Computer solid modeling technologies applied to develop and form mathematical parametric tooth profiles of bevel gear and skew gear sets

This study is based on the parametric conjugate tooth profiles of bevel gear sets having the properties of invariant speed ratios, fixed skew axes (pitch line), zero length of common perpendicular line, two rotating axes intersecting at a point, etc. The geometric characteristics of the tooth profiles of bevel gears can be studied by using the kinematics parametric polar angular (pressure angle) function, the meshing equation and the constraints of continuity conditions. In this paper, the author derives the general profile equations, meshing constraint equations and non-undercut condition equations. By using the above-mentioned equations, gear geometric solid models are constructed. In addition, some gearing examples are presented to verify the developed theories. The non-undercut conditions and curvature properties are discussed in the paper. These developed theories have demonstrated bevel gear tooth profiles that can be parameterized by specifying certain relative parameters and are studied by a series of developed procedures. For the machining of these gears, the CAD/CAM software package from PRO/Engineering is used to transfer the solid models into NC programs. The method of transferring the manufacturing cutting NC codes to protect the tools and avoid impacting fixtures is demonstrated. This study is important for engineering design and for manufacturing factories involved in actual machining.