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Research Papers

Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method

[+] Author and Article Information
J. Bruyère

e-mail: Jerome.bruyere@insa-lyon.fr

P. Velex

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

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received February 19, 2013; final manuscript received April 17, 2013; published online xx xx, xxxx. Assoc. Editor: Qi Fan.

J. Mech. Des 135(7), 071009 (May 24, 2013) (8 pages) Paper No: MD-13-1090; doi: 10.1115/1.4024374 History: Received February 19, 2013; Revised April 17, 2013

A perturbation method is presented which makes it possible to obtain approximate closed-form expressions for profile relief that minimize the fluctuations of quasi-static transmission errors under load. A number of results are displayed which prove the theoretical effectiveness of the proposed solutions for low-contact ratio (LCR) and high-contact ratio (HCR) spur and helical gears. It is also shown that the corresponding relief performance is not significantly downgraded by center-distance (CD) variations. Finally, a number of practical considerations are brought up and commented.

Copyright © 2013 by ASME
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References

Figures

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Fig. 2

Shape function ϕM00(τ) associated with contact point M00 as defined in Fig. 6

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Fig. 3

Profile modification function Λ00 (τ) associated with contact point M00 as defined in Fig. 6

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Fig. 4

Optimum relief curve for LCR spur and helical gears

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Fig. 5

Optimum relief curves for HCR gears

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Fig. 6

Discretized contact lines—Base plane geometry at the initial time τ = 0

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Fig. 7

Modified profile relief

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Fig. 8

Three-dimensional gear model (72 DOFs)

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Fig. 9

RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve as defined in Fig. 4). Gear A in Table 2.

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Fig. 10

RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve labeled (a) as defined in Fig. 5). Gear B in Table 2.

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Fig. 11

RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve labeled (c) as defined in Fig. 5). Gear B in Table 2.

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Fig. 12

RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve labeled (b) as defined in Fig. 5). Gear B in Table 2.

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Fig. 13

RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve as defined in Fig. 4). Gear C in Table 2.

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Fig. 14

RMS of quasi-static transmission error versus the normalized extent of modification (variation along the optimal relief curve as defined in Fig. 4). Gear D in Table 2.

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Fig. 15

Optimum relief for (a) the nominal CD and (b) CD + 0.1 mm—Gear C in Table 2

Tables

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