0
Research Papers: Design of Direct Contact Systems

A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors

[+] Author and Article Information
N. Leque

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: nicholas.leque@pw.utc.com

A. Kahraman

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 17, 2015; final manuscript received December 15, 2016; published online January 16, 2017. Assoc. Editor: Qi Fan.

J. Mech. Des 139(3), 033302 (Jan 16, 2017) (11 pages) Paper No: MD-15-1830; doi: 10.1115/1.4035554 History: Received December 17, 2015; Revised December 15, 2016

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional (3D) formulation of N planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all the three types of manufacturing errors, namely, constant errors such as carrier pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation, and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Hayashi, T. , Li, Y. , Hayashi, I. , Endou, K. , and Watanabe, W. , 1986, “ Measurement and Some Discussions on Dynamic Load Sharing in Planetary Gears,” Bull. JSME, 29(253), pp. 2290–2297. [CrossRef]
Kahraman, A. , 1999, “ Static Load Sharing Characteristics of Transmission Planetary Gear Sets: Model and Experiment,” SAE Paper No. 1999-01-1050.
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]
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]
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]
Hidaka, T. , and Terauchi, Y. , 1976, “ Dynamic Behavior of Planetary Gear-1st Report, Load Distribution in Planetary Gear,” Bull. JSME, 19(132), pp. 690–698. [CrossRef]
Hidaka, T. , Terauchi, Y. , and Dohi, K. , 1979, “ On the Relation Between the Run-Out Errors and the Motion of the Center of Sun Gear in a Stoeckicht Planetary Gear,” Bull. JSME, 22(167), pp. 748–754. [CrossRef]
Hidaka, T. , Terauchi, Y. , and Nagamura, K. , 1979, “ Dynamic Behavior of Planetary Gear: 7th Report, Influence of the Thickness of Ring Gear,” Bull. JSME, 22(170), pp. 1142–1149. [CrossRef]
Seager, D. L. , 1970, “ Load Sharing Among Planet Gears,” SAE Paper No. 700178.
Ma, P. , and Botman, M. , 1985, “ Load Sharing in a Planetary Gear Stage in the Presence of Gear Errors and Misalignments,” J. Mech. Transm. Autom. Des., 107(1), pp. 4–10. [CrossRef]
Kahraman, A. , 1994, “ Load Sharing Characteristics of Planetary Transmissions,” Mech. Mach. Theory, 29(8), pp. 1151–1165. [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]
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. , 2011, “ Epicyclic Load Sharing Map: Development and Validation,” Mech. Mach. Theory, 46(5), pp. 632–646. [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]
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]
OSU GearLab, 2014, “  Windows-LDP, Load Distribution Program,” The Gear and Power Transmission Research Laboratory, The Ohio State University, Columbus, OH.
Kahraman, A. , 1994, “ Dynamic Analysis of a Multi-Mesh Helical Gear Train,” ASME J. Mech. Des., 116(3), pp. 706–712. [CrossRef]
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 Upon Tyne, UK, 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]
Sondkar, P. , and Kahraman, A. , 2013, “ A Dynamic Model of a Double-Helical Planetary Gear Set,” Mech. Mach. Theory, 70, pp. 157–174. [CrossRef]
Visual Numerics, 2006, “ IMSL Fortran Numerical Library,” Visual Numerics, Inc., Houston, TX, pp. 176–180.
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]
Inalpolat, M. , and Kahraman, A. , 2009, “ A Theoretical and Experimental Investigation of Modulation Sidebands of Planetary Gear Sets,” J. Sound Vib., 323(3–5), pp. 677–696. [CrossRef]
Inalpolat, M. , and Kahraman, A. , 2010, “ A Dynamic Model to Predict Modulation Sidebands of a Planetary Gear Set Having Manufacturing Errors,” J. Sound Vib., 329(4), pp. 371–393. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) A sun-planet pi pair, (b) a ring-planet pi pair (a left-handed planet gear is shown (β>0)), and (c) a carrier-planet pi pair

Grahic Jump Location
Fig. 2

Eccentricity errors for each gear and the carrier (adapted from Ref. [11])

Grahic Jump Location
Fig. 3

Comparison of the predicted load sharing factors Li to the experiments of Ligata et al. [3] for a range of sun torques Ts with carrier pin hole error: (a) ec1=35 μm and (b) ec1=70 μm

Grahic Jump Location
Fig. 4

Variation of Li of (a) in-phase, (b) sequentially phased, (c) counter-phased helical planetary gear sets, (d) in-phase, (e) sequentially phased, and (f) counter-phased spur equivalents of the same gear sets

Grahic Jump Location
Fig. 5

(a) Variation of Li with Ts for configurations A–D in Table 2 for ec1=50 μm and (b) variation of (Li)max with ec1 at Ts=200 N⋅m for the same configurations

Grahic Jump Location
Fig. 6

(a) Variation of Li with Ts for configurations E–F in Table 2 for et1=50 μm and (b) variation of (Li)max with et1 at Ts=200 N⋅m for the same configurations

Grahic Jump Location
Fig. 7

Variation of Li with rotation of planets with respect to carrier for (a) configuration H, (b) configuration I, and (c) configuration J, all at Ts=200 N⋅m

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