Analytical modeling of heat conduction for small scale resistance spot welding process

Resistance spot welding (RSW) is one of the most efficient techniques for sheet metal joining and is widely used in industry. However, the size of the weld nugget produced by RSW is not usually feedback-controlled in real time due to technical difficulties in making the nugget size measurements needed to implement such a control. The research presented in this article is based on the idea that a control based on a process model built in the control will greatly benefit the reliability of future controls. For this purpose, an analytical model is more suitable than a numerical model for such a fast process. As a first step, one-dimensional and two-dimensional axis-symmetrical analytical models for heat conduction in the RSW process have been developed. The differential equations with suitable boundary conditions were solved, accounting for resistance heating of bulk materials and simplified faying-interface heating due to contact resistance. Temperature history, temperature profile and steady state from example calculations are presented. Future work to develop a model that could be fit into a real-time monitoring and control scheme is also described.