. Luchinskiy, N. D. (1979). O buksovanii diskovyh pochvoobrabatyvayushchih orudiy. NTB VIM, 39, 13.
  23. Kanarev, F. M. (1983). Rotacionnye pochvoobrabatyvayushchie mashiny i orudiya. Moscow: Mashinostroenie, 142.
  24. Mamatov, F. M. (1977). Eksperimental'noe issledovanie razlichnyh tipov ploskih diskovyh nozhey. Sel'skohozyaystvennye mashiny, ХIV (1), 5–7.
  25. Akimov, A., Konstantinov, Y., Mazyarov, V. (2018). Mathematical model of interaction of free rolling flat disk with soil. Vestnik of Kazan State Agrarian University, 13 (1), 96–101. doi: https://doi.org/10.12737/article_5afc0cc83773a1.96609313
  26. Ahmad, F., Weimin, D., Qishou, D., Rehim, A., Jabran, K. (2017). Comparative Performance of Various Disc-Type Furrow Openers in No-Till Paddy Field Conditions. Sustainability, 9 (7), 1143. doi: https://doi.org/10.3390/su9071143
  27. Ahmad, F., Weimin, D., Qishuo, D., Hussain, M., Jabran, K. (2015). Forces and Straw Cutting Performance of Double Disc Furrow Opener in No-Till Paddy Soil. PLOS ONE, 10 (3), e0119648. doi: https://doi.org/10.1371/journal.pone.0119648
  28. Bianchini, A., Magalhães, P. S. G. (2008). Evaluation of coulters for cutting sugar cane residue in a soil bin. Biosystems Engineering, 100 (3), 370–375. doi: https://doi.org/10.1016/j.biosystemseng.2008.04.012
  29. Magalhães, P. S. G., Bianchini, A., Braunbeck, O. A. (2007). Simulated and Experimental Analyses of a Toothed Rolling Coulter for Cutting Crop Residues. Biosystems Engineering, 96 (2), 193–200. doi: https://doi.org/10.1016/j.biosystemseng.2006.10.014
  30. Dharamkar, M. S., Galhe, D. S. (2017). Design development of self suspended dispenser. International Journal of Engineering Sciences & Research Technology, 6 (2), 688–690.
  31. Karada, P. R., Gaikwad, A. (2018). Design and Analysis of Disk Furrow Opener. International Journal of Engineering Technology Science and Research, 5 (3), 1777–1780.
  32. Blekhman, I. I., Myshkis, A. D., Panovko, Ya. G. (1976). Prikladnaya matematika: Predmet, logika i osobennosti podhodov. Kyiv: Naukova dumka, 270.
  33. Gulin, A. V., Dmitriev, V. I. (Eds.) (2003). Izbrannye trudy A. A. Samarskogo. Moscow: MAKS Press, 531.
  34. Danilov, A. M., Gar'kina, I. A. (2014). Interpolyaciya, approksimaciya, optimizaciya: analiz i sintez slozhnyh sistem. Penza: PGUAS, 168.

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Published

2018-11-27

How to Cite

Akimov, A., Konstantinov, Y., Medvedev, V., Mishin, P., Volkhonov, M., Lekomtsev, P., Obolensky, N., & Yunusov, G. (2018). An approximating mathematical model of interaction between a freely rotating disk and soil. Eastern-European Journal of Enterprise Technologies, 6(1 (96), 17–27. https://doi.org/10.15587/1729-4061.2018.148500

Issue

Vol. 6 No. 1 (96) (2018): Engineering technological systems

Section

Engineering technological systems

License

Copyright (c) 2018 Aleksandr Akimov, Yuriy Konstantinov, Vladimir Medvedev, Petr Mishin, Mikhail Volkhonov, Petr Lekomtsev, Nikolai Obolensky, Gubeydulla Yunusov

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