Coil Power Handling
If you intend to
build a high power coilgun then you must give consideration to the amount of resistive
dissipation which will occur in the coil during a firing sequence. The instantaneous
power dissipation in the coil is given by the product of the square of the current
and the coils resistance
and the total
energy converted to heat is given by the integral of the power dissipation function.
where T0
and T1 are the start
and stop times of the current waveform. If you intend to make reasonably accurate
calculations of the heat energy generated then you'll need to know something about
the shape of the current waveform, that means recording it using a DSO.
Now let's look
at the actual temperature change which comes from the dissipation. Typical current
pulses in a coilgun are of the order of a few ms or less so negligible heat energy
will dissipate to the air during a pulse and we can assume that all the resistive
energy losses will go into heating the coil. The standard equation relating the
change in thermal energy of a body to its change in temperature is
where m is the
mass and c is the specific heat capacity.
We can express
the mass of the coil in terms of its parameters as follows
where
is the density of the wire material and F is the filling factor.
We can now combine these equations and express the temperature
change in the coil as a function of the energy dissipated.
Values of density
and specific heat capacity for copper are; =8.96x10e^{3}Kgm^{3}
and c=385Jkg^{1}K^{1}.
The largest temperature
rise which can be accomodated depends on the insulation rating of the wire. Typically
this is around 125^{0}C so taking a ambient temperature of say 25^{0}C
means that the temperature change in the coil is limited to an absolute maximum
of 100^{0}C. Now it makes sense to stay on the safe of this so limiting
the rise to about 75^{0}C is a safe bet. If you melt the insulation the
coil will be ruined. It's possible to get wire with a higher insulation temperature
rating.
The
time required for cooling between firings is a more complicated
issue from the point of view of calculations. Some of the more obvious
factors are the thermal mass of the coil, the surface area of the
coil, and the heat transfer to the coil matrix material. The matrix
is the material between the windings of the coil. In a low field
coil this can simply be air, but if additional mechanical strength
is required then the coil may be impregnated with a resin, or bound
with glass fibre tape between layers and then impregnated.
This
analysis is simplified by ignoring phenomenon such as the skin and
proximity effects. A more detailed analysis of the issues surrounding
the thermal analysis of pulsed coils can be found in Principles
of Pulsed Magnet Design by R. Kratz and P. Wyder.
Sources:
Engineering Thermodynamics,
Rogers and Mayhew
Engineering Materials
Pocket Handbook, W. Bolton
