621.833.65

dynamic model, speed control device, gear differential, closed-loop hydraulic system, sun gear, ring gear, carrier, planet.

The dynamic processes in the device for speed control with multistage gear differential and closed-loop hydraulic systems through ring gears have been studied for case when the leading link is the sun gear of the first stage, and the driven is a carrier of the last stage. For such a device, the equation of kinetic energy has been compiled and the dynamics equations have been obtained by the Lagrange method, which have been solved. The obtained results are the basis for further computer simulation on and quantitative analysis to assess the performance of such devices and select the necessary closed-loop hydraulic systems to control speed changes.

1. Malashchenko V. О., Strilets O. R., Strilets V. М. Klasyfikatsiya sposobiv i prystroyiv keruvannya protsesom zminy shvydkosti u tekhnitsi. Pidyomno-transportna tekhnika. Odesa: ONPU, 2015, no. 1. P. 70–78. [In Ukrainian].
2. Mаlashchenkо, V., Strilets, О., Strilets, V. Determining performance efficiency of the differential in a device for speed change through ring gear. Eastern-European Journal of Enterprise Technologies, 2017, 6 (7 (90)), 51–57. Doi: http://dx.doi.org/10.15587/1729-4061.2017.110683.
3. Bahk, C.-J, Parker R. G. Analytical investigation of tooth profile modification effects on planetary gear dynamics. Mechanism and Machine Theory, Elsevier, 2013, no. 70. P. 298–319.
4. Qilin, H., Yong, W., Zhipu, H., Yudong, X. Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System. Mathematical Problems in Engineering, 2013, vol. 2013, 12 p. Doi: 10.1155/2013/149046.
5. Salgado, D. R., Castillo, J. M. Analysis of the transmission ratio and efficiency ranges of the four-, five-, and six-link planetary gear trains, Mechanism and Machine Theory, 2014, Vol. 73, pp. 218–243, doi: 10.1016/j.mechmachtheory.2013.11.001
6. Grzegorz, P. Verification Of Gear Dynamic Model In Different Operating Conditions, Scientific Journal of Silesian University of Technology. Series Transport, 2014, 84, 99–104.
7. Fuchun, Y., Jianxiong, F., Hongcai, Zh. Power flow and efficiency analysis of multi-flow planetary
   gear trains. Mechanism and Machine Theory, 2015, Vol. 92, 86–99. Doi: 10.1016/j. mechmachtheory.2015.05.003
8. Pawar1, P. V., Kulkarni, P. R. Design of two stage planetary gear train for high reduction ratio. International Journal of Research in Engineering and Technology, 2015, Vol. 4. Iss. 6, P. 150–157. doi: 10.15623/ijret.2015.0406025
9. Chao, Ch., Jiabin, Ch. Efficiency analysis of two degrees of freedom epicyclic gear transmission and experimental. Mechanism and Machine Theory, 2015, Vol. 87, pp. 115–130. Doi: 10.1016/j. mechmachtheory.2014.12.017
10. Tianli, X., Jibin, H., Zengxiong, P., Chunwang, L. Synthesis of seven-speed planetary gear trains for heavy-duty commercial vehicle, Mechanism and Machine Theory, 2015, Vol. 90, pp. 230–239, doi: 10.1016/j. mechmachtheory. 2014.12.012.
11. Drewniak, J., Garlicka, P., Kolber Design for the bi-planetary gear train. Scientific Journal of Silesian University of Technology. Series Transport. 2016, 91, 5–17. Doi: 10.20858/sjsutst.2016.91.1
12. Li, J., Hu, Q., Zong, Ch., Zhu, T. Power Analysis and Efficiency Calculation of Multistage Micro-planetary Transmission. Energy Procedia, 2017, 141, 654–659. Doi: 10.1016/j.egypro.2017.11.088
13. Wenjian, Y., Huafeng, D. Automatic detection of degenerate planetary gear trains with different degree of freedoms. Applied Mathematical Modelling, 2018, 64, 320–332. Doi: 10.1016/j.apm.2018.07.038
14. Esmail, E. L., Pennestrì, E., Hussein Juber A. Power losses in two-degrees-of-freedom planetary gear trains: A critical analysis of Radzimovsky’s formulas, Mechanism and Machine Theory, 2018, Vol. 128, 191–204, doi: 10.1016/j.mechmachtheory.2018.05.015
15. Dankov, A. M. Planetary Continuously Adjustable Gear Train With Force Closure Of Planet Gear And Central Gear: From Idea To Design. Science & Technique, 2018, 17 (3), 228–237. Doi: 10.21122/2227-1031-2018-17-3-228-237.
