MANUFACTURING PROCESS: ROLLING PROCESS

Question

In the rolling process, Why should the velocity of the strip at the entry before coming in contact with roller be lesser than the velocity of the roller?

Answer 1

Because the cross section of strip decreases during the milling process, its speed will increase to match the roller's speed at the point when it leaves the rollers.

Otherwise the rollers my warp or leave creases on the strip.

It's like a flow of water in a pipe at a slower speed picking up velocity when passing through a nuzzle.

Answer 2

There are many reasons behind, and many ways to justify why it is so.

I'm trying to clarify it by using the conservation of the mass.

1- The density of the rolling material doesn't change, so its volume.

2- We assume that the width of material also stays constant (plain strain) that seems a very rough estimation but if you start with an ingot or slab after passing three or more roll machines that's doesn't change a lot.

Now the mass conservation implies: $$v_iy_i \approx v_\omega y_\omega$$

Here index $i$ indicates the entry speed and thickness and the index $\omega$ indicates the thickness of slab at the moment that its linear velocity is equal to the linear velocity of the rollers. We know for a fact that $y_\omega$ is smaller than $y_i$ then by rewriting the first equation in this form: $$\frac{y_\omega}{y_i} \approx \frac{v_i}{v_\omega}$$

We may now conclude that the entry velocity should be smaller than the velocity of the roller. If $v_i > v_\omega$ then, at the entry the slab begins to decelerate, cause minor damges to component and further energy loss.

Meanwhile the Kamran's answer points out another reason.