Question

A plate of 30 mm thickness is fed through a rolling mill with two powered rolls. Each roll has a diameter of 500 mm. The plate thickness is to be reduced to 27 mm in a single pass. Assume no change in width. The process feasibility and the maximum draft (in mm) can be represented, respectively, as
Use the coefficient of friction as 0.12

• A. NOT feasible and 6.0
• B. NOT feasible and 2.6
• C. feasible and 3.6
• D. feasible and 3.0

Hint:

For rolling problems, the condition \(d \le \mu^2 R\) is the key to determining feasibility. Always distinguish between the actual draft of the operation and the maximum possible draft allowed by friction.

Answer 1

The Correct Option is C

Step 1: Calculate Actual Draft. \(\Delta h = H_i - H_f = 30 - 27 = 3.0\) mm.
Step 2: Calculate Maximum Possible Draft (\(\Delta h_{max}\)). The maximum draft allowed by friction is given by \(\Delta h_{max} = \mu^2 R\). Roll radius \(R = 500/2 = 250\) mm. \(\mu = 0.12\). \[ \Delta h_{max} = (0.12)^2 \times 250 = 0.0144 \times 250 = 3.6 \text{ mm} \]
Step 3: Check Feasibility. Since the actual draft required (3.0 mm) is less than the max draft capacity (3.6 mm), the rolling process is feasible.