16. Dobariya, M. Design of Compound Planetary Gear Train, International Journal for Research in Applied Science and Engineering Technology, 2018, vol. 6, iss. 4, 3179–3184, doi: 10.22214/ijraset.2018.452.
17. Strilets O. R., Malashchenko V. О., Pasika V. R., Strilets V. М. Dynamichna model keruvannya shvydkosti cherez epitsykl pryvoda iz zubchastoyu dyferentsialnoyu peredacheyu. Visnyk Natsionalnoho universytetu “Lvivska politekhnika”. “Dynamika, mitsnist ta proektuvannya mashyn i pryladiv”, 2019, no. 911, pp. 63–67. [In Ukrainian].
18. Strilets O. R., Malashchenko V. О., Strilets V. М. Dynamika prystroyu dlya keruvannya zminamy shvydkosti z zubchastoyu dyferentsialnoyu peredacheyu i zamknutoyu hidrosystemoyu cherez sonyachne zubchaste koleso. Visnyk Natsionalnoho tekhnichnoho universytetu “KHPI”. Seriya: Mashynoznavstvo ta SAPR, 2020, no. 1’2020. P. 93–98. [In Ukrainian].
19. Strilets O. R., Malashchenko V. О., Strilets V. М. Dynamika prystroyu dlya keruvannya zminamy shvydkosti z zubchastoyu dyferentsialnoyu peredacheyu i zamknutoyu hidrosystemoyu cherez vodylo. Naukovyy visnyk KhDMU, 2020, no. 2 (7), pp. 176–182. [In Ukrainian].
20. Strilets O. R., Malashchenko V. О., Strilets V. М. Vyznachennya zvedenykh obertalnykh momentiv rivnyan dynamiky prystroyiv zminy shvydkosti cherez zubchasti dyferentsialy z zamknutymy hidrosystemamy. Visnyk Khmelnytskoho natsionalnoho universytetu. Naukovyy zhurnal. Tekhnichni nauky, 2020, iss. 4, pp. 18–23. [In Ukrainian].
21. Strilets O. R., Malashchenko V. О., Strilets V. М. Dynamic model of a closed-loop hydraulic system for speed control through gear differential. Scientific Journal of TNTU. Tern.: TNTU, 2020, vol. 98, no. 2.
    P. 91–98.
22. Malashchenko V. О., Strilets O. R., Strilets V. М. Keruvannya shvydkistyu rukhu mashyn bahatostupenevoyu zubchastoyu dyferentsialnoyu peredacheyu cherez epitsykl. Visnyk Natsionalnoho universytetu “Lʹvivsʹka politekhnika”. “Dynamika, mitsnist ta proektuvannya mashyn i pryladiv”. 2016. No. 838. P. 57–63. [In Ukrainian].

1. Malashchenko V. О., Strilets O. R., Strilets V. М. Klasyfikatsiya sposobiv i prystroyiv keruvannya protsesom zminy shvydkosti u tekhnitsi. Pidyomno-transportna tekhnika. Odesa: ONPU, 2015, no. 1. P. 70–78. [In Ukrainian].
2. Mаlashchenkо, V., Strilets, О., Strilets, V. Determining performance efficiency of the differential in a device for speed change through ring gear. Eastern-European Journal of Enterprise Technologies, 2017, 6 (7 (90)), 51–57. Doi: http://dx.doi.org/10.15587/1729-4061.2017.110683.
3. Bahk, C.-J, Parker R. G. Analytical investigation of tooth profile modification effects on planetary gear dynamics. Mechanism and Machine Theory, Elsevier, 2013, no. 70. P. 298–319.
4. Qilin, H., Yong, W., Zhipu, H., Yudong, X. Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System. Mathematical Problems in Engineering, 2013, vol. 2013, 12 p. Doi: 10.1155/2013/149046.
5. Salgado, D. R., Castillo, J. M. Analysis of the transmission ratio and efficiency ranges of the four-, five-, and six-link planetary gear trains, Mechanism and Machine Theory, 2014, Vol. 73, pp. 218–243, doi: 10.1016/j.mechmachtheory.2013.11.001
6. Grzegorz, P. Verification Of Gear Dynamic Model In Different Operating Conditions, Scientific Journal of Silesian University of Technology. Series Transport, 2014, 84, 99–104.
