Tool life sensitivity: Arrange cutting speed, feed rate, and depth of cut in decreasing order of their influence on tool life.

Introduction / Context:
Tool life is commonly described by Taylor’s equation V T^n = C, highlighting the dominant role of cutting speed (V). While feed and depth of cut also affect tool life via forces, temperature, and contact conditions, their influence is usually secondary to cutting speed. The question asks you to rank these variables by their impact on tool life.

Given Data / Assumptions:

• Conventional turning with a single-point tool.
• Similar tool material and work material across comparisons.
• No extreme built-up edge or chatter conditions.

Concept / Approach:
In the Taylor relation V T^n = C, small increases in cutting speed dramatically reduce tool life because speed strongly controls cutting-zone temperature and wear mechanisms (diffusion, oxidation). Feed rate increases chip load and contact, moderately reducing life. Depth of cut primarily affects cutting forces and engagement area but typically has the least direct effect on wear rate per unit time compared with speed and feed.

Step-by-Step Solution:

Verification / Alternative check:
Industrial tool-life testing and machining handbooks routinely rank variables the same way, emphasizing careful control of cutting speed to meet life targets.

Why Other Options Are Wrong:
Any order placing feed or depth of cut ahead of speed contradicts the well-established dominance of cutting speed on tool wear and edge temperature.

Common Pitfalls:
Over-attributing rapid wear to feed or depth when speed is too high; ignoring coolant and tool material, which also shift life but do not change the fundamental dominance of speed.

Final Answer:
cutting speed, feed rate, depth of cut