The influence of contact-point position and contact-line trend on entraining velocity and nonzero principal relative normal curvature of cylindrical worm gearing

The object of this paper is to ascertain the influence of contact-point position and contact-line trend on the essential performance indexes (entraining velocity and radius of nonzero principal relative normal curvature) and to find their maximum and minimum values so as to provide criterions for evaluating (or to provide clues for improving) the performances of the existing worm gearings. The formulas for them are derived by the author for the orthogonal worm gearing on condition that the tooth profiles are unknown. The essential findings of this paper are as follows: these performance indexes are functions of both contact-point position and contact-line trend, but their maximum and minimum values are functions of contact-point position only. The maximum entraining velocity vector is equal to a fixed resultant vector in case the contact line is perpendicular to this fixed resultant vector. The minimum entraining velocity vector is equal to zero in case the contact line is tangent to it. The radius of nonzero principal relative normal curvature has its maximum and minimum values of opposite signs in case the contact line is tangent to each of the bisectors of the vertical angles included between the helix and its conjugate curve. It becomes zero in case the contact line is tangent to the helix or its conjugate curve.