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 TCAand LTCAare 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 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 commonto the gear and pinion teeth is predicted by introducing specialized gap elementswith considerations of deflection and deformation due to tooth bending, shearing, local Hertzian contact, and axle stiffness.

The advanced TCAand LTC Aprograms are integrated into GleasonCAGEt for Windows software package. Two numerical examples, a face-hobbing design and a face milling design, are illustrated to verify the developed mathematical models and programs.