The process of longitudinal rolling process is illustrated in Fig. 7.1. The ingot or billet is passed through two rotating rolls mounted in a rigid frame or stand. The gap between the rolls is adjusted to less than the height of incoming billet and hence it gets rolled to a reduced height while it increases in length and width.
Let h1, b1 and v1, be the initial height, width and velocity of the billet, and, h2, b2 and v2 be the corresponding values at exit from the rolls (Fig. 7.1). Since during plastic deformation there is no change in the volume of the body, we can write the following-
In longitudinal rolling, a billet generally elongates more than it widens, particularly if the initial width is large compared to its height. Thus in rolling of wide and thin sheets the widening is negligible and we may take it as a case of plane strain deformation.
ADVERTISEMENTS:
However, when the height of billet is large the widening is not only large it is also non-uniformly distributed over the height of the billet. Figure 7.2 shows the billet shapes of different heights before and after rolling. The billets with high value of h/b (height/width) ratio get a double barrel shape during rolling while those with low value of h/b get a single barrel shape. When the ratio decreases the widening also decreases.
In cold rolling of thin sheets the rigidity of rolling frame is particularly important. Figure 7.3 shows that outgoing sheet thickness h2 is equal to the roll gap (hg) set between the rolls plus the elastic deformation of frame (Δf), the elastic deformation of rolls (Δr) and elastic recovery of sheet (Δs). Thus we may write h2 as under.
The possible reduction that may be carried out in a mill with given diameter rolls is limited by two factors. One of the factors is the entry condition or we may say that too large a billet does not enter the roll gap, so the limit is set by the maximum height of billet that may enter the roll gap.
The second factor is the elastic deformation of strip and rolls. If we increase the ratio of roll diameter to sheet thickness, a stage comes when the sheet does not get rolled at all, it simply suffers elastic deformation and recovers back to original thickness.
Entry Condition and Maximum Reduction:
Figure 7.4 shows the forces acting on the ingot as it contacts the rolls on entry side. The radial pressure of rolls pushes it away from rolls while the frictional force tries to pull it into the roll gap. Let α be the angle of contact. The billet will enter the roll gap if there is net positive force in the direction of rolling.
where D denotes the diameter of rolls. If it is desired to increase the reduction (Δ hmax) further we have to either (i) increase the co-efficient of friction or (ii) increase diameter of rolls or both. In cold rolling the value of coefficient of (µ) is quite small because rolls are ground and well lubricated. It may vary from 0.05 to 0.1 and hence the maximum value of contact angle (αmax) is also small. In hot rolling the co-efficient of friction (µ) is generally high. For hot rolling of steel µ. may be determined from the following empirical relation.
It is observed that the speed of billet on the entry side is less than the surface speed of rolls, so the frictional stress on the billet is directed in the direction of rolling. On the exit side the billet speed is higher than the roll surface speed and frictional stress is directed against the metal flow.
Between entry and exit there is a section called neutral section where the roll speed and billet speed are same. Thus the deformation region may be divided into two zones, i.e. (i) lagging zone which extends from entry to neutral section and (ii) leading zone which extends from neutral section to the exit (Fig. 7.6).
ADVERTISEMENTS:
The direction of frictional stress on the interface in leading zone is opposite to that in lagging zone. Let vr, v1, v2 be the roll surface speed, billet speed on the entry side and billet speed on the exit side respectively. The forward slip and backward slip are defined as follows. The roll surface speed is also equal to the billet speed vγ at the neutral section.
