GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 63 of 65

Marks: +1, -0

Taylor's tool life equation is given by

V T^{n}=C

, where

V

is in

{m} {/} {min}

and

T

is in min. In a turning operation, two tools

X

and

Y

are used. For tool

X, n=0.3

and

C=60

and for tool

Y, n=0.6

and

{C}=90

. Both the tools will have the same tool life for the cutting speed (in

{m} {/} {min}

, round off to one decimal place) of ________

Solution:

According to Taylor’s tool life equation

V T^{n}=C

For tool

X, n=0.3

and

C=60

So,

V T^{0.3}=60

⟹ T=(\;{60}/{V})^{1{ \/} 0.3}

For tool

Y, n=0.6

and

C=90

So,

V T^{0.6}=90

⇒ T=(\;{90}/{V})^{1 {\/} 0.6}

Tool life is same,
Therefore

(\;{60}/{V})^{1 {\/} 0.3}=(\;{90}/{V})^{1 {\/} 0.6}

On solving this, we get

V=39.99 {m} {\/ } {min}

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