Rolling mill configurations — four-high mill geometry In a four-high rolling mill, the diameter of the backup (support) rolls is __________ the diameter of the working (small) rolls.

Introduction / Context:
Rolling mills reduce thickness of metal strip by passing it through rotating rolls. A four-high mill uses two small work rolls to contact the strip and two large backup rolls to support them. Understanding the size relationship is fundamental to mill design and strip flatness control.

Given Data / Assumptions:

• Four-high mill has two work rolls and two backup rolls.
• Work rolls contact the strip; backup rolls prevent work roll bending.
• No unusual special mill (e.g., cluster/Sendzimir) considerations are implied.

Concept / Approach:
Small work rolls reduce roll separating force and improve shape control but are prone to bending under load. Large-diameter backup rolls provide stiffness, minimizing deflection and ensuring uniform thickness across the strip width. Hence the backup rolls must be larger than work rolls.

Step-by-Step Solution:
Identify roll functions: small work rolls contact strip; large backup rolls provide rigidity.Bending stiffness scales strongly with diameter; larger backups better resist deformation.Therefore, backup roll diameter is larger than work roll diameter.

Verification / Alternative check:
Mill catalogs and process schematics consistently show large backup rolls supporting smaller work rolls; advanced mills may add intermediate rolls, but the backup-to-work size ratio remains greater than 1.

Why Other Options Are Wrong:
Equal or smaller backups would not provide sufficient stiffness; 'about half' contradicts standard design logic; 'indeterminate' ignores well-established mill geometry.

Common Pitfalls:
Confusing four-high with two-high or cluster mills; assuming backup rolls contact the strip (they do not); overlooking the effect of roll deflection on crown and flatness.

Final Answer:
larger than