0
Research Papers

Optimal Machine-Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears

[+] Author and Article Information
Vilmos V. Simon

Department for Machine Design,
Faculty of Mechanical Engineering,
Budapest University of Technology
and Economics,
H-1111 Budapest,
Műegyetem rkp. 3, Hungary
e-mail: simon.vilmos@gt3.bme.hu

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 19, 2013; final manuscript received May 1, 2014; published online June 2, 2014. Assoc. Editor: Zhang-Hua Fong.

J. Mech. Des 136(8), 081004 (Jun 02, 2014) (8 pages) Paper No: MD-13-1125; doi: 10.1115/1.4027635 History: Received March 19, 2013; Revised May 01, 2014

In this study, an optimization methodology is proposed to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear (the transmission error), and to reduce the sensitivity of face-hobbed spiral bevel gears to the misalignments. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper. The targeted optimization problem is a nonlinear constrained optimization problem, belonging to the framework of nonlinear programming. In addition, the objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. For these reasons, a nonderivative method is selected to solve this particular optimization problem. That is the reason that the core algorithm of the proposed nonlinear programming procedure is based on a direct search method. The Hooke and Jeeves pattern search method is applied. The effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Litvin, F. L., 1972, Theory of Gear Mesh, Műszaki Könyvkiadó, Budapest, pp. 558–575 (in Hungarian).
Litvin, F. L., Chang, W. S., Lundy, M., and Tsung, W. J., 1990, “Design of Pitch Cones for Face-Hobbed Hypoid Gears,” ASME J. Mech. Des., 112(3), pp. 413–418. [CrossRef]
Kawasaki, K., 2010, “Manufacturing Method for Large-Sized Bevel Gears in Cylo-Palloid System Using Multi-Axis Control and Multi-Tasking Machine Tool,” Proceedings of International Conference on Gears, Munich, VDI-Berichte 2109, pp. 337–348.
Stadtfeld, H. J., 2000, The Basics of Gleason Face Hobbing, Gleason Works, Rochester, NY, pp. 1–26.
Fan, Q., 2006, “Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process,” ASME J. Mech. Des., 128(6), pp. 1315–1327. [CrossRef]
Fan, Q., 2007, “Enhanced Algorithms of Contact Simulation for Hypoid Gear Drives Produced by Face-Milling and Face-Hobbing Processes,” ASME J. Mech. Des., 129(1), pp. 31–37. [CrossRef]
Shih, Y. P., Fong, Z. H., and Lin, D. C. Y., 2007, “Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator,” ASME J. Mech. Des., 129(1), pp. 38–47. [CrossRef]
Vimercati, M., 2007, “Mathematical Model for Tooth Surfaces Representation of Face-Hobbed Hypoid Gears and Its Application to Contact Analysis and Stress Calculation,” Mech. Mach. Theory, 42, pp. 668–690. [CrossRef]
Bibel, G. D., Kumar, A., Reddy, S., and Handschuh, R. F., 1995, “Contact Stress Analysis of Spiral Bevel Gears Using Finite Element Analysis,” ASME J. Mech. Des., 117(2A), pp. 235–240. [CrossRef]
Gosselin, C., Cloutier, L., and Nguyen, Q. D., 1995, “A General Formulation for the Calculation of the Load Sharing and Transmission Error Under Load of Spiral Bevel and Hypoid Gears,” Mech. Mach. Theory, 30, pp. 433–450. [CrossRef]
Fang, Z., Wei, B., and Deng, X., 2004, “Loaded Tooth Contact Analysis for Spiral Bevel Gears Considering Edge Contact,” Proceedings of 11th World Congress in Mechanism and Machine Science, China Machine Press, Tianjin, pp. 838–842.
de Vaujany, J. P., Guingand, M., Remond, D., and Icard, Y., 2007, “Numerical and Experimental Study of the Loaded Transmission Error of a Spiral Bevel Gear,” ASME J. Mech. Des., 129(2), pp. 195–200. [CrossRef]
Simon, V., 2000, “Load Distribution in Hypoid Gears,” ASME J. Mech. Des., 122(4), pp. 529–535. [CrossRef]
Simon, V., 2007, “Load Distribution in Spiral Bevel Gears,” ASME J. Mech. Des., 129(2), pp. 201–209. [CrossRef]
Simon, V., 2009, “Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors,” ASME J. Mech. Des., 131(4), p. 041007. [CrossRef]
Kolivand, M., and Kahraman, A., 2009, “A Load Distribution Model for Hypoid Gears Using Ease-Off Topography and Shell Theory,” Mech. Mach. Theory, 44, pp. 1848–1865. [CrossRef]
Kolivand, M., and Kahraman, A., 2010, “An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gears Having Local and Global Surface Deviations,” ASME J. Mech. Des., 132(7), p. 071004. [CrossRef]
Kawasaki, K., and Tsuji, I., 2010, “Analytical and Experimental Tooth Contact Pattern of Large-Sized Spiral Bevel Gears in Cyclo-Palloid System,” ASME J. Mech. Des., 132(4), p. 041004. [CrossRef]
Shih, Y. P., and Fong, Z. H., 2007, “Flank Modification Methodology for Face-Hobbing Hypoid Gears Based on Ease-Off Topology,” ASME J. Mech. Des., 129(12), pp. 1294–1302. [CrossRef]
Shih, Y. P., and Fong, Z. H., 2008, “Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Generator,” ASME J. Mech. Des., 130(6), p. 062604. [CrossRef]
Kato, S., Ikebe, H., and Hiramatsu, J., 2009, “Study on the Tooth Surface Modification of Hypoid Gear in Face Hob System,” Proceedings of JSME International Conference on Motion and Power Transmissions, Sendai, pp. 109–111.
Fan, Q., 2010, “Tooth Surface Error Corrections for Face-Hobbed Hypoid Gears,” ASME J. Mech. Des., 132(1), p. 011004. [CrossRef]
Kawasaki, K., Tamura, H., and Iwamoto, Y., 1999, “Klingelnberg Spiral Bevel Gears With Small Spiral Angles,” Proceedings of 4th World Congress on Gearing and Power Transmissions, Paris, pp. 697–703.
Hotait, M., Kahraman, A., and Nishino, T., 2011, “An Investigation of Root Stresses of Hypoid Gears With Misalignments,” ASME J. Mech. Des., 133(7), p. 071006. [CrossRef]
Artoni, A., Bracci, A., Gabaccini, M., and Guiggiani, M., 2009, “Optimization of the Loaded Contact Pattern in Hypoid Gears by Automatic Topography Modification,” ASME J. Mech. Des., 131(1), p. 011008. [CrossRef]
Gabiccini, M., Bracci, A., and Guiggiani, M., 2010, “Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments,” ASME J. Mech. Des., 132(4), p. 041010. [CrossRef]
Artoni, A., Kolivand, M., and Kahraman, A., 2010, “An Ease-Off Based Optimization of the Loaded Transmission Error of Hypoid Gears,” ASME J. Mech. Des., 132(1), p. 011010. [CrossRef]
Artoni, A., Gabiccini, M., Guiggiani, M., and Kahraman, A., 2011, “Multi-Objective Ease-Off Optimization of Hypoid Gears for Their Efficiency, Noise, and Durability Performances,” ASME J. Mech. Des., 133(6), p. 121007. [CrossRef]
Artoni, A., Gabiccini, M., and Kolivand, M., 2013, “Ease-Off Based Compensation of Tooth Surface Deviations for Spiral Bevel and Hypoid Gears: Only the Pinion Needs Corrections,” Mech. Mach. Theory, 61, pp. 84–101. [CrossRef]
Simon, V., 2011, “Influence of Tooth Modifications on Tooth Contact in Face-Hobbed Spiral Bevel Gears,” Mech. Mach. Theory, 46, pp. 1980–1998. [CrossRef]
Kolda, T. G., Lewis, R. M., and Torczon, V., 2003, “Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods,” SIAM Rev., 45(3), pp. 385–482. [CrossRef]
Hooke, R., and Jeeves, T. A., 1961, “Direct Search Solution of Numerical and Statistical Problem,” J. Assoc. Comput. Mach., 8(2), pp. 212–229. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Relative position of the head-cutter to the imaginary generating crown gear

