Abstract
This work focuses on the effect of time-dependent errors in the behavior of planetary transmissions. More precisely, this work analyses the response of low-speed planetary transmissions to the presence of time-varying manufacturing errors such as run-out and index errors, which are some of the most common errors inherent to the gear manufacturing process. Thus, in order to observe the interaction of these transmissions to the presence of those errors the analysis focuses on its transmission error. In the context of this work transmissions with in-phase and sequentially phased mesh phasing are considered. These transmissions also implement a pair of state-of-the-art roller bearings modelled in the sun support. As a result of the error modelling, it is possible to see how the results for in-phase transmissions are not affected by the size of the error. However, in the sequentially phased transmissions the change in the geometry of the contacts varies the mesh phasing and leads to discrepancies in the transmission’s behavior.
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References
Inalpolat, M., Kahraman, A.: Dynamic modelling of planetary gears of automatic transmissions. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 222(3), 229–242 (2008). https://doi.org/10.1243/14644193JMBD138
Du, W., Zhao, S., Jin, L., Gao, J., Zheng, Z.: Optimization design and performance comparison of different powertrains of electric vehicles. Mech. Mach. Theory 156, 104143 (2021). https://doi.org/10.1016/j.mechmachtheory.2020.104143
Viadero, F., Fernández, A., Iglesias, M., De-Juan, A., Liaño, E., Serna, M.A.: Non-stationary dynamic analysis of a wind turbine power drivetrain: offshore considerations. Appl. Acoust. 77, 204–211 (2014). https://doi.org/10.1016/j.apacoust.2013.10.006
Diez-Ibarbia, A., Sanchez-Espiga, J., Fernandez-del-Rincon, A., Calvo-Irisarri, J., Iglesias, M., Viadero, F.: Probabilistic analysis of the mesh load factor in wind-turbine planetary transmissions: tooth thickness errors. Mech. Mach. Theory 185, 105341 (2023). https://doi.org/10.1016/j.mechmachtheory.2023.105341
Götz, J., Siglmüller, F., Fürst, M., Otto, M., Stahl, K.: Experimental investigation of the dynamic load sharing of planetary gearboxes. Forsch. im Ingenieurwes. (2021). https://doi.org/10.1007/s10010-021-00507-5
Kurzke, J.: Fundamental differences between conventional and geared turbofans. Proc. ASME Turbo Expo 1, 145–153 (2009). https://doi.org/10.1115/GT2009-59745
Cooley, C.G., Parker, R.G.: A review of planetary and epicyclic gear dynamics and vibrations research. Appl. Mech. Rev. 66(4), 040804 (2014). https://doi.org/10.1115/1.4027812
Vijayakar, S.: A combined surface integral and finite element solution for a three-dimensional contact problem. Int. J. Numer. Methods Eng. 31(3), 525–545 (1991). https://doi.org/10.1002/nme.1620310308
Abousleiman, V., Velex, P., Becquerelle, S.: Modeling of spur and helical gear planetary drives with flexible ring gears and planet carriers. J. Mech. Des. Trans. ASME 129(1), 95–106 (2007). https://doi.org/10.1115/1.2359468
Iglesias, M., Fernandez del Rincon, A., de-Juan, A., Diez-Ibarbia, A., Garcia, P., Viadero, F.: Advanced model for the calculation of meshing forces in spur gear planetary transmissions. Meccanica 50(7), 1869–1894 (2015). https://doi.org/10.1007/s11012-015-0130-3
Guilbert, B., Velex, P., Cutuli, P.: Quasi-static and dynamic analyses of thin-webbed high-speed gears: centrifugal effect influence. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 233(21–22), 7282–7291 (2019). https://doi.org/10.1177/0954406219855411
