GATE ME 2017 Set 1 — Question 55
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Manufacturing Processes → Machining & Machine Tools → Tool Life (Taylor's Equation)
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Question
Two cutting tools with tool life equations given below are being compared:
Tool 1:
Tool 2:
where is cutting speed in m/minute and is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ______ m/minute.
Tool 1:
Tool 2:
where is cutting speed in m/minute and is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ______ m/minute.
Correct answer
105 to 107
Solution
To find the breakeven cutting speed, we equate the tool lives () of both tools.For Tool 1:
For Tool 2:
At the breakeven point, :Taking the root on both sides:Cubing both sides:For m/min, Tool 2 will have a higher tool life. For example, at , and . Thus, the breakeven speed is approximately 106.07 m/min.
For Tool 2:
At the breakeven point, :Taking the root on both sides:Cubing both sides:For m/min, Tool 2 will have a higher tool life. For example, at , and . Thus, the breakeven speed is approximately 106.07 m/min.
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