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Research Papers: Design of Direct Contact Systems

A Mortar-Based Mesh Interface for Hybrid Finite-Element/Lumped-Parameter Gear Dynamic Models—Applications to Thin-Rimmed Geared Systems

[+] Author and Article Information
B. Guilbert

R&T Department,
Turbomeca,
25 Avenue Joseph Szydlowski,
Bordes 64510, France
e-mail: Berengere.Guilbert@insa-lyon.fr

P. Velex

Université de Lyon,
INSA de Lyon,
LaMCoS,
UMR CNRS 5259,
Bâtiment Jean d'Alembert,
20 Avenue Albert Einstein,
Villeurbanne Cedex 69621, France
e-mail: Philippe.Velex@insa-lyon.fr

D. Dureisseix

Université de Lyon,
INSA de Lyon,
LaMCoS,
UMR CNRS 5259,
Bâtiment Jean d'Alembert,
20 Avenue Albert Einstein,
Villeurbanne Cedex 69621, France
e-mail: David.Dureisseix@insa-lyon.fr

P. Cutuli

R&T Department,
Turbomeca,
25 Avenue Joseph Szydlowski,
Bordes 64510, France
e-mail: Philippe.Cutuli@turbomeca.fr

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 8, 2016; final manuscript received July 15, 2016; published online September 13, 2016. Assoc. Editor: Hai Xu.

J. Mech. Des 138(12), 123301 (Sep 13, 2016) (11 pages) Paper No: MD-16-1111; doi: 10.1115/1.4034220 History: Received February 08, 2016; Revised July 15, 2016

An original hybrid gear model is introduced, which combines lumped parameter and finite elements along with a specific interface aimed at coupling mismatched discrete models. A mortar-based interface is presented, which eliminates the numerical errors induced by direct collocations between the tooth contact and gear body models. It is shown that the proposed interface can capture the instant contact conditions in the profile and lead directions for both spur and helical gears. A number of quasi-static and dynamic simulation results are presented, which illustrate the potential and practical interest of the methodology. It is observed that thin rims are more influential in the case of helical gears and that the overall dynamic tooth loads seem largely uncoupled from the local contact conditions on the teeth.

Copyright © 2016 by ASME
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References

Figures

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Fig. 1

Gear element with rigid bodies

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Fig. 2

Base plane discretization (i: contact line number and j: tooth segment number for point Mij)

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Fig. 3

Master nodes chosen for the substructured wheel, with its shaft: (a) rim master nodes for meshing, (b) bearing 1 master nodes, and (c) bearing 2 master nodes

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Fig. 4

Scheme of (a) old model and (b) new model with substructured wheel

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Fig. 5

New gear element with rigid-body pinion and flexible 3D FE wheel model

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Fig. 6

Scheme of discretization used on line of contact element Γ

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Fig. 7

Patch test problem with discrete elements (DE) and finite elements (FE)

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Fig. 8

Displacement along the interface under uniform load for collocation and mortar interface

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Fig. 9

Projection of tooth point Nij on wheel mesh

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Fig. 15

Helical gear example (β = 15 deg) with the new mortar-based interface and three quadratic elements across the face width

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Fig. 16

Dynamic tooth load factor of the spur gear over a range of speed (rad/s)

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Fig. 17

Spur gear dynamic tooth loading at the major critical speed (620 rad/s) for (a) a rigid-body (initial) model and (b) a flexible substructured gear body

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Fig. 14

Spur gear example (β = 0 deg) with the new mortar-based interface and three quadratic elements across the face width

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Fig. 13

Quasi-static tooth load patterns obtained by using noncompatible discrete models. Keys: (a) one element across the face width and (b) three elements across the face width.

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Fig. 12

Load on the contact line with rigid-body gear for (a) the spur gear and (b) helical gear (β = 15 deg) examples as defined in Table 1

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Fig. 11

Thin-rimmed gear geometry (in mm): (a) dimensions and (b) FE mesh

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Fig. 10

Resolution algorithm

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Fig. 18

Spur gear dynamic tooth loading at the major critical speed (620 rad/s) for (a) a rigid-body (initial) model and (b) a flexible substructured gear body with a symmetric profile modification (depth of 13 μm, extent of 25% of active profile)

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Fig. 19

Dynamic load factor versus speed with symmetrical tooth tip relief

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Fig. 20

Dynamic tooth load factor for helical gear (β = 15 deg), comparison between rigid and flexible gear

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Fig. 21

Quasi-static load pattern, helical gear, and pinion lead crowning (40 μm)

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Fig. 22

Dynamic load factor versus speed, helical gear with and 40 μm crowning on pinion

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