A General Approach to Locate Instantaneous Contact Lines of Gears Using Surface of Roll Angle

Determining the locations and orientation of potential instantaneous contact lines between two contacting tooth surfaces of gears is one major step in the prediction of unloaded and loaded gear tooth contacts. This study defines and utilizes new general concept based on the construction of a surface of roll angle to simplify the task of locating instantaneous contact lines of any type of gearing. The position and normal vectors of points on one of the mating surfaces and axes of both gears are used in conjunction with the equation of meshing to define the surface of action and the surface of roll angle. With the surface of roll angle defined, instantaneous contact lines are determined by a novel approach based on an analogy to parallel-axes gears. At the end, the proposed method is applied to various parallel- and cross-axis gear pairs to demonstrate its effectiveness.