Turning on a lathe: maintaining constant cutting speed In a turning operation on a lathe, as machining proceeds the workpiece diameter reduces. To keep the cutting speed (surface speed at the tool–work interface) approximately constant, how should the spindle speed be adjusted as the diameter decreases?

Introduction / Context:
In machining, tool life, surface finish, and productivity depend strongly on cutting speed at the tool–work interface. In turning, the instantaneous cutting speed is set by both spindle revolutions per minute (RPM) and the current workpiece diameter.

Given Data / Assumptions:

• Cylindrical turning on a lathe.
• Cutting speed V is the target value recommended for the tool–work material pair.
• Diameter D decreases during the pass as material is removed.

Concept / Approach:
The relationship between cutting speed V, spindle speed N, and diameter D is V = pi * D * N / 1000 (for V in m/min, D in mm, N in rev/min). To maintain V constant while D decreases, N must increase proportionally.

Step-by-Step Solution:
Start with V_target for the material and tool.Use V = pi * D * N / 1000 to find N = (1000 * V) / (pi * D).As D reduces during machining, the denominator decreases, so N must rise to keep V constant.

Verification / Alternative check:
Example: If V = 120 m/min, D from 60 mm to 40 mm. Initially N ≈ (1000120)/(pi60) ≈ 637 RPM; later N ≈ (1000120)/(pi40) ≈ 955 RPM. RPM increases as expected.

Why Other Options Are Wrong:

• Decrease/keep constant: both reduce surface speed as D shrinks, risking rubbing and poor finish.
• Alternating or back-gear suggestions do not control V systematically and are unrelated to D changes.

Common Pitfalls:
Confusing feed rate with cutting speed; forgetting to adjust RPM on manual lathes during deep roughing cuts.

Final Answer:
Increase the spindle speed