Abstract

Abstract The object of this paper is to show how any worm-wheel contact condition can be determined by analysis and to point out in particular the probable influence of the nature of the contact lines between a worm and a worm wheel upon the lubrication conditions, efficiency, and load-carrying ability. Analyses of three helicoids are made and their equations given. The first of these, a convolute helicoid, had its generatrix tangent to a cylinder of any diameter concentric with the axis of the helicoid. The second, a screw helicoid, had its generatrix passing through the axis of the helicoid, and was one limiting case of the first, with the diameter of the base cylinder reduced to zero. The third, an involute helicoid, had its generatrix tangent to a concentric cylinder of such diameter that the helix angle at this diameter was the same as the angle of the generatrix with a plane perpendicular to the axis. The conjugate action of racks is discussed and equations given. An analysis of worm contact is made. Contact lines of screw helicoids used as worms and those of involute helicoids used as worms are discussed. Contact lines of screw helicoids with large helix angles, and involute helicoids with large helix angles also are treated.

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