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Modelling power transfer in electron beam heating of cylinders Tripp, David William


The electron beam remelting process is used extensively for the refining and recycling of titanium and its alloys. The success of the process relies on its ability to provide a thermal environment capable of removing impurities and deleterious particles while allowing control of chemical composition and solidification. These aspects of the process hinge on the accurate control of power input to the melt stock. Over the years, the effects of various parameters (such as chamber pressure) on the power delivery to the melt stock have largely been ignored. In this work, a series of laboratory scale experiments using instrumented cylinders was conducted. In parallel, a finite element model of the electron beam heating process was developed to analyze the experimental results. The experimental results show that the temperature regime within a target cylinder is affected by variations in chamber pressure. The magnitude of the temperature changes measured as a result of pressure changes was on the order of two to three times the intrinsic error in the thermocouples. Thus these perceived temperature changes were close to the limit of our ability to measure them. The experimental results are self consistent in that a pressure variation produced a similar trend at each thermocouple location. Analysis with the model has shown that the effect of pressure is to alter the power distribution within the beam and not the efficiency of power transfer. The model can be made to reproduce both qualitatively and quantitatively the measured temperature response by varying the beam spreading parameter with chamber pressure. Such a claim cannot be made when varying the power transfer efficiency with chamber pressure. By fitting the model to the experimental thermocouple results it has been shown that that the beam power distribution is adequately represented by a Gaussian or normal distribution. Additional analysis has led to empirical relationships for the effect of chamber pressure on beam focusing characteristics under the conditions used in the laboratory. - The indirect link between chamber pressure and beam power distribution is reinforced using careful and self-consistent experiments, a mathematical model that can reproduce both quantitatively and qualitatively the results of the experiments and the physics of beam - gas particle interactions.

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