Tool life and speed — Taylor’s law insight State the relationship: as cutting speed increases, what happens to tool life (all else equal)?

Introduction / Context:
Taylor’s tool life equation captures the dominant influence of cutting speed on tool life. Recognizing this trend is essential for selecting economical cutting parameters and planning tool-change intervals.

Given Data / Assumptions:

• Taylor’s equation in basic form: V * T^n = C (feed and depth constant).
• Workpiece–tool material pair is fixed.
• Failure criterion for tool wear is predefined (e.g., flank wear land).

Concept / Approach:
According to V * T^n = C, for a given tooling/workpiece combination, increasing speed V requires a compensating decrease in tool life T to maintain the constant C. Higher speed increases cutting temperature and wear rate (diffusion, abrasion, adhesion), thereby shortening life.

Step-by-Step Solution:
Start with V * T^n = C.If V increases ⇒ T must decrease because n > 0.Thus, tool life decreases as speed increases.

Verification / Alternative check:
Shop trials plotting log V versus log T give a straight line with negative slope (−1/n), confirming inverse relation.

Why Other Options Are Wrong:
Options claiming increased or constant life ignore thermal and wear mechanisms that accelerate with speed; non-monotonic behavior requires atypical conditions not implied here.

Common Pitfalls:
Changing feed/depth simultaneously can mask the speed effect; always compare at constant feed and depth.

Final Answer:
Yes — tool life decreases with higher cutting speed