Question

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A low carbon steel bar of $147mm$ diameter with a length of $630mm$ is being turned with an uncoated carbide insert. The observed tool lives are $24min$ and $12min$ for cutting velocities of $90m/min$ and $120m/min$ respectively. The feed and depth of cut are $0.2mm/rev$ and $2mm$ respectively. Use the unmachined diameter to calculate the cutting velocity.

When tool life is $20min$ the cutting velocity in $m/min$ is

• A. $87$
• B. $97$
• C. $107$
• D. $114$

Answer 1

The correct option is B $97$

Taylor's tool life equation:
$V_1{T}_1^n=V_2{T}_2^n$
$\Rightarrow 90\times (24{)}^n=120\times (12{)}^n$
${\left(\frac{24}{12}\right)}^n=\frac{120}{90}$
$\Rightarrow 2^n=1.33$
$\therefore n=0.415$
Now $90\times (24{)}^n=V\times (20{)}^n$
$\therefore V=90\times {\left(\frac{24}{20}\right)}^{0.415}=97m/min$