Determining planetary gearing optimal gear ratio allowing minimize its outer diameter at the specified load torque

Aeronautical and Space-Rocket Engineering

Design, construction and manufacturing of flying vehicles


Аuthors

Abdulin R. R.1*, Podshibnev V. A.1**, Samsonovich S. L.2***

1. Company Avionica, 7, Obraztsova str., Moscow, 127055, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: abdulin@mnpk.ru
**e-mail: podshibneff@mail.ru
***e-mail: samsonovich40@mail.ru

Abstract

Mass and size parameters reduction is one of actual issues of aircraft electromechanical drives design. It concerns especially mechanical transmissions employed in drive systems of mechanical transmission. Harmonic and planetary gears are most compact. They allow obtaining large gear ratio for a single stage. Their application as the output stage of a multi-stage reduction gearbox of an electro-mechanical drive, as a unit transmitting the largest moment, allows mass and size parameters reduction of a drive system.

The goal of this article consists in determining the optimal values of gear ratios at which the outer diameter of planetary transmissions has its minimum size for the specified load moment.

It was demonstrated, that the main parameter affecting the outer diameter of planetary transmissions for the specified load moment was the carrier radius. For a single-row planetary transmission this radius was expressed through the gear tooth module value, the number of teeth of the central sun-gear and gear ratio between the sun-gear and satellites. The article presents substantiation of the above said parameters selection. Minimum acceptable carrier radius was found. It was established, that optimal gear ratio value of the single­row planetary transmission equaled four.

The carrier radius planetary gear with double-row planets was expressed by gear tooth module and two gear ratios, namely between the central sun-gear of the planet gear and first-row satellites, and between planet gear of the second row and the crown-wheel. The dependence of the carrier radius on these gear ratios, which is represented by a surface with «ravine», was plotted. A unified optimal gear ratio value was not obtained for the planetary transmission with double­row satellites was not found. However, a set of quasi­optimal values do exist. The “ravine” direction, along which the quasi-optimal values were located, was determined. The optimal relationship of gear ratios between the central sun-gear and the first-row satellites, and between the second-row satellites and the crown wheel was derived. This relationship allows ensure minimum outer diameter of the planetary transmission with double-row satellites. An example of the minimum outer diameter of the planetary gear with double-row satellites computing is given.

The obtained optimal gear ratio values expand the knowledge on planetary transmissions and allow minimize overall dimensions of aircraft drive systems while developing multi-stage reduction gearboxes for electromechanical drives with output planetary transmission.

Keywords:

planetary gear, double-row satellite gear, optimal gear ratio

References

  1. Sil’chenko P.N., Lekanov A.V., Porpylev V.G., Novikov E.S., Cherepanov D.A., Il’in P.V., Ovechkin G.I. Patent RU2464464 Cl, 20.10.2012.

  2. Krylov N.V., Lalabekov V.I., Ogol’tsov 1.1. et al. Elektromekhanicheskie silovye mini-privody dlya “bolee elektrifitsirovannogo” samoleta (Electromechanical power mini-drives for “more electric” aircraft), Moscow, MAI, 2016, 360 p.

  3. Abdulin R. R., Zudilin A. S., Obolensky Y. G., Rozhnin N. B., Samsonovich S. L., Stitsenko A. N. Developing of an electromechanical actuator of the higher reliability with redundancy. Aerospace MAI Journal, 2018, vol. 25, no. 1, pp. 121-131.

  4. Kirdyashev Yu.N. Mnogopotochnye peredachi differentsial’nogo tipa (Multithreaded differential type transmission), Leningrad, Mashinostroenie, 1981, 232 p.

  5. Nadaraia Ts.G., Shestakov I.Ya., Fadeev A.A. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M.F. Reshetneva, 2014, no. 2(54), pp. 137-140.

  6. Kozyrev V.V. Planetarnye reduktory v sostave robotov i mekhatronnykh system (Planetary gearboxes as a part of robots and mechatronic systems), Vladimir, Vladimirovskii gosudarstvennyi universitet, 2008, 48 p.

  7. Kudryavtsev V.N. Planetarnye peredachi (Planetary gear), Moscow, Mashinostroenie, 1986, 134 p.

  8. Galkin P.A., Nikitina L.Kh. Proektirovanie i analiz zubchatykh mekhanizmov (Gear mechanisms design and analysis), Tambov, Tambovskii gosudarstvennyi tekhnicheskii universitet, 2008, 32 p.

  9. Samsonovich S.L. Osnovy konstruirovaniya elektricheskikh, pnevmaticheskikh i gidravlicheskikh ispolnitel’nykh mekhanizmov privodov letatel’nykh apparatov (Fundamentals of electric, pneumatic and hydraulic actuating mechanisms design of aircraft drives), Moscow, MAI, 2002, 244 p.

  10. Roos F., Spiegelber Ch. Relations between size and gear ratio in spur and planetary gear trains.Technical report, Department of Machine Design, Royal Institute of Technology, KTH, Stockholm, 2004.

  11. Nandeppagoudar S.B., Shaikh S.N., Gote S.R., More S.P., Chaudhari A.S., Borse N.R., Gawande S.H. Design and Numerical Analysis of Optimized Planetary Gear Box. 6th National Conference RDME (17-18 March 2017). DOI: 10.9790/1684-17010030511

  12. Schulze T. Design and Optimization of Planetary Gears Considering All Relevant Influences. Gear Technology. November/December 2013, pp. 96-102.

  13. Tkachenko V.A., Abramov V.T., Korovkin M.D. Proektirovanie planetarnykh mekhanizmov, optimal’nykh po dinamicheskim kharakteristikam (Planetary mechanisms design, optimal on dynamic performance), Kharkov, Kharkovskii aviatsionnyi universitet, 983, 112 p.

  14. Hüseyin Filiz , Olguner S., Evyapan E. A Study on Optimization of Planetary Gear Trains. Special issue of the 3rd International Conference on Computational and Experimental Science and Engineering (ICCESEN 2016), 2017, vol. 132, no. 3, pp. 728-733. DOI: 10.12693/ APhysPolA.132.728

  15. Höhn B.R., Stahl K., Gwinner P. Light-Weight Design for Planetary Gear Transmissions. Gear Technology, September 2013, pp. 96-103.

  16. Abramov V.T., Getya A.N., Matusevich V.A. et al. Vestnik Natsional’nogo tekhnicheskogo universiteta “KhPI”, 2009, no. 29, pp. 45-52.

  17. Tkachenko V.A. Vestnik Natsional’nogo tekhnicheskogo universiteta “KhPI”, 2001, no. 13, pp. 141-147.

  18. Kapelevich A.L., Anan’ev V.M. Vestnik dvigatelestroeniya, 2012, no. 2, pp. 155-160.

  19. Yakovlev P.G., Nikolaev S.N. Resources and Technology, 2003, no. 4, pp. 186-190.

  20. Sushkov S.A. Konstruktsiya i proektirovanie mekhanicheskikhperedachprivoda ustanovok letatel’nykh apparatov (Structure and design of aircraft mechanical transmission drive units), Moscow, MAI, 1983, 82 p.

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