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closed-loop hydraulic system, hydraulic gear pump, gear differential, sun gear, ring gear, planet, dynamic model.

A mathematical dynamic model of a closed hydraulic system for controlling speed changes through a gear differential, which consists of a motor, a gear transmission, a gear hydraulic pump, a closed-loop pipeline, and a control valve, is obtained. The engine can be a solar gear, or an epicycle, or a gear differential, and with the help of a closed hydraulic system, you can change the speed of the solar gear, or an epicycle, or a carrier from when the gear pump pumps fluid in a closed pipe. when the pipeline is closed by the regulating crane, the gear hydraulic pump will be stopped and the link on which the closed hydraulic system is installed will be stopped. The result is an analytical expression to determine the speed of the fluid in a closed hydraulic system, which depends on the angular velocity of the engine – the control links of the solar gear, or epicycle, or carrier.

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. Malashchenko V., Strilets О., Strilets V. Fundamentals of Creation of New Devices for Speed Change Management. Ukrainian Journal of Mechanical Engineering and Materials Science. Lviv, 2015. Vol. 1. No. 2. P. 11–20.
3. Strilets O. R. Keruvannya zminamy shvydkosti za dopomohoyu dyferentsialnoyi peredachi cherez epitsykl. Visnyk Ternopilskoho natsionalnoho tekhnichnoho universytetu. Ternopil: TNTU, 2015. No. 4 (80). P. 129–135. [In Ukrainian].
4. Strilets O. R. Keruvannya protsesom zminy shvydkosti za dopomohoyu dyferentsialnoyi peredachi cherez sonyachne zubchaste koleso. Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky. Khmelnytskyy: KhNU, 2015. No. 5 (229). P. 68–72. [In Ukrainian].
5. Strilets O. R. Keruvannya protsesom zminy shvydkosti za dopomohoyu dyferentsialnoyi peredachi cherez vodylo. Visnyk Kremenchutskoho natsionalnoho universytetu. Kremenchuk: KrNU, 2015. Iss. 6 (95). P. 72–77. [In Ukrainian].
6. Strilets O. R. The efficiency of the differential gear to devices for controlling the speed change through a sun gear. Odes’kyi Politechnichnyi Universytet. Pratsi, Issue 2 (52), 2017. P. 29–38.
7. 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)), P. 51–57. URL: http://dx.doi.org/10.15587/1729-4061.2017.110683.
8. Malashchenko V., Strilets O., Strilets V., Klysz S. Investigation of the energy effectiveness of multistage differential gears when the speed is changed by the carrier. Diagnostyka. Warchava, 2019. Vol. 20. No. 6. P. 57–64.
9. Strilets O. R., Malashchenko V. О., Strilets V. М. Energy effectiveness of the differential of a device for speed change through the sun gear. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. Dniрrо: NHU, 2019. No. 6. P. 52–57.
10. Scheaua Fănel. The Use Of Numerical Analysis In Order To Highlight The Fluid Dynamics Inside A Hydraulic Gear Pump Model. Journal of Industrial Design and Engineering Graphics. 2015. 10 (3). P. 33–36.
11. Rituraj, F., Vacca, A. (2018) External gear pumps operating with non-Newtonian fluids: Modelling and experimental validation. Mech. Syst. Signal Process. 106, P. 284–302.
12. Dawei Liu, Yanbo Ba, Tingzhi Ren (2019) Flow fluctuation abatement of high-order elliptical gear pump by external noncircular gear drive. Mechanism Theory, 134, P. 338–348.
13. Yonghan Yoon, Byung-Ho Park, Jaesool Shim, Yong-Oun Han, Byeong-Joo Hong, Song-Hyun Yun, (2017) Numerical simulation of three-dimensional external gear pump using immersed solid method. Applied Thermal Engineering, 118, P. 539–550.
14. Battarra, M., Mucchi, E., A method for variable pressure load estimation in spur and helical gear pumps. Mechanical Systems and Signal Processing. 76–77, P. 265–282.
15. A. Ransegnola, T., Zhao, X., Vacca, A., (2019) A comparison of helical and spur external gear machines for fluid power applications: Design and optimization. Mechanism and Machine Theory, 142, 103604.
16. Strilets O. R., Malashchenko V. О., Strilets V. М. Otsinka nadiynosti prystroyiv keruvannya zminamy shvydkosti cherez zubchasti dyferentsialy na osnovi yikh enerhetychnoyi efektyvnosti. Naukovyy zhurnal “Tekhnichnyy servis ahropromyslovoho, lisovoho ta transportnoho kompleksiv”. Kharkiv: KhNTUSH, 2018. No. 13. P. 147–154. [In Ukrainian].
17. Malashchenko V. О., Strilets O. R., Strilets V. М. Otsenka energeticheskoy effektivnosti zubchatykh differentsialov ustroystv upravleniya skorostyu opredeleniyem koeffitsiyenta poleznogo deystviya. Sbornik trudov 4-go Moskovskogo Mezhdunarodnogo simpoziuma “Privodnaya tekhnika i komponenty mashin”. M.: ROSPTO – IMASH RAN, 2018. P. 36–41. [In Russian].
