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Research Papers: Design of Mechanisms and Robotic Systems

An Alternative Approach to the Definition of Profile Modifications in High-Contact-Ratio Spur Gears

[+] Author and Article Information
Ph. Velex

Université de Lyon,
INSA Lyon,
LaMCoS, UMR CNRS 5259,
Bâtiment Jean d'Alembert,
20 Avenue Albert Einstein,
Villeurbanne Cédex 69 621, France
e-mail: philippe.velex@insa-lyon.fr

J. Bruyère

Université de Lyon,
INSA Lyon,
LaMCoS, UMR CNRS 5259,
Bâtiment Jean d'Alembert,
20 Avenue Albert Einstein,
Villeurbanne Cédex 69 621, France
e-mail: jerome.bruyere@insa-lyon.fr

X. Gu

Université de Lyon,
INSA Lyon,
LaMCoS, UMR CNRS 5259,
Bâtiment Jean d'Alembert,
20 Avenue Albert Einstein,
Villeurbanne Cédex 69 621, France
e-mail: Xiaoyu.Gu@insa-lyon.fr

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 13, 2014; final manuscript received December 1, 2014; published online January 15, 2015. Assoc. Editor: Qi Fan.

J. Mech. Des 137(3), 032602 (Mar 01, 2015) (9 pages) Paper No: MD-14-1352; doi: 10.1115/1.4029321 History: Received June 13, 2014; Revised December 01, 2014; Online January 15, 2015

An alternative formulation for the definition of profile modifications in high-contact-ratio (HCR) spur gears is presented which makes it possible to select optimum relief with regard to transmission error (TE) fluctuations over a range of loads. General guidelines are presented which can help design optimum relief with minimum effort. It is also confirmed that two-slope profile relief can improve the dynamic behavior of HCR spur gears.

Copyright © 2015 by ASME
Topics: Torque , Stress , Design , Spur gears
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References

Figures

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Fig. 1

The three families of optimum relief for HCR gears (labeled (a), (b), and (c)) and the limit of interference at engagement (λ = 0)

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Fig. 2

Comparisons between the LDP results for TE and the analytical master curves (gear geometry in Table2)

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Fig. 3

Contact length reduction factor λ versus the dimensionless depth of modification χ and extent of modification Γ (symmetric linear relief) for HCR spur gears

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Fig. 4

Measured [7] and predicted quasi-static TEs at different loads for HCR spur gears (short relief)

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Fig. 5

Double slope relief by combining a short and long relief (with contact length reduction)

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Fig. 6

Measured [8] and predicted quasi-static TEs at different loads for a double slope relief (HCR spur gear)

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Fig. 7

Position of the secondary optimum torque

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Fig. 8

RMS of TE versus load—constant mesh stiffness per unit contact length

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Fig. 9

RMS of TE versus load—Weber and Banaschek's mesh stiffness model

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Fig. 10

RMS of dimensionless TE versus load—comparisons between Eq. (17) and the exact calculations based on numerical and analytical results (α=0.2)

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Fig. 11

Characteristic points and slopes for the curves representing the variations of the RMS of TE versus load

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Fig. 12

Sensitivity of the RMS of TE over a torque range (parameter ∇(α) in Eq. (23)) for various values of α and several profile contact ratios ɛα

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Fig. 13

Example of dimensionless maximum mesh force versus torque curves for various values of α

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Fig. 14

MAAG diagram for two slope tooth profile modifications

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Fig. 15

Emax versus dimensionless time

Tables

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