A Novel Approach for Computation of Constraints on Parameters of Modification of the Tooth Addendum of Precision Involute Hobs

In this paper a novel modified scheme and effective computer representation for hobbing operation of precision involute gears is presented. The specific goals of the paper are as follows: (a) to provide a comprehensive understanding of the principal features of addendum modification of an involute gear hob tooth, (b) to come up with a novel approach for the computation of parameters of modification of the hob tooth addendum, (c) to determine the applicability and advantages of the application of the developed approach. The key concept in this paper is satisfaction of the necessary conditions of proper part surface generation (Radzevich, S. P., 2002, Computer Aided Design, 34, pp. 727–740) in gear hobbing operation. The research is performed with the application of the novel $DG∕K$ approach of surface machining earlier developed by the author. The $DG∕K$ approach of surface generation is based on fundamental results obtained in differential geometry of surfaces, and in kinematics of multiparametric motion of a rigid body in $E3$ space. The interested reader may wish to go to the monographs (Radzevich, S. P., 2001, Monograph Kiev, Rastan; 1991, Monograph, Kiev, Vishcha Shkola Publishing) for details. Both of the monographs are available from The Library of Congress. A novel approach for the computation of constraints on the actual values of addendum modification of an involute hob is reported in this paper. The advantages of the developed approach are threefold. It yields the computation: (a) of the minimum and the maximum allowed value of the normal pressure angle; (b) of the maximum allowed value of addendum modification of an involute hob, and (c) of the maximum allowed reduction of addendum of a gear hob. In the way of implementation is also described.