Question

Two metallic sheets, each of 2.0 mm thickness, are welded in a lap joint 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. The properties of the metallic sheets are given as :

ambient temperature = 293 K

melting temperature = 1793 K                        density = 7000 kg/m³

latent heat of fusion = 300 kJ/kg                    specific heat = 800 J/kgK

Assume : i) contact resistance along sheet-sheet interface is 500 micro-ohm and along electrode-sheet interface is zero ;

ii) no 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 is
1. 50.37
2. 60.37
3. 70.37
4. 80.37

Answer 1

Correct Answer - Option 3 : 70.37

Heat generated due to current, H₁ = I²Rt

\({H_1} = {\left( {10 \times {{10}^3}} \right)^2} \times 500 \times {10^{ - 6}} \times 10 \times {10^{ - 3}} = 500J\)

Heat required for melting, \({H_2} = mL + mc{\rm{\Delta }}T\)

\({H_2} = \rho V\left( {L + c{\rm{\Delta }}T} \right)\)

Since fusion zone is spherical in shape, therefore volume = \(\frac{4}{3}\pi {R^3}\) = 33.51 mm³

So, \({H_2} = 7000 \times 33.51 \times {10^{ - 9}}\left\{ {300 \times {{10}^3} + 800 \times \left( {1793 - 293} \right)} \right\} = 351J\)

\(Melting\ \ efficiency = \frac{{{H_2}}}{{{H_1}}} = 70.2\% \)