Tip thickness of circular tooth at the end of a pinion in a semirolling cylindrical transmission

Abstract

Semirolling cylindrical transmissions with round gears consist of a gear that is cut without rolling and a pinion in which the convex and concave sides are cut separately by unidirectional cutting heads [1]. In cut� ting the convex side of the pinion (Fig. 1), its engage� ment with the generating wheel is simulated, so as to ensure rolling (without slip) of the initial pinion cir� cumference (radius rw1) over the initial circumference of the generating wheel (radius rw2). The tooth profile T of the generating wheel is linear, in the middle sec� tion C–C; the tooth surface of the generating wheel is conical (with axis Z); the tooth profile Tt of the gener� ating wheel (in end cross section B–B) is an arc of a hyperbola. It is desirable to reduce the radii of the cutting heads in order to improve the overlap and smooth operation of the transmission. In that case, however, the tip thickness Sta of the tooth in the end plane is reduced in comparison with the middle section C–C, on account of the decrease in tooth thickness of the pinion in the end cross sections (Fig. 2). There is also increased risk of sharpening and weakening of the tooth. Therefore, calculation of the thickness Sta is an important step in designing the transmission.