The curvic coupling was first developed by Gleason Works about sixty years ago. Then, it has been implemented through design and manufacture methods to be used for connecting shafts of gas-turbine engine. The stiffness and the accuracy of centering the coupling have become very important. Therefore, it is necessary to design curvic couplings with the following characteristics: high positioning accuracy, high indexing accuracy, high indexing stiffness, self-centering, and self-improving of indexing accuracy. The process of designing and manufacturing curvic coupling required prior experience as well as a series of trial and error runs. In this paper, mathematical models for designing curvic coupling are developed. First, the parametric and the generalized forms of the quadric surface are presented, and then the mathematical models of cone surface are obtained from the degeneration of quadric surface. Tooth profiles are described by using mathematical model of cone surface in conjunction with design/manufacturing parameters of curvic coupling. The contact patterns are predicted by solving the intersections of all meshing surfaces on the pair of curvic couplings simultaneously. Finally, a computer program is developed for designing curvic couplings with design parameters as input variables to predict the contact patterns of designed curvic couplings and to show them in the form of 3D models. Some design charts are also presented. It is believed that the methodology and the computer program developed in this paper will prove to be an efficient tool for the design and manufacturing of curvic couplings.
MATHEMATICAL MODELS OF INFORMATION PROCESSING AND MANAGEMENT SYSTEMS