Rolf,
As Bob notes, I use 12L14 for all the screws I make. I always hold the material in a collet (more rigid and precise than a chuck) and, depending on the length of the screw required, I do not have any more stock protruding from the collet than I need. I get the cross slide and tool set so that a single pass will take the screw shank to the finished diameter but, for a long screw, I cut in stages. Also, the closer you are working to the collet, the stiffer the workpiece... the bending force is being applied at the point of contact with the tool but the fulcrum of the bending is where the workpiece is held in the chuck / collet. If you take multiple full length passes to get the shank down to final diameter, the work piece is thinner and more flexible each time. If you can take the excess material away in a single pass, the workpiece remains as stiff as the starting diameter of the stock allows.
For example, when making a 8-32 lock screw, 2 inches or so long with a 3/8" diameter head, I start with the 3/8 round stock protruding from the collet about 1/2 inch. I turn about 1/4 inch of length to the final diameter I want to get the tool / cross slide set to turn the right diameter. I move the stock out about 1 inch and turn that much of the shank in a single pass. Then I move the stock out another inch and turn that much more of the stock to final diameter. Once the shank is to the correct diameter, with a die holder in the tail stock, I run the threads on the end of the shank, part off the screw blank, turn it around in the lathe and finish the head.
