Question

Two metallic sheets, each of $2.0$ mm thickness, are welded in a lap join configuration by resistance spot welding at a welding current of $10$ kA and welding time of $10$ millisecond. A spherical fusion zone extending up to the full thickness of each sheet is formed and properties of the metallic sheets are given as:

$\text{Ambient temperature =}293K$
$\text{Melting temperature =}1793K$
$\text{Density =}7000kg/m^3$
$\text{Latent heat of fusion =}300kJ.kg$
$\text{Specific heat =}800J/kgK$

Assume:
(i) contact resistance along sheet-interface is $500$ micro-ohm and along electrode-sheet interface is zero;
(ii) non conductive heat loss through the bulk sheet materials; and
(iii) the complete weld fusion zone is at the melting temperature.

The melting efficiency (in %) of the process

• A. $60.37$
• B. $50.37$
• C. $70.37$
• D. $80.37$

Answer 1

The correct option is C $70.37$

$\text{Given data :}$

$\text{Current: I =}{10}^{4}A$

$\text{Time:}t={10}^{-2}s$

$\text{Resistance:}R=500\times {10}^{-6}\Omega$

$\text{Ambient temperature,}{T}_{\infty }=293K$

$\text{Melting temperature,}{T}_m=1793K$

$\text{Latent heat of fusion,}L=3000kJ/kg$

$\text{Density:}\rho =7000kg/m^3$

$\text{Specific heat,}{c}_p=800J/kgK$

$\text{Radius of sphere,}r=2\times {10}^{-3}m$

$\text{Total heat supplied,}{H}_S=I^{2}Rt$

$=({10}^4{)}^2\times 500\times {10}^{-6}\times 10\times {10}^{-3}$

$=500J$

$\text{Mass}=\frac{4}{3}\pi r^3\times \rho$

$=\frac{4}{3}\pi (2\times {10}^{-3}{)}^3\times 7000$

$=2.346\times {10}^{-4}kg$

$\text{Total heat for melting}{H}_i=mL+m{c}_p(T_m-T_0)$

$=2.346\times {10}^4[300\times 1000+800(1793-293\left)\right]$

$H_i=351.9J$

$\text{Efficiency}=\frac{H_i}{H_S}\times 100$

$=\frac{351.9}{500}\times 100$

$=70.38\text{\%}$