18. Strilets O. R., Malashchenko V. О., Strilets V. М. Obgruntuvannya budovy i pryntsypu roboty zupynnyka dlya lanky keruvannya shvydkistyu zubchastoho dyferentsiala. Visnyk Natsionalʹnoho tekhnichnoho universytetu “KHPI”. Zbirnyk naukovykh pratsʹ. Seriya: Mashynoznavstvo ta SAPR. Kharkiv: NTU “KhPI”, 2018. No. 25 (1301). P. 89–92. [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. Malashchenko V., Strilets О., Strilets V. Fundamentals of Creation of New Devices for Speed Change Management. Ukrainian Journal of Mechanical Engineering and Materials Science. Lviv, 2015. Vol. 1. No. 2. P. 11–20.
3. Strilets O. R. Keruvannya zminamy shvydkosti za dopomohoyu dyferentsialnoyi peredachi cherez epitsykl. Visnyk Ternopilskoho natsionalnoho tekhnichnoho universytetu. Ternopil: TNTU, 2015. No. 4 (80). P. 129–135. [In Ukrainian].
4. Strilets O. R. Keruvannya protsesom zminy shvydkosti za dopomohoyu dyferentsialnoyi peredachi cherez sonyachne zubchaste koleso. Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky. Khmelnytskyy: KhNU, 2015. No. 5 (229). P. 68–72. [In Ukrainian].
5. Strilets O. R. Keruvannya protsesom zminy shvydkosti za dopomohoyu dyferentsialnoyi peredachi cherez vodylo. Visnyk Kremenchutskoho natsionalnoho universytetu. Kremenchuk: KrNU, 2015. Iss. 6 (95). P. 72–77. [In Ukrainian].
6. Strilets O. R. The efficiency of the differential gear to devices for controlling the speed change through a sun gear. Odes’kyi Politechnichnyi Universytet. Pratsi, Issue 2 (52), 2017. P. 29–38.
7. 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)), P. 51–57. URL: http://dx.doi.org/10.15587/1729-4061.2017.110683.
8. Malashchenko V., Strilets O., Strilets V., Klysz S. Investigation of the energy effectiveness of multistage differential gears when the speed is changed by the carrier. Diagnostyka. Warchava, 2019. Vol. 20. No. 6. P. 57–64.
9. Strilets O. R., Malashchenko V. О., Strilets V. М. Energy effectiveness of the differential of a device for speed change through the sun gear. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. Dniрrо: NHU, 2019. No. 6. P. 52–57.
10. Scheaua Fănel. The Use Of Numerical Analysis In Order To Highlight The Fluid Dynamics Inside A Hydraulic Gear Pump Model. Journal of Industrial Design and Engineering Graphics. 2015. 10 (3). P. 33–36.
11. Rituraj, F., Vacca, A. (2018) External gear pumps operating with non-Newtonian fluids: Modelling and experimental validation. Mech. Syst. Signal Process. 106, P. 284–302.
12. Dawei Liu, Yanbo Ba, Tingzhi Ren (2019) Flow fluctuation abatement of high-order elliptical gear pump by external noncircular gear drive. Mechanism Theory, 134, P. 338–348.
13. Yonghan Yoon, Byung-Ho Park, Jaesool Shim, Yong-Oun Han, Byeong-Joo Hong, Song-Hyun Yun, (2017) Numerical simulation of three-dimensional external gear pump using immersed solid method. Applied Thermal Engineering, 118, P. 539–550.
14. Battarra, M., Mucchi, E., A method for variable pressure load estimation in spur and helical gear pumps. Mechanical Systems and Signal Processing. 76–77, P. 265–282.
15. A. Ransegnola, T., Zhao, X., Vacca, A., (2019) A comparison of helical and spur external gear machines for fluid power applications: Design and optimization. Mechanism and Machine Theory, 142, 103604.
16. Strilets O. R., Malashchenko V. О., Strilets V. М. Otsinka nadiynosti prystroyiv keruvannya zminamy shvydkosti cherez zubchasti dyferentsialy na osnovi yikh enerhetychnoyi efektyvnosti. Naukovyy zhurnal “Tekhnichnyy servis ahropromyslovoho, lisovoho ta transportnoho kompleksiv”. Kharkiv: KhNTUSH, 2018. No. 13. P. 147–154. [In Ukrainian].
17. Malashchenko V. О., Strilets O. R., Strilets V. М. Otsenka energeticheskoy effektivnosti zubchatykh differentsialov ustroystv upravleniya skorostyu opredeleniyem koeffitsiyenta poleznogo deystviya. Sbornik trudov 4-go Moskovskogo Mezhdunarodnogo simpoziuma “Privodnaya tekhnika i komponenty mashin”. M.: ROSPTO – IMASH RAN, 2018. P. 36–41. [In Russian].
18. Strilets O. R., Malashchenko V. О., Strilets V. М. Obgruntuvannya budovy i pryntsypu roboty zupynnyka dlya lanky keruvannya shvydkistyu zubchastoho dyferentsiala. Visnyk Natsionalʹnoho tekhnichnoho universytetu “KHPI”. Zbirnyk naukovykh pratsʹ. Seriya: Mashynoznavstvo ta SAPR. Kharkiv: NTU “KhPI”, 2018. No. 25 (1301). P. 89–92. [In Ukrainian].