Question

Tomlinson and Stringer defined the coefficient of spread S in cogging as the ratio of

• A. Increase in length to decrease in width
• B. Increase in width to reduction in height
• C. Reduction in height to increase in length
• D. Reduction in width to increase in height

Hint:

In forging processes, spread increases with higher friction and lower workpiece height.

Answer 1

The Correct Option is B

Concept: Cogging is a primary metal forming process used to reduce the cross-section of large ingots using repeated forging blows. During deformation:
• height decreases due to compressive force
• material spreads laterally in width
• length increases due to volume constancy This deformation behavior is characterized by the concept of spread.

Step 1: Understand deformation in cogging. When a metal billet is compressed:
• vertical height reduces
• material flows sideways (width increases)
• longitudinal elongation occurs However, spread specifically refers to lateral widening.

Step 2: Define coefficient of spread. Tomlinson and Stringer defined coefficient of spread \(S\) as: \[ S = \frac{\text{increase in width}}{\text{reduction in height}} \] This ratio represents how effectively material spreads sideways during deformation.

Step 3: Physical interpretation.
• Higher spread means more lateral flow of material
• Lower spread indicates restricted lateral deformation
• Spread depends on friction, temperature, and die contact conditions

Step 4: Why other options are incorrect.
• (A) Length change is not used in spread definition
• (C) Reduction in height to increase in length is elongation, not spread
• (D) Width reduction is opposite of actual deformation in forging Final Answer: \[ \boxed{\text{Increase in width to reduction in height}} \]