GATE ME 2017 Set 2 — Question 54
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Manufacturing Processes → Machining & Machine Tools → Tool Life (Taylor's Equation)
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Question
During the turning of a mm-diameter steel bar at a spindle speed of rpm, a tool life of minute is obtained. When the same bar is turned at rpm, the tool life becomes minute. Assume that Taylor's tool life equation is valid. When the bar is turned at rpm, the tool life (in minute) is approximately
Correct answer
(B) 32
Solution
Taylor's tool life equation is given by , where is the cutting speed, is the tool life, is Taylor's exponent, and is a constant.Given data:
Case 1: rpm, min
Case 2: rpm, min
Case 3: rpm, minFirst, we use the data from Case 1 and Case 2 to find the value of :
Divide both sides by :
To find , take the logarithm of both sides (e.g., natural logarithm):
Now, we use the value of and data from Case 2 (or Case 1) to find for Case 3:
Rearrange to solve for :
minutesThe closest option is minutes.The final answer is
Case 1: rpm, min
Case 2: rpm, min
Case 3: rpm, minFirst, we use the data from Case 1 and Case 2 to find the value of :
Divide both sides by :
To find , take the logarithm of both sides (e.g., natural logarithm):
Now, we use the value of and data from Case 2 (or Case 1) to find for Case 3:
Rearrange to solve for :
minutesThe closest option is minutes.The final answer is
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