In cold thread rolling, what should be the diameter of the cylindrical blank, relative to the finished thread dimensions, for correct metal flow and accurate profile formation?

Introduction / Context:

Thread rolling forms threads by plastic deformation using dies, without material removal. Choosing the correct blank diameter is essential so that metal flows to create crests and roots to the specified major, minor, and pitch diameters.

Given Data / Assumptions:

• Cold rolling of external threads on a cylindrical blank.
• Standard 60° metric/Unified profiles.
• Elastic spring-back and minor die penetration are accounted for by process practice.

Concept / Approach:

In thread rolling, the blank diameter is set approximately equal to the finished thread’s pitch diameter so that material displaced by the dies builds the crest to the major diameter and compresses the root to the minor diameter without excessive over-fill or under-fill.

Step-by-Step Solution:

Verification / Alternative check:

Process handbooks recommend D_b ≈ d₂ with slight negative/positive corrections (on the order of a few micrometres per pitch) for material and die specifics, confirming the principle answer.

Why Other Options Are Wrong:

• Equal to major diameter: starting too large; difficult metal flow, die overload.
• Equal to minor diameter or a little larger than minor: insufficient material to form crests; under-sized threads.
• A little larger than pitch diameter: risks over-filling and out-of-tolerance crests without careful compensation.

Common Pitfalls:

• Confusing thread cutting allowances with rolling; rolling relies on displacement, not removal.

Final Answer:

equal to the pitch diameter of the thread