Gearing principle and geometric design of conical involute gear pairs with crossed axes

Abstract

A group of formulae for the geometric parameters, such as the gear mounting distance, crossed-axes angle, centre distance and helix angle of the tooth projection on the reference plane of a reference rack, of a crossed-axes gear drive of different arrangements are derived based on the analysis of the spatial mesh relationship between conjugate gears and their reference rack. A set of geometrical design methods for conical involute gear pairs with crossed axes (non-intersecting and non-parallel axes) is presented. The formulae can be applied not only to all of the possible independent forms of crossed-axes gear drives but also to the case of gearing with parallel axes and intersecting axes. The design methods consist of two parts, the sequential and the reverse methods. The former is used to determine the mounting dimensions when the basic dimensions of a pair of conical involute gears are given, while the latter is used to determine basic dimensions of a pair of gears when the mounting dimensions are known. The formulae and the methods are verified through the design and manufacture of a set of testing gears.

Keywords

conical involute gear crossed-axes gear drive gearing principle geometric design

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