Question

A sheet metal drawing is considered feasible if the following conditions are met:

• Reduction ratio < 0.5
• Thickness to diameter ratio > 1%

A sheet metal drawing process is being planned on a sheet metal with a thickness of 2 mm with a punch of diameter 100 mm with various blanks of diameter \( D_b \).
Which ONE of the following blank diameters \( D_b \) (in mm) will result in feasible drawing?

• A. 150
• B. 250
• C. 350
• D. 450

Hint:

Convert both feasibility conditions into inequalities for D_b using t = 2 mm and d_p = 100 mm, then check which option satisfies both.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We are told a sheet metal drawing is feasible only if two conditions hold together: the reduction ratio must be less than 0.5, and the thickness to blank diameter ratio must be greater than 1 percent.
We are given the sheet thickness \( t = 2\ mm \), the punch diameter \( d_p = 100\ mm \), and four candidate blank diameters, and we must find which one satisfies both conditions at once.

Step 2: Key Formulas:
The reduction ratio in deep drawing compares how much smaller the punch is than the starting blank.
\[ \text{Reduction Ratio} = \frac{D_b - d_p}{D_b} \]
The thickness to diameter ratio is simply the sheet thickness divided by the blank diameter.
\[ \text{Thickness to Diameter Ratio} = \frac{t}{D_b} \]

Step 3: Applying the reduction ratio condition:
We need \( \frac{D_b - 100}{D_b} < 0.5 \).
\[ 1 - \frac{100}{D_b} < 0.5 \ \Rightarrow\ \frac{100}{D_b} > 0.5 \ \Rightarrow\ D_b < \frac{100}{0.5} = 200\ mm \]
So the blank diameter must stay below 200 mm just to satisfy the reduction ratio rule.

Step 4: Applying the thickness to diameter condition:
We need \( \frac{2}{D_b} > 0.01 \).
\[ D_b < \frac{2}{0.01} = 200\ mm \]
Interestingly, both conditions independently give the exact same upper limit, \( D_b < 200\ mm \).

Step 5: Testing each option against \( D_b < 200\ mm \):
Option (A) 150 mm is less than 200 mm, so it satisfies both conditions and is feasible.
Option (B) 250 mm is greater than 200 mm, so it fails both conditions.
Option (C) 350 mm is much greater than 200 mm, so it fails both conditions.
Option (D) 450 mm is far above 200 mm, so it also fails both conditions.

Final Answer:
Only a blank diameter of 150 mm keeps the process within both feasibility limits. \[ \boxed{D_b = 150\ mm} \]