Spot Welding Simulation
Theory: current becomes heat, heat changes shape
Overview
Spot welding just passes current — why is it hard to simulate?
Because electrical, thermal and mechanical behaviour interact and change drastically within about 0.1 s. Two steel sheets are clamped between copper-alloy electrodes and several to over ten kA is passed; heating starts at the high-resistance sheet-to-sheet interface. As temperature rises, steel's resistivity grows several-fold and heating concentrates further; softened sheet is pressed by the electrodes, contact area grows, and current path and density change. The electrodes are water-cooled, so most heat flows into them. If the molten nugget grows too large, molten metal is ejected through the gap — expulsion. Simulation solves electric field, temperature and deformation, exchanging data each time step, with the dominant contact resistance given as a function of temperature and pressure.
Heat balance
I is current, R the resistance between electrodes (dynamic resistance), t_w weld time, ρ, c and L density, specific heat and latent heat, T_m melting point, V_n nugget volume, t sheet thickness (mm) and d_n nugget diameter (mm).
Thousands of welds per car
Resistance welding was invented by Elihu Thomson in the United States in 1886. Today's car bodies carry thousands of spot welds, each made by a robot in under a second. As high-strength steels, galvanised sheet and aluminium combinations spread, the window of good conditions narrowed and trial welds alone became insufficient to set parameters — one reason spot welding simulation came into wide use.
Worked examples
Example 1: heat balance for two 1.0 mm steel sheets (100 µΩ, 0.2 s assumed)
| Current | Heat generated |
|---|---|
| 8 kA | 1,280 J |
| 10 kA | 2,000 J |
| 12 kA | 2,880 J |
Treating the nugget as a 5 mm (5√t) diameter, 1.4 mm (70% of total thickness) disc gives 27.5 mm³. Heating steel to melting and melting it takes 9.6 J per mm³, so the nugget needs about 264 J — only 13% of the 2,000 J generated at 10 kA.
If only 13% of the heat goes into the nugget, where does the other 87% go? Does simulation need to care?
Very much so. Most of the rest flows into the water-cooled copper-alloy electrodes and some warms the sheet around the nugget. Nugget size is thus set by the difference between heat generated and heat lost to the electrodes, and depends strongly on electrode cooling and tip geometry (wear that widens the tip lowers current density). Treating electrodes as fixed-temperature boundaries tends to overstate heat loss and underpredict the nugget; model the electrodes including the cooling channel, and give thermal contact resistance between electrode and sheet. Here the current density is about 354 A/mm² with a 6 mm tip; if wear widens the tip to 7 mm it drops about 26%, shrinking the nugget under the same settings.
Practical workflow
- Build a 2D axisymmetric model of sheets and electrodes and split the sequence into squeeze, weld and hold.
- Give resistivity, conductivity, specific heat and strength as functions of temperature, and contact resistance as a function of temperature and pressure.
- Solve the squeeze first for contact pressure, then run coupled electric-thermal-mechanical welding.
- Compare nugget diameter and dynamic resistance history with cross-sections and welder records.
- Vary current and time to map the window between undersized nuggets and expulsion (weld lobe).
“What the dynamic-resistance peak tells you”
Recording electrode voltage and current shows resistance falling right after current starts, rising to a peak and then slowly declining. The initial drop reflects interface seating, the peak the rise in resistivity with temperature, and the later decline nugget growth and electrode indentation enlarging the current area. If simulation reproduces this shape, contact resistance and material data are broadly right. Expulsion causes a sudden drop, so the curve is also used to detect it.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Constant contact resistance | Wrong heat location and amount | Function of temperature and pressure |
| Electrodes at fixed temperature | Nugget underpredicted | Model to the cooling channel |
| Skipping the squeeze step | Inaccurate contact area | Solve squeeze first |
| Ignoring tip wear | Missed nugget shrinkage in production | Evaluate with enlarged tip |
| Ignoring the zinc coating | Required current underestimated | Include coating contact resistance |
I'd like to learn related topics.
Related pages include electrothermal analysis of Joule heating, welding residual stress analysis, arc welding simulation and laser welding simulation.
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