Question

The heat generated in a resistance spot welding operation for joining two metal sheets with a certain set of process parameters is 2000 J. For a second spot welding operation on the same sheets without any change in the overall resistance of the system, the current is increased by 25% and the time for which the current is applied is reduced to half. The heat generated in the second operation (rounded off to one decimal place) in J is ______.

Answer 1

Concept:

The heat generated in resistance spot welding is given as:

\({{{H}}_{{g}}} = {{{I}}^2} \times {{R}} \times {{t}}\)

where, H_g = heat generated, R = electrical resistance of the circuit, t = time during which the current is passing through the circuit.

Calculation:

Given:

R₁ = R₂, current increased to 25 % I₂ = 1.25I₁, time reduced to half t2 = \(\frac{{{{{t}}_1}}}{2}\), H_g1 = 2000 J.

\({{{H}}_{{g1}}} = {{{I}}_1^2} \times {{R_1}} \times {{t_1}}=2000\;J\)

\({{{H}}_{{{{g2}}}}} = {{I}}_2^2 \times {{{R}}_2} \times {{{t}}_2}\)

\({{{H}}_{{{\rm{g2}}}}} = {\rm{}}{\left( {1.25 \times {{\rm{I}}_1}} \right)^2} \times {{\rm{R}}_1} \times {\rm{}}\frac{{{{\rm{t}}_1}}}{2}\)

\({{{H}}_{{{\rm{g2}}}}} = {\rm{}}\frac{{{{\left( {1.25} \right)}^2}}}{2} \times {\rm{}}\left( {{\rm{I}}_1^2 \times {{\rm{R}}_1} \times {{\rm{t}}_1}} \right)\)

\({{\rm{H}}_{{{\rm{g}}_2}}} = {\rm{\;}}\frac{{{{\left( {1.25} \right)}^2}}}{2} \times 2000\)

∴ H_g2 = 1562.5 J.