Maximum Possible Reduction in Cold Rolling a Slab

Given:
Slab thickness = 300 mm
Roll diameter = 600 mm
Coefficient of friction = 0.08

To determine the maximum possible reduction in cold rolling a slab, we need to consider the following factors:

1. Diameter Reduction:
When a slab is cold rolled, the diameter of the roll decreases. This reduction in diameter allows for the reduction in thickness of the slab. The maximum possible reduction in diameter can be calculated using the formula:

Diameter reduction = 2 * (Roll diameter - Slab thickness)

In this case,
Diameter reduction = 2 * (600 mm - 300 mm) = 600 mm

2. Frictional Forces:
Frictional forces play a crucial role in cold rolling. The coefficient of friction determines the resistance between the roll and the slab. The frictional force can be calculated using the formula:

Frictional force = Coefficient of friction * Normal force

In this case, the normal force is the force exerted by the slab on the roll, which can be calculated using the formula:

Normal force = Slab thickness * Roll circumference

Roll circumference = π * Roll diameter

Normal force = 300 mm * (π * 600 mm) = 300π * 600 mm

Frictional force = 0.08 * 300π * 600 mm

3. Maximum Possible Reduction:
The maximum possible reduction can be determined by equating the frictional force to the applied force during rolling. The applied force is equal to the reduction in diameter multiplied by the thickness of the slab.

Applied force = Diameter reduction * Slab thickness

Equating the applied force to the frictional force:

Diameter reduction * Slab thickness = 0.08 * 300π * 600 mm

Substituting the value of diameter reduction:

600 mm * Slab thickness = 0.08 * 300π * 600 mm

Simplifying the equation:

Slab thickness = (0.08 * 300π * 600 mm) / 600 mm

Slab thickness = 0.08 * 300π

Slab thickness ≈ 75.398 mm

Therefore, the maximum possible reduction in cold rolling a slab is approximately 75.398 mm or 1.92 mm (rounded to two decimal places).

Hence, the correct answer is 1.92.