Maximum Reduction in Cold Strip Rolling

Abstract

An analytical equation is derived for the prediction of maximum reductions possible as dependent on the process variables. The results of this equation are presented in graphical form for a wide range of the process variables. A simple experimental procedure is suggested for the determination of the coefficient of friction.

The process variables are: The roll radius R₀, initial t _i and final t _f strip thickness, material yield limit σ₀ at uniaxial tensile test with yield limit σ_oi at initial thickness and σ_of at final exit thickness, front pull stress σxf and back pull stress σxb, the coefficient of friction μ, and the rolling speed U.

The power balance is set for the rolling operation. The powers computed are:

1. (1)

the useful power consumed as internal work of deformation of the strip, called sometimes ‘The homogeneous power’;

(2)

power consumed by the back pull on the strip;

(3)

power supplied by the front pull on the strip;

(4)

power consumed by the friction between the rolls and the strip; and

(5)

power supplied by the rolls.

From the equation: sum of the powers = 0, a dependence of the process variables one on each other is established. From this dependence the coefficient of friction can be computed at maximum reduction, and this gives a simple procedure for the experimental determination of the average coefficient of friction. With the coefficient of friction, yield limit, dimensions of the strip and roll and the values of the front and back pull known, from a given graph the maximum reduction possible can then be computed or picked.