In mechanical drives of machines there is a need to control changes in the speed of their actuators. Stepped and stepless gearboxes are used for this purpose. Known speed control devices have many disadvantages that adversely affect the durability and reliability of drive components and machines in general. These include the design complexity, high material consumption, automation complexity, dynamic loads during transitions from one speed to another, intensive wear of parts due to the friction connections use. The purpose of the work is to develop an algorithm for determining the kinematic, power parameters and dimensions when designing speed change devices through the ring gear of a gear differential with a rotary stopper in the form of a closed-loop hydraulic system based on authors’ previous computer-theoretical research and classical scientific advices. To solve these problems analytical expressions and graphs have been obtained for the relationship between speeds of gear differential links, the efficiency has been determined by the method of potential power – based on friction losses in each gearing. With the help of computer modeling of analytical expressions, using the MATLAB software, graphical dependences of efficiency have been obtained, which made it possible to evaluate the accomplishment of the gear differential in terms of energy consumption and possible self-braking. Based on Lagrange's theory, a dynamic model of a speed change device with a ring gear control has been constructed and a solution of the obtained system of equations has been proposed. The 3D modeling of the device has been executed and at the final choice of the optimum variant of model, after some specifications, development of technical documentation can be started. The results obtained have practical application at the stage of development and design of new speed control devices through the ring gear, allow to evaluate the operation of gear differentials in terms of energy consumption and self-braking and are the basis for further research. The graphical dependences obtained for the efficiency of the gear differentials clearly allow us to trace the change in the value of the efficiency depending on the angular velocity of the ring gear and the gear ratio. For the first time, analytical expressions were obtained to determine the efficiency of the gear differential of a speed-changing device with a driving sun gear, driven carrier, or vice versa, more accurately. The resulting graphical dependences for efficiency visually allow to trace change of efficiency value depending on angular speed of a ring gear, as a control link, and the gear ratio. Results are recommended for introduction into design and engineering practice at development of designs of speed change devices through differential gears of drives of various equipment and in educational process of higher technical educational institutions in discipline of mechanical engineering. Areas of further research – improvement of speed change devices through gear differentials in the design, manufacture, operation and repair.
[1] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “Klasyfikatsiya sposobiv i prystroyiv keruvannya protsesom zminy shvydkosti v tekhnitsi” [“Classification of methods and devices for controlling the process of speed change in technology”], Pidyomno-transportna tekhnika [Hoisting and Transport Equipment], issue 1, pp. 70–78, 2015. [in Ukrainian].
[2] V. Malashchenko, O. Strilets, V. Strilets, “Fundamentals of Creation of New Devices for Speed Change Management”, Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 1, no. 2, pр. 11–20, 2015.
[3] V. M. Strilets, I. P. Rilo, O. R. Strilets, “Zubchastyy dyferentsial z prystroyem dlya keruvannya zminamy shvydkosti” [“Gear differential with a device for controlling speed changes”], UA Patent 7328, June 15, 2005. [in Ukrainian].
[4] V. M. Strilets, I. P. Rilo, O. R. Strilets, V. P. Polishchuk, “Zubchastyy dyferentsial z prystroyem dlya keruvannya zminamy shvydkosti” [“Gear differential with a device for controlling speed changes”], UA Patent 11121, December 15, 2005. [in Ukrainian].
[5] N. M. Kudenko, V. M. Strilets, “Ostanov dlya hruza peremeshchaemoho mekhanyzmom podʹema” [“Stopper for the load moved by the lifting mechanism”], RF Patent 2211796, September 10, 2003. [in Russian].
[6] O. R. Strilets, V. O. Malashchenko, V. M. Strilets, “Zupynnyk obertalnoho rukhu” [“Rotary stopper”], UA Patent 146683, March 10, 2021. [in Ukrainian].
[7] O. R. Strilets, V. O. Malashchenko, V. M. Strilets, “Zapirno-rehulyuvalnyy kran” [“Shut-off and control valve”], UA Patent 147550, May 19, 2021. [in Ukrainian].
[8] O. R. Strilets, “Obgruntuvannya mozhlyvosti keruvannya zminamy shvydkosti za dopomohoyu dyferentsialʹnykh peredach” [“Reasoning of the possibility of speed changes controlling with the help of differential gears”], Visnyk inzhenernoyi akademiyi nauk Ukrayiny [Bulletin of the Engineering Academy of Sciences of Ukraine], issue 2, pp. 177–181, 2015. [in Ukrainian].
