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Research Papers: Design of Direct Contact Systems

Optimization of Profile Modifications With Regard to Dynamic Tooth Loads in Single and Double-Helical Planetary Gears With Flexible Ring-Gears

[+] Author and Article Information
M. Chapron

R&T Department,
Hispano-Suiza,
18 Boulevard Louis-Seguin,
Colombes Cédex 92707, France
e-mail: Matthieu.Chapron@insa-lyon.fr

P. Velex

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

J. Bruyère

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

S. Becquerelle

R&T Department,
Hispano-Suiza,
18 Boulevard Louis-Seguin,
Colombes Cédex 92707, France
e-mail: Samuel.Becquerelle@hispano-suiza-sa.com

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 13, 2015; final manuscript received October 16, 2015; published online November 19, 2015. Assoc. Editor: Hai Xu.

J. Mech. Des 138(2), 023301 (Nov 19, 2015) (11 pages) Paper No: MD-15-1489; doi: 10.1115/1.4031939 History: Received July 13, 2015; Revised October 16, 2015

This paper is mostly aimed at analyzing optimum profile modifications (PMs) in planetary gears (PGTs) with regard to dynamic mesh forces. To this end, a dynamic model is presented based on 3D two-node gear elements connected to deformable ring-gears discretized into beam elements. Double-helical gears are simulated as two gear elements of opposite hands which are linked by shaft elements. Symmetric tip relief on external and internal gear meshes are introduced as time-varying normal deviations along the lines of contact and time-varying mesh stiffness functions are deduced from Wrinckler foundation models. The equations of motion are solved by coupling a Newmark time-step integration scheme and a contact algorithm to account for possible partial or total contact losses. Symmetric linear PMs for helical and double-helical PGTs are optimized by using a genetic algorithm with the objective of minimizing dynamic tooth loads over a speed range. Finally, the sensitivity of these optimum PMs to speed and load is analyzed.

Copyright © 2016 by ASME
Topics: Gears , Stress , Optimization
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References

Figures

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Fig. 3

Potential contact points with respect to beam nodes

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Fig. 6

Influence of a flexible ring-gear on the dynamic factor of (a) external and (b) internal gear meshes—single helical PGT

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Fig. 7

Influence of a flexible ring-gear on the dynamic factor of (a) external and (b) internal gear meshes—double-helical PGT (results on left and right helices are identical)

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Fig. 2

External gear element definition

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Fig. 1

Internal gear element—planet/flexible ring-gear connection

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Fig. 4

Deformed (thin line) and undeformed (thick line) PGT, (a) and (b) in two perpendicular planes (amplification factor = 100, carrier not represented)

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Fig. 5

Deformed (thin line) and undeformed (thick line) double-helical PGT (a), (b) in two perpendicular planes and (c) zoom on the left helix (upper, amplification factor = 100, carrier not represented)

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Fig. 8

PM definition on planet teeth

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Fig. 10

Optimum PMs for a double-helical PGT set with a deformable ring-gear (● for a flexible ring-gear, thick line and line for the modified or not Master Curve)

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Fig. 9

Optimum PMs for a single helical PGT with and without flexible ring-gears (◆, ● for a rigid or flexible ring-gear, thick line and line for the modified or not Master Curve)

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Fig. 11

Influence of long, medium and short PMs on the dynamic factor of (a) external and (b) internal gear meshes

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Fig. 12

Influence of long, medium and short PMs on the dynamic factor of (a) external and (b) internal gear meshes (results for left and right helices are identical)

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Fig. 13

Influence of different optimum PM combinations (external/internal) on the dynamic factor of (a) external and (b) internal gear meshes

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Fig. 14

Influence of optimum PM combinations (external/internal) on the dynamic factor of (a) external and (b) internal gear meshes (results for left and right helices are identical)

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Fig. 15

Influence of torque on the mesh dynamic responses of external gear meshes with (a) long, (b) medium, and (c) short optimum reliefs (helical)

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Fig. 16

Influence of torque on the mesh dynamic responses of internal gear meshes with (a) long, (b) medium, and (c) short optimum reliefs (helical)

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Fig. 17

Influence of torque on the mesh dynamic responses of external gear meshes with (a) long, (b) medium, and (c) short optimum reliefs (double-helical)

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Fig. 18

Influence of torque on the mesh dynamic responses of internal gear meshes with (a) long, (b) medium, and (c) short optimum reliefs (double-helical)

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