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Mathematical model for formation of spur gear teeth by a hyperbolic reference profile
(NTU "KhPI", 2018) Tkach, P. M.; Nosko, P. L.; Revyakina, O. O.; Bashta, O. V.; Kornienko, A. O.; Tisov, O. V.; Tsybri, Yu. O.
The aim of this work is to create a fundamentals of mathematical model which consists in definition of geometry of a generating surface and machining gearing for novel cylindrical spur transmission. The generating surface is considered as rack-cutter with teeth, which profiled by hyperbola – a curve which is smooth at whole addendum and dedendum parts of reference profile. The equations of teeth surfaces which help the basic performances of this generating surface surveyed, namely quadratic forms and normal curvatures in the given directions are presented. The equations of machining gearing which help to obtain the equations of surfaces of teeth which can be applied both for working surfaces and for their fillets are obtained. For these surfaces quadratic forms also defined. Boundaries of a contact zone are defined. The results obtained in a paper can be used for definition of quality indicators of serviceability of novel transmissions which will allow carrying out a comparative estimation of novel transmission with conventional one and with other types of transmissions.