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Research Papers

A Contribution to the Design of Robust Profile Modifications in Spur and Helical Gears by Combining Analytical Results and Numerical Simulations

[+] Author and Article Information
D. Ghribi

 Université de Lyon, INSA Lyon, LaMCoS, UMR CNRS 5259, Bâtiment Jean d’Alembert, 20 Avenue Albert Einstein, 69 621 Villeurbanne Cédex, Francedhafer.ghribi@insa-lyon.fr

J. Bruyère

 Université de Lyon, INSA Lyon, LaMCoS, UMR CNRS 5259, Bâtiment Jean d’Alembert, 20 Avenue Albert Einstein, 69 621 Villeurbanne Cédex, Francejerome.bruyere@insa-lyon.fr

Ph. Velex1

 Université de Lyon, INSA Lyon, LaMCoS, UMR CNRS 5259, Bâtiment Jean d’Alembert, 20 Avenue Albert Einstein, 69 621 Villeurbanne Cédex, Francephilippe.velex@insa-lyon.fr

M. Octrue

CETIM, Pôle d’Activités Mécatronique, Transmissions de Puissance et Capteurs (MEC), 60304 Senlis Cedex, FranceMichel.Octrue@cetim.fr

M. Haddar

 Université de Sfax, Ecole Nationale d’Ingénieurs de Sfax, U2MP. BP. W. 3038, Sfax, Tunisiamohamed.haddar@enis.rnu.tn

1

Corresponding author.

J. Mech. Des 134(6), 061011 (May 18, 2012) (9 pages) doi:10.1115/1.4006740 History: Received February 08, 2012; Revised March 23, 2012; Published May 17, 2012; Online May 18, 2012

This paper addresses the definition of robust profile modifications in spur and helical gears. An original methodology is introduced which relies on closed-form analytical results on transmission errors combined with a gradient descent algorithm and a Gauss quadrature (GQ) based full factorial method. The results compare very well with those delivered by using classic Monte Carlo simulations with a considerable gain in computational time. The influence of the probability distribution law for the design parameters (depth and extent of modification) is analyzed along with the contribution of gear quality grade and load variation. Some optimum robust linear relief is presented which minimizes transmission error fluctuations over a broad range of loads even in the presence of significant geometrical tolerances.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Profile relief definition

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Figure 2

Contour plots of RMS(TEs) in micrometer: Comparison between analytical and numerical results for a constant mesh stiffness per unit of contact length (ISO); (a) analytical formulation and (b) numerical model

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Figure 3

Variation of RMS(TEs) along segment AB

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Figure 4

Illustration of the concept of robustness

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Figure 5

Convergence assessment of Monte Carlo simulations

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Figure 6

Comparisons between MCS and GQ methods, blue: MCS (300 SP) red: GC (N = H2 , H = 4)

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Figure 7

Flowchart of the resolution procedure—numerical simulations

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Figure 8

Probable forms of variability: (a) normal distribution and (b) beta distributions

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Figure 9

areas of robust tooth profile modifications; Frob < 0.3 μm, Cm = 850 Nm, IT-E: Qp7, IT-Γ: 2.5%

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Figure 10

areas of robust tooth profile modifications; Frob < 0.3 μm, normal distribution, Cm = 850 Nm, TI-Γ: 2.5%

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Figure 11

areas of robust tooth profile modifications; Frob < 0.3 μm, normal distribution, Cm = 850 Nm, TI-E: Qp7

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Figure 12

areas of robust tooth profile modifications; Frob < 0.5 μm, normal distribution, TI-E: Qp7, TI-Γ: 2.5%

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