Research Papers

Optimization of Face Cone Element for Spiral Bevel and Hypoid Gears

[+] Author and Article Information
Qi Fan

Senior Gear Theoretician, The Gleason Works, 1000 University Avenue, Rochester, NY 14692 e-mail: qfan@gleason.com

J. Mech. Des 133(9), 091002 (Sep 07, 2011) (7 pages) doi:10.1115/1.4004546 History: Received May 09, 2011; Revised June 24, 2011; Published September 07, 2011; Online September 07, 2011

In the blank design of spiral bevel and hypoid gears, the face cone is defined as an imaginary cone tangent to the tops of the teeth. Traditionally, the face cone element or generatrix is a straight line. On the other hand, the tooth root lines, which are traced by the blade tips, are normally not straight lines. As a result, the tooth top geometry generally does not fit the mating member’s real root shape, providing an uneven tooth root-tip clearance; additionally, in some cases root-tip interference between the tooth tip and the root tooth surfaces of the mating gear members may be observed. To address this issue, this paper describes a method of determining an optimized face cone element for spiral bevel and hypoid gears. The method is based on the incorporation of calculation of tooth surface and root geometries, the conjugate relationship of the mating gear members, the ease-off topography, and the tooth contact analysis. The resulting face cone element may not be a straight line but generally an optimized curve that, in addition, to avoidance of the interference, offers maximized contact ratio and even tooth root-tip clearance. Manufacturing of bevel gear blanks with a curved face cone element can be implemented by using computer numerically controlled machines.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

An example of tooth root-tip interference

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Figure 2

Kinematic model of hypoid generators

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Figure 3

Four sections of blades

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Figure 4

Illustration of cutter head rotation parameter

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Figure 5

Definition of a tooth surface grid

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Figure 6

Finite element model of a hypoid gear drive

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Figure 7

Applied coordinate systems

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Figure 8

An example of ease-off topography (unit: μm)

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Figure 9

Determination of optimized pinion tooth tip line

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Figure 10

Potential contact lines on gear tooth surfaces

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Figure 11

TCA result with root-tip interference

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Figure 12

TCA result with interference eliminated




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