A new method for seeking the optimum gear tooth profiles––the theoretical basis of Wildhaber–Novikov gearing

The object of this paper is to try and develop a new method for seeking the optimum gear tooth profiles. It is illustrated by an example for the line-contact helical gearing. The method developed may be summarized as follows: (1) Determine the essential requirements in accordance with the nature of the service that the gears are to render; (2) Let the paths of contact meet these requirements respectively as well as obey the general law of meshing; (3) Solve the resulting differential equations so that we may obtain the theoretical paths of contact with optimum performances; (4) Finally modify these theoretical paths of contact in order that an optimum basic rack tooth profile of the system may be obtained for practical application. The concrete content involved in the example may be regarded as the theoretical basis of Wildhaber–Novikov gearing. The method embodied in this paper may be regarded as a new field belonging to the theory of gearing.