Grinding and Flotation Characterized with the Parameter Action

Abstract

The product S = E.t, called Action (E — energy, t — time) is well known in physics. It takes several forms such as: Hamilton’s integral S =jJL.dt2 Max Plank’s formula h = E.t and Kinetic monentum k = m.v x E. These forms have dimension Youle. Sec. All natural processes correspond to the principle of the smallest Action (S = E.t = min). All artificial processes including the technological ones are in the most cases rather far from this minimum, but with the technical progress they approach this minimum gradually. Pontryagin’s maximum principle widely used for the optimization of processes is a modification of the principle of the smallest Action.In the area of grinding or flotation the specialists use the parameters power and energy consumption and the time of grinding or flotation. If one juxtaposes power P = P.tδ, energy B = P.t1; and Action S = E.t = P.t2, the essential difference is evident. When they treat grinding and flotation, the best performance criterion is neither P nor B but S. r r the same iniial and final conditions, the best performance of grinuin or flotation process corresponds to the smallest value of the parameter Action S = E.t (E — ener-gy consumption, t — time of flotation or grinding). If the time is the shortest at the egzaal other conditions, the performance is the best one — increased capacity, decreased production cost etc.