[9] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “Novyy sposob besstupenchatoho yzmenenyya skorosty pry pomoshchy zubchatykh dyfferentsyalʹnykh peredach s zamknutoy hydrosystemoy” [“A new way of stepless speed change by means of gear differential transmissions with the closed hydraulic system”], Pryvody y komponenty mashyn [Machine Drives and Components], no. 4–5, pp. 7–10, 2015. [in Russian].
[10] O. R. Strilets, “Keruvannya zminamy shvydkosti za dopomohoyu dyferentsialnoyi peredachi cherez epitsykl” [“Control of speed changes by differential transmission through the epicycle”], Visnyk Ternopilskoho natsionalnoho tekhnichnoho universytetu [Bulletin of Ternopil National Technical University], no. 4 (80), pp. 129–135, 2015. [in Ukrainian].
[11] O. R. Strilets, “Mozhlyvosti bahatoskhodynkovykh zubchastykh dyferentsialnykh peredach z zamknutymy hidrosystemamy keruvaty shvydkistyu” [“Possibilities to control speed by multistage gear differentials with closed hydraulic systems”], in Proc. 9th Int. Sc.-Tech. Conf. “IIRTC-2016”, Kyiv, Ukraine, May 17–18, 2016, pp. 234–236. [in Ukrainian].
[12] O. R. Strilets, “Kinematychni mozhlyvosti zubchastykh dyferentsialnykh peredach z zamknutoyu hidrosystemoyu” [“Kinematic capabilities of differential gears with closed hydraulic system”], in Proc. Int. Sc.-Tech. Conf. of Young Scolars and Students “Urgent Problems of Modern Science”, Ternopil, Ukraine, October 25–26, 2015, vol. 1, pp. 234–235. [in Ukrainian].
[13] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “Keruvannya shvydkistyu rukhu mashyn bahatostupenevoyu zubchastoyu peredacheyu cherez epitsykl” [“Speed control of machines by multistage gear transmission through an epicycle”], Visnyk Natsionalnoho universytetu “Lvivska politekhnika” [Bulletin of Lviv Polytechnic National University], no. 838, pp. 57–63, 2016. [in Ukrainian].
[14] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “Justification of efficiency of Epicyclical Gear Train in Device for Speed Change Management”, Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 3. no. 1. pр. 89–95, 2017.
[15] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “Determining performance efficiency of the differential in a device for speed change through epicycle”, Eastern-European Journal of Enterprise Technologies, no. 6/7 (90). pp. 51–57, 2017.
[16] O. R. Strilets, V. O. Malashchenko, V. M. Strilets, “Otsinka nadiynosti prystroyiv keruvannya zminamy shvydkosti cherez zubchasti dyferentsialy na osnovi yikh enerhetychnoyi efektyvnosti” [“Evaluation of the reliability of speed change control devices through gear differentials based on their energy efficiency”], Tekhnichnyy servis ahropromyslovoho, lisovoho ta transportnoho kompleksiv [Technical service of agro-industrial, forest and transport complexes], no. 13, pp. 147–154, 2018. [in Ukrainian].
[17] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “Zalezhnist koefitsiyenta korysnoyi diyi zubchastoyi dyferentsialʹnoyi peredachi vid peredatochnoho chysla i shvydkosti keruvannya” [“Dependence of the efficiency of the gear differential on the gear ratio and control speed”], in Proc. Conf. to 110 anniversary of S. M. Kozhevnykov, Dnipro, Ukraine, April 11–13, 2017, pp. 145–148. [in Ukrainian].
[18] O. R. Strilets, “KKD zubchastoyi dyferentsialnoyi peredachi koly veduchym ye vodylo, a vedenym – sonyachne koleso” [“The efficiency of the gear differential when the carrier is the driving and the sun gear is driven”], in Proc. 10th Int. Sc.-Tech. Conf. “IIRTC-2017”, Kyiv, Ukraine, May 16–17, 2017, pp. 200–202. [in Ukrainian].
[19] O. R. Strilets, “Vyznachennya KKD bahatoskhodynkovykh dyferentsialʹnykh zubchastykh peredach u prystroyi zminy shvydkosti cherez epitsykl” [“Determination of the efficiency of multi-stage differential gears in the device for changing the speed through the epicycle”], in Proc. 20th Sc. Conf. of TNTU, Ternopil, Ukraine, May 17–18, 2017, pp. 51–52. [in Ukrainian].
