The theory concerns the unsteady conduction of heat occurring within and between billet and die during high-speed hot forging. The analysis comprises an extension of the Fourier heat soakage equation for axial symmetry so as to include the effects on heat flow, and hence temperatures, of the rapid plastic movements in the billet material. A step-by-step solution uses a modification of the Crank-Nicolson technique based on an iterative procedure. Using idealizing assumptions regarding the billet deformation, graphs are produced showing temperature changes in a cylindrical billet.
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References
1.
CrankJ.NicolsonP. ‘A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type’, Proc. Camb. phil. Soc. math, phys. Sci.194743, 50.
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ChanL. T.BakhtarF.TobiasS. A. ‘Design and development of Petro-Forge high energy-rate forming machines’, Proc. Instn mech. Engrs1965–66180 (Pt 1), 689.
