The Properties of Surfaces of Contact for Three Typical Globoid Worms

Abstract

There are three typical forms of globoid worms and their wheels, they are : (1) Hindley worms, (2) helical gears and their enveloping worms, (3) plane toothed wheels and their enveloping worms. The surfaces of contact of these worms and wheels can be analyzed mathematically. In this way, with some assumed data we can get their contour lines, and thus it can be said : (1) Concerning to a Hindley worm and its wheel, their surface of contact is formed of two surfaces, the one is a plane which passes the axis of worm and perpendicular to the axis of wheel, and the other is a curved surface which is very resemble to the above mentioned plane and intersects it. The surface of each wheel tooth has two contact lines on the approach side, but on the recess side there is only one. Thus the tooth bearing on this wheel tooth cannot be said good. (2), (3) As for a toothed wheel and its enveloping worm, the surface of contact is in nearly tangential to the circumference of worm surface. The tooth bearing on a wheel tooth is in their center portion, and in good condition. Now we consider the manufacturing process of these wheels and worms. The Hindley worm can be cut by single tools, but cannot be ground by grinding wheels. Its wheel must be cut by specially made hobs, and also cannot be ground. On the contrary, the plane toothed wheel and its enveloping worm can be easily cut by a milling cutter and ground by a grinding wheel of simple form. In constructing these wheels and worms, the Hindley worm and its wheel must be built with very strictly limited allowance, but the plane toothed wheel and its enveloping worm can be built somehow under less restrictions.