[20] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “Novyy pryvod z dyferentsialom i zamknutoyu hidrosystemoyu dlya keruvannya shvydkistyu mashyny” [“New drive with differential and closed hydraulic system to control the speed of the machine”], Vibratsiyi v tekhnitsi ta tekhnolohiyakh [Vibrations in Engineering and Technology], no. 3 (83), pp.109–116, 2016. [in Ukrainian].
[21] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “Otsenka enerhetycheskoy effektivnosti zubchatyh differentsyalov ustroystv upravlenyya skorostyu opredelenyem koeffitsyenta poleznoho deystvyya” [“Evaluation of energy efficiency of gear differentials of speed control devices by determination of efficiency”], Privodnaya tekhnika y komponenty mashyn [Drive Equipment and Machine Components], pp. 36–41, 2018. [in Russian].
[22] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “KKD zubchastoyi dyferentsialʹnoyi peredachi z vnutrishnim i zovnishnim zacheplennyamy kolis u prystroyi dlya keruvannya zminamy shvydkosti cherez epitsykl” [“Efficiency of gear differential transmission with internal and external gears of wheels in the device for control of changes of speed through an epicycle.”], Visnyk Natsionalnoho universytetu “Lvivska politekhnika” [Bulletin of Lviv Polytechnic National University], no. 866, pp.62–69, 2017. [in Ukrainian].
[23] O. R. Strilets, “Teoretychne obgruntuvannya kinematychnykh ta enerhetyknykh mozhlyvostey prystroyi zminy shvydkosti cherez zubchasti dyferentsialy z zamknutymy hidrosystemamy” [“Theoretical substantiation of kinematic and energy possibilities of the device of change of speed through gear differentials with the closed hydraulic systems”], in Proc. Int. Sc.-Tech. Conf. «Innovative technologies for the development of mechanical engineering and efficient operation of transport systems», Rivne, Ukraine, May 21–23, 2019, pp. 47–49. [in Ukrainian].
[24] O. R. Strilets, “Ohlyad i analiz hidronasosiv dlya zamknutykh hidrosystem u prystroyakh dlya keruvannya zminamy shvydkosti” [“Review and analysis of hydraulic pumps for closed hydraulic systems in devices for speed control”], in Proc. 13th Int. Symp. of Ukrainian Mechanical Engineers in Lviv, Lviv, Ukraine, May 18–19, 2017, pp. 150–151. [in Ukrainian].
[25] V. O. Malashchenko, O. R. Strilets, V. M. Strilets, “Obgruntuvannya budovy ta pryntsypu roboty zupynnyka dlya lanky keruvannya zubchastoho dyferentsiala” [“Substantiation of the structure and principle of operation of the stop for the control unit of the gear differential”], Visnyk Natsionalnoho tekhnichnoho universytetu KHPI [Bulletin of the National Technical University “KhPI”], no. 25 (1308), pp. 89–92, 2018. [in Ukrainian].
[26] O. R. Strilets, “Kinematychni, sylovi i enerhetychni zalezhnosti u zamknutiy hidrosystemi mekhanichnoho pryvodu” [“Kinematic, power and energy dependences in a closed hydraulic system of a mechanical drive”], Visnyk NUVHP [Bulletin of NUWEE], issue 1 (89), pp.152–164, 2020. [in Ukrainian].
[27] O. Strilets, V. Malashchenko, V. Strilets, “Dynamic model of a closed-loop hydraulic system for speed control through gear differential”, Scientific Journal of TNTU, vol. 98, no. 2. pp. 91–98, 2020.
[28] O. R. Strilets, “Teplovyy rozrakhunok zupynnyka obertalʹnoho rukhu u vyhlyadi zamknutoyi hidrosystemy” [“Thermal calculation of a rotary motion stopper in the form of a closed hydraulic system”], Visnyk Khmelnytskoho natsionalnoho universytetu [Bulletin of Khmelnytsky National University], no. 5 (289), pp. 183–187, 2020. [in Ukrainian].
