Project ForgeManufacturing Engineering
Machining Processes
GATE 2010
Hard
For tool A, Taylor's tool life exponent (n) is 0.45 and constant (K) is 90. Similarly for tool B, n=0.3 and K=60. The cutting speed (in m/min) above which tool A will have a higher tool life than tool B is
- 26.7
- B42.5
- C80.7
- D142.9
Explanation
At the crossover speed V, both tools have equal life T: V=90/T^0.45=60/T^0.3. Taking logs and solving: (1/0.45)(ln90-lnV)=(1/0.3)(ln60-lnV), giving lnV≈3.283, V≈26.7 m/min. Above this speed, tool A's shallower slope (lower n) means it retains a longer life than tool B.
Source: GATE ME 2010 (2010)
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