Bodas, A., Kahraman, A.: Influence of carrier and gear manufacturing errors on the static load sharing behavior of planetary gear sets. JSME Int. J. Ser. C 47(3), 908–915 (2004). https://doi.org/10.1299/jsmec.47.908
Iglesias, M., Fernandez del Rincon, A., De-Juan, A., Garcia, P., Diez-Ibarbia, A., Viadero, F.: Planetary transmission load sharing: manufacturing errors and system configuration study. Mech. Mach. Theory 111, 21–38 (2017). https://doi.org/10.1016/j.mechmachtheory.2016.12.010
Sanchez-Espiga, J., Fernandez-del-Rincon, A., Iglesias, M., Viadero, F.: Influence of errors in planetary transmissions load sharing under different mesh phasing. Mech. Mach. Theory 153, 104012 (2020). https://doi.org/10.1016/j.mechmachtheory.2020.104012
Kahraman, A.: Static load sharing characteristics of transmission planetary gear sets : model and experiment. In: Transmission Driveline System Symposium, no. 1, pp. 1–10 (1999). https://doi.org/10.4271/1999-01-1050
Huo, G. Sanchez Espiga, J., Iglesias, M., Fernandez del Rincon, A., Viadero, F., Jiao, Y.: Influence of manufacturing errors on the behaviour of a two-stage planetary gear train. In: DYNA, vol. 98, no. 4, pp. 384–390 (2023). https://doi.org/10.6036/10879
Gu, X., Velex, P.: On the dynamic simulation of eccentricity errors in planetary gears. Mech. Mach. Theory 61, 14–29 (2013). https://doi.org/10.1016/j.mechmachtheory.2012.10.003
Vedmar, L., Henriksson, B.: A general approach for determining dynamic forces in spur gears. J. Mech. Des. 120(4), 593 (1998). https://doi.org/10.1016/j.jalz.2010.01.013
Fernandez del Rincon, A., Viadero, F., Iglesias, M., García, P., Sancibrian, R.: A model for the study of meshing stiffness in spur gear transmissions. Mech. Mach. Theory 61, 30–58 (2013). https://doi.org/10.1016/j.mechmachtheory.2012.10.008
Sanchez-Espiga, J., Fernandez-del-Rincon, A., Iglesias, M., Viadero, F.: Numerical evaluation of the accuracy in the load sharing calculation using strain gauges: Sun and ring gear tooth root. Mech. Mach. Theory 175, 104923 (2022). https://doi.org/10.1016/J.MECHMACHTHEORY.2022.104923
Weber, K., Banaschek, C.: The Deformation of Loaded Gears and the Effect on their Load Carrying Capacity. London (1951)
Zander, G., Kehl, M., Otto, J., Böttcher, M., Stahl, R., Poll, K.: Erweiterung LAGER2 – Erweiterung der Wälzlagerberechnung. In: FVA-Software: Forschungsvorhaben, vol. 701 III. F, no. 1404 (2020)
Jurkschat, T., Otto, M., Lohner, T., Stahl, K.: Determination of the loss behavior and thermal balance of rolling bearings. Forsch. im Ingenieurwesen/Eng. Res. 82(2), 149–155 (2018). https://doi.org/10.1007/s10010-018-0266-0
Fernández-Del-Rincón, A., Iglesias, M., De-Juan, A., Diez-Ibarbia, A., García, P., Viadero, F.: Gear transmission dynamics: effects of index and run out errors. Appl. Acoust. 108, 63–83 (2016). https://doi.org/10.1016/j.apacoust.2015.11.012
Acknowledgements
The authors from Universidad de Cantabria would like to thank the Spanish Ministry of Science and Innovation for financing the project PID2020-116213RB-I00, in which context Dr. J. Sanchez-Espiga completed a postdoctoral research stay at the Gear Research Center (FZG), Technical University of Munich (TUM), Garching, Germany.
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Sanchez-Espiga, J., Fürst, M., Fernandez-del-Rincon, A., Otto, M., Viadero, F., Stahl, K. (2024). Time-Dependent Errors Influence on the Transmission Error in Planetary Gears with Different Mesh Phasing. In: Okada, M. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2023. Mechanisms and Machine Science, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-031-45709-8_12
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