Bright annealing is process of annealing, it is writing in the standard of ASTM A 344 but I could not find "drawing process". If it is easy, can you help me about that process? Any explanation, any document..?
Also look at section 3.4 "Rod and Wire drawing" in "Mechanical Treatment of Metals" R.N. Parkins, pub. G. Allen & Unwin Ltd, 1968, or section 19 "Drawing of rods, wires and tubes", in Mechanical Metallurgy, G.E. Dieter, pub McGraw-Hill Kogakusha, 1976.
Or one of the big Handbooks of Metal Forming, which have excellent descriptions of the main metal forming/working processes.
In the lab you have a wire of diameter A that you wish to convert to wire of a smaller diameter B. When this conversion is achieved by wire drawing, the wire is pulled through a special die with a circular orifice, see the wiki page, on a draw bench. The industrial process is more or less a scaled up version of this, sometimes with in-line multi-dies.
In order to feed the start of wire A through the die, of course you have to reduce its diameter (chicken and egg situation !), in the lab swaging is often used. Basically you push the wire into a machine (again with a circular orifice) where it is cold hammered, sort of from all sides at once (look up swaging too !). Anyway that initially thinned end is passed through the wire drawing die where it is tightly clamped, and tensile forces are applied to pull the rest of the wire through the die. The wire/die is often lubricated (look that up too), and in the lab (many moons ago now for me) we employed a solid lubricant , which I understand was soap based.
If you attempt too great a draw, (i.e. too big a reduction in diameter in one go), you will exceed the tensile strength of the alloy and it will snap, so to achieve the desired reduction you may have to employ more than one drawing stage with intermediate anneals to restore the alloy's ductility for the next drawing pass.
The alloy you refer to is commonly called Nichrome, and in manufacturer's literature they quote an annealing temperature range of 1500-2000F, aka ~1065-1093C.