Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T10:43:34.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Stress optimization and study of the sensitivity to geometricvariations of a spur gear tooth profile

Published online by Cambridge University Press:  02 April 2013

David Guyonneau ,
Emmanuel Mermoz ,
Jean Mailhé ,
Jean-Michel Sprauel  and
Jean-Marc Linares
David Guyonneau*
Affiliation:
Aix Marseille Université, CNRS, ISM UMR 7287, 13288, Marseille Cedex 09, France EUROCOPTER, Aéroport Internationale Marseille Provence, 13725 Marignane, France
Emmanuel Mermoz
Affiliation:
EUROCOPTER, Aéroport Internationale Marseille Provence, 13725 Marignane, France
Jean Mailhé
Affiliation:
Aix Marseille Université, CNRS, ISM UMR 7287, 13288, Marseille Cedex 09, France
Jean-Michel Sprauel
Affiliation:
Aix Marseille Université, CNRS, ISM UMR 7287, 13288, Marseille Cedex 09, France
Jean-Marc Linares
Affiliation:
Aix Marseille Université, CNRS, ISM UMR 7287, 13288, Marseille Cedex 09, France
*
a Corresponding author:[email protected]
Get access

Abstract

This paper presents an approach for obtaining an optimized geometry for the flank of atooth by minimizing the equivalent contact stress. The stress calculation method is basedon Hertz theory. As the majority of tooth profiles are involute, the geometric variationof the flank of the tooth is achieved variationally relative to the involute profile. Theoptimum profile is obtained by Monte Carlo simulation. During this optimization, apolynomial expression of the tooth geometry is used. The parameters influencing thesimulation are the four characteristic contact points. The approach presented has beenapplied in a representative case. A study of the geometric sensitivity was conducted onthe optimized tooth profile. Two different approaches were considered: by Monte Carlosimulation and analytical propagation. The robust and linear nature of the behavior of thetooth profile was demonstrated when it was subjected to geometric variations.

Keywords

Spur GearTooth profileTooth Contact Analysis (T.C.A.)Monte Carlo simulationUncertaintyEngrenages cylindriquesProfil de dentureTooth Contact Analysis (T.C.A.)Simulation de Monte CarloIncertitudes
Type
Research Article
Information
Mechanics & Industry , Volume 14 , Issue 1 , 2013 , pp. 31 - 41
Copyright
© AFM, EDP Sciences 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

G. Henriot, Engrenages – Conception – Fabrication – Mise en œuvre – Ed. DUNOD (2007), 8e
ISO Standard 21771:2007(E), Gears – Cylindrical involute gears and gear pairs – Concepts and geometry, International Organization for Standardization, Geneva, Switzerland, 2007
Spitas, V., Costopoulos, T., Spitas, C., Fast modeling of conjugate gear tooth profiles using discrete presentation by involute segments, Mech. Mach. Theory 42 (2007) 751–762 CrossRefGoogle Scholar
Ye, G., Ye, X.Y., A new method for seeking the optimum gear tooth profiles – the theoretical basis of Wildhaber-Novikov gearing, Mech. Mach. Theory 37 (2002) 1087–1103 CrossRefGoogle Scholar
Simon, V.V., Influence of tooth modifications on tooth contact in face-hobbed spiral bevel gears, Mech. Mach. Theory 46 (2011) 1980–1998 CrossRefGoogle Scholar
Faggioni, M., Samani, F.S., Bertacchi, G., Pellicano, F., Dynamic optimization of spur gears, Mech. Mach. Theory 46 (2011) 544–557 CrossRefGoogle Scholar
Velex, P., Bruyère, J., Houser, D.R., Some analytical results on transmission errors in narrow-faced spur and helical gears: Influence of profile modifications, ASME J. Mech. Desig. 133 (2011) 31010–31010 CrossRefGoogle Scholar
Ghribi, D., Bruyère, J., Velex, P., Octrue, M., Haddar, M., A contribution to the design of robust profile modifications in spur and helical gears by combining analytical results and numerical simulations, ASME J. Mech. Des. 134 (2012) 61011–61011 CrossRefGoogle Scholar
Pedrero, J.I., Pleguezuelos, M., Artés, M., Antona, J.A., Load distribution model along the line of contact for involute external gears, Mech. Mach. Theory 45 (2010) 780–794 CrossRefGoogle Scholar
T. Osman, P. Velex, A model for the simulation of the interactions between dynamic tooth loads and contact fatigue in spur gears, Tribol. Int. (2011) 84–96
Pedrero, J., Pleguezuelos, M., Munoz, M., Contact stress calculation of undercut spur and helical gear teeth, Mech. Mach. Theory 46 (2011) 1633–1646 CrossRefGoogle Scholar
S.C. Hwang, J.H. Lee, D.H. Lee, S.H. Han, K.H. Lee, Contact stress analysis for a pair of mating gears, Math. Comput. Modelling, 2011
Litvin, F.L., Gonzales-Perez, I., Fuentes, A., Hayasaka, K., Yukishima, K., Topology of modified surfaces of involute helical gears with line contact developed for improvement of bearing contact, reduction of transmission errors, and stress analysis, Math. Comput. Model. 42 (2005) 1063–1078 CrossRefGoogle Scholar
J.M. Linares, J.M. Sprauel, S. Aranda, P. Bourdet, Impact of geometric uncertainties onto the operating performance of a mechanical system, in: J.K. Davidson (Ed.), models for computer aided tolerancing in design and manufacturing, Tempe, Arizona, USA, 2005, pp. 225–234
Zamponi, L., Mermoz, E., Linares, J.M., Sprauel, J.M., Impact of geometrical defects on bearing assemblies with integrated raceways in aeronautical gearboxes, Mech. Mach. Theory 44 (2009) 1108–1120 CrossRefGoogle Scholar
Zamponi, L., Mermoz, E., Linares, J.M., Étude des méthodes de calcul des pressions de contact dans les roulements à pistes intégrées des boîtes de transmission aéronautiques, Mécanique Industries 8 (2007) 567–576 CrossRefGoogle Scholar
L. Zamponi, E. Mermoz, J.M. Linares, Contact pressure calculation methodologies in aeronautic gearboxes in the CAD process. The future of product development: proceedings of the 17th CIRP design conference, 2007, pp. 451–462
Xu, H., Kahraman, A., Anderson, N.E., Maddock, D.G., Prediction of mechanical efficiency of parallel-axis gear pairs, ASME J. Mech. Des. 129 (2007) 58–68 CrossRefGoogle Scholar
Linares, J.M., Sprauel, J.M., Bourdet, P., Uncertainty of reference frames characterized by real time optical measurements: Application to computer Assisted Orthopaedic Surgery, CIRP Annals – Manuf. Technol. 58 (2009) 447–450 CrossRefGoogle Scholar
Bruyère, J., Dantan, J-.Y., Bigot, R., Martin, P., Statistical tolerance analysis of bevel gear of tooth contact analysis and Monte Carlo simulation, Mech. Mach. Theory 42 (2007) 1326–1351 CrossRefGoogle Scholar
D.A. Hills, D. Nowell, A. Sackfield, Mechanics of Elastic Contacts, Butterworth – Heinemann Ltd (Oxford), 1993
Guide to the expression of uncertainty in measurement, (1993), 1st Edition, International Organization for Standardization (I.S.O.)