Basically during rolling process thickness of strip is reduced by at least a pair of roll, so thickness of strip coming out of mill will be lesser compared to input thickness. But this will cause material imbalance (volume won't be constant) if, both entry and exit speeds are constant. So reduction in thickness on output size will increase strip speed after rolling, though your speed of rolling (i.e. of rolls) is constant.  For detailed mathematical derivation go through chapter "Rolling of metals"  in Mechanical Metallurgy by Dieter.

Dear Rhushikesh Mane 

Thanks for showing your interest in this problem but the thing i want to know is not clear yet. let me give an example related to my problem .. suppose i am rolling 300 micron sheet to 190 micron, our mill is able to set the maximum speed of say 500 mpm in some condition to get the quality output... now when we move down to thickness .. suppose we need to roll 190 to 100 micron, theory says speed will be more than 500 mpm in the same condition as of 300-190 but practically the mill is not able to run more than this speed if we want good quality foil. .. for getting the required quality we need to reduce the mill speed. 

Yeah just now got your question!!! Okay let me try to answer your question...As you try to produce thinner strips in rolling mill, reduction increases, which causes increase in roll force. At higher roll force, strip tends to bend rolls, but since your rolls are supported at their ends by journal and bearing stuff, bending takes place at centre. So strip rolled in this setup will be thicker at centre than edges by microns. Though this micron wedge is not much, it causes lower length at centre than edges, and shape of the strip will edge wavy rather than flat. But to get flat sheet one can increase speed of rolling which somehow decreases amount of coolant present at mill bite and friction coefficient (CoF) decreases. At higher speeds lubrication regime changes to hydrodynamic from boundary. Since CoF decrease roll force decreases bending of rolls will be lower and you will get relatively flat strip. If speed of mill is restriction, you can do couple of things like increase back and front tension or decreasing reduction per pass. I hope my long answer will answer your question.

First of all, a higher rolling speed will help not only to reduce the roll separating force, but also it lowers the residual stress (which matters a lot in case of foils) in the processed materials. If there exist big difference int the linier velocity of foil and the roll velocity, complete slipping occurs between the roll surfaces and the foil, i.e, there are actually like no neutral points or lines in the deformed zone. This differs from current practices in the industry where the entry speed of the plate is generally controlled to match the horizontal component of the surface velocity of the roll in the feeding direction.

And also if the difference in the relative speed becomes too large, ie. the rolls rotate too fast, then the drawing capacity of roller at entry side may disappear due to the friction loss. And this problem becomes cretical as the initial thickness becomes smaller and smaller. Industries prefer planetory roling mill most of the time for foil production. Hence to get good quality foils, its imp. to controll the entry speed(linier speed of foil or plate which depends upon the thickness reduction done at previous mill) and the roll velocity properly.