Question

In a typical turning tool life test, the following data are generated for tools A and B:

Tool name	Cutting speed (m/min)	Tool life (min)
A	200	20
B	150	58

Assuming the same tool life exponent for the tools, the value of constant in the Taylor’s tool life equation (with cutting speed in m/min and tool life in min) is ______ (round off to 2 decimal places)

Answer 1

Concept:

Taylor's Tool life Equation:

V × Tⁿ = C

Where,

V = Cutting Speed, T = Tool Life, C = Constant.

Calculation:

Given:

V × Tn = C

For Tool A,

200 × 20ⁿ = C   ------(1)

150 × 58ⁿ = C   ------(2)

Equating = (1) & (2)

200 × 20n = 150 × 58n 

\(\frac{200}{150}\) = \(\left ( \frac{58}{20} \right )^n\)

1.33 = 2.9ⁿ

Taking ln both side,

ln(1.33) = n × ln(2.9)

n = 0.27

Then from equation (1),

200 × 20n = C 

C = 200 × 20^0.27

C = 449.33