Meshing Limit Line of Conical Worm Pair

Abstract

Based on the theory regarding algebraic equation of higher degree, a method to compute the meshing limit line for a conical worm drive is brought forward. No iteration is needed to perform this method so the corresponding computer program can be simpler. By employing this method, it is mathematically proved that the meshing limit line does not exist on the internal flank of a conical worm tooth and two meshing limit lines exist on the external flank of the tooth. The numerical results illustrate that the two meshing limit lines on the external flank generally are all outside of the practical tooth surface of the worm and the practical tooth surface is on the useful side of the meshing limit line. This signifies that the working length of a conical worm may fully cover its whole thread length at least theoretically. At the toe of a conical worm, the meshing limit line is nearest to the tooth surface of the worm, and the risk that the meshing limit line enters into the worm tooth surface is the most at that position.