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AGMA 05FTM08:2005 Edition

AGMA 05FTM08:2005 Edition

$14.30

New Developments in Tooth Contact Analysis (TCA) and Loaded TCA for Spiral Bevel and Hypoid Gear Drives

Published By Publication Date Number of Pages
AGMA 2005 14
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Authors: Qi Fan, Ph.D. and Lowell Wilcox, Ph.D., The Gleason Works

Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis (LTCA) are two powerful tools for the

design and analysis of spiral bevel and hypoid gear drives. Typical outputs of TCA and LTCA are the graphs of

contact patterns and transmission errors. TCA and LTCA respectively simulate gear meshing contact

characteristics under light load and under significant load. TCA and LTCA programs have been widely

employed by gear engineers and researchers in their design of high strength and low noise spiral bevel and

hypoid gear drives.

Application of modern CNC hypoid gear generators has brought new concepts in design and generation of

spiral bevel and hypoid gears with sophisticated modifications. This paper presents new developments in

2005 FTM 3

TCA and LTCA of spiral bevel and hypoid gears. The first part of the paper describes a new universal tooth

surface generation model which is developed with consideration of the universal motion capabilities of CNC

bevel gear generators. The new universal model is based on the kinematical modeling of the basic machine

settings and motions of a virtual bevel gear generator which simulates the cradle–style mechanical hypoid

gear generators and integrates both facemilling and face hobbing processes. The tool geometry is generally

represented by four sections, blade tip, Toprem, profile, and Flankrem. Mathematical descriptions of gear

tooth surfaces are represented by a series of coordinate transformations in terms of surface point position

vector, unit normal, and unit tangent. Accordingly, a new generalized TCA algorithm and program are

developed.

In the second part of this paper the development of a finite element analysis (FEA) based LTCA is presented.

The LTCA contact model is formulated using TCA generated tooth surface and fillet geometries. The FEA

models accommodate multiple pairs of meshing teeth to consider a realistic load distribution among the

adjacent teeth. An improved flexibility matrix algorithm is formulated, in which the nonlinear formation of the

area of contact common to the gear and pinion teeth is predicted by introducing specialized gap elements with

considerations of deflection and deformation due to tooth bending, shearing, local Hertzian contact, and axle

stiffness.

The advanced TCA and LTCAprograms are integrated intoGleasonCAGEt forWindows software package.

Two numerical examples, a face–hobbing design and a face milling design, are illustrated to verify the

developed mathematical models and programs.

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