Design basis for a screw-cutting lathe feed gearbox In a screw-cutting engine lathe, the feed gearbox (or Norton/quick-change gearbox) is typically laid out to produce a series of feeds and thread pitches following which mathematical progression?

Introduction / Context:
A quick-change feed gearbox lets machinists select many feed rates and thread pitches quickly. The arrangement of gears determines how uniformly the available settings are distributed, which impacts finish, tool life, and flexibility.

Given Data / Assumptions:

• Conventional screw-cutting lathe with a Norton-style or similar gearbox.
• Objective: evenly spaced, practical feed steps over a range.
• No special electronic variable-speed drives are assumed.

Concept / Approach:
Gearbox design commonly uses a geometric progression for feed steps. With geometric progression, each step is a constant ratio from the previous one, yielding uniform percentage changes across the range. This is advantageous for maintaining consistent changes in surface finish and chip load when stepping up or down feeds. Arithmetic progression would produce equal absolute differences, which is less suitable over wide ranges.

Step-by-Step Solution:

Verification / Alternative check:
Lathe gear charts and design literature routinely present feeds and threads in geometric or near-geometric series (e.g., R20-like series), ensuring practical spacing across low to high feeds.

Why Other Options Are Wrong:
Arithmetic progression: causes overly fine steps at one end and coarse at the other.Harmonic progression: not used for feed step planning.No defined or random series: impractical for standardized machining results.

Common Pitfalls:
Assuming thread pitches can be arbitrarily generated without considering lead screw pitch and change gear ratios. Proper series selection simplifies operator use and documentation.

Final Answer:

Geometric progression