Question

The machining time for an operation of cutting to test metal plates (much harder than both the tool material) when the tool material is changed from brass to cast steel. Metal removal rates with brass and cast steel as the tool material is given by

Given tensile strength of brass is = 135 MPa
Tensile strength of cast steel is = 415 MPa
The percentage change in cutting time when tool is changed from brass to cast steel will be __________
$\frac{Q_b}{Q_{cs}}={\left(\frac{1+r_{cs}}{1+r_b}\right)}^{5/6}$

$\text{Where}$ $r=\frac{\text{Hardness of testing metal}}{\text{Hardness of tool material}}$

• A. -60.78

Answer 1

The correct option is A -60.78
-60.78

Hardness of testing metal is much harder than both the tool material,
$\frac{Q_b}{Q_{cs}}={\left(\frac{r_{cs}}{r_b}\right)}^{5/6}={\left(\frac{H_b}{H_{cs}}\right)}^{5/6}$
Since tensile strength $\left(MPa\right)=3.5\times BHN$

$\frac{H_b}{H_{cs}}=\frac{135}{415}=0.3253$

$\frac{Q_b}{Q_{cs}}=(0.3253{)}^{5/6}=0.3922$

Since metal removal rate, $Q=f$ (Machining time) i.e. inversely proportional
$\frac{t_{cs}}{t_b}=\frac{Q_b}{Q_{cs}}=0.3922$

Now percentage change in cutting time when tool is changed from brass to cast steel is
$\frac{t_{cs}-t_b}{t_b}\times 100$% $=(\frac{t_{cs}}{t_b}-1)\times 100$%$=(0.3922-1)\times 100$%$=-60.78$%