Mathematical Model Of Energy Transferred In A Single Ball Motion In Agitation Mode
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Date
2010-12
Authors
Budin, Salina
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Particle size reduction process using mechanical milling method is an inefficient energy intensive process. Typically, only 1 to 5 percents of the energy supplied to the process are utilized for the size reduction of the particle, and the remaining energy is dissipated mainly into heat. Since energy is one of the predominant operating costs, a lot of efforts have been expanded to understand the mechanism of particle breakage in size reduction process in order to increase the energy efficiency. In industrial practices, this inefficiency is inevitably accepted by allowing longer processing time. However, the longer the processing time, the higher the probability of contamination in the milled work materials will be. In this work, the motion of the vial, the balls and the work materials in the milling mill was studied in order to understand the mechanism of collisions between them. This is considered as the important event where the kinetic energy of the milling ball is being transferred to the work materials for the size reduction process. Thus, a theoretical model of the motion of the vial, the balls and work materials should be developed. To minimize the complexity of the collision event caused by multi ball commonly used in industry, a single ball approach in agitation motion mode was used. Using this arrangement, simulation was performed to examine whether the impact energy generated would be sufficient for work material breakage in the size reduction process. The next step taken was to model the transfer of energy from the milling media to the work material. This is required in order to evaluate the actual energy used in particle size reduction. The model developed is based on the principle of energy conversion, where the energy lost in terms of frictional dissipation and ball bouncing was considered. The model was then validated by free falling test using a milling ball. This is the closest resemblance of direct collision between milling ball, work material, and the internal surface of the vial. The simulation results on the model of motion of the vial, ball and work materials show that the impact energy generated during the collision between the milling ball and internal surface of the vial was higher as compared to impact energy generated in other type of mills in this mode of motion, such as vibratory mill.
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Keywords
Mathematical model of energy transferred , in a single ball motion in agitation mode