Abstract
A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet’s eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear’s supporting stiffness, planet’s bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.
Similar content being viewed by others
References
SEAGER D L. Load sharing among planet gears [C]// SAE Paper. 1970, No.700178.
FANG Zong-de, SHEN Yun-wen, HUANG Zhen-dong. Analysis of dynamic behavior of 2K-H planetary gearing [J]. Journal of Northwestern Polytechnical University, 1990, 8(4): 361–371. (in Chinese)
XIAO Tie-ying, YUAN Sheng-zhi, LU Wei-jie. Calculative method of load balance coefficient in planetary gear [J]. Journal of Northeast Heavy Machinery Institute, 1992, 16(4): 290–295. (in Chinese)
KAHRAMAN A. Load sharing characteristics of planetary transmission [J]. Mech Mach Theory, 1994, 29: 1151–1165.
KAHRAMAN A. Static load sharing characteristics of transmission planetary gear sets: Model and experiment [J]. SAE Trans, 1999, 108(6): 1954–1963.
YUAN Ru, WANG San-min, SHEN Yun-wen. Dynamic optimum design of power shared out equally among the planetary gears [J]. Journal of Aerospace Power, 2000, 15(4): 410–412. (in Chinese)
BODAS A, KAHRAMAN A. Influence of carrier and gear manufacturing errors on the static planet load sharing behavior of planetary gear sets [J]. JSME Int J Ser C, 2004, 47(3): 908–915.
SINGH A, KAHRAMAN A, LIGATA H. Internal gear strains and load sharing in planeteary transmissions: Model and experiments [C]// Proceedings of ASME. Las Vegas, USA: American Society of Mechanical Engineers, 2007: 917–928.
LIGATA H, KAHRAMAN A, SING A. An experimental study of the influence of manufacturing errors on planetary gear stresses and planet load sharing [J]. ASME J Mech Des, 2008, 130: 041701.
LIGATA H, KAHRAMAN A, SINGH A. A closed-form planet load sharing formulation for planetary gear sets using a translational analogy [J]. ASME J Mech Des, 2009, 131: 021007.
SINGH A. Load sharing behavior in epicyclic gears: Physical explanation and generalized formulation [J]. Mech Mach Theory, 2010, 45: 511–530.
LU Jun-hua, ZHU Ru-peng, JIN Guang-hu. Analysis of dynamic load sharing behavior in planetary gearing [J]. Journal of Mechanical Engineering, 2009, 45(5): 85–90. (in Chinese)
GU X, VELEX P. A lumped parameter model to analyze the dynamic load sharing in planetary gears with planet errors [J]. Appl Mech Mater, 2011, 86: 374–379.
MONTESTRUC A N. Influence of planet pin stiffness on load sharing in planetary gear trains [J]. ASME J Mech Des, 2011, 133: 014501.
YE Fu-min, ZHU Ru-peng, BAO He-yun. Static load sharing behavior in NGW planetary gear train with unequal modulus and pressure angles [J]. Journal of Central South University: Science and Technology, 2011, 42(7): 1960–1966. (in Chinese)
LI Tong-jie, ZHU Ru-peng, BAO He-yun. Study on dynamic load sharing behavior of two-stage planetary gear train based on a nonlinear vibration model [J]. Applied Mechanics and Materials, 2011, 86: 611–614.
BOGUSKI B, KAHRAMAN A, NISHINO T A. New method to measure planet load sharing and sun gear radial orbit of planetary gear sets [J]. ASME J Mech Des, 2012, 134: 071002.
HICKS R J. Load equalizing means for planetary pinions: US Patent 3303713 [P]. 1967.
FOX G P, JALLAT E. Epicyclic gear system: US Patent 6994651 [P]. 2006.
FOX G P, JALLAT E. Use of the integrated flexpin bearing for improvement of the performance of epicyclical gear systems [C]// 9th International Power Transmission and Gearing Conference. Chicago, Illinois, USA, 2003: 1003–1011.
MONTESTRUC A N. A numerical approach to calculation of load sharing in planetary gear drives [J]. ASME J Mech Des, 2010, 132: 014503.
HOUSER D R. Gear noise state of the art [J]. Proceedings of Inter-Noise, 1988, 88: 601–606.
KAHRAMAN A, SINGH A. Non-linear dynamics of a spur gear pair [J]. Journal of Sound and Vibration, 2009, 142(1): 49–75.
SUN Zhi-min, SHEN Yun-wen, LI Su-you. Study on dynamic behavior of encased differential gear train [J]. Chinse Journal of Mechanical Engineering, 2002, 38(2): 44–48. (in Chinese)
BAO He-yun, ZHU Ru-peng. Floating displacement static analysis of basic floating part of 2-stages star gear train [J]. Journal of Central South University: Science and Technology, 2006, 37(3): 553–557. (in Chinese)
LU Jun-hua, ZHU Ru-peng, JIN Guang-hu. Basic components’ offset analysis of planetary gearing in need of loading sharing [J]. Journal of Central South University: Science and Technology, 2008, 39(1): 143–148. (in Chinese)
KASUBA R, EVANS J W. An extended model for determing dynamic loads in spur gearing [J]. ASME Mech Des, 1981, 103(2): 398–409.
WANG K L, CHENG H S. A numerical solution to the dynamic load [J]. ASME Mech Des, 1981, 103(1): 177–187.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Projects(NZ2013303, NZ2014201) supported by the National Natural Science Foundation of China; Projects(51375226, 51305196, 51475226) supported by the Fundamental Research Funds for the Central Universities, China
Rights and permissions
About this article
Cite this article
Sheng, Dp., Zhu, Rp., Jin, Gh. et al. Dynamic load sharing characteristics and sun gear radial orbits of double-row planetary gear train. J. Cent. South Univ. 22, 3806–3816 (2015). https://doi.org/10.1007/s11771-015-2925-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-015-2925-8