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ABSTRACT
During the resistance spot welding (RSW), the thermal process plays a crucial role on nugget formation, especially the temperature field at the workpiece–workpiece interface, since it dominates the nugget diameter which is acknowledged generally as the quality criterion for welds, whereas it could hardly be measured experimentally. This work developed a solution for the RSW process of aluminum alloy according to inverse heat conduction problems. A direct transient heat conduction model was first established considering the variation of contact resistance with temperature and electrode force, the temperature-dependent thermophysical material properties, etc. A developed inverse model was then solved via the conjugate gradient method combined with the direct model based on the experimental temperature measurements at the workpiece surface by infrared thermometry. The calculated temperature distributions at the interface of workpieces were examined by the resulting development of the nugget diameter, which agrees well with the experimental results.
Nomenclature
| c | = | specific heat at constant pressure |
| [C(T)] | = | specific heat matrix |
| J | = | electric current density |
| k | = | thermal conductivity coefficient |
| [K(T)] | = | heat transfer coefficient matrix |
| qv, qv1, qv2 | = | internal heat source |
| {Q} | = | heat source vector of nodes |
| Ta | = | surrounding temperature |
| Tm | = | melting point of the workpiece material |
| = | derivative of temperature vector of nodes with respect to time | |
| Ti,j,k | = | temperature of node (i, j, k) in ith ring, jth line, and kth layer |
| {Tknown} | = | temperature vectors of nodes measured at the workpiece surface |
| {Tsurface} | = | temperature vectors of nodes calculated at the workpiece surface |
| σ | = | body electrical resistivity of workpieces |
| σww | = | electrical contact resistivity between workpieces |
| ρ | = | density of materials |
| εf | = | separation between mean surface planes of two workpieces |
| ε1, ε2 | = | small numbers |
| Subscripts | = | |
| e | = | electrode |
| w | = | workpiece |
| Superscripts | = | |
| m | = | iteration number |
| T | = | transposition |
Nomenclature
| c | = | specific heat at constant pressure |
| [C(T)] | = | specific heat matrix |
| J | = | electric current density |
| k | = | thermal conductivity coefficient |
| [K(T)] | = | heat transfer coefficient matrix |
| qv, qv1, qv2 | = | internal heat source |
| {Q} | = | heat source vector of nodes |
| Ta | = | surrounding temperature |
| Tm | = | melting point of the workpiece material |
| = | derivative of temperature vector of nodes with respect to time | |
| Ti,j,k | = | temperature of node (i, j, k) in ith ring, jth line, and kth layer |
| {Tknown} | = | temperature vectors of nodes measured at the workpiece surface |
| {Tsurface} | = | temperature vectors of nodes calculated at the workpiece surface |
| σ | = | body electrical resistivity of workpieces |
| σww | = | electrical contact resistivity between workpieces |
| ρ | = | density of materials |
| εf | = | separation between mean surface planes of two workpieces |
| ε1, ε2 | = | small numbers |
| Subscripts | = | |
| e | = | electrode |
| w | = | workpiece |
| Superscripts | = | |
| m | = | iteration number |
| T | = | transposition |