[29] O. R. Strilets, A. A. Stepanyuk, O. V. Malashchenko, “Zastosuvannya trokhmirnoho modelyuvannya dlya optymizatsiyi rozmiriv zupynnyka obertalnoho rukhu u vyhlyadi zamknutoyi hidrosystemy” [“Application of three-dimensional modeling to optimize the size of the rotary stop in the form of a closed hydraulic system”], Visnyk NUVHP [Bulletin of NUWEE], issue 4 (92), pp. 140–145, 2020. [in Ukrainian].
[30] O. R. Strilets, “Dynamichna model keruvannya shvydkistyu u prystroyi z bahatostupinchastym zubchastym dyferentsialom i zamknutymy hidrosystemamy cherez epitsykly” [“Dynamic model of speed control in a device with a multistage gear differential and closed hydraulic systems through epicycles”], in Proc. Int. Sc.-Pract. Conf. of Young Scolars, Posgraduates and Bachelor Students “Challanges and Opportunities of Modern Science”, Rivne, Ukraine, May 10, 2019, pp. 103–105. [in Ukrainian].
[31] O. R. Strilets, V. O. Malashchenko, V. R. Pasika, V. M. Strilets, “Dynamichna modelʹ keruvannya shvydkosti cherez epitsykl pryvoda iz zubchastoyu dyferentsialʹnoyu peredacheyu” [“Dynamic model of speed control through the epicycle of the drive with gear differential transmission”], Visnyk Natsionalnoho universytetu “Lvivska politekhnika” [Bulletin of Lviv Polytechnic National University], no. 911, pp. 63–67, 2019. [in Ukrainian].
[32] O. Strilets, “Dynamic model of speed control through ring gears in a device with a multistage gear differentials and closed-loop hydraulic system”, Scientific Journal of TNTU, vol. 99, no. 3, pp. 102–111, 2020.
[33] O. R. Strilets, V. O. Malashchenko, V. M. Strilets, “Vyznachennya zvedenykh obertalnykh momentiv rivnyan dynamiky prystroyiv zminy shvydkosti cherez zubchasti dyferentsialy z zamknutymy hidrosystemamy” [“Determination of consolidated torques of equations of dynamics of speed change devices through gear differentials with closed hydraulic systems”], Visnyk Khmelnytskoho natsionalnoho universytetu [Bulletin of Khmelnytsky National University], no. 3 (285), pp. 118–123, 2020. [in Ukrainian].
[34] O. R. Strilets, “Kompyuterne modelyuvannya dyferentsialnykh peredach z prystroyem dlya keruvannya shvydkistyu” [“Computer simulation of differential transmissions with a speed control device”], Mashynoznavstvo [Mechanical Engineering], no. 4 (128), pp. 35–39, 2009. [in Ukrainian].
[35] O. R. Strilets, “Kompyuterne modelyuvannya prystroyu dlya plavnoho keruvannya zminamy shvydkosti” [“Computer simulation of a device for smooth control of speed changes”], Visnyk NUVHP [Bulletin of NUWEE], issue 4 (44), pp. 213–218, 2008. [in Ukrainian].
[36] O. R. Strilets, V. M. Strilets, “Modelyrovanye dyfferentsyalʹnykh peredach s ustroystvom dlya upravlenyya skorostʹyu v systeme KOMPAS-3D” [“Modeling of differential gears with a device for speed control in the KOMPAS-3D”], Sovremennyy nauchnyy vestnyk [Modern Scientific Journal], no. 29 (55), pp. 4–8, 2008. [in Russian].
[37] O. R. Strilets, “Dyferentsialna zubchasta peredacha z prystroyem dlya keruvannya zminamy shvydkosti ta yiyi kompyuterne modelyuvannya” [“Differential gear with speed control device and computer simulation”], Moloda nauka XXI [Young Science XXI], vol. 1, pp. 89–92, 2010. [in Ukrainian].
[38] O. R. Strilets, “Pidvyshchennya efektyvnosti proektuvannya prystroyiv dlya keruvannya shvydkistyu cherez zubchasti dyferentsialy z zamknutoyu hidrosystemoyu zastosuvannyam 3D modelyuvannya” [“Improving the efficiency of design of devices for speed control through gear differentials with a closed hydraulic system using 3D modeling”], in Proc. 2nd Int. Sc.-Tech. Conf. «Innovative technologies for the development of mechanical engineering and efficient operation of transport systems», Rivne, Ukraine, March 25–27, 2020, pp. 36–39. [in Ukrainian].
