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


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
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
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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