A mathematical model for metal flow and heat transfer in centrifuge melt spinning
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I.
INTRODUCTION
C E N T R I F U G E melt spinning (CMS) is a technique tl,2,31 which was developed for improving the manufacturing of rapidly solidified ribbons. Unlike conventional melt spinning, where a molten metal is ejected from a fixed crucible by gas overpressure, CMS uses a rotating crucible. The centrifugal force of the spinning crucible ejects the melt onto the internal surface of a copper rim which rotates in an opposite direction. The centrifugal forces on the rotating rim ensure prolonged contact of the solidifying metal with the heat sink. The ejection pressure of the melt can be varied by changing the velocity of the crucible, and high extraction velocities (up to 100 m s -1) can be achieved in CMS. tL2,3j Cooling rates, calculated from secondary dendritic arm spacings (DAS), as high as 108 K s -t have been achieved with an Al-12 at. pct Ge alloy. The high ejection velocities of the metal stream from the crucible result in a lateral flow of the metal on the rim, causing the thinning of the ribbon. The flow of the melt on the rim produces convection in the melt that enhances heat transfer in the solidifying metal. The increased heat flow through the melt reduces the temperature gradients in the solidifying ribbon and, therefore, affects the microstructural uniformity of the ribbon. In view of the practical limitations in measuring the thermal history of thin solidifying ribbons and in order to understand both the solidification process in CMS and the effect of process parameters on the dimensions and the microstructure of the ribbons, a mathematical model
Z. RIVLIN is with the Dead Sea Works, Sdom, Israel. J. BARAM, Senior Lecturer, Materials Engineering Department, and Leader, Rapid Solidification Processing Laboratory, is with Ben Gurion University of the Negev, Beer-Sheva, Israel. A. GRILL, Professor, Incumbent of the Erik Samson Chair in Steel Processing, Materials Engineering Department, Ben Gurion University of the Negev, is presently with IBM--T.J. Watson Research Center, Yorktown Heights, NY 10598. Manuscript submitted October 5, 1989. METALLURGICAL TRANSACTIONS B
has to be formulated. Mathematical models for rapid solidification processes that were developed previously t4-sl are not suitable for CMS. In those models, when the drag of the melt was taken into consideration, t4,6'7,8~ it was only in the longitudinal direction. In CMS, the volumetric flux and the velocity of the liquid metal prior to impact on the quenching rim are determined by the process parameters which also affect the hydraulics in the casting crucible. In CMS, the lateral flow of the melt is significant in determining the dimensions of the ribbon and, therefore, has to be taken into consideration. The present paper presents a mathematical model developed to take into consideration the specific features of CMS. It is composed of two parts. The first part deals with the hydraulics in the casting crucible and calculates the flow rate of the metal stream and its ejection velocity. These values serve as input for the second
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