Variation of sheet thickness along with its width is called camber. The following three types of cambers are observed on rolled sheets. These are illustrated in Fig. 8.22.
(i) Convex—Sheet is thicker in the middle and thinner towards edges.
(ii) Concave—Sheet is thinner in middle and is thicker towards edges.
(iii) Triangular—Sheet is thicker on one side and thinner on the other.
Out of these three shapes the convex shape is tolerable within the specified tolerances while the other two are not acceptable. The ideal shape, of course, is the straight rectangular cross section with thickness within the tolerance limits.
The camber already rolled on the sheet in hot rolling subsists in cold rolling. It may be slightly reduced. The drastic reduction in camber results in defects as shown in Fig. 8.23.
Cambering of Rolls:
The convex shape of sheet is mainly due to deflection or bending of rolls like a beam. To counter this, camber is ground on rolls in the opposite direction so that after deflection the surface in contact with the sheet becomes flat. However, during rolling a temperature differential builds up in the roll. The middle of roll becomes hotter than its ends and hence roll diameter in the middle of roll increases.
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In hot rolling mills this effect is quite pronounced and should be taken into account while calculating the roll camber. In cold rolling mills the coolant supply at different points on roll surface may be adjusted to minimize this effect. When the roll deflection during rolling is less than the camber ground on the rolls the resulting sheet will have concave camber.
Design of Camber for Two High Rolling Stand:
If the deflection of roll during rolling is equal to the camber ground on the roll the sheet rolled would be flat. Since sheets of various widths may be rolled on the same pair of rolls and with different reductions, no one camber may suit all conditions of rolling. Therefore, we may design the camber on the basis of maximum load that the roll can take if it is uniformly distributed over the entire barrel length.
The weakest part of roll is the section where neck joins the roll barrel. Here the stresses are enhanced due to stress concentration because of unequal cross sections. Figure 8.24 shows the various dimensions of the roll on which a uniformly distributed load Pc is acting. Pc is the load value used for designing camber. It is assumed to be uniformly distributed over the entire roll barrel.
where Δ is stress concentration factor.
From the above equation the Pc is determined as below-
The deflection curves due to PR and the camber curve which is opposite to deflection due to Pc are illustrated in Fig. 8.26. On the figure the values of deflection due to rolling load PR at the middle and at the edge of strip are indicated as ydc and yde respectively. The corresponding values for the camber curve are ycc and yce respectively.
Effect of Temperature Variation along Roll Barrel:
During rolling particularly in hot rolling a temperature differential gets developed between the edge of roll and middle of roll. The experimental observations has shown that the distribution of temperature is of parabolic nature. Such a distribution of temperature adds to the camber of roll surface. It is illustrated in Fig. 8.27.
The fixed camber ground on work rolls cannot take care of the different variations of parameters during rolling. Besides, one of the serious problems is wear of rolls. The rolls wear is more at the edges than at middle of strip. Therefore, it is necessary to have a system in which the roll camber can be varied during rolling, also it is desirable to distribute the wear over the roll length. The different methods employed for the same are described below.
In Process Changing of Roll Camber:
The stringent tolerances on sheet camber and thickness variation has necessitated the development of methods of varying roll camber and thickness during rolling.
For variation of roll camber the following methods are employed:
(i) Bending of work rolls or back up rolls by application of external forces on bearing chokes or on barrel of rolls (Fig. 8.28). Hydraulic forces are applied on the chokes of working rolls to bend it in the positive or negative directions. In some mills two chokes are used to make the force more effective and to increase the range of variation of camber.
(ii) Sliding or shifting of work rolls on either side of center-line of sheet (Fig. 8.29). The application of force as described in factor (i) above has limited effect due to the contact of surface of work roll with the surface of backup roll. The effect can be increased by sliding or shifting the work roll on one or both sides of strip centre-line. A higher range of possible variation in roll camber can be achieved.
(iii) Use of shaped rolls (surface ground to predetermined profile) along with axial sliding. In this method positive as well as negative roll camber may be achieved but at a higher cost. However, the range of camber variation that can be controlled is further increased (Fig. 8.30a-c).
(iv) Rotation of axes of work rolls with respect to axes of backup rolls in the horizontal plane (Fig. 8.31). By rotating the axis of working rolls with respect to that of backup rolls the contact between the two gets limited to the central portion.
During rolling the working roll ends would deflect towards backup roll, thus creating a camber on working roll surface which is in contact with the sheet. The method is highly useful in automatic control of camber. This type of control is easily adaptable in computer control of cold rolling mills.
Rolling Practice V/S Anisotropy in Sheet Metal:
The measurement of planer anisotropy and anisotropy ratio. The anisotropy ratio is useful in getting deeper draws while planer anisotropy gives rise to earnings during drawing.
The extent of reduction given in cold rolling affects the development of anisotropy ratio and hence the deep drawing characteristics of the sheet metal. Figure 8.32 shows the effect of reduction in cold rolling on anisotropy ratio. The maximum benefit results if this reduction is around 70-80 %.
Besides, the coiling temperature after hot rolling and alloying elements also affect the drawabillity.