Question

During turning of a metallic rod at a given condition, the tool life was found to decrease from 100 min. to 25 min. when cutting speed was increased from 50 m/min. to 100 m/min. How much will be life of tool if machined at 80 m/min.?
1. 38.06 min.
2. 39.06 min.
3. 40.06 min.
4. 41.06 min.

Answer 1

Correct Answer - Option 2 : 39.06 min.

Concept:

Taylor’s tool life equation gives the relation between velocity and tool life

VTⁿ = C

Where V = velocity in (m/min)

T = tool life in min

n = Taylor’s tool life exponent

Calculation:

Given V₁ = 50 m/min, and T₁ = 100 min, V₂ = 100 m/min, and T₂ = 25 min,

Let us first try to find out ‘n’ by equating two given conditions

\({{V}_{1}}T_{1}^{n}={{V}_{2}}T_{2}^{n}=C\)

50 ⋅ 100ⁿ = 100 ⋅ 25ⁿ

\({{\left( \frac{100}{25} \right)}^{n}}=\frac{100}{50}\)

\({{\left( 4 \right)}^{n}}=2~;{{\left( 2 \right)}^{2n}}={{2}^{1}}~;2n=1~;n=\frac{1}{2}\)

n  = 0.5

Now the velocity given is, 80 m/min again we can find the unknown time by equating two conditions;

80 × T^0.5 = 100 × 25^0.5

T = 39.06 min