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RESEARCH PAPERS

A Static and Dynamic Model of Geared Transmissions by Combining Substructures and Elastic Foundations—Applications to Thin-Rimmed Gears

[+] Author and Article Information
M. N. Bettaïeb, M. Ajmi

Laboratoire de Mécanique des Contacts et des Solides, UMR CNRS 5514, INSA de Lyon, Bâtiment Jean d’Alembert, 20 Avenue Albert Einstein, 69 621 Villeurbanne Cédex, France

P. Velex1

Laboratoire de Mécanique des Contacts et des Solides, UMR CNRS 5514, INSA de Lyon, Bâtiment Jean d’Alembert, 20 Avenue Albert Einstein, 69 621 Villeurbanne Cédex, Francephilippe.velex@insa-lyon.fr

1

Corresponding author.

J. Mech. Des 129(2), 184-194 (Feb 06, 2006) (11 pages) doi:10.1115/1.2406088 History: Received November 07, 2005; Revised February 06, 2006

The present work is aimed at predicting the static and dynamic behavior of geared transmissions comprising flexible components. The proposed model adopts a hybrid approach, combining classical beam elements, elastic foundations for the simulation of tooth contacts, and substructures derived from three-dimensional (3D) finite element grids for thin-rimmed gears and their supporting shafts. The pinion shaft and body are modeled via beam elements which simulate bending, torsion and traction. Tooth contact deflections are described using time-varying elastic foundations (Pasternak foundations) connected by independent contact stiffness. In order to account for thin-rimmed gears, a 3D finite element model of the gear (excluding teeth) is set up and a pseudo-modal reduction technique is used prior to solving the equations of motion. Depending on the gear structure, the results reveal a potentially significant influence of thin rims on both quasi-static and dynamic tooth loading.

FIGURES IN THIS ARTICLE
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Copyright © 2007 by American Society of Mechanical Engineers
Topics: Gears
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References

Figures

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Figure 1

Elastic foundation model for a pair of mating teeth

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Figure 2

Thin slice modeling of the teeth

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Figure 3

Geometrical parameters for pinion-gear meshes

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Figure 4

Hybrid model—schematic representation (for clarity, damping is not shown and only one tooth pair model is represented)

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Figure 5

Gear geometry (10) (tooth number on pinion/on gear is 50∕50, module is 4mm, pressure angle of 20deg, torque on pinion of 294Nm)

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Figure 8

Quasi-static tooth load distributions—spur gear examples: (a) solid gear 100mm; (b) thin-rimmed gear 100mm; (c) solid gear 200mm; and (d) thin-rimmed gear 200mm.

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Figure 9

Quasi-static tooth load distributions—helical gear examples (β=30deg): (a) solid gear 100mm; (b) thin rimmed gear 100mm; (c) solid gear 200mm; and (d) thin-rimmed gear 200mm

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Figure 12

Dynamic tooth load factor versus pinion speed—solid and thin-rimmed spur gears (face width of 200mm)

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Figure 13

Dynamic tooth load factor versus pinion speed—solid and thin-rimmed helical gears (face width of 100mm)

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Figure 6

Dynamic tooth load factor versus pinion speed—comparisons between the hybrid model and a lumped parameter model for the solid spur gear defined in Fig. 5.

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Figure 7

Gear geometry (output member)

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Figure 10

Spectra of quasi-static transmission errors: (a) face width of 100mm; and (b) face width of 200mm

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Figure 11

Dynamic tooth load factor versus pinion speed—solid and thin-rimmed spur gears (face width of 100mm)

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Figure 14

Dynamic tooth load factor versus pinion speed—solid and thin-rimmed helical gears (face width of 200mm)

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