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RESEARCH PAPERS

Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator

[+] Author and Article Information
Yi-Pei Shih

Department of Mechanical Engineering, National Chung Cheng University, No. 168, University Road, Min-Hsiung, Chia-Yi, Taiwan, R.O.C.

Zhang-Hua Fong1

Department of Mechanical Engineering, National Chung Cheng University, No. 168, University Road, Min-Hsiung, Chia-Yi, Taiwan, R.O.C.imezhf@ccu.edu.tw

Grandle C. Lin

 HOTA Industrial Mfg. Co., Ltd., 115, Ren-hua Road, Ta Li, Taichung County, Taiwan, R.O.C.

1

Corresponding author.

J. Mech. Des 129(1), 38-47 (May 17, 2006) (10 pages) doi:10.1115/1.2359471 History: Received June 29, 2005; Revised May 17, 2006

Based on the theory of gearing and differential geometry, a universal hypoid generator mathematical model for face hobbing spiral bevel and hypoid gears has been developed. This model can be used to simulate existing face hobbing processes, such as Oerlikon’s Spiroflex© and Spirac© methods, Klingelnberg’s Cyclo-Palloid© cutting system, and Gleason’s face hobbing nongenerated and generated cutting systems. The proposed model is divided into three modules: the cutter head, the imaginary generating gear, and the relative motion between the imaginary generating gear and the work gear. With such a modular arrangement, the model is suitable for development of object-oriented programming (OOP) code. In addition, it can be easily simplified to simulate face milling cutting and includes most existing flank modification features. A numerical example for simulation of the Klingelnberg Cyclo-Palloid© hypoid is presented to validate the proposed model, which can be used as a basis for developing a universal cutting simulation OOP engine for both face milling and face hobbing spiral bevel and hypoid gears.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Coordinate systems for the left handed dual cutter heads of the Cyclo-Palloid© method

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Figure 2

Coordinate systems for the left handed single cutter head

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Figure 3

Coordinate systems between the cutter head and imaginary generating gear

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Figure 4

The circle arc motion versus the epicycloidal motion

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Figure 5

Coordinate systems between the generating gear and work gear

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Figure 6

The relative position between the outer and inside blades

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Figure 7

The tooth surfaces and relative positions for the example: (a) pinion and imaginary generating gear and (b) gear and imaginary generating gear

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Figure 8

Coordinate systems for assembly of the gear pair

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Figure 9

The result of TCA for the hypoid gear drive example

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