0
Research Papers: Design of Direct Contact Systems

A Load Distribution Model for Planetary Gear Sets

[+] Author and Article Information
Y. Hu, A. Kahraman

Gear and Power Transmission
Research Laboratory,
The Ohio State University,
Columbus, OH 43210

D. Talbot

Gear and Power Transmission
Research Laboratory,
The Ohio State University,
Columbus, OH 43210
e-mail: talbot.11@osu.edu

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 31, 2017; final manuscript received January 17, 2018; published online March 9, 2018. Assoc. Editor: Mohsen Kolivand.

J. Mech. Des 140(5), 053302 (Mar 09, 2018) (14 pages) Paper No: MD-17-1597; doi: 10.1115/1.4039337 History: Received August 31, 2017; Revised January 17, 2018

A load distribution model of planetary gear sets presented is capable of simulating planetary gear sets having component- and system-level design variations such as component supporting conditions, different kinds of gear modifications and planetary gear sets with different numbers of equally or unequally spaced planets as well as different gear set kinematic configurations while considering gear mesh phasing. It also accounts for classes of planetary gear set manufacturing and assembly related errors associated with the carrier or gears, i.e., pinhole position errors, run-out errors, and tooth thickness errors. Example analyses are provided to indicate the need for a model of this type when studying load distribution of planetary gear sets due to unique loading of the gear meshes associated with planetary gear sets. Comparisons to measurements existing in the literature are provided.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Vijayakar, S. , 1991, “A Combined Surface Integral and Finite Element Solution for a Three-Dimensional Contact Problem,” Int. J. Num. Method Eng., 31(3), pp. 525–545. [CrossRef]
Kahraman, A. , and Vijayakar, S. , 2001, “Effect of Internal Gear Flexibility on the Quasi-Static Behavior of a Planetary Gear Set,” ASME J. Mech. Des., 123(3), pp. 408–415. [CrossRef]
Bodas, A. , and Kahraman, A. , 2004, “Influence of Carrier and Gear Manufacturing Errors on the Static Load Sharing Behavior of Planetary Gear Sets,” JSME Int. J., Ser. C, 47(3), pp. 908–915. [CrossRef]
Kwon, H. S. , Kahraman, A. , Lee, H. K. , and Suh, H. S. , 2014, “An Automated Design Search for Single and Double-Planet Planetary Gear Sets,” ASME J. Mech. Des., 136(6), p. 061004. [CrossRef]
Colbourne, J. R. , 1981, “The Design of Undercut Involute Gears,” ASME Paper No. 80-C2/DET-67.
Colbourne, J. R. , 1987, “The Geometric Design of Internal Gear Pairs,” ASME Paper No. 87FTM2.
Polder, J. W. , 1984, “Interference and Other Limiting Conditions of Internal Gears,” ASME Paper No. 84-DET-180.
Talbot, D. , Li, S. , and Kahraman, A. , 2013, “Prediction of Mechanical Power Loss of Planet Gear Roller Bearings Under Combined Radial and Moment Loading,” ASME J. Mech. Des., 135(12), p. 121007. [CrossRef]
Talbot, D. C. , Kahraman, A. , Stilwell, A. W. , Singh, A. , and Napau, I. , 2015, “Power Losses of Full-Complement Needle Bearings of Planetary Gear Sets: Model and Experiments,” Proc. Inst. Mech. Eng. Part C, 230(5), pp. 839–855.
Lim, T. C. , and Singh, R. , 1990, “Vibration Transmission Through Rolling Element Bearings—Part I: Bearing Stiffness Formulation,” J. Sound Vib., 139(2), pp. 179–199. [CrossRef]
Harris, T. A. , and Kotzalas, M. N. , 2007, Rolling Bearing Analysis, 5th ed., CRC Press, Boca Raton, FL.
Ligata, H. , Kahraman, A. , and Singh, A. , 2008, “An Experimental Study of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing,” ASME J. Mech. Des., 130(4), p. 041701. [CrossRef]
Ligata, H. , Kahraman, A. , and Singh, A. , 2009, “Closed-Form Planet Load Sharing Formulae for Planetary Gear Sets Using Translational Analogy,” ASME J. Mech. Des., 131(2), p. 021007. [CrossRef]
Singh, A. , 2005, “Application of a System Level Model to Study the Planetary Load Sharing Behavior,” ASME J. Mech. Des., 127(3), pp. 469–476. [CrossRef]
Boguski, B. , Kahraman, A. , and Nishino, T. , 2012, “A New Method to Measure Planet Load Sharing and Sun Gear Radial Orbits of Planetary Gear Sets,” ASME J. Mech. Des., 134(7), p. 071002. [CrossRef]
Leque, N. , and Kahraman, A. , 2017, “A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors,” ASME J. Mech. Des., 139(3), p. 033302. [CrossRef]
Windows-LDP, 2017, “Windows-LDP, Load Distribution Program,” Gear and Power Transmission Research Laboratory, The Ohio State University, Columbus, OH.
Kahraman, A. , Ligata, H. , Kienzle, K. , and Zini, D. , 2004, “A Kinematics and Power Flow Analysis Methodology for Automatic Transmission Planetary Gear Trains,” ASME J. Mech. Des., 126(6), pp. 1071–1081. [CrossRef]
Conry, T. F. , and Seireg, A. , 1971, “A Mathematical Programming Method for Design of Elastic Bodies in Contact,” ASME J. Appl. Mech., 38(2), pp. 387–392. [CrossRef]
Conry, T. F. , and Seireg, A. , 1973, “A Mathematical Programming Technique for the Evaluation of Load Distribution and Optimal Modifications for Gear Systems,” ASME J. Eng. Ind., 95(4), pp. 1115–1122. [CrossRef]
Singh, A. , Kahraman, A. , and Ligata, H. , 2008, “Internal Gear Strains and Load Sharing in Planetary Transmissions—Model and Experiments,” ASME J. Mech. Des., 130(7), p. 072602. [CrossRef]
Talbot, D. , Kahraman, A. , and Singh, A. , 2012, “An Experimental Investigation of the Efficiency of Planetary Gear Sets,” ASME J. Mech. Des., 134(2), p. 021003. [CrossRef]
Talbot, D. , and Kahraman, A. , 2014, “A Methodology to Predict Power Losses of Planetary Gear Sets,” International Gear Conference, Lyon-Villeurbanne, France, Aug. 26–28, pp. 625–635.
Kahraman, A. , 1994, “Planetary Gear Train Dynamics,” ASME J. Mech. Des., 116(3), pp. 713–720. [CrossRef]
Kahraman, A. , and Blankenship, G. W. , 1994, “Planet Mesh Phasing in Epicyclic Gear Sets,” International Gearing Conference, Newcastle, WA, Sept. 7–9, pp. 99–104.
Parker, R. G. , and Lin, J. , 2004, “Mesh Phasing Relationships in Planetary and Epicyclic Gears,” ASME J. Mech. Des., 126(2), pp. 365–374. [CrossRef]
Yau, E. , Busby, H. R. , and Houser, D. R. , 1994, “A Rayleigh-Ritz Approach to Modeling Bending and Shear Deflections of Gear Teeth,” Comput. Struct., 50(5), pp. 705–713. [CrossRef]
Stegemiller, M. E. , and Houser, D. R. , 1993, “A Three-Dimensional Analysis of the Base Flexibility of Gear Teeth,” ASME J. Mech. Des., 115(1), pp. 186–192. [CrossRef]
Cornell, R. W. , 1981, “Compliance and Stress Sensitivity of Spur Gear Teeth,” ASME J. Mech. Des., 103(2), pp. 447–459. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic representations of (a) a sun-planet mesh and (b) a ring-planet mesh for phasing formulations

