Question

force. 2 3 Stand 1 30 17.7 10.7 078**000 028 0 0 0 4 5 6.6 4.1 m/s 2.6 m/s 10. __o 0 0.90 1.45 2.25 mm Pay-off reel 0.34 0.56 Take-up reel Stand 4 3. Rolling Velocities (20 pts) a. Using the following figure, calculate the strip velocity after each roll stand if the initial velocity is reduced to 2.0 m/s. b. Calculate the required roll velocity for the work rolls at each roll stand in order to maintain a forward slip of zero. (use the velocities for the strip shown in the figure) (Moro 0.90 mm 1.45 mm 2.25 mm

Answer 1

from the continuity equation we know that

A1U1A2v2 A2U2 bhivi bh2u2 h2v2

here A is the cross section area, b is the width and h is the height of the strip. 1 is for inlet in the roll stand and 2 is for outlet from the roll stand.

a).

for stand 5

height of strip is 2.25 and V is reduced to 2, i.e V1 is 2. or Vin is 2 and h in is 2.25

we get V2 or

hinVin Vout hin

from here we get Vout=3.10 m/s similarly for all the stands, outlet velocity of previous stand will become inlet for the next one.

Similarly values for all the stands can be calculated using the above formula.

using the above formula, all the velocities are written in table below.

	h in	V in (m/sec)	h out	v out(m/sec)
stand 5	2.25	2.00	1.45	3.10
stand 4	1.45	3.10	0.90	5.00
stand 3	0.90	5.00	0.56	8.04
stand 2	0.56	8.04	0.34	13.24
stand 1	0.34	13.24	0.26	17.31

b.)Formula for forward slip is given by

Uroll Vout Uroll

for zero forward slip, this formula has to be zero.

which gives

Vout Uroll = 0 Uroll =0 Vout Uroll Vout= Uroll

so the velocity of strip coming out of the stand will be the velocity of roll for respective stand for zero forward slip.

	v out(m/sec)	v roll(m/sec)
stand 5	4.10	4.10
stand 4	6.60	6.60
stand 3	10.70	10.70
stand 2	17.70	17.70
stand 1	30.00	30.00