Question

In case of plane strain rolling derive an expression for the length of arc of
contact of the workpiece and the roll from entry to exit.
= √∆ℎ
Where R is the roll radius and ∆ℎ is the change in thickness.

Answer 1

Answer:

Rolling is the process of reducing the thickness or changing the cross section

of a long workpiece by compressive forces applied through a set of rolls, as

shown in figure (5-1).

Fig. (5-1)

Most rolling is carried out by hot working, called hot rolling, owing to the large

amount of deformation required. Hot-rolled metal is generally free of residual

stresses, and its properties are isotropic. Disadvantages of hot rolling are that

the product cannot be held to close tolerances, and the surface has a

characteristic oxide scale.

Steelmaking provides the most common application of rolling operations.

Figure (5-2) illustrates the sequence of steps in a steel rolling mill to show the

variety of products made. Similar steps occur in other basic metal industries.

The work starts out as a cast steel ingot that has just solidified. While it is still

hot, the ingot is placed in a furnace where it remains for many hours until it

has reached a uniform temperature throughout, so that the metal will flow

consistently during rolling. For steel, the desired temperature for rolling is

around 1200_C (2200_F). The heating operation is called soaking, and the

furnaces in which it is carried out are called soaking pits. From soaking, the

ingot is moved to the rolling mill, where it is rolled into one of three

intermediate shapes called blooms, billets, or slabs, as shown in figure (5-2).