Patent Application
20070285198
Joule or resistance heating is achieved by the dissipation associated with internal resistance and the corresponding voltage drop when a DC or AC current flows through the workpiece. This phenomena is well understood, and of course is the basis for many types of electrical heating elements. For application to a rotor coil, consideration must be given to the materials and construction and resulting extremely low resistance of the workpiece, and the resulting large current that is likely to be required. The amount of current will depend on the heat capacity of the workpiece and heat loss due to convection and radiation from the workpiece, and the required curing temperature. For a particular embodiment of interest, with an overall coil length of about 30 feet and a cross section of approximately 1 inch by ¼ inch, initial evaluations indicated that heat loads are on the order of 3000 W per coil in the steady state heating condition, and that a corresponding current on the order of 800 amps would be required. This is the basic information that is required to design a transformer suitable for this application. A critical aspect of the system is to make good electrical contact between the coils and the transformer. Further, the secondary winding of the transformer must be kept within acceptable temperature limits.
In connection with
Joule Heating: Qj=i2R
Convection: Qc=hAs (T28)
Radiation: Qr=σAs(TA'T4∞)
Storage: Qs=vol·ρmcp (−T∞)
The resistance is a critical factor in calculating the Joule heating. The nominal resistance R0 depends on geometry and material properties where L is length, As is cross-sectional area and ρR is the resistivity at nominal temperature T0. The actual resistance R0 varies with temperature T with proportionality α which is the thermal coefficient of expansion. Power P depends on the resistance R and the current i as follows:
An approximation of the values for temperature coefficient of resistance can be used by assuming the values for pure copper, whereas in fact the coils are made using a copper alloy containing a small amount of silver. The other relevant constants used in the subsequent calculations are tabulated below:
α=0.004 C−1
ρR=0.67 μΩ−cm
c
p=0.39 J/gm-C
ρm=8.9 gm/cm3
T
∞
=T
0=20 C
Using the relationships expressed above, one can determine the resistance in a winding of a given size and configuration, and also determine the voltage necessary to produce a current that will raise the temperature of the winding sufficiently to cure the powder coating.
With reference now to
The primary winding (not shown) of the transformer 12 is energized with AC current (preferably 50 or 60 Hz), creating a magnetic field in the transformer core (also not shown). The magnetic field creates an electric field in the secondary winding 20, and a resulting current i is generated in the series loop formed by the rotor coils. The predetermined required current is sufficient to heat the coil elements 14, 16 to the temperature necessary to cure the powder coating, for example, 150 C.
Preferably, the temperature of the rotor coil elements 14, 16 is monitored while the primary coil is energized, and used as an input to an otherwise conventional proportional-integral-derivative feedback control loop for continual regulation of the temperature. Thus, the temperature can be measured directly and the voltage adjusted as necessary to vary the current to produce the desired temperature. Alternatively, the temperature can be inferred from the voltage and current characteristics, since resistance in the coil elements is temperature dependant.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
