Research Papers

Mathematical Model for Face-Hobbed Straight Bevel Gears

[+] Author and Article Information
Yi-Pei Shih

 Department of Mechanical Engineering, National Taiwan University of Science and Technology, No. 43, Sec. 4 Keelung Rd., Taipei, 106, Taiwan, ROCshihyipei@mail.ntust.edu.tw

J. Mech. Des 134(9), 091006 (Aug 09, 2012) (11 pages) doi:10.1115/1.4007151 History: Received December 18, 2011; Revised June 28, 2012; Accepted July 13, 2012; Published August 09, 2012; Online August 09, 2012

Face hobbing, a continuous indexing and double-flank cutting process, has become the leading method for manufacturing spiral bevel gears and hypoid gears because of its ability to support high productivity and precision. The method is unsuitable for cutting straight bevel gears, however, because it generates extended epicycloidal flanks. Instead, this paper proposes a method for fabricating straight bevel gears using a virtual hypocycloidal straight-line mechanism in which setting the radius of the rolling circle to equal half the radius of the base circle yields straight lines. This property can then be exploited to cut straight flanks on bevel gears. The mathematical model of a straight bevel gear is developed based on a universal face-hobbing bevel gear generator comprising three parts: a cutter head, an imaginary generating gear, and the motion of the imaginary generating gear relative to the work gear. The proposed model is validated numerically using the generation of face-hobbed straight bevel gears without cutter tilt. The contact conditions of the designed gear pairs are confirmed using the ease-off topographic method and tooth contact analysis (TCA), whose results can then be used as a foundation for further flank modification.

Copyright © 2012 by American Society of Mechanical Engineers
Topics: Gears , Equations
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Figure 1

Straight motion as a hypocycloid for ρm/ρb=1/2

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Figure 2

Face-hobbing method for a straight bevel gear

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Figure 3

Coordinate systems for a left-handed cutter head

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Figure 4

Coordinate systems for cutting edges

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Figure 5

Coordinate systems for the standard imaginary generating gear

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Figure 6

Coordinate systems of a cutter head and an imaginary generating gear without cutter tilt

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Figure 7

Face-hobbed imaginary generating gear

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Figure 8

Universal cradle-type bevel gear generator

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Figure 9

Coordinate systems of the imaginary generating gear and work gear

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Figure 10

Dimensions for face-hobbed gear blank

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Figure 11

Coordinate systems of a virtual pinion cutter and conjugated ring gear

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Figure 12

Normal deviations between the face-hobbed and standard generating gears of a pinion and ring gear

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Figure 13

3D model of a face-hobbed straight bevel gear pair modeled by SolidWorks

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Figure 14

Normal deviations of tooth surfaces in face-hobbed versus standard straight bevel gears

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Figure 15

Ease-off topography in the numerical example

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Figure 16

Tooth contact analysis of the circular-edge face-hobbed cutter head




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