Sharif Digital Repository

We derive a new non-linear two dimensional model for melt flows and interface instability in aluminum reduction cells. This model is based on non-linear de St. Venant shallow water equations and contains the main features of an aluminum reduction cell. In this model we consider linear friction terms but in a new way that has not been considered in previous works. Our results are in good agreement with the results of simulation of viscous flow. This model is applicable both in determination of melt flows in molten aluminum and cryolite layers and also in finding the extreme limit for stability of interfacial waves in an aluminum reduction cell  

The production with high quality at the lowest production time can be a key means to success in the competitive environment of manufacturing companies. Therefore, in recent years, the need for extra precise and high-speed machine tools has been impressively increased in manufacturing applications. One of the main sources of errors in the motion of high-speed spindles is the occurrence of non-repetitive runouts (NRRO) in the bearing. The NRRO can be caused by some factors such as the form of balls, the waviness of rings, the number of balls, and the permutation of one or two balls in the ball bearing. In this paper, a Taguchi-based approach is proposed for the optimal design of high-speed...