Improved method of incremently drawing fibers

In the process of drawing fibers in small increments by passing said fiber with plural helical turns between a plurality of spaced-apart spindles, each of said spindles being elongated about an axis that extends transversely to the helical turns of said fiber thereon and is canted relative to said axis of the other spindle, and each of said spindles having a rotating fiber-bearing outer surface the radius of which changes along said axis thereof so as to tapered, said fiber-bearing surface being formed of a plurality of discrete circumferential microterraces of different radii which are substantially parallel to said axis of rotation of the corresponding one of said spindles, said fiber-bearing surface being designed and disposed for engaging each helical turn of said fiber frictionally and for supporting each said turn without imposing any substantial axially-directed restraint on said fiber, the improvement comprising:

• providing each said microterrace on the first said spindle with a width dimension dependent on the draw increment imposed on the portion of said fiber contacting said microterrace and equal to the pitch of said helical turn of said fiber substantially defined by a first equation:
• p.sub.i =[(DI.sub.i +cos .phi.)r.sub.i -a.sub.i sin .phi.[ sin .phi.
• where:
• .phi. is the angle of cant of said spindle axes as measured in the projection along the perpendicular common to said spindles;
• a.sub.i is the axial distance between the point of intersection of said spindle axes and the "i"th intersection of said wrap of said fiber with said first spindle axis in said projection;
• and a.sub.i is other than a.sub.1 and is related to a.sub.1 by a second equation:
• ##EQU4## a.sub.1 being the axial distance between the point of intersection of said spindle axes in said projection and the first intersection of said fiber with said axis of said first spindle;
• p.sub.i is said pitch, which is distance as measured on said first spindle axis between consecutive intersections of said wrap of said fiber with said first spindle axis;
• DI.sub.i is the draw ratio increment imposed on said fiber as it moves from said first spindle to the second said spindle, at position a.sub.i ;
• and is equal to the ratio of the radius r'.sub.i to r.sub.i, which is the ratio of the second spindle fiber receiving radius to the first spindle fiber sending radius;
• r.sub.i is the radius of said first microterraced spindle at axial distance a.sub.i ;
• r.sub.i being substantially equal to r.sub.1 times the product of all draw increments preceding microterrace r.sub.i, r.sub.1 being the radius of said surface of first contact on said first spindle.