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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

Anderson, N. E., and Loewenthal, S. H., 1986, “Efficiency of Nonstandard and High Contact Ratio Involute Spur Gears,” ASME J. Mech. Des., 108(1), pp. 119–126. [CrossRef]
Lee, C., Oswald, F. B., Townsend, D. P., and Lin, H. L., 1991, “Influence of Linear Profile Modification and Loading Conditions on the Dynamic Tooth Load and Stress of High-Contact-Ratio Spur Gears,” ASME J. Mech. Des., 113(4), pp. 473–480. [CrossRef]
Rosen, M. K., and Frint, H. K., 1982, “Design of High-Contact-Ratio Gears,” J. Am. Helicopter Soc., 27(4), pp. 65–73. [CrossRef]
Elkholy, A. H., 1985, “Tooth Load Sharing in High-Contact-Ratio Spur Gears,” ASME J. Mech. Des., 107(1), pp. 11–16.
Wang, J., and Howard, I., 2005, “Finite Element Analysis of High-Contact-Ratio Spur Gears in Mesh,” ASME J. Tribol., 127(3), pp. 469–483. [CrossRef]
Lin, H. L., Oswald, F. B., Townsend, D. P., and Lee, C., 1993, “Computer Aided Design of High-Contact-Ratio Gears for Minimum Dynamic Load and Stress,” ASME J. Mech. Des., 115(1), pp. 171–178. [CrossRef]
Yildirim, N., and Munro, R. G., 1999, “A Systematic Approach to Profile Relief Design of Low and High Contact Ratio Spur Gears,” Proc. Inst. Mech. Eng., Part C, 213(6), pp. 551–562. [CrossRef]
Yildirim, N., and Munro, R. G., 1999, “A New Type of Profile Relief for High Contact Ratio Spur Gears,” Proc. Inst. Mech. Eng., Part C, 213(6), pp. 563–568. [CrossRef]
Tsai, M. H., and Tsai, Y. C., 1998, “Design of High-Contact-Ratio Spur Gears Using Quadratic Parametric Tooth Profiles,” Mech. Mach. Theory, 33(5), pp. 551–564. [CrossRef]
Ajmi, M., and Velex, P., 2002, “Multi-Criterion Design of Tooth Modifications on High-Contact-Ratio Spur Gears,” Proceedings of the International Conference on Gear, VDI, Münich, Germany, Vol. 2, pp. 737–749.
Niemann, G., and Baethge, J., 1970, “Drehwegfehler, Zahnfederhärte und Geräusch bei Stirnrädern (Mesh Errors, Tooth Flexibility and Noise in Spur Gears),” VDI-Z, 112, pp. 205–276 and pp. 495–499.
Yildirim, N., 1994, “Theoretical and Experimental Research in High Contact Ratio Spur Gearing,” Ph.D. thesis, University of Huddersfield, Yorkshire, UK.
Yildirim, N., Gasparini, G., and Sartori, S., 2008, “An Improvement on Helicopter Transmission Performance Through Use of High Contact Ratio Spur Gears With Suitable Profile Modification Design,” Proc. Inst. Mech. Eng., Part G, 222(8), pp. 1193–1210. [CrossRef]
Velex, P., Bruyère, J., and Houser, D. R., 2011, “Some Analytical Results on Transmission Errors in Narrow-Faced Spur and Helical Gears—Influence of Profile Modifications,” ASME J. Mech. Des., 133(3), p. 031010. [CrossRef]
Bruyère, J., and Velex, P., 2013, “Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method,” ASME J. Mech. Des., 135(7), p. 071009. [CrossRef]
Velex, P., and Maatar, M., 1996, “A Mathematical Model for Analyzing the Influence of Shape Deviations and Mounting Errors on Gear Dynamics,” J. Sound Vib., 191(5), pp. 629–660. [CrossRef]
Houser, D. R., Harianto, J., Iyer, N., Josephson, J., and Chandrasekaren, B., 2000, “A Multi-Variable Approach to Determining the ‘Best’ Gear Design,” Proceedings of the 8th ASME International Power Transmission and Gearing Conference, Sept. 10–13, Baltimore, Paper No. DETC2000/PTG-111.
Bruyère, J., and Velex, P., 2014, “A Simplified Multi-Objective Analysis of Optimum Profile Modifications in Spur and Helical Gears,” Mech. Mach. Theory, 80(1), pp. 70–93. [CrossRef]
Weber, C., and Banaschek, K., 1953, Formänderung und Profilrücknahme bei Gerad-und Schrägverzahnten Antriebstechnik (Shape Modifications and Profile Relief in Spur and Helical Gears), Vol. 11, Vieweg, Braunschweig, Germany. [PubMed] [PubMed]
Lundberg, G., 1939, “Elastische Berührung zweier Halbraüme (Contact Between Two Elastic Half-Spaces),” Forsch. Geb. Ingenieurwes., 10(5), pp. 201–211. [CrossRef]

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

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