- Published:
Planetary gear profile modification design based on load sharing modelling
Chinese Journal of Mechanical Engineering volume 28, pages 810–820 (2015)
Abstract
In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical system. Through the development of models capable of reproduce the system behavior, research in this area contributes to improve gear transmission insight, helping developing better maintenance practices and more efficient design processes. A planetary gear model used for the design of profile modifications ratio based on the levelling of the load sharing ratio is presented. The gear profile geometry definition, following a vectorial approach that mimics the real cutting process of gears, is thoroughly described. Teeth undercutting and hypotrochoid definition are implicitly considered, and a procedure for the incorporation of a rounding arc at the tooth tip in order to deal with corner contacts is described. A procedure for the modeling of profile deviations is presented, which can be used for the introduction of both manufacturing errors and designed profile modifications. An easy and flexible implementation of the profile deviation within the planetary model is accomplished based on the geometric overlapping. The contact force calculation and dynamic implementation used in the model are also introduced, and parameters from a real transmission for agricultural applications are presented for the application example. A set of reliefs is designed based on the levelling of the load sharing ratio for the example transmission, and finally some other important dynamic factors of the transmission are analyzed to assess the changes in the dynamic behavior with respect to the non-modified case. Thus, the main innovative aspect of the proposed planetary transmission model is the capacity of providing a simulated load sharing ratio which serves as design variable for the calculation of the tooth profile modifications.
References
SMITH J D. Gear noise and vibration[M]. Cambridge: Marcel Dekker Inc., 1999.
HENG A, ZHANG S, TAN A, et al. Rotating machinery prognostics: State of the art, challenges and opportunities[J]. Mechanical Systems and Signal Processing, 2009, 23(3): 724–739.
HAYASHI T, LI Y, HAYASHI I, et al. Measurement and some discussions on dynamic load sharing in planetary gears[J]. Bulletin of the JSME, 1986, 29(253): 2290–2297.
HIDAKA T, TERAUCHI Y. Dynamic behavior of planetary gear-1st report, load distributions in planetary gear[J]. Bulletin of the JSME, 1976, 19(132): 690–698.
SINGH A. Load sharing behavior in epicyclic gears: Physical explanation and generalized formulation[J]. Mechanism and Machine Theory, 2010, 45(3): 511–530.
ABOULEISMAN V, VELEX P, BECQUERELLE S. Modeling of spur and helical gear planetary drives with flexible ring gears and planet carriers[J]. Journal of Mechanical Design, 2007, 129: 95–106.
PALMER W, FUEHRER R. Noise control in planetary transmissions[J]. SAE Technical Paper No. 770561, 1977.
ABOULEISMAN V, VELEX, P. A hybrid 3D finite element/lumped parameter model for quasi-static and dynamic analyses of planetary/epicyclic gear sets[J]. Mechanism and Machine Theory, 2006, 41(6): 725–748.
INALPOLAT M, KAHRAMAN A. A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors[J]. Journal of Sound and Vibration, 2010, 329(4): 371–393.
AL-SHYYAB A, KAHRAMAN A. A non-linear dynamic model for planetary gear sets[J]. Proceedings of the Institution of Mechanical Engineers, Part K, 2007, 221(4): 567–576.
BAHK C J, PARKER R G. Analytical investigation of tooth profile modification effects on planetary gear dynamics[J]. Mechanism and Machine Theory, 2013, 70: 298–319.
SEAGER D L. Conditions for the neutralization of excitation by the teeth in epicyclic gearing[J]. Proceedings of Institution of Mechanical Engineers, 1975, 17(5): 293–298.
INALPOLAT M, KAHRAMAN A. A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors[J]. Journal of Sound and Vibration, 2010, 329(4): 371–393.
LIU G, PARKER R G. Dynamic modeling and analysis of tooth profile modification for multimesh gear vibration[J]. ASME Journal of Mechanical Design, 2008, 130(12): 121402.
VELEX P, FLAMAND L. Dynamic response of planetary trains to mesh parametric excitations[J]. ASME Journal of Mechanical Design, 1996, 118(1): 7–14.
LIN J, PARKER R G. Planetary gear parametric instability caused by mesh stiffness variation[J]. Journal of Sound and Vibration, 2002, 249(1): 129–145.
PARKER R G, AGASHE V, VIJAYAKAR S M. Dynamic response of a planetary gear system using a finite element/contact mechanics model[J]. ASME Journal of Mechanical Design, 2000, 122(3): 304–310.
FERNANDEZ DEL RINCON A, VIADERO F, et al. A model for the study of meshing stiffness in spur gear transmissions[J]. Mechanism and Machine Theory, 2013, 61: 30–58.
FERNANDEZ A, IGLESIAS M, DE-JUAN A, et al. Gear transmission dynamic: Effects of tooth profile deviations and support flexibility[J]. Applied Acoustics, 2014, 77: 138–149.
FERNANDEZ DEL RINCON A. An advanced model for the study of the vibratory behavior of gear transmission systems[D]. Santander: University of Cantabria, 2010.
LITVIN F L, FUENTES A. Gear geometry and applied theory[M]. 2nd ed. Cambridg: Cambridge University Press, 2004.
VEDMAR L. On the design of external involute helical gears, Transactions of machine elements division[M]. Lund: Lund Technical University, 1981.
ANDERSSON A, VEDMAR L. A dynamic model to determine vibrations in involute helical gears[J]. Journal of Sound and Vibration, 2003, 260(2): 195–212.
HÖNH B. Improvements on noise reduction and efficiency of gears[J]. Meccanica, 2010, 45(3): 425–37.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the Project DPI2013-44860 funded by the Spanish Ministry of Science and Technology
IGLESIAS Miguel is a research professor and received his PhD degree at University of Cantabria, Spain in 2013. His research activities are focused on machinery condition monitoring and gear dynamic modelling.
FERNÁNDEZ DEL RINCÓN Alfonso is an associate professor and a PhD candidate supervisor at University of Cantabria, Spain. He received his PhD degree from University of Cantabria, Spain in 2010. His research interests include rotordynamics and machinery condition monitoring.
DE-JUAN Ana Magdalena is an assistant professor at University of Cantabria, Spain. She received her PhD degree from University of Cantabria, Spain in 2011. Her research interests fall in the kinematics synthesis and multibody modeling.
GARCIA Pablo is currently an associate professor at Mechanical Engineering Research Group, University of Cantabria, Spain. His main research activities include kinematics synthesis, machine dynamics and NVH assessment.
DIEZ Alberto is an engineer and an assistant lecturer at University of Cantabria, Spain, and is a PhD candidate in the field of gear efficiency modeling. He received his master degree on industrial engineering in 2011.
VIADERO Fernando is a full professor and the head at the Mechanical Engineering Research Group, University of Cantabria, Spain. He received his PhD degree from Faculty of Engineering of Bilbao, Spain, in 1984. His research interests include dynamics of gear transmissions, analysis and synthesis of mechanisms, and vehicle suspension design.
Rights and permissions
About this article
Cite this article
Iglesias, M., Fernández Del Rincón, A., De-Juan, A.M. et al. Planetary gear profile modification design based on load sharing modelling. Chin. J. Mech. Eng. 28, 810–820 (2015). https://doi.org/10.3901/CJME.2015.0307.025
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3901/CJME.2015.0307.025