Grahic Jump Location
Fig. 2

Schematic representation of sun gear coordinate system and six possible rigid body motions as well as the contact normal vector of a point j on gear tooth

Grahic Jump Location
Fig. 5

Influence of gear face width and planet bearing tilting stiffness kθxθx=kθyθy=kθθ on maximum tilting motion of planet 2, θxp2, under Ts=200 Nm

Grahic Jump Location
Fig. 3

A carrier-planet i pair

Grahic Jump Location
Fig. 4

Schematic representations of (a) a carrier pinhole position error and (b) gear and carrier runout errors

Grahic Jump Location
Fig. 8

Contact stress distribution for varying load and planet gear modification

Grahic Jump Location
Fig. 9

Measured [12] and predicted load sharing of four-planet gear set with (a) Ts=600 Nm, (b) Ts=800 Nm, and (c) Ts=1000 Nm

Grahic Jump Location
Fig. 10

Measured [12] and predicted load sharing of five-planet gear set with Ts=800 Nm

Grahic Jump Location
Fig. 11

Measured [12] and predicted load sharing of six-planet gear set with Ts=800 Nm

Grahic Jump Location
Fig. 12

((a1)–(c1)) Measured [15] and ((a2)–(c2)) predicted sun gear orbit of in-phased ((a1) and (a2)), sequentially phased ((b1) and (b2)) and CP ((c1) and (c2)) gear set

Grahic Jump Location
Fig. 6

Load distribution of a SP planetary gear set with 40 mm face width and planet bearing tilting stiffness of 6(10)4 N·m/rad under Ts=200 Nm

Grahic Jump Location
Fig. 7

Load sharing factor for varying load and planet gear modification

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In