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.

[1]  J. H. Poynting.  XV. On the transfer of energy in the electromagnetic field , 1884, Philosophical Transactions of the Royal Society of London.

[2]  Oscar Lucía,et al.  Computational Modeling of Two Partly Coupled Coils Supplied by a Double Half-Bridge Resonant Inverter for Induction Heating Appliances , 2013, IEEE Transactions on Industrial Electronics.

[3]  Diego Puyal,et al.  Load-Adaptive Control Algorithm of Half-Bridge Series Resonant Inverter for Domestic Induction Heating , 2009, IEEE Transactions on Industrial Electronics.

[4]  Mark William Kennedy,et al.  Review of Classical Design Methods as Applied to Aluminum Billet Heating with Induction Coils , 2011 .

[5]  J. Bakken,et al.  Analytical and Experimental Validation of Electromagnetic Simulations Using COMSOL ® , re Inductance, Induction Heating and Magnetic Fields , 2011 .

[6]  E. Davies.  Conduction and Induction Heating , 1990 .

[7]  H. A. Wheeler.  Simple Inductance Formulas for Radio Coils , 1928, Proceedings of the Institute of Radio Engineers.

[8]  Paul P. Biringer,et al.  An Improved Method of Calculating the Power Generated in an Inductively Heated Load , 1974 .

[9]  J. Bakken,et al.  Improved short coil correction factor for induction heating of billets , 2012 .

[10]  N. Mclachlan.  Bessel functions for engineers , 1934 .

[11]  H. Nagaoka,et al.  The Inductance Coefficients of Solenoids , 1909 .

[12]  John Henry Poynting,et al.  On the transfer of energy in the electromagnetic field , 1883, Proceedings of the Royal Society of London.

[13]  J. W. Williamson,et al.  Design of induction-heating coils for cylindrical nonmagnetic loads , 1945, Electrical Engineering.

[14]  E. B. Rosa,et al.  Formulas and tables for the calculation of mutual and self-inductance (Revised) , 1912 .

[15]  M. Enokizono,et al.  Designing of suitable construction of high-frequency induction heating coil by using finite-element method , 2005, IEEE Transactions on Magnetics.

[16]  L. Lorenz,et al.  Ueber die Fortpflanzung der Electricität , 2022 .

[17]  J. Bakken,et al.  Analytical and Fem Modeling of Aluminum Billet Induction Heating with Experimental Verification , 2012 .