# Rolling, Metal

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Rolling, Metal

a means of pressure shaping metals and metal alloys by compressing the metals between rotating rolls. The rolls, generally cylindrical in shape, are either smooth or with depressions (passes) that form grooves when two rolls come together.

Because of the continuous operation of the process, rolling is the most efficient method of imparting required shapes to items. During rolling, the metal generally undergoes significant plastic compression deformation involving destruction of the original cast structure and the formation of a flatter and closer-grained structure; the metal’s quality is thereby improved. Thus, rolling serves not only to change the shape of the metal but also to improve its structure and properties.

Like other methods of pressure shaping, rolling is based on the ductility of metals. A distinction is made between hot, cold, and warm rolling. Most rolled products (billets, merchant and sheet metals, tubes, balls) are produced by hot rolling at initial temperatures of 1000°-1300°C for steel, 750°–850°C for copper, 600°–800°C for brass, 350°–400°C for aluminum and its alloys, 950°-1100°C for titanium and its alloys, and about 150°C for zinc. Cold rolling is used primarily to produce sheets and strips less than 1.5–6 mm thick and precision sections and tubes. Hot-rolled metal is later cold-rolled to obtain smoother surfaces and better mechanical properties. Cold rolling is also used because of the difficulty of heating and rapidly cooling thin items. Warm rolling, unlike cold rolling, is carried out at a somewhat elevated temperature in order to reduce the hardening (cold working) of the metal during deformation.

In special cases, metals are rolled in a vacuum or in a neutral atmosphere to protect the surface of the metal from oxidation.

The three major methods of rolling are longitudinal, transverse, and rotary (slantwise) rolling. In longitudinal rolling (Figure 1,a), the metal is deformed by rolls, usually parallel to each other, that rotate in opposite directions. The friction between the roll surfaces and the metal pulls the metal through the gap between the rolls so that the metal is plastically deformed. Longitudinal rolling is much more common than the other two methods.

Transverse rolling (Figure 1,b) and rotary (slantwise) rolling (Figure 1,c) are only used to treat solids of revolution. In transverse rolling, the metal is subjected to rotational motion relative to its axis and is thus worked in the transverse direction. In rotary rolling, in addition to rotational motion, translational motion is imparted to the metal body along its axis through slantwise positioning of the rolls. If the translational speed of the metal is less than the circumferential speed of rotation, the rolling operation is called transverse rotary rolling; if the translational speed is greater, the operation is called longitudinal rotary rolling. Transverse rolling is used for working gear teeth and other parts, and rotary rolling is used in the manufacture of seamless rolled tubes, balls, axles, and other solids of revolution (Figure 2). Longitudinal rotary rolling is used to manufacture drill bits.

In longitudinal rolling, the height of the cross section of the metal decreases as the metal passes between the rolls, whereas the length and width increase (Figure 3). The difference in the heights of the cross sections of the metal before and after passing between the rolls is called the linear (absolute) reduction. Δh = h_{0} – h_{1}. The ratio of this value to the original height h_{0}, expressed as a percentage 100Δ/h_{0}, is called the percent reduction, which is usually from 10 to 60 percent per pass but may be as much as 90 percent. The increase in the length of the metal is characterized by the reduction ratio—the ratio of the length of the metal after exiting the rolls to the original length. The deformation of the metal relative to the width of the cross section is called spreading—the difference between the width of the cross section before and after rolling. Spreading increases with reduction, roll diameter, and the coefficient of friction between the metal object and the surface of the rolls.

The area between the rolls where the workpiece comes into direct contact with the rolls is called the zone of deformation; it is here that the metal is reduced. The small regions adjacent to both sides of the zone of deformation are called the noncontact zones of deformation; in these zones, the metal is only slightly deformed. The zone of deformation consists of two major segments: the lag zone, or zone of slippage on the entry side, in which the speed of the metal is less than the horizontal component of the circumferential speed of the rolls, and the advance zone, or zone of slippage on the delivery side, in which the speed of the metal is relatively greater. Thus, the exit speed of the workpiece from the rolls is 2 to 6 percent greater than the circumferential speed of the rolls. The boundary between these zones is called the neutral cross section. In the lag zone the frictional forces from the rolls acting on the workpiece are in the direction of exit, whereas in the advance zone they are opposite the direction of exit.

