Review of Classical Design Methods as Applied to Aluminum Billet Heating with Induction Coils

"In the present study classical induction design tools are applied to the problem of heating nonmagnetic metal billets, using 50 Hz AC. As an example of great practical industrial interest, the induction heating of aluminum billets is addressed specifically. The predicted work piece power is compared with the measured work piece power for a long and a short coil, using well established methods, such as those of Burch and Davis, introduced in 1926/28, Dwight and Bagai in 1935, Baker in 1944/57, Vaughan and Williamson in 1945, and by Tudbury in 1960. A calculation methodology based on a combination of the available tools is also introduced and discussed. The method has proven to give an error of <10% of the actual work piece power. An equation for Tudbury's work piece shortness correction factor is disclosed for the first time.IntroductionInduction heating of metal billets is a practical problem, with a geometry suitable for solution using analytical methods. This paper will examine solutions related specifically to round work pieces in round coils, although the methods presented can be extended to other regular shapes of work pieces and coils[l]. The methods can also be extended to ferromagnetic materials with slight changes[2-3]. It is assumed that the coil and work piece have a consistent diameter over their entire length and that the work piece is at least as long as the coil. Correction factors can be derived for the cases where the work piece is shorter than the coil.The study of induction heating by coils began in the late 19th century with theoreticians like Heaviside[ 4]. The work of Burch and Davis[ 5-7] in the 1920' s greatly improved the theoretical understanding of induction applied to metallurgy. Many investigators in the 1930's-1950's: Dwight and Bagai[8], Baker[l-2, 9], Vaughan and Williamson[3, 10] and others[l 1-12] added to our understanding with clearer mathematics, solutions for specific applications, semi-empirical modifications and practical design tools. Much of the accumulated knowledge is available in books, such as Tudbury's practical text or Simpson's engineering guide from 1960[13-14]. Perhaps the best description and derivation of the theoretical and semi-empirical solutions can be found in Davies[15]."