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Research Papers: Design of Direct Contact Systems

Analytical Investigations on the Mesh Stiffness Function of Solid Spur and Helical Gears

[+] Author and Article Information
X. Gu

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

P. Velex

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

P. Sainsot

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

J. Bruyère

Université de Lyon,
INSA Lyon, LaMCoS, UMR CNRS 5259,
Bâtiment Jean d'Alembert,
20 Avenue Albert Einstein,
Villeurbanne Cédex 69621, France
e-mail: Jerome.Bruyere@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 December 1, 2014; final manuscript received March 5, 2015; published online April 16, 2015. Assoc. Editor: Qi Fan.

J. Mech. Des 137(6), 063301 (Jun 01, 2015) (7 pages) Paper No: MD-14-1762; doi: 10.1115/1.4030272 History: Received December 01, 2014; Revised March 05, 2015; Online April 16, 2015

Approximate formulae are presented which give the time-varying mesh stiffness function for ideal solid spur and helical gears. The corresponding results compare very well with those obtained by using two-dimensional (2D) finite element (FE) models and specific benchmark software codes thus validating the proposed analytical approach. More deviations are reported on average mesh stiffness which, to a large extent, are due to the modeling of gear body deflections.

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References

Figures

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Fig. 1

Point of reference M00 on the base plane

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Fig. 2

FE models: (a) FE model for a complete pinion, (b) FE mesh for a five-tooth sector, and (c) loaded profile (detail)

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Fig. 3

Mesh stiffness functions–comparisons between FE results and (10): (a) 25/25 pinion-gear (full FE model), (b) 25/25 pinion-gear (five-tooth sector), and (c) 25/83 pinion-gear (five-tooth sector)

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Fig. 4

Comparisons between Eqs. (9) and (10), the numerical integration of Weber and Banaschek's formulae (referred to as VSA) and the results from LDP. Spur gear example (25/33).

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Fig. 5

Comparisons between Eqs. (9) and (10), the numerical integration of Weber and Banaschek's formulae (referred to as VSA) and the results from LDP. Helical gear example (26/141).

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Fig. 6

Contour plots of the RMS of k∧(τ) (using Eq. (10)) for various profile (ɛα) and transverse (ɛβ) contact ratios

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Fig. 7

Contour plots of the RMS of k∧(τ) using Eq. (10) for the first four mesh harmonics versus profile and transverse contact ratios

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