Reconsideration of the LogiX Gear Using a General Mathematical Model of Composite Gear Profiles

Abstract

A general mathematical model is derived for describing the conjugate tooth profiles and meshing properties of composite gears. Via a typical gear parameter, the pressure angle, necessary conditions that determine the continuity of composite gears in tooth geometry and meshing properties are introduced. The peculiarity of the presented model is that composite gears can be parametrically characterized by the specific functions in terms of pressure angle. An example is demonstrated that the discontinuity in composite gears will be efficiently and logically solved. In this paper the LogiX gear, a special composite gear which consists of many segmental “S” curves in gear profiles and possesses zero values of relative curvature and specific sliding at the joints of connected segmental profiles, will be parametrically investigated by this model. The “ideal” LogiX gear profile, theoretically, is constructed by infinite numbers of segmental profiles such that it may have infinite numbers of zero values of relative curvature and specific sliding. However, this “ideal” LogiX gear profile is characterized as a linear parametric profile that is a monotonous curve substantially and no more has infinite numbers of the zero values. Finally, many parametric gears which own power relative curvature and specific sliding than that of the “ideal” LogiX gear profile are presented.