Question

In rolling of metals, when reduction per pass is increased while all other conditions are kept constant, the required rolling force

• A. decreases due to smaller contact length
• B. Increases because deformation zone and strain work increase
• C. Remains constant
• D. Becomes zero at large reductions

Hint:

A higher draft ($\Delta h$) means more material is deformed simultaneously under higher strain, which always requires more rolling torque and rolling force.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question deals with the metal rolling process in manufacturing.
It asks how the required rolling force changes when the reduction per pass is increased.

Step 2: Key Formula or Approach:
The rolling force ($F$) is given by:
\[ F = L \cdot w \cdot \sigma_m \]
where:
$L$ is the contact length ($L = \sqrt{R \Delta h}$),
$w$ is the width of the sheet, and
$\sigma_m$ is the mean flow stress of the material.

Step 3: Detailed Explanation:

• Increasing the reduction per pass means increasing the draft ($\Delta h = h_i - h_f$).

• As the draft $\Delta h$ increases, the contact length $L = \sqrt{R \Delta h}$ increases, expanding the contact area and the deformation zone.

• Additionally, a higher reduction induces more plastic strain, which increases the average flow stress ($\sigma_m$) of the material due to work hardening.

• Both the enlarged deformation zone (larger contact area) and the increased work of strain lead directly to a higher required rolling force.

Step 4: Final Answer:
The rolling force increases because the deformation zone and strain work increase.