7. Fuchun, Y., Jianxiong, F., Hongcai, Zh. Power flow and efficiency analysis of multi-flow planetary
   gear trains. Mechanism and Machine Theory, 2015, Vol. 92, 86–99. Doi: 10.1016/j. mechmachtheory.2015.05.003
8. Pawar1, P. V., Kulkarni, P. R. Design of two stage planetary gear train for high reduction ratio. International Journal of Research in Engineering and Technology, 2015, Vol. 4. Iss. 6, P. 150–157. doi: 10.15623/ijret.2015.0406025
9. Chao, Ch., Jiabin, Ch. Efficiency analysis of two degrees of freedom epicyclic gear transmission and experimental. Mechanism and Machine Theory, 2015, Vol. 87, pp. 115–130. Doi: 10.1016/j. mechmachtheory.2014.12.017
10. Tianli, X., Jibin, H., Zengxiong, P., Chunwang, L. Synthesis of seven-speed planetary gear trains for heavy-duty commercial vehicle, Mechanism and Machine Theory, 2015, Vol. 90, pp. 230–239, doi: 10.1016/j. mechmachtheory. 2014.12.012.
11. Drewniak, J., Garlicka, P., Kolber Design for the bi-planetary gear train. Scientific Journal of Silesian University of Technology. Series Transport. 2016, 91, 5–17. Doi: 10.20858/sjsutst.2016.91.1
12. Li, J., Hu, Q., Zong, Ch., Zhu, T. Power Analysis and Efficiency Calculation of Multistage Micro-planetary Transmission. Energy Procedia, 2017, 141, 654–659. Doi: 10.1016/j.egypro.2017.11.088
13. Wenjian, Y., Huafeng, D. Automatic detection of degenerate planetary gear trains with different degree of freedoms. Applied Mathematical Modelling, 2018, 64, 320–332. Doi: 10.1016/j.apm.2018.07.038
14. Esmail, E. L., Pennestrì, E., Hussein Juber A. Power losses in two-degrees-of-freedom planetary gear trains: A critical analysis of Radzimovsky’s formulas, Mechanism and Machine Theory, 2018, Vol. 128, 191–204, doi: 10.1016/j.mechmachtheory.2018.05.015
15. Dankov, A. M. Planetary Continuously Adjustable Gear Train With Force Closure Of Planet Gear And Central Gear: From Idea To Design. Science & Technique, 2018, 17 (3), 228–237. Doi: 10.21122/2227-1031-2018-17-3-228-237.
16. Dobariya, M. Design of Compound Planetary Gear Train, International Journal for Research in Applied Science and Engineering Technology, 2018, vol. 6, iss. 4, 3179–3184, doi: 10.22214/ijraset.2018.452.
17. Strilets O. R., Malashchenko V. О., Pasika V. R., Strilets V. М. Dynamichna model keruvannya shvydkosti cherez epitsykl pryvoda iz zubchastoyu dyferentsialnoyu peredacheyu. Visnyk Natsionalnoho universytetu “Lvivska politekhnika”. “Dynamika, mitsnist ta proektuvannya mashyn i pryladiv”, 2019, no. 911, pp. 63–67. [In Ukrainian].
18. Strilets O. R., Malashchenko V. О., Strilets V. М. Dynamika prystroyu dlya keruvannya zminamy shvydkosti z zubchastoyu dyferentsialnoyu peredacheyu i zamknutoyu hidrosystemoyu cherez sonyachne zubchaste koleso. Visnyk Natsionalnoho tekhnichnoho universytetu “KHPI”. Seriya: Mashynoznavstvo ta SAPR, 2020, no. 1’2020. P. 93–98. [In Ukrainian].
19. Strilets O. R., Malashchenko V. О., Strilets V. М. Dynamika prystroyu dlya keruvannya zminamy shvydkosti z zubchastoyu dyferentsialnoyu peredacheyu i zamknutoyu hidrosystemoyu cherez vodylo. Naukovyy visnyk KhDMU, 2020, no. 2 (7), pp. 176–182. [In Ukrainian].
20. Strilets O. R., Malashchenko V. О., Strilets V. М. Vyznachennya zvedenykh obertalnykh momentiv rivnyan dynamiky prystroyiv zminy shvydkosti cherez zubchasti dyferentsialy z zamknutymy hidrosystemamy. Visnyk Khmelnytskoho natsionalnoho universytetu. Naukovyy zhurnal. Tekhnichni nauky, 2020, iss. 4, pp. 18–23. [In Ukrainian].
21. Strilets O. R., Malashchenko V. О., Strilets V. М. Dynamic model of a closed-loop hydraulic system for speed control through gear differential. Scientific Journal of TNTU. Tern.: TNTU, 2020, vol. 98, no. 2.
    P. 91–98.
22. Malashchenko V. О., Strilets O. R., Strilets V. М. Keruvannya shvydkistyu rukhu mashyn bahatostupenevoyu zubchastoyu dyferentsialnoyu peredacheyu cherez epitsykl. Visnyk Natsionalnoho universytetu “Lʹvivsʹka politekhnika”. “Dynamika, mitsnist ta proektuvannya mashyn i pryladiv”. 2016. No. 838. P. 57–63. [In Ukrainian].