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Research Papers

Study on the Anti-Twist Helical Gear Tooth Flank With Longitudinal Tooth Crowning

[+] Author and Article Information
Van-The Tran

Department of Mechanical and
Computer-Aided Engineering,
Feng Chia University,
100 Wenhwa Road, Seatwen,
Taichung 40724, Taiwan
e-mail: vanct4.hut@gmail.com

Ruei-Hung Hsu

Assistant Professor
Department of Mechanical and
Computer-Aided Engineering,
Feng Chia University,
100 Wenhwa Road, Seatwen,
Taichung 40724, Taiwan
e-mail: rhhsu@fcuoa.fcu.edu.tw

Chung-Biau Tsay

Professor
Department of Mechanical and
Computer-Aided Engineering,
Feng Chia University,
100 Wenhwa Road, Seatwen,
Taichung 40724, Taiwan
e-mail: cbtsay@mail.nctu.edu.tw

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 8, 2013; final manuscript received February 27, 2014; published online April 17, 2014. Assoc. Editor: Zhang-Hua Fong.

J. Mech. Des 136(6), 061007 (Apr 17, 2014) (10 pages) Paper No: MD-13-1399; doi: 10.1115/1.4027166 History: Received September 08, 2013; Revised February 27, 2014

To attain an anti-twist helical gear tooth flank with longitudinal tooth crowning, a novel additional rotation angle is proposed for the work gear during its hobbing process. A congruous nonlinear function with two variables is proposed and supplemented to this additional rotation angle of work gear. Two numeral examples are presented to illustrate the effects of coefficients of the proposed nonlinear function on the twist and evenness of generated helical gear tooth flanks. The twist of the crowned helical tooth flank is reduced significantly by applying the proposed longitudinal crowning gear method.

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References

Litvin, F. L., 1994, Gear Geometry and Applied Theory, PTR Prentice Hall, Englewood Cliffs, NJ, pp. 412–468.
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Chen, K.-H., Chen, C.-J., and Fong, Z.-H., 2009, “Computer Simulation for the Cutting Process of a CNC Hobbing Machine,” Chinese Society of Mechanism and Machine Theory Conference, Chia-Yi, Taiwan, pp. 154–161.
Tseng, J.-T., and Tsay, C.-B., 2004, “Mathematical Model and Surface Deviation of Cylindrical Gears With Curvilinear Shaped Teeth Cut by a Hob Cutter,” ASME 7th Biennial Conference on Engineering Systems Design and Analysis, Manchester, UK, pp. 271–277.
Simon, V., 2011, “Optimized Polynomial Function for Inducing Variation to Machine Tool Settings in Manufacturing Hypoid Gears,” 13th World Congress in Mechanism and Machine Science, Guanajuato, Mexico.
Lin, C.-Y., Tsay, C.-B., and Fong, Z.-H., 2001, “Computer-Aided Manufacturing of Spiral Bevel and Hypoid Gears Applying Optimization Techniques,” J. Mater. Process. Technol., 114, pp. 22–35. [CrossRef]
Tang, J., Zhou, C., and Wu, C., 2007, “Studies on FEM Geometrical Model of Gear Machined by Pre-Grinding Hob With Protuberance,” ASME International Power Transmission and Gearing Conference, Las Vegas, NV, Sept. 4–7, DETC2007-34914.
Wang, W.-S., and Fong, Z.-H., 2008, “A Dual Face-Hobbing Method for the Cycloidal Crowning of Spur Gears,” Mech. Mach. Theory, 43, pp. 1416–1430. [CrossRef]
Hsu, R.-H., and Fong, Z.-H., 2011, “Novel Variable-Tooth-Thickness Hob for Longitudinal Crowning in the Gear-Hobbing Process,” Thirteenth World Congress in Mechanism and Machine Science, Gearing and Transmissions, Guanajuato, Mexico.
Witte, D., 2006, “A Revolution in Hobbing Technologies,” Gear Solutions Mag., 4, pp. 38–43.
Fette GmbH and Liebherr–Verzahntechnik, 2006, “Finish Hobbing Crowned Helical Gears Without Twist,” Gear Solutions Mag., 1/2, pp. 12–13.
Lange, J., 2009, “How are you Dealing With the Bias Error in Your Helical Gears,” AGMA Fall Technical Meeting.
Xu, H., Chakraborty, J., and Wang, J. C., 2009, “Effects of Axle Deflection and Tooth Flank Modification on Hypoid Gear Stress Distribution and Contact Fatigue Life,” AGMA Fall Technical Meeting, 05FTM09, Detroit, MI.
Winkel, O., 2005, Utility Patent No. DE 20 2005 014 619U1.
Winkel, O., 2010, “New Developments in Gear Hobbing,” Gear Technol., 3/4, pp. 47–55.
Shih, Y.-P., and Fong, C.-H., 2007, “Flank Modification Methodology for Face-Hobbing Hypoid Gears Based on Ease-Off Topography,” ASME J. Mech. Des., 129(12), pp. 1294–1302. [CrossRef]
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Figures

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Fig. 1

Surface parameters of the standard rack cutter

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Fig. 2

Coordinate systems for the schematic generation mechanism of standard involute helical gear

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Fig. 3

Definition of axes on a gear hobbing machine of SIEMENS

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Fig. 4

Coordinate systems for the hobbing of work gear with longitudinal crowning teeth

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Fig. 10

Simulated topography of crowned work gear surfaces generated with modified additional rotation angle function and an increment of coefficient aza=1×10-6

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Fig. 11

Simulated topography of crowned work gear surfaces generated with modified additional rotation angle function and an increment of coefficient aφ1=1×10-6

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Fig. 12

Simulated topography of crowned work gear surfaces generated with modified additional rotation angle function and an increment of coefficient aφ1za=1×10-6

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Fig. 9

Simulated topography of crowned work gear surfaces generated with modified additional rotation angle function

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Fig. 8

Simulated topography of crowned work gear surfaces generated with the additional rotation angle function

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Fig. 7

Simulated topography of crowned work gear surfaces generated with original formula

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Fig. 6

Normal deviation of the tooth flank position vector

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Fig. 5

Flow chart for determination of coefficients of the proposed additional rotation angle function

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