Grahic Jump Location
Fig. 2

Relative position of the pinion and the gear in mesh

Grahic Jump Location
Fig. 3

Tooth contact pressure distributions along the potential contact lines when the pinion and gear tooth surfaces are fully conjugate

Grahic Jump Location
Fig. 4

Tooth contact pressure distributions along the potential contact lines when the pinion tooth is manufactured by optimized head-cutter and machine-tool settings

Grahic Jump Location
Fig. 5

Tooth contact pressure distributions when the pinion and gear tooth surfaces are fully conjugate, and the transmitted torque is 20 Nm

Grahic Jump Location
Fig. 6

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on torque 80 Nm, and the really transmitted torque is 20 Nm

Grahic Jump Location
Fig. 7

Tooth contact pressure distributions when the pinion and gear tooth surfaces are fully conjugate, and the transmitted torque is 200 Nm

Grahic Jump Location
Fig. 8

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on torque 80 Nm, and the really transmitted torque is 200 Nm

Grahic Jump Location
Fig. 9

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on the assumed misalignments and no misalignments are in the gear pair

Grahic Jump Location
Fig. 10

Tooth contact pressure distributions when the pinion and gear tooth surfaces are fully conjugate, and the pinion offset is Δa = -0.5 mm

Grahic Jump Location
Fig. 11

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on the assumed misalignments and the actual pinion offset is Δa = -0.5 mm

Grahic Jump Location
Fig. 12

Tooth contact pressure distributions when the pinion and gear tooth surfaces are fully conjugate, and the horizontal angular misalignment of the pinion axis is ɛh = -0.5 deg

Grahic Jump Location
Fig. 13

Tooth contact pressure distributions when the optimization of head-cutter geometry and machine-tool settings is based on the assumed misalignments and the actual horizontal angular misalignment of the pinion axis is ɛh = -0.5 deg

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In