A Method of Local Synthesis of Gears Grounded on the Connections Between the Principal and Geodetic Curvatures of Surfaces

Abstract

A spatial gear-mechanism with double curvature tooth surfaces is discussed. The following results are obtained: a) the relationship between the principal curvatures of the surfaces, b) the conditions under which the path of the contact point on the surface is a geodetic line in the local sense. A method of synthesis of mismatched gearing proposed here permits determination of optimal conditions of meshing in the vicinity of the main contact point.

Research on geometrical characteristics of straight bevel gears with a small shaft angle with a non-generated gear and generated pinion

“…The long-term experience in manufacturing bevel and hypoid gears demonstrates that we can simplify the gear cutting process by means of bevel gears with a small shaft angle [11,12,18]. Their distinguishing characteristics are that gears can be crowned in a profiled direction.…”

“…Due to the rolling motion when generating the pinion tooth surface, the matrix of relative motion 12 A is a function of the parameter 1 ϕ :…”

“…The cost of bevel gear mass-production on Gleason machines is reduced significantly when bevel gears with a small shaft angle are used [11,12].…”

“…Gleason experts have developed such methods as FORMATE, HELIXFORM. Despite a more complex task of determining the optimal tooth modification [11,12], ], such gear technology is more progressive. Bevel gears with cyclo-poloidal teeth are cut using Klingelnberg and Oerlikon gear-cutting machines [13,14,15,16,17].…”

“…Providing for the required geometrical parameters of meshing of contacting gears for each particular method is a complex mathematical task generally reducing to solving systems of transcendental equations or to minimizing functions of many variables with limited equality and inequality [11,12,16,17,19,20].…”