In cold rolling of steel strips and sheets, the yield strength of strip material is fairly high and very high specific roll pressures and hence rolling loads are experienced. Consequently high elastic deformations are also associated along with the plastic deformations.
The elastic deformation of roll surface makes the roll surface flatter or in other words it increases the effective roll diameter and hence length of contact (L) also increases. The deformed roll radius is determined from Hitchcock’s formula which is given below-
The sheet or strip also suffers elastic deformation. The elastic recovery of strip takes place after it crosses the center line of rolls on the exit side. Thus the contact between the rolls and the sheet/strip continues beyond the center line of rolls. Both the elastic deformations, i.e. of rolls and of strip, increase the length of contact, specific roll pressure and hence the rolling load.
ADVERTISEMENTS:
Contact Length with Elastic Deformation of Rolls and Strip:
Figure 7.12 illustrates the effect of elastic deformations on the length of contact. The undeformed roll surfaces are shown by dotted circular lines in the figure. If there were no elastic deformation the strip would enter the roll gap at the point A and leave the roll gap at the point D. But due to elastic deformation of roll surface the rolls have to be brought nearer'(roll gap has to be decreased) so as to maintain the strip thickness.
Each roll has to be brought nearer to centerline of strip by a distance Δ1. Also strip recovers on exit from rolls by 2Δ2. Hence each roll has to be further brought nearer to the centerline of rolls by a distance Δ2. Because of elastic deformations the strip enters the roll gap at A’ instead of A and leaves the roll gap at the point F instead of D. The contact length now becomes equal to L’ which is given by
where vr and Er are respectively the Poisson ratio and Young’s modulus for roll material, and, vs and Es are similar quantities for the strip material. For steel the values of v and E may be taken as 0.3 and 207 × 109 N/m2 respectively. Substitution of Eqns. (7.67a, b – 7.68) in Eqn. (7.62) gives the length of contact as given below-
