Load distribution along the pinion rim width of a multi-threaded planetary gear with the teeth increased pliability at the ends

The paper presents results of studying a multi-thread planetary gear with one external and one internal pinion gearing, which load capacity is limited by the teeth contact strength. The pinion is positioned on two rolling bearings, its teeth at the end are made in the form of cantilevers to reduce rigidity in the engagement and lower the maximum linear load caused by the teeth initial non-fitting due to errors in the mechanism manufacture. To determine the laws of load distribution in the wheels engagement, equations were compiled for the teeth displacement compatibility in two sections of the contact. Linear load on the tooth cantilever section was determined by solving a fourth-order differential equation obtained from equations relating to deformation of the tooth cantilever and force factors taking into account the angle of the teeth initial non-fitting. Engagement rigidity in this section was calculated using formulas for the material resistance and the broken sections hypothesis. Numerical solution of the resulting equations made it possible to determine coefficient of the uneven load distribution along the pinion rim width with cantilever teeth at its end, which was necessary to calculate the transmission strength and to assess influence of the specified gearing parameters on the pinion mechanism load parameters. Comparative analysis of gears with flexible and rigid pinion teeth showed that the first of these gears had the load capacity approximately 10% higher than the second.
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References

[1] Suntsov A.S., Vychuzhanina E.F., Perminova O.M. Optimization of parameters of the two-speed manual drive of the stopping pipe valves with automatic speed change. Khimicheskoe i neftegazovoe mashinostroenie, 2021, no. 5, pp. 30–32. (In Russ.).

[2] Plekhanov F.I., Yakimovich B.A. Recent developments in the field of mechanical drives and their possible application to military technology. Vestnik akademii voennykh nauk, 2015, no. 1, pp. 144–146. (In Russ.).

[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] Ermolaev M.M., Zakharov M.N., Sinitsyna Yu.V. Experimental verification of methods for calculation of the distribution of forces in planetary pin gearboxes. Vestnik mashinostroeniya, 2020, no. 12, pp. 12–15. (In Russ.).

[5] 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

[6] Plekhanov F.I., Vychuzhanina E.F. A study of the stress-strain state of the planetary carrier cheek. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2019, no. 8, pp. 3–9, doi: http://dx.doi.org/10.18698/0536-1044-2019-8-3-9 (in Russ.).

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

[8] 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)

[9] 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

[10] 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, vol. 51, pp. 117–137, doi: https://doi.org/10.1007/978-3-319-60399-5_6

[11] Reshetov L.N. Samoustanavlivayushchiesya mekhanizmy [Self-aligning mechanisms]. Moscow. Mashinostroenie Publ., 1991. (In Russ.).

[12] Pervushin G.N., Suntsov A.S., Vychuzhanina E.F. Mnogosatellitnaya planetarnaya peredacha [Multi-satellite planetary gear]. Patent RU 2791077. Appl. 02.11.2022, publ. 02.03.2023.

[13] Ayrapetov E.L., Genkin M.D. Deformativnost planetarnykh mekhanizmov [Deformability of planetary mechanisms]. Moscow, Nauka Publ., 1973. (In Russ.).

[14] Kudryavtsev V.N., Kirdyashev Yu.N., Ginzburg E.G. Planetarnye peredachi [Planetary gears]. Leningrad, Mashinostroenie Publ., 1977. 563 p. (In Russ.).

[15] Plekhanov F.I., Muzafarov R.S. Planetarnaya peredacha [Planetary gear]. Patent RU 2664608. Appl. 17.10.2016, publ. 21.08.2018. (In Russ.).