Question

The coefficient of friction increases by 5 times when a slab is hot rolled in a specific mill. The maximum possible reduction:

• A. increases by 5 times
• B. increases by 25 times
• C. decreases by 5 times
• D. decreases by 25 times

Hint:

Maximum possible reduction in rolling is proportional to the square of the friction coefficient: if \( \mu \) increases by 5 times, reduction increases by \( 5^2 = 25 \) times.

Answer 1

The Correct Option is B

In rolling operations, the maximum possible reduction (\( r_{max} \)) in thickness during a single pass is related to the coefficient of friction (\( \mu \)) and the roll radius (\( R \)) by the equation: \[ r_{max} = \mu^2 R \] From this relationship, it's clear that the maximum possible reduction is proportional to the square of the coefficient of friction.
Now, if the coefficient of friction increases by 5 times: \[ \mu' = 5\mu ⇒ r'_{max} = (5\mu)^2 R = 25\mu^2 R = 25 \times r_{max} \] So, the maximum possible reduction increases by 25 times when friction is increased by 5 times.