REQUIREMENT FOR LIMITS OF ACTION AND WILDHABER'S LIMIT NORMAL

摘要

One of the most important criteria to design a gear pair which has smooth tooth surfaces around a given design point is how far the design point is from the limits of action. However, in the present theories, the definition is obscure and the calculation methods are not clear except for cylindrical gears. In this paper, when a path of contact and its contact normals are given according to the unified designing method applicable to all kinds of gears having the same equations defined in the common coordinate systems which are determined by the disposition of the gear axes and the angular velocities, the infinitesimal surface of action along the path of contact and the corresponding tooth surfaces are determined and the requirement for limit of action for all kinds of gears is obtained. To design a smooth tooth surface around the design point, it is convenient to look for the limit path of contact with its contact normal whose limit of action coincides with the design point, from which a design path of contact must be inclined adequately. Finally, it is shown that Wildhaber's limit normal is the contact normal of the limit path of contact solved under the condition that the given path of contact is an arc around the gear axis and is just one solution of the limits of action of a hypoid gear pair.