Empirical Verification of a Short-Coil Correction Factor

The magnetic field produced in the air gap by any particular “short coil” at a fixed current is affected by a highly complex interaction between the coil and workpiece geometries, as well as changes in frequency. A frequency-modified semiempirical short-coil correction factor, based upon the formula published by Vaughan and Williamson in 1945, is presented and experimentally verified. This new equation is shown to predict the total system reactive power and the average magnetic flux at the surface of the workpiece with typical differences of less than 2% at 50 Hz ac and to accurately predict workpiece heating rates typically within 5% for aluminum billets at 50 Hz to 500 kHz ac. The workpiece real and reactive powers, as well as total system reactive power, are compared with both analytic and 2-D axial symmetric finite-element modeling (FEM) model solutions as a function of operating frequencies from 50 Hz to 500 kHz. The measured flux density is compared to FEM and analytical predictions at 50 Hz.