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: Understanding the Question:
We need to determine if a given rolling operation is feasible and calculate the maximum possible draft. The feasibility depends on whether the actual draft required is less than or equal to the maximum draft allowed by the friction conditions.
Step 2: Key Formula or Approach:
The actual draft, \(d\), is the difference between the initial thickness (\(h_i\)) and the final thickness (\(h_f\)). \[ d = h_i - h_f \] The maximum possible draft, \(d_{\text{max}}\), is determined by the coefficient of friction (\(\mu\)) and the roll radius (\(R\)). \[ d_{\text{max}} = \mu^2 R \] The process is feasible if \(d \le d_{\text{max}}\).
Step 3: Detailed Explanation:
Given data:

• Initial thickness, \(h_i = 30\) mm
• Final thickness, \(h_f = 27\) mm
• Roll diameter = 500 mm, so Roll radius, \(R = 250\) mm
• Coefficient of friction, \(\mu = 0.12\)

First, calculate the actual draft for the operation: \[ d = 30 - 27 = 3 \text{ mm} \] Next, calculate the maximum possible draft: \[ d_{\text{max}} = (0.12)^2 \times 250 \] \[ d_{\text{max}} = 0.0144 \times 250 = 3.6 \text{ mm} \] Now, check for feasibility by comparing the actual draft to the maximum draft: \[ d \le d_{\text{max}} \implies 3 \text{ mm} \le 3.6 \text{ mm} \] The condition is satisfied, so the process is feasible.
The question asks for the feasibility and the maximum draft. The maximum draft we calculated is 3.6 mm.
Step 4: Final Answer:
The process is feasible, and the maximum draft is 3.6 mm.