Coil thermal management: losses, paths and the hot spot

Where the heat comes from

The main source of heat in a coil is copper loss, the resistance of the winding multiplied by the square of the current. Because the current is squared, a 20 per cent overcurrent adds about 44 per cent to the loss. A small error in the current rating becomes a large error in the temperature rise.

AC coils add core loss. The alternating flux heats the core through hysteresis and eddy currents. The loss depends on the material, the flux density and the frequency. A core that is fine at 50 Hz can run hot at 400 Hz, even with the same copper loss.

There are other sources. A shaded pole motor, a brake coil or a solenoid may have a shorted turn that carries current. A coil near a hot surface absorbs heat from it. A coil in a sealed enclosure is cooled by the enclosure, not by the room. The thermal design has to account for all of them, not just the winding.

Why the hot spot matters

Heat is generated in the copper throughout the winding, but it can only leave through the surfaces. The centre of a thick winding is far from a surface, so it runs hotter than the outside. The difference between the hot spot and the average can be 15 to 30 K in a thick build. That is illustrative, not a fixed rule.

The insulation ages fastest at the hot spot. A class 180 system that averages 150 C may still have a hot spot near 180 C, which leaves no margin. A temperature rise test that reports only the average can therefore look acceptable while the insulation is at its limit.

The build, the wire diameter, the varnish and the potting all affect the internal gradient. A vacuum impregnated winding fills the air gaps and conducts better. A dry winding with trapped air has a higher internal resistance. The same copper and the same current can run at different hot spots depending on the impregnation.

The conduction path

The thermal path from the hot spot is a chain. Heat crosses the copper, the enamel, the air or varnish in the winding, the bobbin wall, the core, the mounting interface and finally the enclosure or the air. Each link has a thermal resistance, and the largest one sets the temperature rise.

Copper conducts well, so the along-the-wire path is not usually the limit. The weak links are the insulation, the air gaps and the interfaces. A bobbin wall of 2 mm of filled plastic can drop more temperature than several metres of copper. A mounting foot with a small contact area is a bottleneck even if the bracket is large.

Potting can improve the path by replacing air with a material of higher conductivity, but only if the potting fills the voids and bonds to the surfaces. A potting compound that shrinks away from the bobbin leaves an air gap and adds resistance instead of removing it.

Convection and radiation

Convection moves heat from the outer surfaces to the air. It depends on the surface area, the orientation, the air speed and the temperature difference. A coil mounted horizontally and a coil mounted vertically do not shed heat at the same rate.

In a sealed enclosure, the coil heats the air inside, and the enclosure heats the room. The enclosure surface becomes the real heat sink. A small sealed box with no external fins can run much hotter than the same coil on an open frame.

Radiation becomes useful at higher temperatures, but it depends on the surface emissivity and the view to cooler surfaces. A shiny metal surface radiates less than a black one. Dust, oil and conformal coating change the surface and the convection, sometimes in ways that are not obvious from a clean bench test.

Losses and paths in one view

The table links each loss or path to the design response. It is a checklist for the thermal review, not a substitute for a measurement.

Duty and protection

A continuous coil reaches a steady temperature. An intermittent coil may never reach it, which is why a short duty cycle can carry a higher current. The rating should state the duty, the ambient and the mounting condition, not just a voltage.

A stalled actuator is a special case. The current may be limited only by resistance, and the coil can reach its limit quickly. A thermal cutout, a PTC thermistor or a current-limited supply can protect the winding, but the protection has to be matched to the thermal time constant. A slow protector will not save a fast hot spot.

The class rating is an endurance statement. Running a class 180 coil at a 180 C hot spot for its full life is not the same as running it there for a short test. The insulation ages, and the rate depends on the temperature and the time. A design with margin runs cooler or accepts a shorter life.

Verification

Measure the winding resistance before and after a temperature run. The change gives an average copper temperature, using the temperature coefficient of copper. It is a good average, but it does not show the hot spot.

Use thermocouples or resistance temperature detectors in the winding, at the centre and near the surface, to estimate the gradient. A thermal camera shows the outside of the coil, which is useful for the enclosure and the mounting, but it cannot see the centre. Combine the methods rather than trusting one.

Run the test at the worst-case ambient, the maximum voltage and the longest duty. Soak the coil until the temperature is stable, then record the ambient, the current, the resistance and the surface temperature. Compare the result with the class limit and with the thermal model. A single spot check at room temperature is not a thermal qualification.