Analyses of the energy-size reduction of mixtures of narrowly sized coals in a ball-and-race mill

Mixture breakage of particles in various sizes is common in industrial mills, and breakage behavior is influenced by size composition. But studies on particle breakage are conducted to narrowly sized samples. In this paper, tentative works are made to investigate interaction among super clean coal in mixture breakage from aspects of breakage rate, energy consumed characteristics and energy split factors. Experimental results demonstrate that breakage rate of coarse particles in mixture breakage increases if compared with that in single breakage. Particle size is modelled into classical breakage equation, and the modified model is successfully applied to mixture breakage. Energy split factor of component is determined based on the balance of specific energies of components in heterogeneous breakage and energy-size equation, and consumed energy (W) of component in multi-component grinding is calculated. Calculated energy split factors of components are all above one in various mixed conditions, so energy efficiency (value of product t₁₀ at the same specific energy) decreases if compared with that of single breakage. Energy split analyses are also conducted for mixture breakage of middling coals, which illustrates that the method is robustness for energy-size reduction process influenced by associated minerals in coal.     

Using Krylov‐Padé model order reduction for accelerating design optimization of structures and vibrations in the frequency domain

In many engineering problems, the behavior of dynamical systems depends on physical parameters. In design optimization, these parameters are determined so that an objective function is minimized. For applications in vibrations and structures, the objective function depends on the frequency response function over a given frequency range, and we optimize it in the parameter space. Because of the large size of the system, numerical optimization is expensive. In this paper, we propose the combination of Quasi‐Newton type line search optimization methods and Krylov‐Padé type algebraic model order reduction techniques to speed up numerical optimization of dynamical systems. We prove that Krylov‐Padé type model order reduction allows for fast evaluation of the objective function and its gradient, thanks to the moment matching property for both the objective function and the derivatives towards the parameters. We show that reduced models for the frequency alone lead to significant speed ups. In addition, we show that reduced models valid for both the frequency range and a line in the parameter space can further reduce the optimization time. Copyright © 2012 John Wiley & Sons, Ltd.