RI 7151 A Model For Molten Pools In Arc Melting

The use of consumable.-electrode arc melting as a production technology is growing. One advantageous feature of this process is that it avoids ingot contamination by soluble crucible materials by employing a chilled metal crucible. Because the thermal balance under these conditions is rather delicate and does not necessarily provide a favorable environment for solidification, catastrophic imbalances can occur. The effectiveness and mechanistic roles of various factors are mostly unknown, and more intelligent insight regarding the distribution of temperature and heat is needed. Experience has provided several pertinent observations, some of which are quite superficial. The most meaningful data have resulted from studies of molten pool shapes and sizes and from measurements of heat flow through crucible walls. Overall experience, intuitively interpreted and supplemented, is sufficient nevertheless as a basis for a boundary-value treatment of the problem. A mathematical analysis based on a separation of variables, using conventional differential equation methods, provides a useful solution. For a cylindrical ingot, the temperature varies as a Bessel function of an argument proportional to the radius and as an exponential function of longitudinal position. Trial calculations using the problem solution seem to verify the general correctness of the result as compared with experience. The role and nature of solution parameters are also clarified, though not entirely resolved. It is revealed that the barrier to heat flow at the ingot-crucible surface has a prominent influence. Utility of the model embodied in the problem solution is readily demonstrated by considering a variety of contemporary questions about arc melting, and it is hoped that utility can be enhanced by improvement of the model.