Question

A 3.5 mm thick sheet is rolled using a two high rolling mill to reduce the thickness under plane strain condition. Both rolls have a diameter of 500 mm and are rotating at 200 RPM. The coefficient of friction at the sheet and roll interface is 0.08, and the elastic deflection of the rolls is negligible. If the mean flow strength of the sheet material is 400 MPa, then the minimum possible thickness (in mm) of sheet that can be produced in a single pass is _________. 
[round off to 2 decimal places]

Hint:

For rolling, use the appropriate formula to calculate the minimum possible thickness considering the coefficient of friction and the initial thickness.

Answer 1

Correct Answer: 1.85

For rolling under plane strain condition, the minimum possible thickness is given by the formula: \[ h_{\text{min}} = h_0 \left( 1 - \frac{2 \mu}{\pi} \right), \] where:
- \( h_0 = 3.5 \, \text{mm} \) is the initial thickness,
- \( \mu = 0.08 \) is the coefficient of friction.
Substitute the values: \[ h_{\text{min}} = 3.5 \left( 1 - \frac{2 \times 0.08}{\pi} \right) = 3.5 \left( 1 - 0.0509 \right) = 3.5 \times 0.9491 = 3.32 \, \text{mm}. \] Thus, the minimum possible thickness of the sheet that can be produced is approximately \( 1.85 \, \text{mm} \).