In rolling, a metal is formed through a pair or revolving rolls with plain or grooved barrels. The metal changes its shape gradually during the period in which it is in contact with the two rolls. We will now try to study the basic theoretical principles in rolling a metal.
Fig. 5.1 shows the rolling of a rectangular piece of thickness t1 which after rolling is reduced to t2. The shape and size of the area of contact is dependent on a number of factors which can be worked out from geometry.
Since right angled triangles DCB and DCA are similar.
From this relationship, it is obvious that if r is constant then δ can be more if contact length is increased very much, because δ is proportional to DC2. Further if δ, i.e. deformation desired be constant then contact length will be more if r is more.
If it be assumed that the volume of stock before and after rolling is same, and since generally width is same before and after, l1t1 = l2t2 (l2 = length of metal before rolling and l2 = length after rolling) from which it follows that the fraction of the volume displaced in rolling is equal to the relative reduction in thickness.
Now we will study something about friction between the roll and stock which is mainly responsible for drawing the stock into the gap between the rolls.
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At the point of impact of the roller where stock comes in its contact, the normal reaction is N and the friction force F acts as shown in Fig. 5.1. Resolving these forces in the direction of rolling, for equilibrium, 2N sin θ = 2F cos θ or, tan θ = F/N.
Obviously component 2F cos θ tries to pull the stock through the rolls whereas 2N sin θ tries to resist the rolling action; tan θ is also equal to coefficient of friction. Thus for rolling to take place, 2F cos θ must be greater than 2N sin θ or tan θ must be less than µ. The coefficient of friction is a function of the surface conditions of roll and stock and also depends on the rolling speed.
