The Method of Substitutive Circles Family: Application in Catia Design Environment for Gear Shaped Tool Profiling

Tools which generate by enveloping using the rolling method may be profiled using various methods. The substitutive circles family method is a complementary method developed based a specifically theorem, in which is determined a family of circles associated with the blank’s centrode, family which envelop the profile to be generate. The method assumes the determination of the circles family, transposed in the rolling process between the blank and tool centrodes. In this paper is proposed an algorithm for curling surfaces in enveloping, associated with a pair of rolling circular centrodes. The graphical algorithm is based on the representation of the circles family enveloped the blank’s profile. It is generated the circles family transposed on the centrode associated with the gear shaped cutter and is determined a new position of contact points with the blank. The assembly of these points forms the profile of the gear shaped cutter. The numerical data proof the proposed method quality.