Mathematical model for tooth surfaces representation of face-hobbed hypoid gears and its application to contact analysis and stress calculation

An accurate geometrical representation of gear tooth surfaces is the fundamental starting point for developing a reliable computerized gear design which includes tooth contact analysis under light and heavy loads and stress analysis. Goal of this paper is just to propose a mathematical model able to represent tooth surfaces of a complex gear drive: hypoid gears cut by face-hobbing method. With this aim, an analytical description of the cutting process is firstly formulated: Formate® and generated cut are simulated, complex blade shapes, including protuberance (Toprem®), are studied. Starting from here, by using theory of gearing, the mathematical representation of gear tooth surfaces is derived; the proposed model is very accurate allowing to handle also undercutting occurrence. The discussion is ended by an application of the model to a real case: a truck transmission is modelled and the results are critically discussed; then, the so computed tooth surfaces are provided as input to an advanced contact solver making possible to analyze the performance of such gear drive.