[39] O. R. Strilets, “Vykorystannya 3D modelyuvannya dlya optymizatsiyi rozmiriv pry proektuvanni prystroyu keruvanni zminoyu shvydkosti cherez epitsykl” [“Using 3D modeling to optimize dimensions when designing a speed change device through an epicycle”], in Proc. Int. Sc.-Tech. Conf. «Fundamental and Applied Problems of Modern Technologies», Ternopil, Ukraine, May 14–15, 2020, pp. 113–114. [in Ukrainian].
[40] O. R. Strilets, A. A. Stepanyuk, O. V. Malashchenko, “Zastosuvannya trʹokhmirnoho modelyuvannya dlya optymizatsiyi rozmiriv prystroyu keruvannya zminoyu shvydkosti zupynnykom obertalʹnoho rukhu u vyhlyadi zamknutoyi hidrosystemy” [“Application of three-dimensional modeling for optimization of the sizes of the control device of change of speed by a stop of rotational movement in the form of the closed hydraulic system”], Visnyk Natsionalnoho tekhnichnoho universytetu KHPI [Bulletin of the National Technical University “KhPI”], no. 1, pp. 141–154, 2021. [in Ukrainian].
[41] O. R. Strilets, “Etapy proektuvannya prystroyu zminy shvydkosti cherez epitsykl zubchastoho dyferentsiala z zupynnykom obertalnoho rukhu” [“Stages of design of the device of change of speed through an epicycle of a gear differential with the stop of rotational movement”], in Proc. Int. Sc.-Pract. Conf. of Young Scolars, Posgraduates and Bachelor Students “Challanges and Opportunities of Modern Science”, Rivne, Ukraine, May 13, 2021, pp. 168–170. [in Ukrainian].
[42] Y. Y. Artobolevskiy, “Teoriya mekhanizmov i mashyn” [“Theory of mechanisms and machines”]. Moskow, Russia: Nauka Publ., 1988. [in Russian].
[43] Ya. T. Kinytskyy, “Teoriya mekhanizmiv i mashyn” [“Theory of mechanisms and machines”]. Kyiv, Ukraine: Naukova Dumka Publ., 2002. [in Ukrainian].
[44] K. V. Frolov, et al., “Teoriya mekhanizmov i mashyn” [“Theory of mechanisms and machines”]. Moskow, Russia: Vysshaya shkola Publ., 2003. [in Russian].
[45] L. A. Andryenko, B. A. Baykov, Y. K. Hanulych, et al., “Detali mashyn” [“Machine parts”]. Moscow, Russia: MHTU Publ., 2004. [in Russian].
[46] V. O. Malashchenko, V. M. Strilets, Ya. M. Novitskyy, O. R. Strilets, “Detali mashyn i pidyomno-transportne obladnannya” [“Machine parts and Hoisting and Transport Equipment”]. Rivne, Ukraine: NUWEE Publ., 2017. [in Ukrainian].
[47] V. V. Yushkyn, “Osnovy rascheta obyemnoho hidropryvoda” [“Basics of calculation of the volume hydraulic drive”]. Minsk, Belarus: Vyshcha Shkola Publ., 1982. [in Russian].
[48] Razrabotka i proizvodstvo gidravlicheskikh silovykh mashin i komponentov gidrosistem [Design and manufacture of hydraulic power machines and hydraulic components]. [Online]. Available: https://www.hydrosila.com/. Accessed on: April 30, 2021. [in Russian].
[49] G. A. ‘Barsov, L. V. Bezmenova, L. S. Hrodzenskaya, et al., “Teoryya ploskikh mekhanizmov i dinamika mashyn” [“Theory of plane mechanisms and dynamics of machines”]. Moskow, Russia: Vysshaya shkola Publ., 1961. [in Russian].
[50] N. Dudaeva, S. Zahayko, “Samouchytelʹ Solid Works 2010” [“Solid Works Tutorial 2010”]. St. Peterburh, Russia: VNV-SPb Publ., 2011. [in Russian].
[51] M. I. Kydruk, “Kompas – 3D V10”. St. Peterburh, Russia: Piter Publ., 2009. [in Russian].
[52] M. M. Kozyar, Yu. V. Feshchuk, O. V. Parfenyuk, “Kompyuterna hrafika. SolidWorks” [“Computer graphics. SolidWorks”]. Kherson, Ukraine: OLDI-PLUS Publ., 2018. [in Ukrainian].