Study of the stressed-deformed state of the axis of satellite of multi-threaded planetary transmission

Planetary gears with their multi-threaded (multi-satellite) design have a high load capacity. However, unavoidable errors in their manufacture lead to uneven load distribution in wheel gearings. Deformation of the elements of the planetary mechanism (especially the axis of the satellite) contributes to load balancing, but at unfavorable values of the transmission parameters, it can lead to the appearance of unacceptably high stresses and failure of the axis and parts mated with it. In this regard, it is important to establish the effect of deformation of the satellite axis on the distribution of load and stress in the areas of its mating with the jaw of the carrier and with the bearing. The article presents the results of the study of the stress-strain state of the axis of the planetary gear satellite, taking into account the compliance of the elements mating with it (the jaw of the carrier and the bearing ring). Multisatellite structure is considered, in which carrier is arranged in the form of two cheeks, which are rigidly connected to each other with jumpers. The solution of the problem of stress-strain state was carried out using differential equations of the curved axis of the satellite, presented in the form of a beam on an elastic base. The obtained dependences and calculations made on them make it possible to determine coefficients of non-uniformity of distribution of load and stresses in areas of coupling of the axis of the satellite with elements of the planetary mechanism and to rationally design the gear.
EDN: EXXEAH, https://elibrary/exxeah

References

[1] Drewniak I., Kopek I., Zawislak S. Kinematical and efficiency analysis of planetary gear trains by means of various graph-based approaches. In: Theory and practice of gearing and transmissions. Springer, 2016, pp. 263–284, doi: https://doi.org/10.1007/978-3-319-19740-1_12

[2] Sondkar P., Kahraman A. A dynamic model of a double-helical planetary gear set. Mech. Mach. Theory, 2013, vol. 70, pp. 157–174, doi: https://doi.org/10.1016/j.mechmachtheory.2013.07.005

[3] Timofeev G.A., Panyukhin V.V., Sashchenko D.V. Studying self-braking planetary gears with single-crown satellites. Problemy mashinostroeniya i nadezhnosti mashin, 2020, no. 4, pp. 44–50, doi: https://doi.org/10.31857/S0235711920040148 (in Russ.). (Eng. version: J. Mach. Manuf. Reliab., 2020, vol. 49, no. 4, pp. 308–313, doi: https://doi.org/10.3103/S1052618820040147)

[4] Kahraman A., Ding H. A methodology to predict surface wear of planetary gears under dynamic conditions. Mech. Based Des. Struct. Mach., 2010, vol. 38, no. 4, pp. 493–515, doi: https://doi.org/10.1080/15397734.2010.501312

[5] Sidorov P.G., Pashin A.A., Plyasov A.V. Multi-threaded gears: structure, education, kinematic and force relationships, classification and application prospects. Privodnaya tekhnika, 2010, no. 4, pp. 25–30. (In Russ.).

[6] Grabskiy A.A., Plekhanov F.I., Grabskaya E.P. et al. Strategy of structural and parametric improvement of multisatellite planetary gears in mining machines. Gornyy zhurnal, 2022, no. 3, pp. 54–57, doi: https://doi.org/10.17580/gzh.2022.03.08 (in Russ.).

[7] Inalpolat M., Kahraman A. A theoretical and experimental investigation of modulation sidebands of planetary gear sets. J. Sound Vib., 2009, vol. 323, no. 3–5, pp. 677–696, doi: https://doi.org/10.1016/j.jsv.2009.01.004

[8] Plekhanov F.I., Ovsyannikov A.V., Suntsov A.S. et al. Mnogosatellitnaya planetarnaya peredacha [Multi-satellite planetary gear]. Patent RU 2799777. Appl. 27.03.2023, publ. 11.07.2023. (In Russ.).

[9] Goncharov Yu.A., Baranova I.A. Rational design of planetary gears. Vestnik mashinostroeniya, 2019, no. 7, pp. 3–7. (In Russ.).

[10] Kudryavtsev V.N., Kirdyashev Yu.N., Ginzburg E.G. Planetarnye peredachi [Planetary gears]. Leningrad, Mashinostroenie Publ., 1977. 536 p. (In Russ.).

[11] Plekhanov F.I., Goldfarb V.I., Vychuzhanina E.F. Load distribution in meshing of planetary gearwheels and its influence on the technical and economic performance of the mechanism. In: Advanced gear engineering. Springer, 2018, pp. 117–137, doi: https://doi.org/10.1007/978-3-319-60399-5_6

[12] Dvornikov L.T., Zhukov I.A. Fundamentals of a unified theory of planetary gears. Vestnik mashinostroeniya, 2022, no. 3, pp. 3–9. (In Russ.). (Eng. version: Russ. Engin. Res., 2022, vol. 42, no. 6, pp. 541–547, doi: https://doi.org/10.3103/S1068798X22060090)

[13] Boguski B., Kahraman A., Nishino T. A new method to measure planet load sharing and sun gear radial orbit of planetary gear sets. J. Mech. Des., 2012, vol. 134, no. 7, art. 071002, doi: https://doi.org/10.1115/1.4006827

[14] Plekhanov F.I., Vychuzhanina E.F. Research of the flexibility of elements of a rational design of a multi-satellite planetary gear and its influence on the distribution of load over power flows. Vestnik mashinostroeniya, 2020, no. 11, pp. 3–7, doi: https://doi.org/10.36652/0042-4633-2020-11-3-7 (in Russ.).

[15] Plekhanov F.I., Molchanov S.M., Suntsov A.S. Study of Influence of element deformation and manufacturing errors of an epicyclic gear train on the load distribution among satellites. Russ. Engin. Res., 2024, vol. 44, no. 4, pp. 493–497, doi: https://doi.org/10.3103/S1068798X24700643