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RESEARCH PAPERS

Modeling of Spur and Helical Gear Planetary Drives With Flexible Ring Gears and Planet Carriers

[+] Author and Article Information
V. Abousleiman, S. Becquerelle

 Hispano-Suiza, 18 Boulevard Louis Seguin, 92707 Colombes Cedex, France

P. Velex1

LaMCoS, INSA Lyon, Bâtiment Jean D’Alembert, 20 Avenue A. Einstein, 69 621 Villeurbanne, Francephilippe.velex@insa-lyon.fr

1

Corresponding author.

J. Mech. Des 129(1), 95-106 (Feb 22, 2006) (12 pages) doi:10.1115/1.2359468 History: Received April 29, 2005; Revised February 22, 2006

A model is presented which enables the simulation of the three-dimensional static and dynamic behavior of planetary/epicyclic spur and helical gears with deformable parts. The contributions of the deflections of the ring gear and the carrier are introduced via substructures derived from 3D finite element models. Based on a modal condensation technique, internal gear elements are defined by connecting the ring-gear substructure and a planet lumped parameter model via elastic foundations which account for tooth contacts. Discrete mesh stiffness and equivalent normal deviations are introduced along the contact lines, and their values are recalculated as the mating flank positions vary with time. A constraint mode substructuring technique is used to simulate the planet carrier as a superelement which is connected to the planet center. Planetary/epicyclic gear models are completed by assembling lumped parameter sun gear/planet elements along with shaft elements, lumped stiffness, masses and inertias. The corresponding equations of motion are solved by combining a time-step integration scheme and a contact algorithm for all simultaneous meshes. Several quasistatic and dynamic results are given which illustrate the potential of the proposed hybrid model and the interest of taking into account ring gear and carrier deflections.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Example of FE model and geometry of planet carrier

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Figure 2

Pin axle-planet bore connection

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Figure 3

Planet bearing element

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Figure 4

Geometrical parameter for internal gear modeling

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Figure 5

Examples of ring-gear FE models

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Figure 6

Connection between teeth and ring-gear substructure: (a) thin-slice model of ring-gear teeth (The reference frame(Sc,Tc,Z)is fixed to the ring-gear) and (b) position of Mpi and ring-gear finite element grid

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Figure 7

Radial position error on planet j

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Figure 8

Static deformed shape of the planetary gear (helical gear example): (a) static deformed shape of the planetary gear (in the plane of symmetry, displacement magnification factor of 100) and (b) static deformed shape of the planetary gear (in the axial direction, displacement magnification factor of 200)

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Figure 9

Static deformed shape of the planet-carrier (helical gear example)

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Figure 10

Quasi-static tooth load distributions for various planet bearing stiffness (helical gear example—see Table 5 for stiffness variations): (a) case 1 and 2 and (b) case 3

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Figure 11

Dynamic tooth loads on external and internal meshes versus sun-gear speed—spur gear example: (a) sun-gear/planet meshes and (b) planet/ring-gear meshes

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Figure 12

Dynamic tooth loads on external and internal meshes versus sun-gear speed—helical gear example: (a) sun-gear/planet meshes and (b) planet/ring-gear meshes

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Figure 13

Dynamic tooth loads versus sun-gear speed—influence of the ring-gear rim thickness—spur gear example

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Figure 14

Dynamic tooth loads on planet/ring-gear meshes for ring-gear (B)

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Figure 15

Influence of the carrier flexibility on the dynamic tooth loads on external and internal meshes. Spur gear example: (a) sun-gear/planet meshes and (b) planet/ring-gear meshes.

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Figure 16

Influence of radial planet position errors on the quasi-static gear mesh stiffness variations: (a) sun-gear/planet meshes and (b) planet/ring-gear meshes

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Figure 17

Influence of radial planet position errors on the sun-gear trajectory at three different speeds

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Figure 18

Influence of centrifugal effects on the planet trajectory at three different speeds (key: vis the radial displacement, wis the tangential displacement)

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Figure 19

Influence of centrifugal effects on mesh stiffness functions (time is normalized with respect to the mesh period): (a) sun-gear/planet mesh stiffness functions and (b) planet/ring-gear mesh stiffness functions

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Figure 20

Influence of centrifugal terms on dynamic tooth loads (epicyclic train—spur gears)

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