How hot does the workpiece get in electromagnetic forming?

Less than you might expect. Here (10 kJ, 92.7 kA peak) one shot raises the aluminium tube about 32 K. Current crowds into the skin layer (about 0.95 mm) but flows for only about 0.4 ms, limiting deposited heat. The workpiece's strength hardly drops from heating, which is why electromagnetic forming is treated as cold working.

Where does heating become a problem?

In the coil. Each shot carries current comparable to the workpiece's, leaving 189 J of heat here. A single shot only raises the surface layer about 23 K, but repeated shots accumulate heat that can't escape in time, damaging coil insulation and structure. In production, shot interval and coil cooling become design constraints.

What does it mean that skin-layer heating doesn't depend on resistivity?

When the same current flows in the skin layer, heat per volume goes as resistivity over the layer thickness squared, and thickness squared is proportional to resistivity, so resistivity cancels. Here both aluminium and copper see 7.84×10⁷ J/m³. Total heat still differs with layer thickness, and temperature rise depends on density and specific heat.

Thermal Analysis in Electromagnetic Forming

Category: Coupled Analysis – Electromagnetic-Thermal | Revised 2026-10-01

Theory: heat left in the skin layer by a brief huge current

Overview

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Electromagnetic forming uses currents of 100,000 amperes, so why doesn't the workpiece melt?

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Because it flows so briefly. Dumping a capacitor bank into the coil drives current to peak in tens of microseconds and it decays in under a millisecond. Current crowds into the skin layers of workpiece and coil and heats them resistively, but total heat is set by the time integral of current squared (the action integral), so a short pulse limits it. Here the workpiece warms only about 32 K. The coil, however, takes this current every shot, so repeated firing accumulates heat. Thermal analysis in EM forming is more often about how many shots, at what interval, the coil can take than about changes in workpiece properties.

Discharge current and action integral

$$ I(t) = \frac{V_0}{\omega L}\,e^{-\alpha t}\sin\omega t,\qquad \alpha = \frac{R}{2L},\qquad S = \int_0^\infty I^2\,dt $$

C = 200 μF, V₀ = 10 kV (10 kJ), L = 2 μH, total circuit resistance R = 10 mΩ (assumed). Frequency 7.95 kHz, decay time constant 400 μs, first peak 92.7 kA, action integral 1.0×10⁶ A²s.

Skin-layer heating

$$ q = \rho\,\frac{S}{(l\,\delta)^2},\qquad \delta^2 = \frac{2\rho}{\omega\mu_0}\ \Rightarrow\ q = \frac{\omega\mu_0\,S}{2\,l^2},\qquad \Delta T = \frac{q}{\rho_m c} $$

l is coil length (20 mm), δ skin depth, ρ resistivity, ρ_m and c density and specific heat. Current is approximated as uniform within the skin layer. Heat per volume q is independent of resistivity.

Coffee Break Trivia

Strong fields from short pulses

In the 1920s at Cambridge, Kapitza drove large currents through coils to produce fields of tens of tesla. The problems were coil heating and coils torn apart by magnetic forces. His solution was to cut pulse duration to around a hundredth of a second, finishing the experiment before the coil could melt. Passing huge currents in short pulses and finishing before heat accumulates carries straight over to electromagnetic-forming coil design.

Worked examples

Example 1: heating per shot (10 kJ)

Part	Skin depth	Peak current density	Heat per volume	Temperature rise	Heat per shot
Al tube (25 mm radius, 1 mm)	0.945 mm	4.90×10⁹ A/m²	7.84×10⁷ J/m³	32.3 K	233 J
Cu coil (26 mm inner radius)	0.736 mm	6.29×10⁹ A/m²	7.84×10⁷ J/m³	22.7 K	189 J

Of the 10 kJ stored, about 0.42 kJ in total stays as heat in the skin layers of workpiece and coil. Copper's higher volumetric heat capacity gives a smaller temperature rise for the same heat per volume.

Example 2: mean coil temperature under repeated shots

Shot interval	Mean coil heating	Mean rise (hA = 1 W/K)
60 s	3.1 W	3.1 K
10 s	18.9 W	18.9 K
2 s	94.3 W	94.3 K

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Even at 2 s intervals the mean is 94 K, about 120 °C from 25 °C. Copper won't melt, so isn't that fine?

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The copper is fine, but the materials holding the coil aren't. EM forming coils embed conductors in resin and fibre to withstand the large magnetic force each shot (around 15 MPa here). Many resins lose much of their strength above 100 °C, and with repeated loading, delamination and cracks grow until the coil fails. The surface layer also rises another 23 K or so each shot above the mean, so the hottest spot is higher still. Copper's resistance also rises with temperature, lowering current and magnetic pressure at the same voltage and scattering forming results. So coil temperature distribution is solved over time to set cooling channels and shot interval — a problem of magnetic force acting on heat-weakened resin, evaluated by coupling electromagnetics, heat and structure.

Modelling workflow

Solve the bank, cabling and coil circuit for the current waveform.
Solve eddy currents in workpiece and coil over time for heating distribution.
Couple workpiece deformation, including current changes as the gap opens.
Thermal analysis of the coil with repeated shots and cooling.
Estimate coil life from resin temperature and magnetic force.

Coffee Break Trivia

“Forming that weakened every afternoon”

On an automotive-parts EM forming line, tubes were crimped correctly in the morning but grip weakened in the afternoon. Analysis showed continuous operation raising coil temperature, increasing copper resistance, lowering peak current and leaving magnetic pressure short. Adding coolant channels to the coil and a temperature-based small increase in charging voltage made forming consistent throughout the day.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Single-shot evaluation only	Coil heat build-up missed	Simulate repetition
Uniform current in conductor	Heating underestimated	Resolve skin layer
Constant resistivity	Current wrong when hot	Temperature-dependent resistivity
Resin strength at room temperature	Coil life overestimated	Use strength at temperature
Stationary workpiece	Current and force wrong	Couple with deformation

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