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RESEARCH PAPERS

Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process

[+] Author and Article Information
Qi Fan

 The Gleason Works, 1000 University Avenue, Rochester, NY 14692qfan@gleason.com

J. Mech. Des 128(6), 1315-1327 (Dec 24, 2005) (13 pages) doi:10.1115/1.2337316 History: Received June 27, 2005; Revised December 24, 2005

The Gleason face hobbing process has been widely applied by the gear industry. But so far, few papers have been found regarding exact modeling and simulation of the tooth surface generations and tooth contact analysis (TCA) of face hobbed spiral bevel and hypoid gear sets. This paper presents the generalized theory of the face hobbing generation method, mathematic models of tooth surface generations, and the simulation of meshing of face hobbed spiral bevel and hypoid gears. The face hobbing indexing motion is described and visualized. A generalized description of the cutting blades is introduced by considering four sections of the blade edge geometry. A kinematical model is developed and analyzed by breaking down the machine tool settings and the relative motions of the machine elemental units and applying coordinate transformations of the elemental motions. The developed face hobbing generation model is directly related to a physical bevel gear generator. A generalized and enhanced TCA algorithm is proposed. The face hobbing process has two categories, non-generated (Formate®) and generated methods, applied to the tooth surface generation of the gear. In both categories, the pinion is always finished with the generated method. The developed tooth surface generation model covers both categories with left-hand and right-hand members. Based upon the developed theory, an advanced tooth surface generation and TCA program is developed and integrated into Gleason CAGEfor Windows Software. Two numerical examples are provided to illustrate the implementation of the developed mathematic models.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Basic concept of bevel gear generation

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Figure 2

Generation of extended epicycloids

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Figure 3

Concept of bevel gear cutting

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Figure 4

Model of Phoenix®II hypoid generators

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Figure 5

Kinematical model of hypoid generators

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Figure 6

Face hobbing tool and blades

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Figure 7

Basic geometry of blades

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Figure 8

Hook, rake and offset angles

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Figure 9

Coordinate systems Sm and Ss

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Figure 10

Coordinate systems Ss and Sr

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Figure 11

Coordinate systems Sm and Sc

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Figure 12

Coordinate systems Sr and Sp

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Figure 13

Coordinate systems Sp and So

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Figure 14

Coordinate systems So and Sw

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Figure 15

Coordinate systems Sm and Se

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Figure 16

Coordinate systems Sj and Se

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Figure 17

Coordinate systems Sj and Si

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Figure 18

Pinion tooth surface model

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Figure 19

Gear tooth surface model

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Figure 20

Model of a hypoid gear drive

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Figure 21

Coordinate systems applied for TCA

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Figure 22

Condition of tooth surface contact

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Figure 23

Single meshing of design A

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Figure 24

Single meshing of design B

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Figure 25

TCA output of design A - mean

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Figure 26

TCA output of design A - toe

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Figure 27

TCA output of design A - heel

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Figure 28

TCA output of design B - mean

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Figure 29

TCA output of design B - toe

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Figure 30

TCA output of design B - heel

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