Page 340 - Manufacturing Engineering and Technology - Kalpakjian, Serope : Schmid, Steven R.

320 Chapter 13 Metal-Rolling Processes and Equipment

EXAMPLE |3.l Calculation of Roll Force and Torque in Flat-rolling
An annealed copper strip 228 mm wide and 25 mm (80 + 280)/2 = 180 MPa. We can now define the roll
thick is rolled to a thickness of 20 mm in one pass. force as
The roll radius is 300 mm, and the rolls rotate at 100 38.7 250
rpm. Calculate the roll force and the power required F- Lwyavg- X X MPa
in this operation.
= 1.74 MN.
Solution The roll force is determined from Eq. (13.2),
The total power is calculated from Eq. (13.4), with
in which L is the roll-strip contact length. It can be
N = 100 rpm. Thus,
shown from simple geometry that this length is given
approximately by _ 211'FLN _ 5
Power--166,000 --2/7TX 1.74 >< 10
L =\/R(F(, - hf) ='\/ 300(25 - 20) = 38.7 mm.
38.7 100
Xmxajm =705 W
The average true stress, Yavg, for annealed copper is
determined as follows: First note that the absolute
value of the true strain that the strip undergoes in Exact calculation of the force and the power
requirements in rolling is difficult because of the uncer-
this operation is
tainties involved in (a) determining the exact contact
.13 = ln(%`§-> = 0223. geometry between the roll and the strip and (b) accu-
rately estimating both the coefficient of friction and
Referring to Fi _ 2.6, note that annealed copper has a the strength of the material in the roll gap, particu-
true stress of about 80 MPa in the unstrained condi-
tion, and at a true strain of 0.223, the true stress larly for hot rolling because of the sensitivity of the
is 280 MPa. Thus, the average true stress is strength of the material to strain rate (see Section 2.2.7.)

Reducing Roll Force. Roll forces can cause significant deflection and flattening of
the rolls (as it does in a rubber tire). Such changes in turn will affect the rolling
operation. Also, the columns of the roll stand (including the housing, chocks, and
bearings, as shown in Fig. 133) may deflect under high roll forces to such an extent
that the roll gap can open up significantly. Consequently, the rolls have to be set
closer than originally calculated in order to compensate for this deflection and to
obtain the desired final thickness.
Roll forces can be reduced by the following means:

° Reducing friction at the roll-workpiece interface
° Using smaller diameter rolls to reduce the contact area
° Taking smaller reductions per pass to reduce the contact area
° Rolling at elevated temperatures to lower the strength of the material
° Applying front and/or back tensions to the strip

Among these strategies, the last requires some elaboration. An effective method of
reducing roll forces is to apply longitudinal tension to the strip during rolling (as a
result of which the compressive stresses required to plastically deform the material
become smaller). Because they require high roll forces, tensions are important par-
ticularly in rolling high-strength metals. Tensions can be applied to the strip at either
the entry zone (back tension), the exit zone (front tension), or both. Back tension is
applied to the sheet by applying a braking action to the reel that supplies the sheet
into the roll gap (pay-off reel) by some suitable means. Front tension is applied by
increasing the rotational speed of the take-up reel. Although it has limited and spe-
cialized applications, rolling also can be carried out by front tension only, with no
power supplied to the rolls-a process known as Steckel rolling.