The capture of the metal by the rolls and the stability of the process result from the frictional forces arising on the contact surface between the metal and the rolls. For capture to occur, the tangent of the angle of bite α—the angle between the radii extended from the roll axes to points *A* and *B* (see Figure 3)—must not exceed the coefficient of friction: tan α ≤ *μ*. When a very smooth surface is not required, the surface roughness is added to the rolls in order to increase the angle of bite and, thus, of draft.

In practice, the angles of bite are 20°-26° in hot rolling with smooth rolls, 27°–34° in hot rolling with notched surfaces, and 2°–6° in cold rolling with a lubricant.

The force on the rolls during rolling is determined by multiplying the area of the contact surface by the mean specific force *P* = *F*×*p*_{m}. The specific force is distributed over the contact surfaces unevenly: the maximum is near the neutral cross section

and decreases in the directions of entry and exit. In rolling bands with a rectangular cross section, the contact surface is calculated by the formula , where *r* is the radius of the roll. In cold rolling of bands, the actual contact area is large because of the elastic compression of the rolls at points of contact with the metal.

The mean specific force, which is also called the normal bearing stress, depends on many factors and may be expressed by the formula *p*_{m} = *n*_{1}*n*_{2}*n*_{3}σ. Where *n*_{1} is the coefficient of the state of stress of the metal, which depends mainly on the ratio of the length of the arc of bite—the arc between points *A* and *B* on the circumference of the cross section of the roll (Figure 3)— to the mean thickness and width of the rolled band, on the coefficient of friction, and on the stretching of the rolled metal (stretching is widely used in cold rolling); *n*_{2} is the coefficient that accounts for the effect of the rolling speed; *n*_{3} is the coefficient that accounts for the effect of the cold working of the metal; and *σ* is the yield point (resistance to deformation) of the metal at the temperature used in the rolling process. Coefficient *n*_{1} is the most important and varies widely—from 0.8 to 8—depending on the factors mentioned above. This coefficient increases as frictional forces on the contact surfaces increase and the thickness of the workpiece decreases. In practical calculations, *n*_{3} is taken as 1 in hot rolling and *n*_{2} is taken as 1 in cold rolling.

For carbon steels, the mean specific force is in the range 100–300 newtons per m^{2} (10–30 kilograms-force per mm^{2}) in hot rolling and in the range 800–1,500 newtons per m^{2} (80–150 kilograms-force per mm^{2}) in cold rolling. The resultant forces on the rolls under the most common conditions of rolling are directed parallel to a line connecting the axes of the rolls, that is, vertically (Figure 4).

The relationship between the force *P* and the moment *M* required for the rotation of each roll is given by the formula *M = P(a +* ρ), where *a* is the arm of force *P*, which is in the range (0.35–0.5), and ρ is the radius of the friction circumference of the roll bearings, equal to the coefficient of friction of the bearing multiplied by the radius of the bearing trunion. The force on a roll in rolling steel wire and steel bands varies from about 200 to 1,000 kilonewtons (kN), that is, 20 to 100 tons-force; the force in rolling sheets from 2 to 2.5 m wide reaches 30 to 60 MN (3,000 to 6,000 tons-force). The moment required for rotating both rolls in rolling steel wire and small sections varies from 40 to 80 kN-m (4 to 8 tons-force-m), and the moment required for rolling slabs and wide sheets reaches 6.000–9,000 kN-m (600–900 tons-force-m).

### REFERENCES

Tselikov, A. I.*Osnovy teorii prokatki*. Moscow, 1965.

Smirnov, V. S.

*Teoriia prokatki*. Moscow, 1967.

Tselikov, A. I., and A. I. Grishkov.

*Teoriia prokatki*. Moscow, 1970.

Teterin, P. K.

*Teoriia poperechno-vintovoi prokatki*. Moscow, 1971.

Tret’iakov, A. V., and V. I. Ziuzin.

*Mekhanicheskie svoistva metallov i splavov pri obrabotke davleniem*. Moscow, 1973.

Lugovskoi, V. M.

*Algoritmy sistem avtomatizatsii listovykh stanov*. Moscow, 1974.

A. I. TSELIKOV