Improved Short Coil Correction Factor for Induction Heating of Billets

"To determine the heating rate of billets using ‘short coils’, an appropriate correction factor must be applied to the theoretical relationship. In 1945, Vaughan and Williamson published a semi-empirically modified Nagaoka coefficient applicable for moderate frequency induction heating processes (10 kHz). Recently it was demonstrated that the method of Vaughan and Williamson gives <10% error in the estimated power when heating aluminum billets at 50 Hz.In the present study, experiments have been conducted on aluminum billets in order to verify an empirical frequency corrected ‘short coil’ equation. Measurements of electrical conductivity (<± 0.5%), current (± 1%), heat (± 1-3%), and magnetic flux density (± 1-2%) have been performed. The results are compared with 1D analytical calculations, and 2D axial symmetric FEM modeling using COMSOL 4.2®. The frequency corrected equation has proven to provide accurate predictions of power (<4% error) within the frequency range 50 Hz to 500 kHz.IntroductionInduction heating is commonly applied to the re-heating of billets before forging or extrusion processes. The resistive heating produced by eddy currents in the solid or semi-solid work piece during this procedure, is driven by the time varying magnetic flux density in the air-gap between the work piece and the coil. The flux in the air-gap is created by the current flowing in the induction coil, i.e. the magneto-motive force. In Figure 1 it can be seen that the currents present in the work piece are concentrated in the outer ‘shell’, or the first electromagnetic penetration depth (dw), and flow in a direction which opposes the magnetic field produced by the induction coil."